Bachs Numbers

Bach’s Numbers

In eighteenth-century Germany the universal harmony of God’s creation and the perfection of its proportions still held philosophical, moral and devotional significance. Reproducing proportions close to the unity (1 : 1) across compositions could render them beautiful, perfect and even eternal. Using the principles of her ground-breaking theory of proportional parallelism and the latest source research, Ruth Tatlow reveals how Bach used the number of bars to create numerical perfection across his published collections, and explains why he did so. The first part of the book illustrates the wide-ranging application of belief in the unity, showing how planning a wellproportioned structure was a normal compositional procedure in Bach’s time. In the second part Tatlow presents practical demonstrations of this in Bach’s works, illustrating the layers of proportion that appear within a movement, within a work, between two works in a collection, across a collection and between collections. British-Swedish musicologist Ruth Tatlow is an independent scholar based in Stockholm. Her research into Bach’s use of numbers led from her classic monograph Bach and the Riddle of the Number Alphabet (Cambridge, 1991) to this sequel, Bach’s Numbers, through publications on methodology, inventive techniques and the theory of proportional parallelism. In 2004 she co-founded Bach Network UK (BNUK), establishing its open-access web-journal Understanding Bach in 2006. She is currently Chair of the BNUK Council, joint editor of Understanding Bach, and a member of the Editorial Board of the American Bach Society. Her research has attracted awards and grants from numerous sources including the Swedish Research Council, the Royal Swedish Academy of Music, the Society of Authors of Great Britain, the British Council, The Hinrichsen Foundation, The Leverhulme Trust and the Royal Swedish Academy of Letters.

Bach’s Numbers Compositional Proportion and Significance ruth tatlow

University Printing House, Cambridge CB2 8BS, United Kingdom Cambridge University Press is part of the University of Cambridge. It furthers the University’s mission by disseminating knowledge in the pursuit of education, learning and research at the highest international levels of excellence. www.cambridge.org Information on this title: www.cambridge.org/9781107088603 © Ruth Tatlow 2015 This publication is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published 2015 Printed in the United Kingdom by CPI Group Ltd, Croydon CR0 4YY A catalogue record for this publication is available from the British Library Library of Congress Cataloguing in Publication data Tatlow, Ruth, author. Bach’s numbers: compositional proportion and significance / Ruth Tatlow. pages cm ISBN 978-1-107-08860-3 (Hardback) 1. Bach, Johann Sebastian, 1685–1750 – Criticism and interpretation. 2. Symbolism of numbers in music. I. Title. ML410.B13T25 2015 780.92–dc23 2015000588 ISBN 978-1-107-08860-3 Hardback Cambridge University Press has no responsibility for the persistence or accuracy of URLs for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate.

To Mark Louisa, Emily Benjamin and Anita with love

Contents

List of figures [page ix] List of tables [x] Acknowledgements [xv] List of abbreviations [xvii]

part i foundations

[1]

1 Bach’s numbers [3] 2 Symmetry, proportion and parallels [36] 3 Unity, proportions and universal Harmony in Bach’s world

[73]

4 Bars, compositional planning and proportional parallelism [102] part ii demonstrations 5 Three collections for strings

[131]

[133]

6 Four in two collections for keyboard [159] 7 Two further collections for keyboard [182] 8 Two small late collections [204] 9 Two large late collections [224] 10 Collections of concertos [255] 11 Collections of organ works [275] 12 Great passions and cantatas [294] 13 Festive cut-and-paste projects: masses and oratorios [326]

vii

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contents

14 Lost compositional blueprints [354] Appendix: A theology of musical proportions and Harmony in Bach’s time [370] Bibliography [383] Index of sources [396] Index [400]

Figures

2.1

2.2

2.3

2.4 2.5

3.1

3.2

4.1

4.2

Puttenham, The Arte of English Poesie (London, 1589), 72 Proportion by situation. Courtesy of Sterling Library, Senate House Library, University of London [page 40] Puttenham, The Arte of English Poesie (London, 1589), 76 Proportion in figure. Courtesy of Sterling Library, Senate House Library, University of London [41] Pachelbel, Hexachordum Apollinis (Nürnberg, 1699). Chronogram by Beer. Courtesy of Sibley Music Library, Eastman School of Music, University of Rochester [48] Buttstett, Wieder das Beschützte Orchestre (Erfurt, 1718). Courtesy of Library of Congress Music Division, Washington, DC [54] ‘Johann Sebastian Bach’ in Kircher’s musical alphabets (Kircher, Musurgia Universalis (Rome, 1650), Tome II, Book IX, 362. Alphabetum steganographicum musicum. Courtesy of Kungliga Biblioteket, Stockholm. Callmark: 147 A. a. Fol. [63] Puttenham, The Arte of English Poesie (London, 1589), 53. Of Proportion Poeticall. Courtesy of Sterling Library, Senate House Library, University of London [76] Mattheson, Das Beschützte Orchestre (Hamburg, 1717), 478. Courtesy of Sibley Music Library, Eastman School of Music, University of Rochester [82] Mizler, Musicalische Bibliothek, Vol. IV, Part 1 (Leipzig, 1754), 108. Courtesy of Sibley Music Library, Eastman School of Music, University of Rochester [117] Müller, Wohlmeynender Unterricht (Leipzig, 1743), 172–3. Courtesy of Kungliga Biblioteket, Stockholm [124]

ix

Tables

2.1 2.2 2.3 4.1 4.2 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 5.10 5.11 5.12 5.13 5.14 5.15 5.16 5.17 5.18 6.1 x

B/H-A-C key pattern across Clavier Übung I and II. Original print [page 64] Statistical survey of Bach’s signatures [66] Bach’s signatures in three common number alphabets [67] Symmetry of intervals in the hexachord [103] Symmetry of semitones in B-A-C-H [103] Six Solos. Autograph score, P 967 [135] Proportioned pair: Sonata 1 and Partita 1. Autograph Score, P 967 [137] Proportion in Partita 3 in E major. Autograph score, P 967 [138] Six Solos. Autograph score, P 967. Six Sonatas. Copyist Altnickol, P 229 [140] Large-scale movements. Fuga and Ciaccona. Autograph score, P 967 [142] Five Solos for violin. Copyist Kellner, P 804 [144] Revisions to the Six Solos. P 804, and P 967 [145] Six Sonatas for violin and harpsichord. Copyist Altnickol, P 229 [147] Six Sonatas. Early and final versions compared. St 162 and P 229 [148] Changes to Sonata 6. St 162 and P 229 [148] Parallels between two violin collections. P 967, St 162 and P 229 [149] Six Cello Suites. Copyist Anna Magdalena Bach, P 269 [152] D-major Cello Suite. Copyist Anna Magdalena Bach, P 269 [153] Proportion formed between movements. Cello Suites, P 269 [154] A second large-scale proportion. Cello Suites, P 269 [154] Further evidence of proportioning. Cello Suites, P 269 [155] An earlier version of the Cello Suites? P 269 and autograph score of BWV 998 [156] Proportioning in an earlier version of the Cello Suites [157] WTC Book 1. Autograph score. P 415 [161]

list of tables

6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 6.10 6.11 6.12 6.13 6.14 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 7.10 7.11 8.1 8:2

Early preludes expanded. Clavier-Büchlein, Kayser’s copy, P 401 and P 415 [163] Aufrichtige Anleitung. Autograph score, P 610 [165] Earlier names and orders. Clavier-Büchlein, 1722/3 and copy by Kayser, P 219 [167] Two additional collections. Autograph score, P 415 and copy by Kayser, P 219 [169] WTC I. Autograph score, P 415 with Aufrichtige Anleitung, P 610 and P 219 [170] A chronological overview. WTC I and Aufrichtige Anleitung [171] Clavier Übung I and II. Original print [173] Proportional integration of two sets of two keyboard collections [174] Partitas in A and E minors. Autograph score, P 225, and print (BWV 827, 830) [175] Partitas in A and E minor. Autograph score, P 225, 1725 [176] Evolving plans for Clavier Übung I. Print. Autograph score, P 225, P 226 [177] Early ordering of Clavier Übung I and II. Print. Autograph score, P 226 [179] Clavier Übung Parts 1-IV. Original prints [180] Earliest fifteen movements. Clavier Übung III. Original print [185] Twelve later movements. Clavier Übung III. Original print [187] Clavier Übung III. Original print [187] Twelve consecutive thematic groups. Clavier Übung III. Original print [188] Perfect proportioning in consecutive movements. Clavier Übung III. Original print [189] Goldberg Variations. Numerical structure. Original print [192] Proportions in the canons. Goldberg Variations, Clavier Übung IV. Original print [195] Time and keyboard attributions. Goldberg Variations, Clavier Übung IV. Original print [196] 1742 plans. Clavier Übung III and Clavier Übung IV. Original prints [198] Canons, BWV 1087. Autograph score, F-Pn Mus. Ms. 17669 [200] Large-scale Clavier Übung series. Original prints [202] Canonic Variations. Engraving of three original variations [206] Canonic variations. Numerical value of engraved title page [207]

xi

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list of tables

8.3 8.4 8.5 8.6 8.7 8.8 8:9 9.1 9.2 9.3 9.4 9.5 9.6 9.7 9.8 9.9 9.10 9.11 9.12 9.13 9.14 9.15 9.16 10.1 10.2 10.3 10.4 10.5

Canonic Variations. Comparison of 1747 print and autograph score, P 271 [210] Canonic Variations, Schübler Chorales and Goldberg Canons. Original prints [213] Collections of canons, 1739 and 1747. Original prints [214] A collection for organ? Autograph score, P 271 [215] Schübler Chorales. Sources and proportions. Original print [219] Schübler Chorales. Title page. Original print [221] Original binding of Bach’s Handexemplar of Clavier Übung III and Schübler Chorales [222] Musical Offering. Original print [228] Sonata and Canons in Sections C and D. Musical Offering. Original print [231] Number values of title words. Musical Offering [232] Parallel values. Musical Offering. Original print [233] Title page. Musical Offering. Original print [235] Reichardt’s handwritten title page. Musical Offering, A.Wn. S. H. J. S. Bach 102 [236] The Art of Fugue. Original print [244] Contrapunctus 1–10. The Art of Fugue. Original print [245] Fourteen movements. The Art of Fugue. Original print [246] Possible ground plans. The Art of Fugue. Original print [247] A possible ground plan. The Art of Fugue. Original print [248] The Art of Fugue. Autograph score, P 200 [249] Transformation process. The Art of Fugue, P 200 and original print [249] Transformation process. The Art of Fugue, P 200 and original print [250] Title page. The Art of Fugue. Copyist, Altnickol, P 200, and original print [251] Schübler Chorales; Fuga a 3 Soggetti. Original prints [253] Early Keyboard Transcriptions. Mixed copyists, P 804 [258] Twelve concerto transcriptions. Copyist, Johann Bernhard Bach, P 280 [260] Two sets of six transcriptions. Copyist, Johann Bernhard Bach, P 280 [262] A proportionally related collection of twelve. Copyist, Johann Bernhard Bach, P 180 [262] Brandenburg Concertos. Autograph score, Am. B. 78 [269]

list of tables

10.6 10.7 11.1

Reconstruction of Bach’s numerical plans. Am. B. 78 [271] Rastration of BWV 1050/1. Autograph score, Am. B. 78 [272] ‘Great Eighteen’ organ chorale preludes. Autograph score, P 271, 56–99 [278] 11.2 The ‘Great Fifteen’, P 271, and Fifteen mass settings from Clavier Übung III in 1739 [283] 11.3 Additions to P 271. Organ chorales and Canonic Variations [283] 11.4 Six Trio Sonatas. Autograph score, P 271, 2–55 [286] 11.5 Two Trio Sonatas in C minor: coincidental parallelism? [289] 11.6 Large-scale parallels between five collections [290] 11.7 Parallel proportions between keyboard collections: Clavier Übung III, The Art of Fugue, Schübler Chorales and P 271 [292] 12.1 St Matthew Passion. Autograph score, P 25 [296] 12.2 St Matthew Passion. Picander’s text and Bach’s autograph score, P 25 [299] 12.3 St Matthew Passion. Layout of autograph score, P 25 [305] 12.4 St John Passion. Partial autograph score, P 28 [308] 12.5 Chorales in St John Passion. Partial autograph score, P 28 [311] 12.6 Arias, Chorales and Recitatives in St John Passion. Partial autograph score, P 28 [312] 12.7 St John Passion, layout and proportion. Partial autograph score, P 28 [314] 12.8 Cantata ‘Wo soll ich fliehen hin’, BWV 5. Autograph score, BL Stefan Zweig Collection Ms. 1 [320] 12.9 Cantata ‘Gott ist mein König’, BWV 71. Printed text and autograph score, P 45 [322] 12.10 Psalm 74:12 in BWV 71/1. Printed text and autograph score, P 45 [324] 13.1 Three Lutheran masses. Copyist Altnickol, P 15/1–3 [328] 13.2 Mass in A, BWV 234. Autograph score, D-DS Mus. Ms. 971 [329] 13.3 Missa in B minor. Autograph score, P 180 [331] 13.4 Symbolum Nicenum–Sanctus–Osanna in B minor. Autograph score, P 180 [332] 13.5 B-minor Mass. Autograph score, P 180 [334] 13.6 Christmas Oratorio. Autograph score, P 32 [337] 13.7 Free-texted material in Christmas Oratorio. Autograph score, P 32 [338] 13.8 Original performance schedule of Christmas Oratorio, Leipzig, December 1734–January 1735 [339]

xiii

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list of tables

13.9 13.10 13.11 13.12 13.13 13.14 13.15 14.1 14.2 14.3 14.4 14.5 14.6 14.7 14.8

Recitatives, Duet and Trio in Christmas Oratorio. Autograph score, P 32 [342] Choruses and Chorales in Christmas Oratorio. Autograph score, P 32 [343] Layout of Christmas Oratorio. Autograph score, P 32 [345] Christmas Oratorio title page. Printed text booklet, Leipzig 1734 [347] Easter Oratorio. Autograph score, P 34 [349] Ascension Oratorio. Autograph score, P 44 fascicle 5 [351] A proportionally related pair: the Easter and Ascension Oratorios [352] English Suites. Copyist, Kayser, P 1072 [357] French Suites. Copyist, Altnickol, US ML 96.B186 [357] The Neumeister Collection, LM 4708 and Bach’s Orgelbüchlein, P 283 [358] Five Great Preludes and Fugues. Mixed copyists [360] 1738/9 plan for three grand organ collections [361] Six Great Preludes and Fugues. Unknown Berlin copyist, Am. B. 60 [362] Four solo concertos for keyboard. BWV 1052–5. Autograph score, P 234 [364] A collection of six concertos for harpsichord. Mixed copyists [365]

Acknowledgements

Research for this book could not have been undertaken with the conventional tools available fifty years ago, and I would like to begin by expressing my gratitude to the numerous unseen sponsors and librarians, who have worked diligently to put online so many seventeenth- and eighteenthcentury sources, and to the scholars who painstakingly compiled and produced the Bach documents and diplomatic source research on which Bach scholars today can build with confidence. Over the past two decades I have received generous funding from many sources, including The Leverhulme Trust, The Hinrichsen Foundation, Kungliga Musikaliska Akademien, Kungliga Vitterhetsakademien, Vetenskaprådet and the Society of Authors, and I would like to thank the trustees of these foundations for their confidence and interest in my research questions. I am grateful too for the help of many librarians, including my Swedish colleagues at Statens Musikverk in Stockholm, the staff at the Bach-Archiv Leipzig, the Kungliga Bibliotek in Stockholm and the Senate House Library in London, and specifically David Coppen at the Special Collections of the Sibley Music Library in Rochester NY, Brigitte Geyer in Special Music Collections of the Stadtbibliothek, Leipzig, and Steffen Voss of RISM at the Bayerische Staatsbibliothek. One of the privileges of my research journey has been the pleasure of exchanging notes with friends and colleagues, some of whom have generously read and responded to my discoveries, including Cécile BardouxLovén, Christine Blanken, Gregory Butler, John Butt, Raymond Erickson, Fred Fehleisen, Don O. Franklin, John Eliot Gardiner, Helen Gough, Wendy Heller, Paula Higgins, Michael Marissen, Jennie Nell, Szymon Paczkowski, Stephen Rose, Ulrich Siegele, Peter Smaill, Reinhard Strohm, Burkhard Schwalbach and Christoph Wolff. Thanks are due also to Jeffrey Sposato, Andrew Talle and Joyce Irwin for kindly trusting me with their unpublished research results, and to Barbara Reul for her invaluable help with the translations in the Appendix. And a special thank you to four colleagues whose longstanding friendship and wise words have meant so much to me during the evolution of this book: Jonathan Dunsby, Robin A. Leaver, Joel Speerstra and Yo Tomita.

xv

xvi

acknowledgements

Being part of a loving family has been my anchor throughout. The church family of Immanuel International, Stockholm has been an inspiration and has provided deep friendships. The encouragement of my parents-in-law Mary and David Tatlow, and daughter-in-law Anita is a source of great joy. I owe a profound debt of gratitude to my parents, Olive and Frank († 4.11.14) Ballard, not least because they first showed me the love of Bach’s music. Above all, though, it has been the unfailing and unconditional love, tolerance, humour and faith of Mark, Benjamin, Louisa and Emily that empowered me to bring this work to fruition.

Abbreviations

AA BD I–VII Benary

BJ Buttstett, Ut, Mi, Sol

BWV BWV2a CÜ I–IV D-B Fritsch, Lexicon JP Mattheson, Capellmeister Mattheson, Orchestre 1 Mattheson, Orchestre 2 Mattheson, Orchestre 3 MP NBA KB NBR

J. S. Bach, Aufrichtige Anleitung (Two- and Three-Part Inventions and Sinfoniae). Bach Dokumente, vols. I–VII, 1963– . Peter Benary, ed., Johann Gottfried Walther. Praecepta der Musicalischen Composition, 1955. Bach-Jahrbuch, 1904– . Johann Heinrich Buttstett,Ut, Mi, Sol, Re, Fa, La, Tota Musica et Harmonia Aeterna, [1716]. Bach-Werke-Verzeichnis, 1950; rev. and enlarged, 1990. Bach-Werke-Verzeichnis, kleine Ausgabe, 1998. J. S. Bach, Clavier Übung, parts I–IV. Staatsbibliothek zu Berlin. Thomas Fritsch,Teutsch-Englisches Lexicon, 1716. J. S. Bach, The Passion according to St John. Johann Mattheson, Der Vollkommene Capellmeister, 1739. Johann Mattheson, Das Neu-Eröffnete Orchestre, 1713. Johann Mattheson, Das Beschützte Orchestre, 1717. Johann Mattheson, Das Forschende Orchestre, 1721. J. S. Bach, The Passion according to St Matthew. Neue Bach-Ausgabe: Kritischer Bericht. The New Bach Reader, rev. and enlarged, 1998. xvii

xviii

list of abbrev iations

New Grove P St Walther, Lexicon Walther, Praecepta Wolff, Essays Wolff, Learned Musician WTC I–II Zedler, Lexicon

New Grove Dictionary of Music and Musicians, 2nd edn, 2001. D-B Mus. ms. Bach P[artitur]. Original score held at Staatsbibliothek, Berlin. D-B Mus. ms. Bach St[immen]. Original parts held at Staatsbibliothek, Berlin. Johann Gottfried Walther, Musicalisches Lexicon, 1732. Johann Gottfried Walther, Praecepta der Musicalischen Composition, 1708. Christoph Wolff, Bach: Essays on His Life and Music, 1991. Christoph Wolff, Johann Sebastian Bach: The Learned Musician, 2000. J. S. Bach, Das Wohltemperirte Clavier, books 1–2. Johann Heinrich Zedler, Grosses vollständiges Universal-Lexicon aller Wissenschafften und Künste, 1732–54.

part i

Foundations

1 Bach’s numbers

Sonnet Du edle Musica, die du das Hertz bewegst, Du schönes Himmel-Kind, wer wolte doch nicht lieben; Die sind von guter Art, die dich rechtmässig üben, Die du im innern Grund Zahl, Maaß, Gewichte hegst. Und die Proportion von Erd’ und Himmel trägst: Dein Werck besteht in sechs, und deine Ruh in sieben; Du bist mit Heimligkeit und Kunst durchaus beschrieben, Die du des Himmels Bild in deine Wercke prägst. Du must dich zwarten auch offt übel zerren lassen; Der Mißbrauch lässet dich in deinen Würden nicht; Und ob Apollo dich mit allem Ernst verficht; So finden sich doch die, die deine Schöne hassen. Du aber bleibest wol: Ob sie nicht achten dein; So wirstu doch das Spiel der Frommen ewig seyn. Henr. Georg. Neuss, Past. Gvelpherbyt., 1691

The dangers of playing with numbers are many and legendary. The humiliation of the sixteenth-century mathematician and pastor Michael Stiefel, whose calculations on biblical verses enabled him to predict that Christ would return at 8 a.m. on 18 October 1533,1 was matched by the shame of his cold and hungry parishioners after their disappointing vigil. The embarrassment of theologian and musicologist Friedrich Smend four hundred years later was less public, but it still had a significant influence on the inhibition of number research. His interpretation of the number ‘84’ epitomises the problems: Bach noted a symbolic number in the autograph score of the B-minor Mass. At the end of the ‘Patrem Omnipotentem’ he writes the bar number of the movements ‘84’ (7
12) . . . [This] chorus is about creation (‘factorem coeli et terrae’) . . . Earth and heaven are contained in 7 [3 symbolises heaven and 4 earth] . . . We hear

1

Zedler, Lexicon, s.v. ‘Stiefel, Michael’.

3

4

foundations

the word ‘Credo’ forty-nine times, and its continuation ‘in unum Deum’ eightyfour times. Yet again numbers with symbolic content appear.2

Eighty-four quickly became a buzzword for the folly of symbolic numbers in music when it was discovered that the annotation had been written into the score by one of C. P. E. Bach’s copyists3 decades after J. S. Bach’s death. In spite of the inherent risks, this book is nonetheless devoted to compositional numbers, tackling their form, purpose and meaning in Bach’s music.

I

How numbers became associated with Bach

Bach left no description of his methods of composition, or of whether or not he used numbers when he composed. One of the earliest allusions to the mathematical bases of his music dates to the early 1740s. It can be read in a published collection of musicians’ autobiographies,4 in which Lorenz Mizler (1711–78) wrote that he had been influenced by ‘reading good books, listening to good music, perusing many scores by good masters and also in his association with Capellmeister Bach’.5 This entry enraged the editor of the compilation, Johann Mattheson (1681–1764), causing him to add that ‘Bach no more taught Mizler the mathematical bases of music than I did myself’,6 referring to an earlier discussion of the value of mathematics for music in which he had named Mizler’s training in mathematics, philosophy and music.7 Mattheson’s comments should have killed any later rumours that Bach was interested in the use of mathematics in music, but they did not. A century later the great music historian Philipp Spitta unwittingly revived the topic when he drew attention to the Mizler– Mattheson dialogue. Although intended to demonstrate that Bach had no interest in the mathematical basis of composition,8 it had the opposite effect. In the 1920s Arnold Schering (1877–1941) further raised the profile of numbers in music when he unearthed traditions of permutation in compositional

2 3

4 6 7 8

F. Smend, J. S. Bach Kirchen-Kantaten (Berlin, 1947; rev. edn 1966), vol. IV, 14 and 19. Score, P 180, on page 105 in Bach’s pagination. The same scribe wrote the figure 84 in the corresponding place in the soprano solo part, St 118/2 in C. P. E. Bach’s 1786 copies of the parts of the Credo, St 118, thus ruling out the possibility that J. S. Bach wrote the figure. 5 J. Mattheson, Grundlage einer Ehrenpforte (Hamburg, 1740). BD II, Doc. 470, 380. Mattheson, Ehrenpforte, 231. Ibid., 230, where Mattheson issued a lengthy diatribe against mathematics in music. P. Spitta, Johann Sebastian Bach: His Works and Influence on the Music of Germany (1685–1750), trans. A. C. Bell and J. A. Fuller-Maitland. 3 vols. (London, 1884; reprint edn New York, 1951), vol. III, 24.

Bach’s numbers

invention.9 He steered the number discussion towards Bach studies when he demonstrated the presence of four types of symbolism in Bach’s cantata ‘Du sollt Gott, deinen Herren, lieben’ (BWV 77), spicing the commentary with provocative phrases such as ‘the esotericism of Bach’s vocal canons’ and ‘holy and mysterious numbers’.10 Many musicologists were eager to run with Schering’s ideas before the ground had been fully prepared. Friedrich Smend (1893–1980) was at the forefront, introducing the term ‘cabbalism’ and using number alphabets to interpret patterns he had found in Bach’s music.11 A frisson rippled through the musical world. Amateurs and less discerning scholars lovingly nurtured the ideas, while professional musicologists openly voiced their disdain. The paragram,12 which used one of more than thirty different alphabets to substitute numbers for letters, was Smend’s major stumbling block. As a widely read theologian with a particular interest in church history, he had met similar numero-alphabetical techniques in Jewish mysticism, which duped him into making an association between Bach’s numbers and religious symbolism. It was a fabulous premise with which to work, as it promised to reveal the unseen depths of Bach’s spiritual motivation, although, like the allure of the sirens’ call, it proved treacherous. Nonetheless, numerical readings of Bach’s compositions continued to be published. Many contained fanciful and fallacious interpretations, some were downright illogical,13 and the majority fell short of their promise not only because of weak methodology, but because of their lack of solid historical or documentary evidence.14 The shaky historical foundations on which number and interpretation structures were built made their collapse inevitable. What could have become a valuable scientific discipline of numbers within musicology became known as ‘numerology’, in all its notoriety. And this is where my research enters the history. An examination of Smend’s work led to a study of number alphabets; from their origins, through the quagmires of mystical cabbalism, black and white magic and two centuries of Lutheran exegesis, to the poetical paragram. The results, 9

10 11

12 13 14

A. Schering, ‘Geschichtliches zur ars inveniendi in der Musik’, in Jahrbuch der Musikbibliothek Peters für 1925, ed. Rudolf Schwartz (Leipzig: Peters, 1926), 25–34. Schering cites Glareanus (1547), Kircher (1650), Heinichen (1738), Mattheson (1739) and Sulzer (1778). Schering, ‘Bach und das Symbol’, BJ (1925), 44. Ruth Tatlow, Bach and the Riddle of the Number Alphabet (Cambridge University Press, 1991), 130–8. See Chapter 2, §III. Malcolm Boyd, Bach, The Master Musicians (London: Dent, 1983), 223. Notable exceptions include the number research of Ulrich Siegele and Don O. Franklin, to whom I am enormously grateful for their generosity in sharing their expertise, and lending their support as I pursued my research paths.

5

6

foundations

given first in my doctoral thesis15 and later revised in the monograph Bach and the Riddle of the Number Alphabet, prove conclusively that numbers and numerical interpretations were an integral part of Bach’s heritage. Word and number conceits, including the anagram, chronogram, acrostic and paragram, were popular drawing room pastimes as well as useful tools for the more serious poet or orator in need of creative inspiration. Research for this book began where Bach and the Riddle left off, addressing the question of whether Bach and his contemporaries actually used numbers and number alphabets when they composed. It was originally designed to be a comprehensive survey of theoretical evidence showing where numbers and numerical constructions fitted into compositional theory in Bach’s time, with the anticipated conclusion that composers made little or no use of numbers in practice. The structure and contents changed radically, however, with the unexpected discovery of proportional parallelism in all the collections and multi-movement works that Bach revised for publication.16 At its most basic, the theory of proportional parallelism shows that Bach created layers of 1 : 1 and 1 : 2 proportions, using the numbers of bars in the parts and sections of compositions. The original theoretical survey is included in Part I of this book, while the demonstration of Bach’s use of numbers, including evidence of the changes Bach made as he transformed early works into perfectly proportioned collections, forms Part II. Proportional parallelism would have seemed a self-evident practice to any composer living in Bach’s time and locality, which is not to say that all composers used it. Symmetrical organisation, parallel techniques, perfect proportions and unity were all commonplace, were found in everyday life, in every academic discipline and creative pursuit, and were also described by music theorists in books about how to compose. Numerous observations of the symmetrical organisation found in Bach’s multi-movement works have been accepted into the canon of Bach scholarship. For example, in recent years Christoph Wolff has been a long-term champion for Bach’s architectural designs; their symmetry, order, organisation, connection and proportion.17 Many of these observations can now be confirmed empirically by proportional parallelism. Furthermore, since Smend’s work, there has been a widely held assumption that numbers in Bach’s music would be symbolic. Proportional parallelism shows something subtly, but significantly, different: it is the proportions, rather than the specific numbers, that hold the meaning. 15 16 17

Tatlow, ‘Lusus Musicus vel Poeticus’. King’s College, University of London, 1987. Tatlow, ‘Collections, bars and numbers’, Understanding Bach 2 (2007), 37–58. Many examples in Wolff, Essays.

Bach’s numbers

Several types of evidence combine to demonstrate Bach’s use of proportional parallelism. There is the numerical evidence found in the scores. By comparing the numbers of bars in his early and later versions, or by tracing the changes he made as he compiled a new collection from pre-existing movements, one can see how Bach introduced the layers of perfect proportion. There is documentary evidence to demonstrate the specific role that numbers, unity, symmetry, proportion and Harmony18 played in compositional organisation and planning in Bach’s time. And there is documentary evidence to show how these numerical concepts would have been viewed and understood at the time. There is also a body of evidence hidden by the eighteenth-century language that has been lost in translation, both literally and culturally. At all times I have aimed to incorporate results from the most up-to-date diplomatic evidence and source studies. The majority of results shown in Part II confirm the conclusions drawn by these source studies, but occasionally my demonstrations and numerical reconstructions suggest a new interpretation. The discovery of proportional parallelism in Bach’s collections raises the fundamental and challenging question of why he spent time striving to create proportional order within his compositions. The answer lies in the philosophical and theological understanding of Harmony and harmonic proportions, which had been an essential element in philosophy, science and the arts since classical times, and was still prevalent in Lutheran Germany.19 In the late seventeenth and early eighteenth centuries thought-patterns associated with the Enlightenment began to spread across Europe. Although the ancient proportional world view survived longer in some areas, its final rejection in the early nineteenth century caused an intellectual paradigm shift that would have a profound and lasting effect on the formation of twentieth-century European culture. Bach was living, working and using proportions at this tumultuous time of philosophical change.

II

Parallels, proportions and Harmony

It was the first four numbers, the perfect tetrachys, expressed as the ratios 1 : 1, 1 : 2, 2 : 3 and 3 : 4 and as the proportion 6 : 8 : 9 : 12,20 that the ancient 18

19 20

Harmony, with a capital ‘H’, will be used throughout as a translation of harmonia and Harmonie. See Chapter 3, and the Sonnet by Neuss on the first page of this chapter. Nicomachus’ tenth proportion. See Tatlow, ‘The Use and Abuse of Fibonacci Numbers and the Golden Section in Musicology Today’, Understanding Bach 1 (2006), 77–9.

7

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foundations

Greeks esteemed as the most perfect for music and Harmony.21 The first six sounding numbers, or the senarius, would later be considered perfect because, through the ratios 1 : 1, 1 : 2, 2 : 3, 3 : 4, 4 : 5 and 5 : 6, they were the source of the musical scale, and in sequence formed the unison, the octave, the fifth, the fourth and the major and minor thirds respectively, which is one reason why the Guidonian mnemonic Ut, re, mi, fa, sol, la for the six degrees of the hexachord was also considered perfect.22 Later still the seven ‘harmonic’ numbers 1, 2, 3, 4, 5, 6, 8, called the septenarius,23 or numeri harmonici,24 became popular, the sequence omitting the number seven, or the ‘Ruh-Zahl’.25 In Bach’s time Euclid’s demonstration of the number six as the first perfect number was used to endorse the universal perfection of the senarius;26 those who found the septenarius more perfect also came up with numerous reasons.27 A theology of creation based on proportions and harmonia gradually evolved. Harmonic proportions in the cosmos, in the world and in the measurement of the human being were understood to be a reflection of the ‘indescribable wisdom and perfection’ of the Creator God.28 The proportional perfection of musical intervals gave rise to the terms ‘perfect unison’, ‘perfect octave’, ‘perfect fifth’ and ‘perfect fourth’. The term trias harmonica was coined to describe the consonant triad, because its perfection reflected the perfect Harmony of the Holy Trinity,29 and because its intervals, the fifth and the major and minor thirds, expressed in the

21

22

23

24 25

26

27 28

29

Pythagoras considered it the perfect number as 1þ2þ3þ4 equals 10, from which numbers the proportions 1 : 1, 1 : 2, 2 : 3 and 3 : 4 form the unison, octave, fifth and fourth. T. Christensen, The Cambridge History of Western Music Theory (Cambridge University Press, 2002), 253–4, 276–8. For example in Walther, Praecepta, 36 (Benary, 83), and Buttstett, Ut, mi, sol, 26–8, citing Andreas Werckmeister, Musicalische Temperatur (Quedlinburg, 1691), and Conrad Matthäi, Kurtzer, doch ausführlicher Bericht von den Modis Musicis (Königsberg: Matthäi, 1652), 14–15. Walther, Praecepta, ‘Musica Poetica’, 8 (Benary, 76). Matthäi, Modis musicis, 15, calls seven a ‘rest’ number because one cannot make any musical interval out of the seventh number on the monochord, and because God rested on the seventh day. A perfect number is one whose divisors add up exactly to the number itself. The number 6 has the divisors 1, 2, 3 and 1þ2þ3 equal 6. 28 is the next perfect number because its divisors 1, 2, 4, 7 and 14 add up to 28. 496 is the third, and 8128 is the fourth perfect number. Euclid described this in his Prop. IX 36. Walther, Lexicon, s.v. ‘numerus perfectus’, citing Euclid. J. F. Riederer, Gründliche Untersuchung der Zahl Sieben. (Franckfurt; Nürnberg, 1719). Appendix, 1691-IV 8, 1691-IV 9. (Sources relevant to the doctrine of music have been assigned a short year/number reference (as here) to the Appendix, where full bibliographic references and full text in parallel English-German translation are given.) Walther, Lexicon, s.v. ‘Lippius’ does not name Lippius as the author of the term trias harmonica.

Bach’s numbers

proportions 4 : 5 : 6, were contained within the God-given senarius.30 The triad thus became a powerful reminder for Lutheran Christians of the centrality of music to God and His created order. This view of the world was still alive and current in Bach’s time. Harmony embraced both silent universal proportions and sounding music. A sonnet by Heinrich Georg Neuss (1654–1716), printed in the preface to a music treatise by Andreas Werckmeister (1645–1706) and also on the first page of this chapter, illustrates the centrality of Harmony to Germanspeaking Lutherans in 1691. Within a few decades, though, there would be many changes in the understanding of music and philosophy in Europe. Thomas Christensen explains: Music theory gradually receded from its Boethian heights through the robust growth of musica practica as a discipline. By the eighteenth century, music theory had become only a shell of its former glory. (Rameau felt obliged on numerous occasions to defend the honour and dignity of music theory, while at the same time conceding such knowledge might be of little practical use to musicians.) Yet for every defender of music theory – such as Rameau or Lorenz Mizler (1711–78), the founder of the ‘Corresponding Society of Musical Science’ – there were critics such as Johann Mattheson (1681–1764), who would lambaste much theoria (or, as he preferred to call it, ‘musical mathematics’) as a discredited remnant of unenlightened prejudice . . . With the weapons of empirical philosophy bequeathed by Locke, writers such as Mattheson could militantly hoist the Aristoxenian flag of sensus over that of ratio.31

Philosophical ideas from France and Britain were gaining popularity within Lutheran Germany, and gradually eroding confidence in the centrality of the unison and proportions. The catastrophe was not unforeseen. In 1728, in a book that Bach knew well,32 the Dresden Capellmeister Johann David Heinichen (1683–1729) made the following prediction about the effect of this new philosophy upon music: The beginning has already been made in our times; no doubt daily progress will be made in our century to this end for those supposedly paradoxical hypotheses, and finally all the remaining weak and partly-worn pillars of the musical past will be torn completely asunder.33

30

31 32 33

Walther, Lexicon, s.v. ‘Trias harmonica oder musica’ terms a major triad ‘Trias harmonica perfecta’, and a minor triad ‘Trias harmonica imperfecta’. Christensen, ed., The Cambridge History of Western Music Theory, 8. NBR Doc. 140, and appendix, 529. Bach was Leipzig sales agent for the treatise, and he owned a copy. J. D. Heinichen, Der Generalbass in der Composition, 2nd edn (Dresden, 1728), 5, note (a); translation in Buelow, Thorough Bass Accompaniment According to Johann David Heinichen, rev. edn (Ann Arbor: UMI, 1986), appendix B, 310–11.

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foundations

Bach grew up in this climate of change, when the proportional world view was under attack and gradually falling out of favour, which makes understanding the presence and significance of proportions in his music even more challenging.34 The complexity of this musical and philosophical transition can best be understood from the writings of Mattheson, who was determined to prove that the traditional Lutheran understanding of musical Harmony was erroneous, fighting tooth and nail to prove that true Harmony must be sounding and not silent. ‘Mr Organist’, he wrote, addressing Johann Heinrich Buttstett (1666–1727), ‘why don’t you distinguish primarily between what is properly called Harmony (Harmonia propriè sic dictam), and Harmony in Music (Harmonia in Musicis)?’35 His zeal to divide the traditional Lutheran understanding of Harmony explains many of his curious statements about musical mathematics, not least his seemingly illogical charge about Mizler and Bach.36 From a single united concept that embraced both non-sounding universal harmony and the sounding harmony of pitches and intervals, Mattheson made two distinct harmonies, i.e. Harmony proper (universal harmony) and Harmony in music (the proportions of pitch, intervals and rhythm). In contrast to contemporary theorists such as Mizler and Spiess, Mattheson saw music as a science for the ear alone and not a theory to be studied in terms of proportions and arithmetic. Nonetheless, he continued to believe in many of the philosophical and theological aspects of universal Harmony, sharing some fundamental views about proportions with theorists traditionally understood to be his opponents. Attempting to persuade Buttstett of his erroneous understanding of Harmony, Mattheson demonstrated his personal belief in proportions, writing: There is no doubt whatsoever that the Lord God is pleased with proportions, and the universe demonstrates this . . . God is pleased with musical sounds and their proportions: I doubt that as little as I doubt Christ’s Birth, because music is His creation, indeed one of His best creations and gifts.37

This shows that even Mattheson, reputedly the great opponent of musical mathematics, still profoundly believed that God was pleased with both non-sounding and sounding proportions. It was a belief that motivated him and many other authors and musicians of the period to recommend proportional organisation in musical composition. Mattheson papered 34 36

35 Implications discussed in Chapter 3. Appendix, 1717-I. 37 Mattheson, Ehrenpforte, 231. See also note 7. Appendix, 1717-III.

Bach’s numbers

over the logical cracks of his position, qualifying his recommendation to proportion pieces of music ‘for there is nothing more pleasing to the ear’. Theorists who held the traditional view of Harmony as a united entity recommended proportional ordering in compositions without qualification: to them it made no difference if the proportions were heard or not.

III

The unison and Harmony applied

A proverb cited frequently in music treatises of Bach’s time reads: ‘the closer a proportion is to the unity [or equality] the more perfect it is: the further a proportion is from the unity the more imperfect’.38 This simple formulation holds the essence of much that lies behind the concept of proportional parallelism in Bach’s compositions. The unity and the unison of the 1 : 1 proportion had become the ultimate expression of both equality and perfection. Using Christensen’s phrase, it was truly a ‘generative unison’.39 Whole lifestyle applications and artistic techniques were based on belief in the unity because of its position in universal Harmony, regardless of the practitioner’s stand on the sensus–ratio or sounding/ non-sounding debate. The generative unison fell within Mattheson’s classification of non-sounding Harmonia propriè, the proportions of which even he believed pleased God. How this unison generated many structural forms, including symmetry and parallelism, is the subject of Chapter Two. The 1 : 1 kinship between symmetry and parallelism sheds light on the significance of their use in the arts in Bach’s time. The dual meaning of emblems has been well researched and documented, but I set their parallel image-meaning into the larger context of belief in the philosophical, theological and aesthetic significance of the unity and Harmony. Eurythmia was a synonym for symmetry, which, because of its 1 : 1 nature, was considered to be the epitome of beauty and perfection. According to Johann Gottfried Walther (1684–1748) and other theorists, eurythmia in music could be demonstrated numerically by numerus musicus. There was symmetry in poetry, both in the rhyme scheme and in the metrical organisation, which Morhof described as numerus poeticus. Bach was surrounded by a world of symmetry and parallel forms. Appreciating

38 39

Appendix, 1708-VI. T. Christensen, Rameau and Musical Thought in the Enlightenment (Cambridge University Press, 1993), 84–90 – although Christensen applied the phrase solely to musical properties.

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the underlying philosophy that may have influenced their proliferation and popularity lends further weight to our understanding of why Bach chose to use parallels and proportions in his compositional practice. The acrostic could be used to create a parallel meaning to a poem or a hymn text when the letters of a specific name were woven into the structure, commonly in the first letter of the first word of each consecutive stanza. The poetical paragram is literally a 1 : 1 parallel, with the numerical value of each word in the parallel columns reaching the same total. There were parallels used for compositional invention, one of the most common being a parallel piece of music, created when a new bass line was set to a pre-existent melody, then a new melody to the new bass line, followed by a second new bass line made for the new melody, and so on ad infinitum. Hybrid parallel forms were created from any combination of parallel techniques, such as numero-alphabetical substitutions, emblematic images or arithmetical or algebraic procedures. Bach would have recognised the term lusus ingenii as a description of parallel techniques.40 In a keyboard publication that Bach knew well, his predecessor as Leipzig Thomaskantor, Johann Kuhnau (1660–1722), claimed that his entire keyboard publication, Musicalische Vorstellung einiger biblischer Historien, was nothing more than such a lusus, implying that he might have embedded many more compositional parallels than the mere musical description of the cited biblical stories. There were also parallels with printing symbols. Indeed symbolism, including number symbolism, is nothing more than a parallel expression. Bach’s use of parallel forms can be seen in some of his album entries, where he uses a Latin dedication with a dual meaning. But above all it is the documented use of the family name in music notes – B-A-C-H – that bears witness to his knowledge and use of lusus ingenii and parallel techniques. To what extent Bach developed this practice and toyed with the numerical value of his names can only be guessed. Evidence of what appears to be a reference to his name appears so frequently throughout his published works that I decided to include it as one of the three characteristics of proportional parallelism.41 Bach’s birthday on 21 March (213) happens to be parallel to the numerical value of the first three letters of his surname in the natural order and milesian number alphabets. The parallel use of B and H in music for B♮ makes it possible for B-A-C also to stand for B/H-A-C.42 Permutation was commonplace and second nature to 40 42

41 Tatlow, Bach and the Riddle, 8 and 109. Tatlow, ‘Collections, Bars and Numbers’, 37–58. The idea that ‘B’ always stood for B♭ and ‘H’ for B is a common twentieth-century misconception.

Bach’s numbers

any master of fugal writing. Thus when the letters and numbers 213 appear as 132 or 312 or 123, these too may be a parallel to the 213 of the Bach surname. Chapter 3 explains how belief in the unison and Harmony became intertwined with the Lutheran doctrine of music, and how musicians with a vested interested in Harmony generated conceptual and behavioural regulations, or moral norms from the belief. Proportions in any artistic pursuit gave an objective means of capturing perfection and beauty. Striving to achieve this perfection was an important life goal for those who believed in Harmony, because, as Werckmeister wrote: ‘God Himself created nature through His omniscient counsel so that everything might strive to achieve unity and therein take pleasure.’43 It was his belief in Harmony that caused Buttstett to put in writing what he understood to be the true, correct, biblical view of music,44 to rectify Mattheson, whose views in Orchestre 1 ‘contravened the word of God’.45 Buttstett most probably knew Werkmeister’s book The Noble Art of Music: Its Greatness, Use and Abuse, with its notion of God-pleasing music, which implied its opposite, that music could be composed and used in a way that was definitely not pleasing to God. This belief led to behavioural guidelines for musicians, in which some activities, such as playing in pubs and accompanying the drinking rounds, were classified as sinful.46 More interesting than the prohibitions, however, are the positive practices that this belief encouraged. Developing piety, godliness and virtues were among the practices that Bach and his contemporaries were challenged to strive to achieve. The guideline given by Bach’s second cousin Walther, that good Harmony will result not only when it is ‘composed after the artistic rules, but above all and primarily when it is used in virtuous and God-pleasing practices’,47 implies that he adhered to a belief in the moral and behavioural applications of Harmony. Bach’s choice of wording for the title pages of his Clavier Übung publications implies the same. The hours of hard work Bach must have put into revising his compositions to introduce the unity and layers of literal 1 : 1 or 1 : 2 parallel proportions also speak of a man striving to achieve something specific. He would have saved a lot of time and patience had he left what were perfectly good works unrevised and unproportioned. By making his collections harmoniously structured (i.e. by introducing unsounding parallel proportions, as in Mattheson’s 43 45 46

44 Appendix, 1687-I. Chapter 3, §II. Note the phrase ‘das rechte Fundamentum Musices’. Buttstett, Ut, Mi, Sol, 3. ‘Es ist auch solches kühnes Unterfangen wieder Gottes Wort.’ 47 Appendix, 1691-IX, 1691-XI and 1723-III. Appendix, 1708-II.

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Harmonia propriè) Bach may have been ensuring they would survive the Rapture and last for eternity. Buttstett believed this; Mattheson did not. Chapter Four presents many new sources to show how belief in proportions and the unison influenced methods of musical composition. The ideal of the 1 : 1 and 1 : 2 proportions as the most perfect persisted among German-speaking theorists until the mid eighteenth century. Mattheson wrote more extensively than any other theorist of the period about compositional planning, and, regardless of his view that harmony must be sounding, he recommended that the composer should organise an entire composition so that ‘every part demonstrates a true proportion, uniformity and unison’.48 Perhaps the most direct description he gives is the fifth in his list of rules for loveliness in a melody or in a whole composition, where he writes that the composer should ‘Observe well the proportion of all sections, parts and terms’.49 His belief in well-proportioned music extends to rhythm, the numerus musicus, and to the number of bars as they display a specific progressio arithmetica. Theorists recommend that proportions are formed by the number of bars, the number of beats within a bar, the rhythmic flow within a phrase and the number of bars making up a section. Mattheson makes clear that, although he has for practical reasons used a melody to illustrate this, the same applies to the order and disposition of a complete musical work.50 All this presupposes that the composer, in this case Bach, kept an eye on the number of bars in his composition. And we know he did. When transcribing a part or an entire score, the copyist used the number of bars to determine the length of the finished manuscript, to dictate the size and number of staves to be drawn on each sheet of paper, and to check that the correct number of bars had been copied. Bach used this method, sometimes recording the cumulative total of bars in his scores.

IV

Historically informed methodology

At every stage of the research presented in this book I have aimed to use tools the composer himself could have used, to formulate any discoveries in terms and concepts the composer would have recognised, and to ensure 48

49 50

Tatlow, ‘Theoretical Hope’, Understanding Bach 8 (2013), 39–40; Mattheson Capellmeister, Part II, chapter 14, §30, 240. Mattheson, Capellmeister, part II, chapter 5, §52, 141. Mattheson, Capellmeister, part II, chapter 14, §4, 235.

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that, as far as possible, every claim or concept is supported by appropriate historical sources.51 Twenty-first-century definitions, preconceptions and ‘common sense’ can seriously hamper the historian trying to discover how a musician living in Bach’s time and location thought about specific subjects. It was a systematic use of the principles of what I have termed historically informed theory (HIT) that enabled me to discover proportional parallelism while searching documents and scores for answers to questions about Bach’s possible use of compositional numbers. There are many subtle traps in the process. Recognising aspects of Bach’s physical environment and studying the philosophical and theological ideas of his time can easily encourage us to falsely assume that we have an accurate grasp of life in the early eighteenth century. Similarly, recognising concepts in scores and music treatises of Bach’s time can persuade us that we understand music as Bach and his contemporaries did. Although many of Bach’s techniques and concepts are familiar to us, the image is distorted by all manner of personal and collective modern assumptions. Translations, whether modern or original, frequently mask the intended meaning or the implications of a word or phrase that would have spoken clearly to the original reader. The problems become more complex when we attempt to understand the specific mindset of a historical figure such as Johann Sebastian Bach, whose compositions have become such an integral part of modern-day cultural experience. Although his life story and position in music history are so familiar, can we really know whether what he read caused him to compose differently?

Intellectual influences There are many resources that help decipher cultural codes in Bach studies, including dictionaries and reference works published in the Leipzig area during Bach’s lifetime. The most comprehensive is undoubtedly Zedler’s encyclopedia (Zedler, Lexicon), and for understanding how German was translated into English in Leipzig at this time, Fritsch’s German–English dictionary (Fritsch, Lexicon). To avoid falling into the very time-bound trap one is trying to escape, it is essential to remember that Fritsch’s synonyms reflect early eighteenth-century English usage. Books that Bach knew or that he might have read are also invaluable resources. Although he made no inventory of his library,52 we know he 51 52

Tatlow, ‘Theoretical Hope’, 33–60. K. Beißwenger, Johann Sebastian Bachs Notenbibliothek (Kassel; Basel: Bärenreiter, 1992).

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would have had access to many more books than he possessed. Borrowing literature from family members,53 or from wealthy pastors and supporters, commonly supplemented personal ownership at this time. Bach could also have visited public lending libraries in Eisenach, Erfurt, Lüneburg, Weimar, Cöthen and Leipzig, where the majority of readers were middleclass professionals, as the detailed records of the public library in Weißenfels show. Among their thirty-six volumes of music books and scores were Werckmeister’s Musicae mathematicae hodegus curiosus and Athanasius Kircher’s (1602–80) Musurgia Universalis, if Bach had not been able to borrow these classics from friends.54 It is important not to ignore the fact that ideas may also have been transmitted by personal contact, through word of mouth, or in private correspondence. Bach probably never met Andreas Werckmeister. Their connection was through Johann Gottfried Walther. Bach and Walther were cousins through their respective mothers, Maria Elisabetha Lämmerhirt (1644–94) and Martha Dorothea Lämmerhirt (1655–1727).55 The boys were born within six months of each other and seem to have kept in regular contact throughout their lives. As a 19-year-old in 1704 Walther journeyed to Halberstadt and Magdeburg specifically to get to know the ‘famous musician Mr Werckmeister’.56 The purpose of the trip may have been to discuss the latest musical ideas and possible content for Walther’s own music treatise that he would complete four years later.57 He acquired Werckmeister’s complete works and other ‘stumme Lehrmeister’58 on this trip, and they may have exchanged the names and addresses of useful contacts.59 There may also have been an exchange of musical

53

54

55

56

57 58

59

See Johann Gottfried Walther Briefe, ed. K. Beckmann and H.-J. Schulze (Leipzig: VEB, 1987), 34–54 for Walther’s 1729 catalogue of music books and scores in a letter to Bokemeyer, dated 4 April 1729. M. Raabe, Leser und Lektüre im 18. Jahrhundert, Vol. 4 (München; London: K. G. Saur, 1989), 4 and 534–5. The library purchased Zedler, Lexicon later in the century. H. Bokemeyer c. 1726, J. G. Schwanberger in 1766, and Bach’s biographer J. N. Forkel from 1799, were all readers at this library. A related Martha Lämmerhirt married the Erfurt theorist and organist J. H. Buttstett, whose writings are discussed in Chapter 3. Walther, Briefe, 219. Letter 37 to Johann Mattheson, 28 December 1739. Werckmeister died on 26 October 1706, two years after the visit. Walther, Praecepta. Walther, Briefe, 68 and 219 and editorial comment on page 84, naming Robert Fludd’s Utriusque Cosmi (1617) and Kircher’s Musurgia Universalis (1650) in addition to Werckmeister’s works. For example, Werckmeister may have recommended to him the work of his Wolffenbüttelbased theologian friend Heinrich Georg Neuss.

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manuscripts. In 1729 Walther told Heinrich Bokemeyer (1679–1751) that he owned over 200 organ pieces, the majority given to him by Werckmeister (manuscripts in German tablature by Buxtehude),60 and the remainder given to him by Bach,61 whom he describes as his ‘Vetter’ and ‘Gevatter’.62 Bach would no doubt have seen Walther’s Buxtehude manuscripts and probably have been interested to hear what his cousin had discussed with Werckmeister. Given Walther’s personal association with cantor Johann Heinrich Buttstett and the cousins’ mutual association with Erfurt, there can be no doubt that Bach and Walther would have been interested readers of the Buttstett–Mattheson battle publications,63 and we know that by 1729 Walther owned copies.64 Whatever their response to the dispute, Bach and Walther would definitely have understood Buttstett’s thoughtprocesses and the doctrinal issues that caused Mattheson’s zealous and largely unprovoked invective. Fifteen years later, while Walther was compiling material for his musical dictionary alongside his duties as court organist in Weimar,65 Bach and his second wife found themselves based in the cosmopolitan university city of Leipzig. Located conveniently on the trade routes, Leipzig attracted international visitors to the thrice-yearly fairs, and had a thriving publishing industry. Together with Halle, Leipzig was a host city to the massive lexicographical project initiated by Johann Heinrich Zedler (1706–51), who aimed to record all world knowledge of the time. It was also in Leipzig that Walther decided to publish his dictionary, which was available from 1729 for the pre-publication entries beginning with letter ‘A’, with full publication from 1732, when Bach was its Leipzig sales agent.66

60 61

62

63

64

65

66

Walther, Briefe, 62–3, and BD II, Doc. 263, 193. Bach might have received manuscripts when Walther died in 1748, if the Neuss manuscripts were in Walther’s possession. However, there is no documentary evidence to support this suggestion. Fritsch, Lexicon. ‘Er ist mein Gevatter’ means ‘He was godfather to a child of mine’. In 1712 Bach stood godfather to Walther’s son Johann Gottfried the younger. Vetter means ‘cousin’. Walther and Bach were not cousins, but Walther’s assignation shows that he thought of Bach as a close relative. It would be interesting to know how Walther reacted to the publications, in view of his bad experience of Buttstett as a teacher. Walther, Briefe, 35, letter 4 April 1729 includes two catalogues of books, including ‘(11) Matthesonii Opera omnia, (32) Buttstedts [sic] Ut re mi fa sol la, and (41) Matthesons Orchestre 1. 2. u. 3 Theil’. J. G. Walther was organist at the church of St Peter and St Paul, Weimar from 29 July 1707, and Court Musician from 1721 until his death on 23 March 1748. BD II, Doc. 260, 191.

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Bach owned a copy of the dictionary, and also acted as sales agent for Heinichen’s 1728 treatise Der Generalbass in der Composition, with its masterly introductory analysis of current conflicts within music.67 His promotion of the treatise suggests that he was not offended by Heinichen’s manner or approach to music. The same cannot be said of his attitude towards Mattheson, whose publications were conspicuously absent from Bach’s sales stock. Moreover, Bach seems to have ignored two invitations to contribute a short biography to Mattheson’s Grundlage einer Ehrenpforte, in spite of Mattheson’s praise of Bach in Orchestre 2 (1717),68 and their possible meeting in St Catherine’s church, Hamburg, in 1722.69 Why Bach did not promote Mattheson’s books, when to do so would have been commercially advantageous, and why he did not foster the contact and reply to Mattheson’s invitation when others from the Thüringian region responded,70 are tantalising questions. Perhaps Bach formed a negative opinion of Mattheson’s morality and theology through the battle with Buttstett, or found his comments inaccurate or blasphemous, or even considered Mattheson himself to be an abuser of music, an author who sinfully sought his own glory rather than God’s.71 Unfortunately we cannot know.

Views of composition Even though Bach accepted Mizler’s invitation to join his corresponding society, whose aim was to study the science of music, Mizler understood that Bach never intended to ‘occupy himself with deep theoretical speculations on music’,72 choosing rather to contribute musical compositions that demonstrated theoretical principles. When Bach was teaching he could not avoid covering the theoretical basis of music. Several short sets of his music theory guidelines have survived,73 copied by his pupils C. F. Richter and Carl August Thieme (1721–95) in 1738.74 The guidelines are a free adaptation of sections from Niedt’s 67 68 70 72 73

74

NBR Doc. 140, and appendix, 529. Wolff Learned Musician, 342. 69 Mattheson, Orchestre 2, 222 footnote comment. Wolff, Learned Musician, 213–15. 71 Mattheson, Ehrenpforte, s.v. ‘Walther’, 387. Appendix I, 1691-V, 1716-I. BD III, Doc. 666, 89; NBR, 306. NBA Supplement, ed. P. Wollny (2011), 37–38, rules for figured bass from P 225, 123–4; 41–44, rules for syncopation in double counterpoint; 45–64, rules for canons. Ibid., 3–38. Facsimile in Pamela L Poulin (ed.), Johann Sebastian Bach: Precepts and Principles for playing the Thorough-Bass of Accompanying in Four Parts. Leipzig, 1738 (Oxford: Clarendon Press, 1994), 59–107.

Bach’s numbers

Musicalische Handleitung, whose descriptions exude a clear and strong theology of music. We do not know exactly what Bach would have considered deep theoretical speculations, or what exactly Mizler meant by Bach demonstrating theoretical principles in his music, but I suspect both men would have considered proportional parallelism a practical expression and demonstration of the theoretical principles of music. Trying to paint a true picture of the concepts Bach might have used when he spoke or thought about the construction of music is hindered by the lack of surviving personal papers. Therefore to use concepts that his peers used in books he would have read is the next best route towards catching a glimpse of Bach’s mental imagery and intellectual framework. Several authors described the composition and construction of music in terms used by rhetoricians, dividing the creative process into three: disposition, elaboration and decoration. Some used the imagery of the human being, describing the different parts of music and art in terms of the soul, the body and the clothing. The most popular image, however, was that of architecture, and this is the image I will use to explain the parameters of my own analyses of Bach’s collections in Part II. In music treatises that Bach knew and read, the composer’s task is likened to that of the architect as he designs and builds a new mansion. Just as the architect draws up a plan of a building, detailing the size and position of specific rooms and features within a house, the composer should do likewise, and draft a detailed plan of the parts and sections of a composition. The numerical analyses in Part II are the musical equivalent of an architectural plan. Proportional parallelism has enabled me to reconstruct Bach’s lost constructional drawings. The reconstructed plans show the literal 1 : 1 and 1 : 2 proportions that Bach designed using the ratios of the numbers of bars between movements, within works and between works in a collection. Sometimes two collections are parallel, just as an architect might design two or more proportionally related pairs of mansions in a palace complex. Sometimes old buildings retain vestiges of older structures, which allow a historical architect to reconstruct the position of an original wall, or the shape of an original foundation before its rebuilding or renovation. In the same way, it has occasionally been possible, through vestigial numerical evidence, to detect Bach’s early plans for a collection, and to reconstruct their original shape and size. Whenever numerical evidence of this kind is available, it is discussed in the context of the latest source evidence. Architectural ground plans are simply a parallel image or an analogy to Bach’s musical ground plans. When reading the ground plans in Part II, it

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is important to remember that the specific numerical dimensions of Bach’s collections are of little importance: it was the proportions and not the numbers that he was striving to achieve. In emulating the 1 : 1 unison and the 1 : 2 octave, he was aspiring to create a musical structure that would render his compositions the most perfect, the most beautiful, the most eurythmic, and the most lasting.

Evidence in Bach’s scores The success of a historically informed theory is dependent upon accurate data. If Bach added bars and movements of specific lengths to collections in order to make them perfectly proportioned, it is only by ascertaining how exactly he counted the bars in his works that his numerical planning will be discovered. Many number experiments of the past have fallen at this point, as they use artificial data gathered from the layout of rationalised modern editions, and therefore show nothing more than that symmetrical ordering and numerical coincidence are naturally occurring phenomena. To be able to claim that a composer deliberately incorporated numerical patterns into a work, the data must be pure, based upon the composer’s original scores. Schmieder’s thematic catalogue (BWV) has been a fabulous resource for Bach scholars for over sixty years. The beauty of the catalogue for number research is that it includes a bar total for each movement that Bach composed. Taking over from Wolgast and Ruthardt, Wolfgang Schmieder aimed to include all known works by Bach when he began to compile his catalogue in 1937. The first edition was published in 1950 after the loss of many sources in the Second World War and in time for the celebration of the bicentenary of Bach’s death. Forty years later Schmieder produced a revised edition, assigning a BWV number to newly discovered works and demoting those of doubtful authenticity to an appendix.75 However, much as the catalogues are a useful reference for the number researcher, their authority can be misleading, because the figures can disguise Bach’s compositional intentions. All repeats are included in the bar totals of the Schmieder catalogue, whereas in the shortened version, BWV2a, they are not. Printing errors apart, the bar numbers in the

75

‘Schmieder, Wolfgang’, in J. S. Bach, ed. Malcolm Boyd. Oxford Composer Companions (Oxford University Press, 1999).

Bach’s numbers

catalogues reflect the consistencies of a rationalised editorial policy, rather than the inconsistencies Bach introduced when he laid out his scores. Similarly the latest scholarly editions with full critical commentaries can never be a substitute for working from Bach’s original scores, although their clean modern typeface is a welcome aid to deciphering Bach’s often complex orthography. Bach occasionally noted the bar total at the end of a movement or page, and he quite regularly wrote the number of bars’ rest into orchestral parts. This documented usage shows that he counted bars much as we do today. However, there are several ambiguous features in his scores that can complicate the acquisition of accurate data. These features include the da capo or dal segno indication, the repeat, the half bar line feature and what I call the TS feature, when the time signature is used as a bar line. I will discuss each in turn.

The da capo or dal segno The ABA structure of a da capo aria or movement is normally notated with crystal clarity in Bach’s compositions. Bach usually, but not always, indicates a return to the A section at the end of the last bar of the B section with the words ‘Da capo al fine’ or ‘D’ or with a simple sign %. Sometimes he adds the first bar of the A section after the last bar of the B section, in which case the performer returns to the second bar of the A section. The lengths of the sections are not affected by the notation, but Bach’s layout requires space for one more written bar. If he was working out his proportions from the groundplan of the score, rather than the repeats, it is important to observe this feature literally. Bach’s D indication in his fair copy of the ‘Gavotte en Rondeau’ BWV 1006/3, P 967,76 illustrates the tremendous importance of score layout for number studies. Had I relied upon the NBA edition or the Schmieder catalogues (100 and 108 bars respectively) I would have missed Bach’s design of the 92-bar layout, and the large-scale proportions within the Six Solos for violin (BWV 1001–6), and the theory of proportional parallelism might never have been formulated. Bach’s two different notations of the D return in the Allegro movement used in both BWV 1049 and BWV 1057 show his flexibility in a situation that might originally have been caused by a copying oversight. In Brandenburg

76

D-B Mus. ms. Bach P 967.

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Concerto no. 4 (BWV 1049/1) he notated the movement as 352 (D 75) bars, whereas, in his arrangement of the same movement as a concerto for solo harpsichord and orchestra (BWV 1057/1), he notated it more logically as 344 (D 83), with the da capo return at the end of the last bar of the B section.

The repeat Bach used the repeat sign liberally in his scores, writing at a double bar either two or four dots, centrally between the five lines of the stave. Observing the repeat indications in a movement frequently doubles its length, making the bar total of an entire collection extremely large and unwieldy. A composer creating parallel layers of proportion with the number of bars is therefore most likely to ignore repeats in his bar totals. Where the repeated bars are integral to the meaning of a text, as is the case in texted chorales, Bach frequently notated twelve bars with a repeat, even though the text demands sixteen bars. I was first confronted with this problem when exploring the numerical structure of the St Matthew Passion (MP). According to the shorter Schmieder thematic catalogue, the Passion has exactly 2800 bars, a figure that includes all the da capo indications and the repeats in the chorales. However, despite the seductive beauty of a 2800 bar total, it was necessary to explore the logical possibility that Bach was also aware of the literal layout of the score with the number of written bars, including the non-repeated chorales and without the da capo repeats: this showed a parallel structure with 2400 bars. A repeat can also be indicated in words. In the full score of the St Matthew Passion, for example, there is no music for Chorale 17 ‘Ich will hier bey dir stehen’. Instead, Bach inserted a written indication that Chorale 15 should be repeated with a new text.77 Similarly the ‘Osanna’ of the B-minor Mass (BWV 232 IV/1) is not written out a second time; instead Bach writes the words ‘Osanna repetatur’ after the ‘Benedictus’. In the Goldberg Variations Bach uses words to indicate a repeat of the opening Aria after the Quodlibet variation 30, as he does in the Christmas Oratorio, to indicate a repeat of the opening chorus BWV 248/24 after Chorale 248/35. 77

Table 12.1.

Bach’s numbers

I had to explore whether Bach did this simply to save paper and time, or if the notational feature was integral to his numerical design. Results strongly suggest that Bach was aware of the bar total both with and without the repeated movements, and that when he wished to make a compositional change that destroyed a numerical structure, he could make a virtue of necessity and use the flexible elements of the layout, the D or repeats to facilitate a new numerical plan.

The non-conformist bar There is a notational anomaly in some of Bach’s scores that I term the ‘non-conformist’ bar. Nowadays one expects a careful composer to create the value of a full bar from the combined value of the anacrusis before the opening full bar and the value of the final partial bar of each movement. Bach nearly always complies with this standard, but on several occasions, sometimes in publications, he does not. This orthographic ‘error’, if indeed Bach considered it so, may have been forced by a later amendment to the score, as seems to be case in the extra half bar at the beginning of Recitative (BWV 244/18) ‘Da kam Jesus mit ihnen zu einem Hofe’ in MP.78 Or it may, in publications, have been because engravers considered it too messy, pedantic or technically unnecessary to add small rests when the final bar of a movement was either a full bar or a crotchet short of a full bar, and the opening anacrusis to a movement was a quaver or semiquaver. This can be seen in the anacruses and final bars of the Courante movements in Partita 2 (BWV 826/3) and Partita 4 (BWV 828/3) of Clavier Übung part I (CÜ I). There are several similar cases in Bach’s autograph fair copies where the notational anomaly cannot be blamed on an impatient or unobservant engraver. A more logical explanation for the ‘non-conformist’ bar is when it appears to emphasise the musical phrase. An example is the D minor Ciaccona for solo violin (BWV 1004/5), where the first bar consists of two crotchets in 34 time without a crochet rest, and the final bar has a full three crotchets, instead of the expected one crochet of modern practice. By beginning the first entry as if it were the first beat of the bar (i.e. without a crotchet rest) the performer is given an entirely different impression of the subject that is about to unfold.

78

The recitative is literally fifteen-and-a-half bars long, but is counted as fifteen whole bars in BWV, BWV2a and NBA.

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Ambiguity of the half-bar line In movements using stile antico notation, with their or time signature, Bach writes a full-length bar line at the breve and frequently adds a shorter vertical line after each semibreve. This short bar line raises the question of whether he counted the bar at the semibreve or the breve. The Schmieder catalogue counts each breve as the ‘bar’, as indicated by Bach’s full-length bar line, and we have evidence that Bach also counted such movements at the semibreve. For example, when he copied the parts of the B-minor Mass for both the second ‘Kyrie’ and the ‘Gratias agimus’, Bach wrote bar lines at the breve in the score and yet counted the bars’ rest in the parts at the semibreve.79 The semibreve count would make things much easier for the instrumentalists and thus for accurate ensemble performance. However, as this ambiguous notation appears also in keyboard music where no other instruments or players are involved, the reason for it cannot have been solely to facilitate ensemble playing. Bach had to know the number of bars in either form to create the correct layout of his score and parts. The numerical evidence strongly suggests that he was aware of the bar totals both at the breve and at the semibreve in such movements and that he actively exploited the duality. His inconsistent use of the qualifying term ‘alla breve’ for these movements emphasises and highlights this ambiguity. Occasionally Bach introduced a similar feature in movements with a time signature of 68 or 64 . For example in the Presto of Sonata 1 for solo violin (BWV 1001/4), which has a time signature of 68 , he wrote short bar lines at 38 , and in the Corrente of Partita 1 (BWV 1002/3), which has a time signature of 64 , he wrote short bar lines at 34 . These notational ambiguities will be pointed out in Part II whenever they affect the bar count.

The TS feature: a time-signature as barline It was the coincidence of the double 1 : 1 proportion between Bach’s first keyboard collections, 2 : 2 sets in 3120 : 3120 bars, that forced me to take the TS notational anomaly seriously.80 The 1722/3 pair has exactly 3120 bars with several layers of proportion, whereas CÜ I and II appear to have 3121 bars. With only one bar difference, it was strangely close and yet so far from 79

80

Tatlow, ‘Parallel Proportions, Numerical Structures and Harmonie in Bach’s Autograph Score’, in Exploring Bach’s B Minor Mass, ed. Yo Tomita, Robin A. Leaver, Jan Smazcny (Cambridge University Press, 2013), 142–62. Table 6.8.

Bach’s numbers

perfection. Had Bach been striving to achieve the perfection of 1 : 1 between his first two published sets of CÜ and his set of two keyboard collections lovingly transcribed in autograph fair copy a decade earlier, it is highly unlikely that he would have missed the total by one bar. Because he had taken so much time and care over the construction and publication of CÜ I and II, I initially suspected that the error was mine. But discovering later that the total of the Six Trio Sonatas for two manuals and pedal (BWV 525–30), appeared to be 1561 bars – just one bar more than would create a 1 : 2 proportion with 3120 bars – caused me to scour the autograph scores and original prints of these collections for any notational peculiarity. It was then that I discovered the common feature. In both CÜ I and the Six Trio Sonatas there is a single example of a time signature used in place of a bar line in the middle of a movement at a time change. In the thirtieth bar of the first movement of Partita 2 (BWV 826/1), there is no bar line when the movement changes to 34 time. In the Six Trio Sonatas there is no bar line when the movement changes to 34 time in the fourth bar of the first movement of the fourth sonata (BWV 528). Further observations showed that Bach was inconsistent, or perhaps intentional, in his notation of the bar line at a change of a time signature. Usually when the change of time signature coincides with a repeat indication, he inserts a double bar line, for example, at the change from to 98 time in the first movement of Partita 4 (BWV 829/1). At the end of the first movement of the French Overture, CÜ II (BWV 831/1), he omits the bar line at the change to 68 necessitated by the repeat indication at bar 163, which affects the bar count when the movement is repeated. Modern editors invariably choose to insert an extra bar line before the time signature. Bach did not. When he published the B-flat major Partita (BWV 826) individually in 1727, the lack of a bar line between bars 29 and 30 created a movement that contained simultaneously 90 and 91 bars, giving a margin of numerical flexibility to part of an incomplete collection, that would be a useful numerical loophole in extremis if required as the larger numerical plan evolved. Bach did not amend the feature when the set of six partitas was republished in 1731 as Opus 1, even though he made other small notational adjustments. There are notable incidences of the time-signature as barline in many of Bach’s vocal works. It can be seen three times in the B-minor Mass (BWV 232), many times in two recitative sections of his autograph score of MP (BWV 244/ 11 and 41c), and in the mixed choral/recitative section of the Christmas Oratorio (BWV 248/7), where the tight rhythm of the choral sections contrasts strongly with the flexibility of the Evangelist’s recitatives.

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Wherever it occurs in Part Two this time signature as bar line feature will be highlighted in the tables, and indicated by the abbreviation TS. The TS feature might seem more characteristic of a lapse in orthographic consistency than of deliberate design, but the numerical results and Bach’s usage suggest that he left it in intentionally. An element of numerical flexibility was well known to paragrammatists as a well-tried and tested technique to facilitate creating the perfect parallel 1 : 1 proportion with the numerical value of words and mottos.81

V

Proportional parallelism

Overlooked for almost three hundred years, the three characteristics of proportional parallelism can now be seen in every collection and multimovement work that Bach published or left in autograph fair copy, their understated simplicity unifying complex works of art.

Bar total as a multiple of 10, 100, or 1000 All of Bach’s collections, whether published or in autograph fair copy have a bar total that is a multiple of 10, 100 or even 1000. In the few collections where the bar number is not a multiple of 10, 100 or 1000, the round bar total is seen when two companion collections associated by a common title or an indisputable compositional timeline are viewed together. For example it is only when book 1 of Das Wohltemperirte Clavier (WTC), The Well-Tempered Clavier, is viewed with the companion collection that Bach prepared at the same time, the Inventions and Sinfonias, Aufrichtige Anleitung (AA), that one sees the total 3120 bars. And it is only when CÜ I and CÜ II are viewed together that the self-referential key pattern and the overall plan of 3120 bars, parallel to the earlier pair, can be seen.82 Unfortunately we do not have documentary evidence to demonstrate conclusively how Bach achieved such an exact total over such a long period of time. The occasional recorded bar totals in his music suggest he was keeping an eye on the length of a movement, either because it was a copying habit, or because he was aiming to achieve a specific numerical 81

82

J. F. Riederer, Catalogus derer eintausend fünfzig Paragrammatum Cabbalisticorum Trigonalium (Nürnberg, 1719). Introduction, 4. Table 6.8.

Bach’s numbers

total, or both. Above all, though, it is the additions and extensions that Bach made as he compiled and revised a collection that provide empirical evidence of his intention to create a perfect structure imbued with the characteristics of proportional parallelism.

Numerical reference to Bach’s name The second characteristic of proportional parallelism is a recognisable Bach signature, formed either in the total number of bars or in the overall key pattern. A common numerical allusion is the combination of the numerals 2-1-3, with numbers 14, 41 and 158.83 Because the numbers 21-3 are also the component parts of the first numerus perfectus 6 it is dangerous to interpret the bar totals formed from these numerals as a selfreferential conceit. It is quite possible however that this numerus perfectus / parallel signature duality pleased Bach. The signature is sometimes formed by key patterns across a work, as in both the collections for violin, the Six Solos (BWV 1001–6) and the Six Sonatas (BWV 1014–19). In each case the pattern B-A-C is clearly seen when the 1600 bars of the 2 : 1 proportion are grouped together (Tables 5.1 and 5.4). In Bach’s time the musical letters B and H for B natural were interchangeable, contrary to a common twentieth-century misconception. Parts I and II of the CÜ series have signatures in both the bar totals and the keys: 3120 bars and B-A-C-H, facilitated by Bach’s transposition of the French Overture from C minor to B minor.84 It has been suggested that Bach deliberately copied the Six Solos for violin onto forty-one sides of music as an allusion to the numerical value of one of his signature forms; ‘J. S. Bach’. This is possible, although if Bach had intended forty-one sides, he could have numbered each side of music, as he did for the Missa of the B-minor Mass (P 180). In the event, he foliated the solos on consecutive recto sides from 2 to 22. The different numerical totals of Bach’s name as a whole have been the subject of speculation and problematic interpretations since Friedrich Smend first introduced the notion to musicology in the 1940s. It would be ludicrous to claim that Bach intended every occurrence of the numbers 14, 41, 70, 100, 108 and 158 to be a self-reference. The multiple possibilities generated by each number when their divisors and multiples are ‘allowed’ mean that almost any number in a Bach score could be considered 83

See Chapter 2, §IV.

84

Table 6.8.

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signatory. There are nonetheless some notable occurrences of these numbers in obvious structural positions which suggest they were planned. Framing the collection of Leipzig organ chorales transmitted in P 271 is a perfect 2 : 1 proportion formed by the Bach name numbers 158 : 79. The first and last chorale preludes in this collection together have 158 bars, and the two central preludes have 79. The proportion would have had to be planned before Bach began to copy the collection. Strongly implied as one of the numerical ground plans of the posthumously published The Art of Fugue is a similar perfect 1 : 2 proportion on the name number 158, although multiplied by 10. The first eight movements have exactly 790 bars, after which is the much discussed emblematic signature. The remaining movements have 1300 bars, and the final incomplete fugue 239 bars, just 41 bars short of the anticipated 1580 bars. Planning to publish the collection posthumously, Bach might have introduced the puzzle of the unfinished final fugue so that the reader would ask both ‘what’ and ‘who’ is missing; its solution, highlighted by the emblematic seal after bar 790, pointing to the overall 1 : 2 structure with its missing 41 bars, which in turn points to the missing author, J. S. Bach (41). The number 14 appears relatively frequently in the large-scale totals of collections. 1400 bars in the B-minor Mass, 1400 bars of the Ascension and Easter Oratorios, possibly 1400 bars in Six Keyboard Concertos, 2800 in the MP and possibly 2800 bars in the two keyboard collections CÜ III and IV. Interpreting the number 28 as self-referential rather than as the second numerus perfectus raises the same problem as the interpretation of permutations of 1-2-3. Embracing their parallel significance is perhaps the best solution. The annotations in his copy of Calov’s Bible commentary show that Bach was interested in eschatological numbers. For example, he wrote in the margin beside Daniel 12: 7–13 the following numbers that occur in the printed text: 1260, 1290, 1335, 1941 and 2408.85 Besides 2408,86 these figures have not occurred in the bar totals in Bach’s scores and so I suspect we should take Bach’s annotations at face value, as evidence of a lively intellect, intrigued by figures while reading his Bible carefully. Friedrich Smend was keen to systematise a Lutheran interpretation of

85

86

R. A. Leaver, J. S. Bach and Scripture: Glosses from the Calov Bible Commentary (St Louis: Concordia, 1985), 113–15. 2408 is the bar total of BWV 1001–6 in the modern NBA layout.

Bach’s numbers

numbers and apply it to Bach’s music.87 Laudable as Smend’s aim was, it proved impossible due to the difficulty of amassing reliable data and the multiple ambiguities of parallel techniques.

Parallel layers of 1 : 1 or 1 : 2 proportions The most significant of the three characteristics of proportional parallelism, however, is the layers of 1 : 1 and 1 : 2 proportions that divide the bar total, the movements and the works of a collection into rationally and frequently symmetrical structures. The prevalent view of the perfection of proportions close to the unity (1 : 1 and 1 : 2) was good reason for a composer like Bach to take the time and effort to introduce them so precisely into the structural layers of his published collections. These perfect proportions88 coexist at several layers in the structure of the publications: between sections of a movement, between movements of a work, between two works in a collection, between parts of the collection as a whole and between two related collections. In the Six Solos for violin (BWV 1001–6), for example, there are five distinct layers of proportion, and in the Christmas Oratorio (BWV 248), at least three. To save space, the smallest-scale layer of proportion, formed between sections of a movement and commonly found in binary-form dances, will not be included in the demonstrations in Part II. Strangest of all the proportions in Bach’s compositions is that found between two or more collections. It seems too large and too theoretical to have been intentional, and too speculative and invisible to be of any scientific value. Nonetheless, having discovered it, it has been noted with supporting documentary evidence. In the case of the violin solos, a double 1 : 1 proportion is formed with the Six Sonatas for violin and harpsichord (BWV 1014–19), which also have exactly 2400 bars. This is particularly persuasive because their next layer of proportion is identical – a double 2 : 1 proportion with four works having exactly 1600 bars and the other two 800 bars.89 The largest-scale proportion is also found between Bach’s first two keyboard collections and his first two published keyboard collections. In spite of the time gap, Bach created a double 1 : 1 proportion between the four collections and their identical totals (2 : 2 collections in 87 88

89

Tatlow, Bach and the Riddle, 8–36. By using the word ‘proportion’ rather than ‘ratio’ I am following usage of the early eighteenth century, when theorists used ‘proportion’, although aware of its technical inaccuracy. Walther, Praecepta (1708), Book II, 10 (Benary, 76). Tables 5.9 and 5.11.

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3120 : 3120 bars), adding a hitherto unseen relationship between them – a relationship that perhaps Bach alone knew.

The extent The three characteristics can be seen in all of the collections and multimovement works Bach published or wrote out in best top copy. The word ‘collection’ in this definition is used to mean works in which two or more compositions are united by title, e.g. CÜ I and II, or in which two or more compositions are collected under one title, e.g. the six partitas in CÜ I, or the six works of the Brandenburg Concertos. The term ‘multi-movement works’ includes large compositions with many movements under one title, e.g. MP and the B-minor Mass, as well as smaller works such as the Canonische Veränderungen on the melody ‘Vom Himmel hoch’, known as the Canonic Variations. The ten works printed during Bach’s lifetime are ‘Gott ist mein König’ (BWV 71); CÜ I (BWV 825–30), for which five partitas were published separately before publication of the collection of six partitas; CÜ II (BWV 831 and 971); CÜ III; the Aria with Thirty Variations, the ‘Goldberg Variations’ (BWV 988); Musicalisches Opfer (BWV 1079); the Canonic Variations (BWV 769); Sechs Choräle von verschiedener Art known as the ‘Schübler Chorales’ (BWV 645–50); Die Kunst der Fuge, The Art of Fugue, largely overseen by Bach although published posthumously (BWV 1080); and two canons, the Canon Triplex à 6 voci (BWV 1076) and an untitled canon (BWV 1074). Of these ten, all but the two canons are collections according to the definition above, and all display the three characteristics of proportional parallelism. Bach was also responsible for the sixty-nine engraved musical settings in the hymn book Musicalisches Gesang-Buch published by G. C. Schemelli, for which he composed some new melodies and revised some harmonisations. Although the hymn book is a collection, Bach’s contribution to its musical content does not fall within the definition of a Bachian collection. The autograph fair copies are manuscripts that Bach intended to stand as a neat and definitive version, normally written in meticulous calligraphic script and containing very few errors.90 In many cases early versions of these works survive, making it possible to trace the revisions Bach made as he created the perfect parallel proportions. Particularly interesting in this 90

Yo Tomita, ‘Sources. 1. Manuscript Sources’, in J. S. Bach, ed. Malcolm Boyd. Oxford Composer Companions (Oxford University Press, 1999).

Bach’s numbers

respect are the Brandenburg Concertos (BWV 1046–51); the Six Solos for violin (BWV 1001–1006), WTC I (BWV 846–69); AA (BWV 772–801); the Six Trio Sonatas (BWV 525–30); the so-called Leipzig Chorale Preludes, or the Great Eighteen (BWV 651–68); MP (BWV 244); the Missa in A major (BWV 234); the Christmas Oratorio; the Easter Oratorio (BWV 249) and the Ascension Oratorio (BWV 11). Many of Bach’s collections are in mixed calligraphy, either mixed in the sense that the manuscript score includes a copyist’s hand, or that Bach himself mixed calligraphic styles, with corrections and sometimes with newly composed material, demonstrating that he was revising or adding to the composition even as he was making the fair copy. The three characteristics shed light on the status of such manuscripts, which include: St John Passion (BWV 245) and the B-minor Mass (BWV 232). The status of collections transmitted in the hand of a copyist for which no autograph has survived can also be tested against the three characteristics. Collections in this category include the Six Sonatas for violin and harpsichord (BWV 1014–19a), six Cello Suites (BWV 1007–12), and the Early Keyboard Transcriptions of concertos by various composers (BWV 972–87). A number of well-known collections in Bach’s hand have come down to us in separate parts, or as an incomplete collection. These include WTC II (BWV 870–93); the French Suites (BWV 812–17); the English Suites (BWV 806–11) and the Orgelbüchlein (BWV 588–644). There are also several collections known today as Bach collections that are nothing more than compilations of works of similar genre and instruments put together by librarians and editors in the nineteenth and early twentieth centuries. As these were not designed or revised by Bach, they will be disregarded in this study. Bach’s annual cantata cycles fall outside any of these categories. They are in the widest possible variety of handwriting, and the current state of documentary evidence makes it impossible to test whether Bach designed them as collections. Nonetheless examples from several cantatas have been included in Chapter 12 because they indicate that Bach aimed for numerical proportion even when he was composing quickly on such a small scale.

Evidence from Bach’s revisions In the early days of my research I assumed that Bach had a single, rather than several, well-defined concepts of a work when he made the first sketch, and that the numerical plan, if he had one, would be found in the earliest versions. Gregory Butler has persuasively demonstrated, from

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erasures in the original engraved prints, that Bach made many dramatic changes to the original concept of CÜ III to the extent of altering the entire stucture of the collection after he had sent it, presumably ‘complete and finished’, to the publisher.91 Every single change has significant implications for the overall bar total and the internal proportions. Tracing the revisions through to the perfect proportions in the final publication of CÜ III suggests that Bach had a numerical plan for each stage. Making changes to handwritten works was not such a serious or expensive business as amending engravings. However, paper was expensive and Bach’s early versions were in no way lacking structural forethought. The clearest example of Bach discarding an excellent numerical plan in favour of something even more perfect can be found in the construction of the B-minor Mass, from the 1733 Missa, through the implied construction of parts II–IV, to the final 1749 Missa tota.92 When Bach was revising a collection he frequently reordered its constituent parts. Studying the original order can sometimes show what the earliest numerical plan was, although it is not always possible to trace the original beneath an amended version. In the case of AA (BWV 772–801), however, we have both Wilhelm Friedemann’s Clavier-Büchlein and Kayser’s later copy of the earlier ordering. The embryonic 500 : 500 bar structure of Friedemann’s copy is visible, although several of the movements are left unfinished, as if father were instructing son in the art of proportion. In his own calligraphic autograph copy of the collection, Bach reordered the thirty movements to mirror and complement the key patterns of WTC I and in this reordering the constructional blocks of 500 and 500 bars disappeared.93 Editors have been at a loss to explain why Bach made small and seemingly insignificant bar changes to what was already perfectly good music. Hans Eppstein noted that these changes frequently occur in the final work of a collection. Observing that in the sixth sonata (BWV 1019) Bach defied the formal logic set up in the first five sonatas of this collection for violin and harpsichord, Eppstein asked ‘What might be the cause of Bach’s action?’94 Bach’s documented revisions to create layers of parallel proportion in all his polished collections provide an explanation.

91 92 94

G. Butler, Clavier-Übung III: The Making of a Print (Duke University Press, 1990). 93 Tatlow, ‘Parallel Proportions’, 142–62. Tables 6.4 and 6.6. H. Eppstein, ‘Fragen der Ordnungsprinzipien’, in Leipziger Beiträge zur Bach-Forschung 5, ed. U. Leisinger (Zürich: Olms, 2002), 133.

Bach’s numbers

The numerical demonstrations in Part II often show blocks of bars, or ‘building blocks’, with a rational total, sometimes even proportioned. These readily recognisable units are usually unrelated to the final proportion of the finished structure, but may well have facilitated the construction of the larger-scale whole. For example, the consecutive 1300-bar unit visible in the published version of The Art of Fugue, the contiguous blocks of 500 bars and 500 bars in Kayser’s copy of the Inventions and Sinfoniae, and the 900 bars in Six Solos for violin could all have helped Bach as he created the proportioned collections. The arrangement of movements forming perfect proportions can appear consecutively, or in a symmetrical, interlocking, dovetail pattern with two ends and a middle, as in Puttenham’s ‘proportion by situation’.95 Symmetry is the quintessential 1 : 1 proportion over a central axis. Of course Bach did not design all the symmetrical arrangements that can be found in his scores: random groups and random numbers will naturally form proportions and symmetry. Nonetheless the recurrence of some very specific patterns and symmetrical features strongly implies intentionality.

Summary Although the theory of proportional parallelism has been formulated in the twenty-first century, the ambition has been to keep the thought-processes consistent with eighteenth-century ideas and practice. Although it was the intentional application of the principles that led to the discovery of proportional parallelism, there remain many dangers in pursuing a method based on numbers. The number of notes or bars in a score offers the illusory promise of a direct line to the composer’s thought-processes, a promise beyond the aspiration of the majority of music analytical techniques. If the composer was not aware of how many notes or bars he wrote, the patterns the analyst isolates will reveal nothing about the compositional method, and subsequent interpretations based upon these patterns will be little more than fantasy. The main problem, though, is not the patterns. Patterns are good and important, helping to explain how music works and how a composition is constructed. The problem is when the analyst assumes, without external evidence, that the patterns are proof of the composer’s intentional design. External source evidence supporting the 95

George Puttenham, The Arte of Poesie (London, 1589). This work is discussed in Chapter 2.

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method, the data and the interpretation is essential before the analyst can with any integrity claim that the composer designed the patterns. And even then there must be room for doubt. The age-old issue of how we listen and think also affects our interpretation of a musical score. Bach and many of his contemporaries heard and understood music in terms of modes, hexachords, tones and keys.96 We have experienced atonality. Bach knew that the harmonic proportions he used in his compositions were central to the created order in the universe. Today we believe otherwise. The many philosophical and musical differences between Bach and ourselves are increasingly irreconcilable. A face-to-face conversation with Bach would be the simplest way to answer many of these questions, but as this is impossible, the musicologist has to confront the problem and decide: either to give up any ambition to hear and think as Bach did, content to discover twenty-first-century resonances in his music; or to continue to attempt to hear as Bach did, and strive to understand the universe and music as he understood it. I chose the latter, and using terms that Bach could have used, I decided to name the phenomenon I had discovered ‘proportional parallelism’. The idea for using the term ‘parallelism’ originated with Heinrich Schenker’s concept of motivic parallelism, even though its parallels are very different from the layers of parallel proportions I had found in Bach’s scores.97 I originally chose the Schenkerian paradigm of background, middleground and foreground to differentiate between these layers of proportion, but rejected them and the word ‘level’ in favour of the word ‘layer’ because it was less hierarchical.98 Furthermore, Zedler’s encyclopedia shows that the words parallelismus and parallelistica methodus had a specific meaning in theological circles in Bach’s time: Parallelismus is a juxtaposition or a comparison of diverse passages by an author, used to explain or clarify the meaning of something difficult, with something clearer, which is a necessary technique in the art of exegesis.99

96

97

98

99

For example Kirnberger’s annotations in red ink on the copy by Anon. 42 of WTC, D-B Am. B. 57. I am grateful to Yo Tomita for alerting me to this example. D. Beach, Aspects of Unity in J. S. Bach’s Partitas and Suites (University of Rochester Press, 2005) and C. Burkhart in his classic analysis of Schubert’s ‘Erlkönig’ in ‘Schenker’s “Motivic Parallelisms”’, Journal of Music Theory 22/2 (1978), 145–75. I am grateful to Jonathan Dunsby for his invaluable help in the process of clarifying the conceptual properties of proportional parallelism. A pilot version of the theory was presented in Oxford at the Third J. S. Bach Dialogue Meeting of Bach Network UK in 2006, where delegates posed many valuable and searching questions. Zedler, Lexicon, s.v. ‘Parallelismus’.

Bach’s numbers

The technique has two branches, ‘parallelism of words’ and ‘parallelism of things’, which are subdivided into two species, ‘historical parallelism’ and ‘dogmatic parallelism’, and two orders ‘parallelism of the first order’ and ‘parallelism of the second order’. This contemporary definition shows that the word was used in the context of methodology, and that it would have been natural for Bach and his contemporaries to clarify the meaning of something with a parallel technique. The three characteristics raise many questions, not least why a composer such as Bach would introduce proportions that cannot be heard. Heinrich Schenker believed that his parallel motives were aurally detectable, that the motives nesting in each other at the different structural levels were mentally retained by the listener across the length of a composition. He believed that this accounted for a perceived unity within a musical work. Although the aesthetic bases of the theory of proportional parallelism and Schenker’s parallel motives are entirely different, both may be part of why and how a large-scale Bachian collection is perceived as a whole. With this skeletal introduction to the methodology and parameters of the subject area of this book, the reader may, without too much detriment, proceed directly to the analyses in Part Two. The remainder of Part One will add chapter and verse, flesh and bones to the evidence summarised and referenced in this chapter. Naturally, though, I hope that the majority of readers will enjoy the detailed historical discussion and the documentary evidence presented in the following three chapters, as they aim to awaken a deeper appreciation of the beauty and complexity of what numbers, proportions and Harmony meant in Bach’s world and in his music.

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2 Symmetry, proportion and parallels

Proportio quo vicinior aequalitati eo perfectior Proportio quo remotior ab aequalitate eo imperfectior. J. G. Walther, 1708

Hybrid parallel forms, including number games, word play and the permutation of numbers, characters, notes and letters, cropped up in every area of daily life in Bach’s time and permeated every creative pursuit. Bach would have seen them in the construction and decoration of buildings, in literature, poetry and imagery, and he would have heard them in speeches and in music. Nonetheless modern research has overlooked the kinship between parallelism, symmetry and eurythmia.1 Many of the parallel techniques transmitted over the centuries have their roots in the culture of ancient Greece. They have been adopted and adapted by different cultures in different ways, appearing in various pure and corrupt forms in the writings and artworks of authors with vastly conflicting intentions and philosophies. Failure to appreciate this inherent diversity has led to many an inappropriate interpretation of the parallel techniques of Bach’s time. This chapter aims to correct the distortion and remove the mystique surrounding parallel techniques.

I

Symmetry as an ideal

Symmetrical forms are simultaneously a proportion and a parallel: a proportion because they are a literal 1 : 1 ratio around a central axis, and a parallel because they consist of two contrasting concepts that run side by side. Parallels are always both symmetrical and proportional. Proportions, although always parallel, are not always symmetrical. In the German–English dictionary published by Fritsch in 1716 (Fritsch, Lexicon), the entry on ‘Symmetrie’ reads: ‘Symmetrie eines gebäu[d]es 1

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Even though the parallel totals of its texts are a literal 1 : 1 proportion and ‘para’ its prefix, the significance of parallelism in the poetical paragram escaped my attention in Bach and the Riddle.

Symmetry, proportion and parallels

(die) die geschicklichkeit und gleichförmigkeit aller theile desselben, the symmetry of a building; the uniformity, or regular proportion of all its parts’. Twenty years later, Mattheson used the word Gleichförmigkeit (uniformity/symmetry or regular proportion) in a recommendation about the best way to order a complete composition ‘so that each part demonstrates true proportion, uniformity and unison’.2 Symmetry was still an ideal of beauty and perfection in Lutheran Leipzig in the 1740s. Emphasising the harmonious quality of the 1 : 1 unison and the centrality of symmetry, Zedler’s entry s.v. ‘Eurythmia’ reads: Eurythmia, die Wohlgereimheit, is a term used in architecture to mean the agreement (Uebereinstimmung) of the sections and decoration, and applied to the whole building, such that all parts of a building coordinate well together with the aim that a building is harmonious, e.g. that in small houses one also has small stair cases, in large rooms large doors etc. . . . Vitruvius defined Eurythmia as a fine exterior and a comfortable concept in the compositions of different works. What is termed here Eurythmia is the French word Symmetrie, which in Vitruvius can be recognised in the proportion of the parts of a building.3

The entry on ‘Beauty in Architecture’ begins: ‘The rules of beauty for a building are based on symmetry, or the proportional unison (Uebereinstimmung) and well-disposed ordering of all the parts of a building,’ but ends with a more modern and significant qualification: ‘what some find beautiful others do not’.4 This element of subjective taste also appears in the article ‘Zierrath’. Nonetheless the traditional understanding of symmetry and proportion as the objective, measurable ideal for beauty and perfection continued to dominate, with no suggestion that this ancient aesthetic had yet gone out of fashion in Leipzig and Halle. Dividing ‘decoration’ into the intrinsic and the natural, the article ‘Zierrath’ continues: Intrinsic decoration consists of Symmetrie and Eurithmie. Symmetry requires that all the parts of a building, both between itself and against the building as a whole, are well proportioned in length, breadth and height. Eurithmie, however, demands that each part of the house is positioned in the correct direction and positioned in its proper place. Without question the best and most pleasing proportions are those that can be expressed in single and small numbers, because they can be easily and accurately recognised and distinguished at a glance. This pleases our emotions most, and does not require too much or too astute sharp reflection. Therefore note the following proportions: 1 : 1, 1 : 2, 1 : 3, 1 : 4, 2 : 3,

2 4

3 Mattheson, Capellmeister, 240. Zedler, Lexicon, s.v. ‘Eurythmia’. Ibid., s.v. ‘Schönheit in der Baukunst’.

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3 : 4, 4 : 5, 5 : 6. We meet the same proportions in every part of our own bodies, and in all its joints when they are measured against each other or against the whole body.5

Notice that the author includes the senarius, the first six proportions of Harmony, within the definition of symmetry and eurythmia. Citing Vitruvius book III chapter 1 and Albrecht Dürer in his book of human proportions, the writer continues: ‘Another reason they [proportions of the senarius] please us is that they please our ears . . . Whichever proportions please our ears, our eyes find pleasing too.’6 According to Walther eurythmia in music also requires numbers: ‘Eurythmia is decoration and beauty, which in music consists of numbers, when a melody is well-constructed numerically.’7 He also cited and upheld the Aristotelian proverb that the closer a proportion is to unity or equality (i.e. 1 : 1), the more perfect it is; the further a proportion lies from unity or equality, the more imperfect and confusing it is.8 Music theorists including Mattheson, Walther and Niedt discussed the technicalities of eurythmia in music in terms of progressio arithmetica and numeri musici. Mattheson recommended Gleichförmigkeit, symmetry, proportion and unison as the ideal for making a plan for a complete composition.9 Details in the published conflict (1713–18) between Mattheson and Buttstett show that they disagreed over whether the proportions of Harmony in music actually had to be heard in order to be pleasing to God. Mattheson was adamant that non-sounding Harmony was not musical harmony, whereas Buttstett believed the opposite. In fact, as Part II demonstrates, all of Bach’s publications and autograph fair copies display non-sounding eurythmia and symmetry, created by large- and small-scale 1 : 1 and 1 : 2 proportions between sections, movements and works in collections. The majority of his proportions cannot be heard.

II Proportion poetical as a model Symmetry could be expressed in poetic forms. Book two of the widely circulated three-part poetry treatise, The Arte of English Poesie (1589) by George Puttenham (1529–90), is devoted entirely to poetical 5 8

Ibid., s.v. ‘Zierrath’. Appendix, 1708-VI.

6 9

7 Ibid. Walther, Lexicon, s.v. ‘Eurythmia’. Mattheson, Capellmeister, 240 §30.

Symmetry, proportion and parallels

proportion.10 Starting with the mathematical basis of proportion, Puttenham’s descriptions include: (i) proportioning of the staff or stanza through the number of verses in each;11 (ii) proportioning of the measure or mensura through the number of feet and/or syllables,12 including the caesura, through the correct symmetrical positioning of the comma, colon and period;13 (iii) proportioning of rhyme14 through the accent or stress,15 and cadence through the metre and feet;16 (iv) proportion by situation, through the symmetrical arrangement of rhymes;17 (v) proportion in figure, through the symmetrical arrangement of line length,18 which includes many forms such as the anagram. Puttenham’s categorisation of proportions by situation and in figure gives a documentary basis for patterns found in Bach’s works. These patterns of rhymes and feet were commonplace in the poetry of Bach’s time, and there is every reason to assume that such patterning was also applied to musical units. Puttenham likened these proportions to the stones or bricks used by the mason as he constructs a building.19 The example in Figure 2.1 shows seven alternative ‘proportions’ formed by the permutations of metre and rhyme within five lines. Importantly, this demonstrates that patterns formed between non-consecutive units were still classified as proportions; many such non-consecutive units forming numerical proportions are found in Bach’s works.20 Puttenham also describes two proportions working at different levels simultaneously, writing: Of Proportion by situation. This proportion consisteth in placing of every verse in a staffe or ditty by such reasonable distances, as may best serve the ear for delight, and also to shew the Poets art and variety of Musick, and the proportion is double. One by marshalling the meetres, and limiting their distaunces having regard to the rime or concorde how they go and returne: another by placing every verse, having a regard to his measure and quantitie onely, and not to his concorde.21

10

11 12 14 15 16 17 18 20

21

G Puttenham, The Arte of English Poesie (London, 1589). Book Two, chapter I, ‘Of Proportion Poeticall’, 53–4. See Figure 3.1. Ibid., chapter II, ‘Of proportion in Staffe’, 54–5. 13 Ibid., chapter III ‘Of proportion in measure’, 55–61. Ibid., chapter IV ‘Of Cesure’, 61–3. Ibid., chapter V ‘Of Proportion in Concord, called Symphonie or rime’, 63–4. Ibid., chapter VI ‘Of accent, time and stir’, 64–5. Ibid., chapter VII, ‘Of your Cadences’, 65–7. Ibid., chapter X ‘Of proportion by situation’, 69–75. 19 Ibid., chapter XI ‘Of proportion in figure’, 75–85. Ibid., 89. For example, the double 2 : 1 proportion with 4 : 2 movements and 1600 : 800 bars across BWV 1001–6 formed by non-consecutive units. See Table 5.4. Puttenham, Poesie, Book Two, chapter XI.

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Figure 2.1 Proportion by situation, The Arte of English Poesie (1589), 72

This is evidence of the practical concept of a double proportion, a term I have adopted when it occurs in Bach’s works, and of parallelism between proportions.22 Although less important for proportional parallelism, the examples of proportion in figures which follow are included here in Figure 2.2 to help disprove some of the more extreme symbolic interpretations in musicology, such as those propounded by number hunters aspiring to find the chalice or holy grail in Bach’s compositions. The symmetrical shapes classified by Puttenham as Proportion in figure are visual forms of poetical proportion, created by the length of lines in verses. Puttenham writes: Your last proportion is that of figure, so called for that it yields an ocular representation, your meeters being by good symmetrie reduced into certaine Geometrical figures, whereby the maker is restrained to keepe him within his bounds and sheweth not onely more art, but serveth also much better for briefenesse and subtilitie of device.23

Just as introducing parallel proportions would have been a creative restraint for Bach as he revised his works, Puttenham explains how this visual constraint of symmetrical figure served the poet well. Although Bach is unlikely to have read The Arte of Poesie, he may well have read about Puttenham’s techniques in other poetic treatises. For example, in a widely distributed German text Unterricht von der Teutschen Sprache und Poesie, Daniel Georg Morhof (1639–91) devotes five chapters to similar techniques; chapter 6 to Numerus Poëticus, describing syllables, metre and feet (i.e. rhythm in poetry),24 and chapters 7–12 to various rhyming schemes.25 Another example that Bach would have known can be 22

23 24

25

The double proportion across BWV 1001–6 is formed both by the number of bars and number of movements. Ibid., 75. Morhof, Unterricht von der Teutschen Sprache und Poesie rev. edn. (Lübeck; Franckfurt, 1700), 496–509. Morhof, Unterricht, 509–87.

Symmetry, proportion and parallels

Figure 2.2 Proportion in figure, The Arte of English Poesie (1589), 76

found in a script stolen from Pastor Erdmann Neumeister (1671–1756) and published by Christian Friedrich Hunold (1680–1721) as Die Allerneueste Art zur Reinen und Galanten Poesie zu gelangen in 1707.26 The authors recommend creating order in a poem by measuring the number of syllables or feet.27 Symmetrical ordering in poetry composition was classified as ‘proportion poetical’. This is fundamental to understanding the phenomenon of proportional parallelism; it implies that a technique of symmetrical ordering in musical composition such as proportional parallelism would have been classified as ‘proportion musical’. 26

27

Tatlow, Bach and the Riddle, 92–3. In Geheime Nachrichten und Briefe (Cöln, 1731), Hunold claims that he stole Neumeister’s notes and published them under his own name. Christian Friedrich Hunold, Die allerneueste Art zur Reinen und galanten Poesie zu gelangen (Hamburg: Liebernickel, 1707), chapter 6, ‘Von den Versen’, 56.

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The breadth of technique embraced by Puttenham’s term ‘Proportion Poeticall’ is staggering. Particularly important for the theory of proportional parallelism in Bach’s music are Puttenham’s ‘Proportion by situation’ and ‘Proportion in figure’ because they show that proportions could be formed between non-consecutive units, as happens continually in Bach’s revised works. When a proportion was formed by consecutive movements in a work, Bach would often reorder them later. Over the past decades, leading Bach scholars have observed the symmetrical arrangement of texts and movements in his multi-movement works without giving any historical evidence for the use or significance of formal symmetry. Puttenham’s description of proportion by situation and in figure, together with early eighteenth-century discussions of similar techniques, now gives a historical and philosophical context for observations of symmetry in Bach’s works. Bach and his contemporaries knew and used many forms of ‘proportion poetical’. Listed by Puttenham, and among the most popular in Bach’s time, was the anagram or ‘poesie transposed’. Not listed by Puttenham but also commonly used and popular in German-speaking regions was the paragram. Both paragram and anagram appear in Hunold’s list of techniques to give the poet creative ideas when inspiration is running dry:28 (1) derivation; (2) double or parallel meaning;29 (3) the synonym; (4) the anagram; and (5) the artistic/creative cabbala, which includes the acrostic and the poetic paragram.30All are parallel forms and all use techniques such as letter and word permutation, equivalent meaning and numerical values. In his example of an acrostic Hunold uses a proper name in exact retrograde. These parallel techniques were regularly used in Mühlhausen, Weißenfels, Erfurt and Weimar while Bach lived there. In 1690, for example, Johann Georg Ahle (1651–1706) published two acrostics on the word ‘Musica’: ‘Mit Uns Sei Iesus Christus, Amen’, and in retrograde as the final words of his treatises,: ‘Allein Christus Iesus Sei Unser Musik!’31 Nineteen years later, the birthday of the Weimar Duke Wilhelm Ernst was marked by the performance of a newly composed song, ‘Alles mit Gott’ (BWV 1129). The twelve-stanza text was written by Superintendent Johann Anton Mylius (1657–1724). The first letter of the third word of the second line of each stanza is printed in prominent, capitalised type, the twelve 28

29 30 31

Ibid., 542. The original terms are (i) derivatio, (ii) aequivocatio, (iii) synonyma, (iv) anagramma, and (v) artificium cabbalae. In Tatlow, Bach and the Riddle, 92–4, (ii) and (v) are translated inaccurately. Zedler, Lexicon, s.v. ‘Aequivocatio’. Zedler, Lexicon, s.v. ‘Artificium’, where ‘Artificium’ is described as a ‘Kunst-Stück’ or ‘Meisterwerk’. J. G. Ahle, Anleitung zur Singekunst (Mühlhausen, 1704), 2 and 85.

Symmetry, proportion and parallels

stanzas spelling in order the name WJLHELM ERNST.32 Thanks to Duke Wilhelm’s patronage, Mylius had been promoted in just seven years from the position of Deacon at St Andrew’s Church in Erfurt, to first bishop of Buttstädt. Writing a poem on the duke’s life motto ‘Alles mit Gott und nichts ohn’ ihn’ for the birthday celebrations was an excellent and appropriate way for Mylius to express his gratitude. As Bach was also hoping for promotion within the musical hierarchy of the court, he had good reason to be involved in the venture.33 The birthday ode text was printed; the music was not. However there was space for Bach to write the fifty-five bars of music by hand on the final two blank pages. Classified by Hunold as a part of ‘false cabbala’ (1707), the acrostic was a popular device that Bach used on several occasions in a musical context. The acrostic on the name ‘Wjhelm Ernst’ in the Birthday Ode (BWV 1127) demonstrates that Bach was familiar with the form by 1713. In 1747 he created an acrostic on the word ‘Ricercar’ for the dedication copy of the Musical Offering (BWV 1079): Regis Iussu Cantio Et Reliqua Canonica Arte Resoluta. Unlike Hunold, he did not use a retrograde of the word to complete the acrostic, but as a proven master of permutation, he is likely to have noticed that the retrograde version of its plural form RICERCARI is IRA CRE[S]CIR; ‘the wrath of growth’. The two words ‘Canonica Arte’ from the acrostic may also have held a parallel meaning, alluding to the numerical structure of the collection.34 In conjunction with another parallel conceit, the musical alphabet, Bach used the acrostic, ‘Fidelis Amici Beatum Esse Recordari Bonae Artis Cultorem Habeas’, to accompany the puzzle canon BWV 1078.35 Variations on this kind of ‘Proportion in figure’ seem to have been commonplace, frequently used in texts printed in Leipzig until at least the late 1740s. Publisher, engraver and printer C. F. Geßner describes both the chronogram and acrostic in his book for apprentice printers, and explains how to set them so that the embedded names are clear:36 The following songs in our hymn books can be included because in each verse one letter of a name stands out. ‘Allein auf Gott setz dein Vertrauen’, has the complete

32

33 35 36

J. S. Bach, ‘Alles mit Gott und nichts ohn’ ihn’, ed. M. Maul. Documenta Musicologica: Handscriften-Faksimiles, Band 33 (Kassel; Basel; London: Bärenreiter, 2005). 34 Ibid., Maul, ‘A “Miraculous Blessing” from Bach’, 14. See Chapter 9, §I. BD IV, Image 585, BD I, Doc. 177. Speculative online discussion of one such puzzle recently prompted an article in BJ. Hans Joachim Schulze, ‘Rätselhafte Auftragswerke Johann Sebastian Bachs Anmerkungen zu einigen Kantatentexten’, BJ 96 (2009), 69–74.

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alphabet and is called the ‘golden’; ‘Mein Herz ruht und ist stille’, spells the name ‘Maria’; ‘Jesu wollst uns weisen’ spells Johannes Casimir Hertzog zu Sachsen; ‘Valet will ich dir geben’ spells ‘Valerius’; ‘Brich an du liebe Morgenröthe’ spells ‘Burchardt Großmann’; ‘Hilff Gott daß mirs gelinge’ spells ‘Heinrich Müller ’. NB: The beginning of each verse must be typeset with a Latin capital letter.37

Hunold completed his explanation of inventive techniques with a description of the poetical paragram, listing just five of many possible number alphabets.38 Substituting numbers for letters is an age-old tradition found in different cultures for many different purposes. Although black magic and sorcery were not common in Bach’s Lutheran society, theological purists were still wary of any practice that might tend towards superstition or doctrinal error. For this reason the cabbalistic tradition of using number–letter equivalents to interpret scripture was frowned upon, whereas the inventive use of number alphabets was considered entirely harmless and suitable for everyone.39 Hunold listed the paragram alongside the acrostic as a ‘false cabbala’, describing it as his fifth method of invention. Commonly going by the name paragramma cabbalisticorum or simply paragramma, paragrams were commissioned and personalised for occasions such as weddings, funerals and birthdays. Writing paragrams became a serious commercial enterprise under the business acumen of Johann Friedrich Riederer (16781734), who, based in Nuremberg, published three sales catalogues in 1715, 1719 and 1732 advertising over 5000 different paragrams that, for a fee, could be printed or handwritten on request.40 In the introduction to his first sales catalogue Riederer included a description of his compositional process, showing the compromises and alterations required in a parallel number–letter technique to achieve a specific numerical total. ‘I begin by opening the Bible and looking for a suitable verse which expresses the main idea.’ He chooses Sirach 31:33–4, ‘What is life without wine? For wine is made to make man happy’. He works out the numerical value of this verse, letter by letter, writing the verse one word per line in a vertical row on a long sheet of paper. The numerical total is 5593, and this becomes the fixed point in the procedure. The next stage is to find a name with the same numerical total. He chooses the amusing fictitious character ‘Adam Krazbürste Wirth in 37 38

39

C. F. Geßner, Der in der Buchdruckerei wohl unterrichtete Lehr-Junge (Leipzig, 1743), 381–2. Hunold, Die Allerneuste Art, 545, where the natural order (A=1 to Z=24), the trigonal (A=1 and Z=300), and the milesian (A=1 to Z=400) are included. See Tatlow, Bach and the Riddle, 93. 40 Tatlow, Bach and the Riddle. Ibid., 94–102.

Symmetry, proportion and parallels

der halb papernen wanze in Schlauraffenland’, which has a total of 4801, 792 short of the 5593 of Sirach 31:33–4. Small adjustments to the spelling are then made until the two totals are identical, i.e. exactly parallel. Riederer explains the procedure: ‘What to do here? I could insert the letter “n” and get a further 91, but that’s still not enough. How about if I put in the word “Herr”, adding 357, so the total is now 5158, but we are still 435 short.’ He then has the idea of adding ‘mein’ before ‘Herr’, generating a further 226, but he is still 206 short; and so on until he reaches exactly 5593.41 Exploiting the non-standard spelling of words such as wenn, wann, dann or denn, auff or auf was invaluable to the successful paragram, with equivalent expedients used in other parallel techniques. Riederer’s description of the procedure shows the effort required to reach exact totals to achieve a 1 : 1 proportion. This is important historical and philosophical evidence of the striving required to create unity, and formal symmetry. The revision procedure Bach undertook to introduce proportional parallelism into his collections involved similar effort and numerical refinements as he added or cut out bars and movements. Features he could exploit to facilitate his numerical efforts include the Da Capo, the repeat, stile antico notation and the TS feature, all described in Chapter 1. Riederer was a sufficiently eminent figure to earn an entry in Zedler’s Lexicon.42 The connection between J. F. Riederer, his catalogues and paragrams, and J. S. Bach was through the Pachelbel family and St Egidien’s church in Nuremberg, where Wilhelm Hieronymus Pachelbel (1686–1764), organist there from 1706, was a boyhood friend of Bach’s cousin J. G. Walther.43 Johann Pachelbel, Wilhelm’s father and tutor to Bach’s eldest brother, had died in Nuremberg in March 1706, where he had been organist of St Sebald’s since 1695. W. H. Pachelbel remained organist at St Egidien’s from 1719 until his death in 1764.44 It was during this period that Riederer wrote paragrams for the consecration of the newly restored St Egidien’s,45 and to raise money for the Salzburg emigrants – a political event that also touched Bach.46 A Riederer paragram that Bach might have seen can be found in the preface to Benjamin Schmolck’s collection of cantata texts for each Sunday 41 43

44 45

42 Riederer, Catalogus, Introduction. Zedler, Lexicon, s.v. ‘Riederer, Johann Friedrich’. On 28 December 1739, Walther wrote to Mattheson: ‘In 1706 I visited my compatriot, former neighbour and playmate of my tender years, Mr Wilhelm Hieronymus Pachelbel, in Nuremberg, to learn from him and other musicians.’ Walther, Briefe, 219. New Grove, s.v. ‘Pachelbel, Wilhelm Hieronymus’. 46 Image reproduced in Tatlow, Bach and the Riddle, 96–7. BD IV, Image 423.

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of the church year, published in 1720.47 A decade later Bach’s colleague Christian Friedrich Henrici (1700–64) composed and published a paragram under his pen name ‘Picander’.48 Bach and Picander worked together on texts for church cantatas at this time, and also on the text of the St Matthew Passion which Picander had published in his second volume of texts.49 In the preface to his third collection of poems, the volume in which he published the paragram, Picander claims that Bach had written music to a whole cycle of his texts.50 These close associations strongly suggest that Bach and professionals in his immediate circles knew these inventive parallel methods, and even commissioned paragrams.

III

Parallelism as the basis of hybrid forms

The idealism of the 1 : 1 proportion and symmetry seems to have provided favourable conditions in which many forms of parallelism in the creative arts, theology and philosophy could grow. The philosophical and theological concept of predestined Harmony, developed with varying emphasis on God’s will and human action by Gottfried Wilhelm Leibniz (1646–1716), Isaac Newton (1643–1727) and Christian Wolff (1679–1754) has parallelism and dualism at its heart.51 Parallelism was an important rhetorical tool, in which statements by a single author are compared and contrasted,52 and many parallel methods are listed in Zedler’s dictionary under ‘Parallelistica Methodus’, ‘Loca parallela’ and ‘Parallel–Loca’,53 including concepts such as parallelism of words, parallelism of things, historical parallelism, dogmatic parallelism, parallelism of the first order and parallelism of the second.54 47

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Saitenspiel des Hertzens (Bresslau, 1720). Bach’s famous contemporary Gottfried Heinrich Stölzel (1690–1749) set at least one cantata from this collection. I am grateful to Jeffrey Sposato for alerting me to this source. Picander [C. F. Henrici], Ernst-Schertzhaffte und Satyrische Gedichte, vol. III (Leipzig, 1732), 27. See also Tatlow, Bach and the Riddle, 6–8, 92–102. Picander, Ernst-Schertzhaffte und Satyrische Gedichte, vol. II (Leipzig, 1729), 101–12. Picander’s wife, Johanna Elisabetha, was godmother to one of Bach’s daughters, Johanna Carolina Bach, in 1737. See the overview given of the contribution of these philosophers to the discussion of predestined harmony in Zedler, Lexicon, s.v. ‘Vorherbestimmte harmonie’. Zedler, Lexicon, s.v. ‘Parallelismus’ Zedler, Lexicon, s.v. ‘Parallelistica Methodus’, and s.v. ‘Loca parallela’. Zedler, Lexicon, s.v. ‘Parallelismus der Wörter’, ‘Parallelismus der Sachen’, ‘historischer Parallelismus’, ‘dogmatischer Parallelismus’, ‘Parallelismus primi ordinis’ and ‘Parallelismus secundi ordinis’.

Symmetry, proportion and parallels

Parallel method of compositional invention Perhaps one of the most widely used parallel methods in music is the invention of a new bass line to a pre-existent melody. Today, this might be regarded as controlled plagiarism, but in the eighteenth century it was a respectable form of invention used by composers and recommended by teachers. In 1739 Mattheson encouraged the beginner learning to write two-part counterpoint to use this method,55 while in 1765 Löhlein suggested its use in improvisation as a means for the keyboardist to develop free and fixed fantasies.56 Almost twenty years later Bach’s pupil Kirnberger wrote: One takes a piece by a good composer or if you want to make it even more hidden, one by yourself, and make from the bass a totally new melody . . . Then one writes a new bass to the newly written melody, thereby rendering neither bass-line nor descant recognisably similar to their original. The method is extremely common and stands up to the closest scrutiny. It can even be adapted so that a second bass is written for a melody, and a second melody then created to this.57

C. P. E. Bach’s description of his father’s teaching method suggests that Bach senior used a similar parallel method: His pupils had to begin their studies by learning pure four-part thorough-bass. From this he went to chorales; first he added the basses to them himself, and they had to invent the alto and tenor. Then he taught them to devise the basses themselves.58

Paragrams and chronograms: Beer and Pachelbel In 1699 Johann Beer (Bähr) (1655–1700) used a hybrid parallel form. combining a name, a date, a milesian alphabet and a music publication for the foreword to Pachelbel’s published keyboard collection, Hexachordum Apollinis (1699) (see Figure 2.3). The name is converted to numbers through a milesian-type number alphabet, A=1, B=2, both I and J=9, K=10, L=20 to T=100, both U and V=200 etc. The unusual spelling of NORIBERGHENSIVM in the title, with the additional H between the G and E, was probably the means by 55 56

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Mattheson, Capellmeister, part III, chapter 16, ‘Von Zwostimmigen Sachen’, §3 and §4, 338–9. Georg Simon Löhlein, Clavier-Schule (Leipzig, 1765), chapter 20, 179–90. I am grateful to John Lutterman for alerting me to this source. Kirnberger, Methode Sonaten aus’m Ermel zu schüddeln (Berlin, 1783). NBR, Doc. 395; BD III, Doc. 803.

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Figure 2.3 Pachelbel, Hexachordum Apollinis (Nürnberg, 1699), preface. Chronogram by Beer

which Beer achieved the exact totals. There may be further parallels between the emblem and the composition itself. The conceit generates many possibilities. For example, with the milesian alphabet used in the chronogram, Pachelbel’s name has the unfortunate total 666,59 a parallel that neither he nor Beer would have wished to draw to public attention. In the natural order alphabet however, the value of his name is 189, and, with the title of the collection a 3 : 1 proportion is formed: Johannes Pachelbelius Hexachordum=303: Apollinis=101.60 Although we cannot know if Pachelbel or Beer were aware of the 303 : 101 proportion, the examples show how easily an exact proportion can be formed with number-letter substitutions. Johann Beer and Pachelbel had been friends since their student days in the 1670s at the Gymnasium Poeticum in Regensburg. By 1699 Johann Beer was still Concert Master in the Weissenfels court 59

60

Johannes=243 Pachelbelivs=423, in spite of its satisfying combination of 2, 3 and 4. See p. 59 below. Johannes=81 Pachelbelivs=108 Hexachordum=114=303: Apollinis=101.

Symmetry, proportion and parallels

orchestra,61 while Pachelbel was organist at St Sebald’s church, Nuremberg, having moved from Erfurt in 1690 via Stuttgart (1690–2) and Gotha (1692–5). On 15 August 1690 the Pachelbel family moved from their home in Erfurt to Nuremberg, taking their 4-year-old son Wilhelm Hieronymous from his 5-year-old playmate Johann Gottfried Walther, Bach’s second cousin, whom Mattheson was later to call ‘the second Pachelbel’.62 The move touched the Bach family too, as Johann Pachelbel was godfather to Johann Sebastian’s elder sister, Johanna Judith, and more importantly, the trusted music teacher to Johann Christoph Bach (1671–1721), eldest brother of Johann Sebastian. Johann Pachelbel could easily have been Johann Sebastian’s teacher had the untimely death of his parents not left him penniless. Becoming an orphan forced Johann Sebastian to accept gratefully the next best thing, being tutored by a student of Pachelbel. Although we do not know how much time the young Johann Sebastian Bach spent in Erfurt during his childhood, we do know that family and musical connections were highly valued, and for this reason I suspect that both Bach and cousin Walther would have felt a personal pride in Pachelbel’s Hexachordum when it was published in Nuremberg in 1699. The prominent position of the parallel chronogram/alphabet conceit by two such highly respected musicians may well have set a benchmark for the impressionable teenagers.63 Some time before 1729, Bach himself would be awarded a title similar to Beer’s, given in the chronogram as ‘Hochfürstl. Sächsischer Weissenfelsischer Concert-Meister’. Although Bach’s title ‘Hochfürstlicher Sachsen Weissenfelsischer Capell-Meister’, was honorary and he was based in Leipzig, just over twenty miles away (‘vom Haus aus’), it raised Bach’s status a level higher than that of Court Concert-Master Beer. Did Pachelbel’s keyboard publication plant a seed in the teenage Bach that blossomed later to encourage his application for the honorary Weißenfels title? In 1735 Bach chose the Nuremberg publisher, Christoph Weigel, Jr (1702–77) to produce the second part of his Clavier Übung. Weigel’s father had published compositions by Johann Pachelbel, and perhaps Bach’s long-term respect for Pachelbel influenced this choice of a publisher so far from Leipzig. Pachelbel’s use of a parallel conceit in his

61 62 63

He had held the position since 1685. New Grove, s.v. ‘Beer, Johann’. Mattheson, Ehrenpforte, s.v. ‘Walther’, 387–90. K. Welter, ‘A Master Teacher Revealed: Johann Pachelbel’s Deutliche Anweisung’, in About Bach, ed. Gregory G. Butler, George B. Stauffer and Mary Dalton Greer (Urbana; Chicago: University of Illinois Press, 2008), 3–13.

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Hexachordum may also have stimulated Bach to include something similar in his own publications. If nothing else, Beer’s chronogram proves that a hybrid parallel form was used in a 1699 music publication known to Bach.

Words, numbers, letters: Kuhnau Some time around the turn of the century, Johann Kuhnau (1660–1722) created an original parallel form for the preface of his keyboard publication, Musicalische Vorstellung einiger biblischer Historien. After a contagiously enthusiastic background description of the sonatas, Kuhnau included a device involving a name, the natural order number alphabet and an arithmetical puzzle, the solution to which is the name ‘Stephani’, whose admiration and influence Kuhnau wished to acknowledge. Steffani was also greatly admired by Mattheson, for his method of compositional planning,64 and by Werckmeister, who published Steffani’s Quanta certezza abbia da’ suoi principii la musica (1695) in German translation in 1700.65 Kuhnau states that he encrypted the name through the puzzle lest he offend any others to whom he also owed a debt of admiration and gratitude. The solution is found by using the natural order number alphabet (A=1 to Z=24) to decipher the results of a variety of arithmetical processes: But if anyone is so curieux and would be glad to know his name, I will give him an Algebraical Problem, by which he may guess it by way of a pastime, or a lusus ingenii (indeed, this entire work of mine is nothing more than such a lusus, as My Lady Muse makes plain on the first engraved plate). But he should first know that I have assigned to each letter the number that falls to it according to the alphabetical order: 1 signifies A, 2 B and so on. Secondly, I leave the reader in doubt as to whether I have used 1 or 2 letters too few or too many at the end.66

It is intriguing to know what exactly Kuhnau meant by his parenthentical comment that ‘this entire work of mine is nothing more than such a Lusus’. He teasingly challenges the reader to decipher the parallel meanings of the first engraved plate, which may then lead to a parallel meaning in the 64 65

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Mattheson, Capellmeister, part II, 240 J. Hawkins, A General History of the Science and Practice of Music (London, 1776), Book III, 303. The preface, dated 30 April 1700, was thought so important it was reproduced with the solution ‘Stephani’ in the announcement of the publication in Historische Remarques über die neuesten Sachen in Europa, 26. Woche, 28 Junii 1701, 207. I am grateful to Robin A. Leaver for alerting me to this source.

Symmetry, proportion and parallels

musical collection of sonatas. At face value the purpose of Kuhnau’s preface is to introduce the work; the many secondary purposes are hidden or alluded to in common parallel techniques. If Kuhnau wanted his readers to understand the secondary purposes of the collection, why did he not state them in plain words? We know that readers pored over such puzzles and published the solutions.67 And we know that the majority of parallels in emblem books were designed to lead the reader to devotional contemplation; they were not simply amusing and diverting puzzles in the modern sense.68 On 15 March 1700, a little over five months before Kuhnau’s work was published, Bach left Ohrdruf for Lüneburg. If he did not see a copy of this collection in Lüneburg, Mühlhausen or Arnstadt, he would definitely have had access to it through Walther when he moved to Weimar in 1708. Was Bach able to decipher and to understand the emblematic image? Did the form, style and content of Kuhnau’s collection inspire his own keyboard compositions?69 Was this the first time Bach had seen a natural order number alphabet? When Bach met Kuhnau in person,70 did they discuss the publication, the pros and cons of including lusus ingenii, and even their solutions? Within a year of publishing the collection Kuhnau was appointed Thomaskantor, a post he held until his death in 1722, which precipitated Bach’s appointment to the post in 1723. There is no indication from the developments in Kuhnau’s career that using parallel forms in composition was frowned upon; quite the opposite. Kuhnau enjoyed a fine reputation. His compositions, even with their emblematic puzzles, would therefore have been a role model for Bach.

Emblems, words, numbers: Kuhnau, Mattheson, Buttstett The parallel 1 : 1 nature of image, word and meaning in emblems is spelt out in Zedler’s entry ‘Sinnbild’, which explains that the art of Emblema is highly developed ‘nowadays’ and very well known.71

67

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70 71

Ibid. The 1701 announcement above proudly announced that Hamburg mathematician Herr Heinrich Meißner had solved the puzzle. Zedler, Lexicon, s.v. ‘Sinnbild’. Some also had offensive interpretations. For example Bach’s ‘Capriccio sopra la lontananza del suo fratello dilettissimo’ (BWV 992), in the Möller manuscript collection, with its story line described in music; and Capriccio in E in honorem Johann Christoph Bachii Ohrdrufiensis, P 804 (BWV 993), 33–6. In 1716 at the Halle Liebfrauenkirche. NBR, Doc. 59; BD I, Doc. 85. The entry cites G. P. Harsdörffer’s Frauenzummer Gesprechspiele. 8 vols. (Nürnberg, 1644–9), and D. G. Morhof, Unterricht von der Teutschen Sprache und Poesie (Lübeck; Franckfurt, 1700), 700–5.

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Fundamental to an emblem is an equality [Gleichheit] found between the picture and the meaning of the motto, and its beauty lies in the fact that the picture cannot be understood without the text, nor the text without the picture.72

Typical of the many catalogues of emblems available at this time is the anonymous collection Devises et Emblèmes Anciennes & Modernes which was published in many editions, the fourth in Augsburg in 1699, describing 715 emblems with mottos in German, Latin, French and Italian.73 Puzzling out the meaning of an emblem was an intellectual exercise, and the art of emblem writing was a lusus ingenii that aimed to exploit double entendre. Zedler continues: An emblem is a picture with an image and a few accompanying words, which contains a hidden message and leads to deeper reflection. The picture stimulates the body while the text stimulates the soul . . . Many emblems can have contrary interpretations (‘Widerwärtige Deutungen’), which are disguised by their superscript.74

Frequently combining significant numbers, imagery and a motto, emblems were regularly reproduced in biblical commentaries and books of illustrated sermons to aid a reader’s devotion. There are many examples among the commentaries Bach owned.75 Zedler continues: The motto should be short and meaningful, and it is much better if it is taken from a famous Poet. Sinnbilder or emblems are primarily used to communicate moral teachings, mysterious meanings and profound reflections, but also praise outstanding deeds, and can be created not only on paper, or in speeches, or explained in short poems, but also stamped on coins, plaques and memorials and gravestones.76

Emblems were a form of art appreciation, in which the representative images had a literal meaning. Morhof classified the riddle as an emblem.77 Männling saw the emblem as the inventive part of rhetoric.78 Mattheson devised his own emblematic frontispiece in Orchestre II in response to Buttstett’s critique of Orchestre I, and his image is not subtle, even for a modern reader. It

72 73

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Zedler, Lexicon, s.v. ‘Sinnbild’. Devises et Emblemes Anciennes & Modernes tirées des plus celebres Auteurs. Oder: Emblematische Gemüths-Vergnügung. 4th edn (Augsburg, 1699). Zedler, Lexicon, s.v. ‘Sinnbild’. See R. Steiger, Gnadengegenwart. Johann Sebastian Bach im Kontext lutherischer Orthodoxie und Frömmigkeit. Doctrina et pietas II/2 (Stuttgart-Bad Cannstatt, 2002). 77 Zedler, Lexicon, s.v. ‘Sinnbild’. Morhof, Unterricht, 704. J. Chr. Männling, Expediter Redner, 13–50. Referred to in Peter-André Alt, Begriffsbilder: Studien zur literarischen Allegorie zwischen Opitz und Schiller (Tübingen: Niemeyer, 1995), 331–4.

Symmetry, proportion and parallels

caused strong reactions at the time.79 Buttstett in his turn replied very simply in 1718 with a plain one-side manifesto Wieder das Beschützte Orchestre, written in the form of a letter, at the end of which there is an emblematic seal that could easily be overlooked (see Figure 2.4). Beneath what might be deemed a provocative dictum, dixi et confitendo salvavi animam meam’ (‘I spoke and by confessing saved my soul’) and between the date and signature, Buttstett placed the circular engraving of a half-filled goblet on a flat surface, above which is the word ANISUM. The words ‘authorised by the Author’s stamped seal’ in the first sentence of the manifesto confirm that the image is Buttstett’s seal. A letter seal at this time usually had both a meaningful (sinnreich) picture and a motto.80 Since none of Buttstett’s other publications or surviving letters uses this seal,81 it is probable that he devised it and its emblem specifically for this final response to Mattheson. The capitalised motto-word ‘Anisum’ is the key to understanding its potentially ‘contrary interpretation’. The entries on ‘anisum’ (anise) in several contemporary encyclopedias show that the plant was grown throughout Europe and, specifically, in particularly vast quantities, in Thuringia, in the Bamberg counties and in Little Poland.82 The seed and flower of anise, and also anise wine, had many medicinal properties for every kind of pain in the digestive tract, and were particularly used for the relief of flatulence.83 Since Buttstett’s hometown of Erfurt is in the heart of Thuringia, a symbol of anisum would have been a natural and innocentlooking emblem for a seal. But its well-known medicinal properties may have been hiding parallel and contrary connotations ‘disguised by the superscript’. Was Buttstett offering a glass of anise wine to his readers, was he taking the medicine himself, or most insultingly, proffering the drink to Mattheson?84 One wonders who had the last laugh in the battle. Bach used emblems and mottos in an album entry for Johann Gottfried Fulde, dated 15 October 1747, when he wrote that the symbolum was ‘Christus Coronabit Crucigeros’.85 Some have taken this to mean that 79 80 82

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Mattheson, Critica Musica (Hamburg, 1725), 257–82, esp. 265. 81 Zedler, Lexicon, s.v. ‘Siegel’. I am grateful to Michael Maul for confirming this. Zedler, Lexicon, s.v. ‘Anisum’, reproducting the exact entry in Lémery’s Vollständiges Materialien-Lexicon (Leipzig, 1721), which itself is a translation and revision from the original Greek. ‘Für die Aufblähung der Miltz, sonsten löset er auf alle innerliche Verstopfung, zertheilet die Winde, stillet das sauere Ausstossen des Magens . . . Es ist gut für alle Verstopffung und Anhäuffung, für alle Blähung des Leibes.’ Tatlow, ‘Goblet of Anise: A Case Study’, unpublished paper, 2010. BD IV, Image 584, ‘Album entry for Johann Gottfried Fulde with canon BWV 1077, 15 October 1747. Also BD I, Doc. 174

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Figure 2.4 Buttstett, Wieder das Beschützte Orchestre (1718)

Symmetry, proportion and parallels

Bach’s life motto was ‘Christus Coronabit Crucigeros’,86 but as the format is similar to other dedicatory verses he wrote, this claim cannot be substantiated. For example the album entry dated 2 November 1725 has a similar format, although the canon is missing, and its symbolum, or life motto is: ‘Omnia tunc bona, clausula quando bona est’.87 Another album entry in Bach’s hand, dated 10 January 1734,88 lacks a symbolum, but includes a canon. The word symbolum is again associated with Bach on the title page of ‘Alles mit GOTT und nichts ohn’ Ihn’ (BWV 1127), explaining that the chosen symbolum of Wilhelm Ernst is Omnia cum DEO, & nihil sine eo. Did this sentiment find its way into the music of BWV 1127?89

Symmetry in printed images and vignettes Was there any parallel meaning in the ubiquitous and fabulously engraved scrolls, swirls and flowers that frequently separate page sections or form borders around title pages? Zedler’s article ‘Vignette’ explains that dedicatory engravings usually represent something related in some way to the book.90 The vignette, originally a vine leaf with tendrils, became a standard decoration. At the end of the lengthy article on ‘Zierrath’ describing the essential symmetry and harmonic proportion of decoration, there is a short paragraph on decoration in the art of book printing that begins: ‘Ornaments (in book engraving) should not stand for nothing, but must have a reason, use or meaning.’91 In the twenty-first century a reader of early eighteenthcentury music frontispieces may notice symmetrical 1 : 1 patterns and the engraved decoration, but frequently miss their original purpose.92 Not all printed images and symbols had emblematic meaning, however. Christian Friedrich Geßner’s manual includes many standard printing signs and abbreviations used in Leipzig in the early 1700s.93 Over half of Geßner’s publication reproduces Johann Caspar Müller’s unpublished

86 87 88

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T. A. Smith, www2.nau.edu/tas3/crownofthorns.html, accessed 14 April 2015. BD IV, Image 313, BD I Doc. 154 BD IV, Image 439. Johann Matthias Gesner, Rector of St Thomas School, is presumed to have been the recipient; BD I, Doc. 167. Michael Maul, ‘“Alles mit Gott und nichts ohn’ ihn” – Eine neu aufgefundene Aria von Johann Sebastian Bach’, BJ 91 (2005), 7–34. 91 Zedler, Lexicon, s.v. ‘Vignette’. Zedler, Lexicon, s.v. ‘Zierrath’. See J. Speerstra, ‘Bernardo Pasquini’s Cuckoo: An Opera for Keyboard in One Act’, Quaderni Trentino Cultura (2012), 260–74. C. F. Geßner, Der in der Buchdruckerei wohl unterrichtete Lehr-Junge (Leipzig, 1743).

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text on how to teach a printing apprentice speed and accuracy.94 Müller was a highly respected printer renowned for the intellectual foresight of his publication policy, which included printing many learned tomes from Thomas Fritsch Verlag. Müller worked in Leipzig from 1702 until his death in 1717, after which his widow Maria Sophia ran the business alone for two years until she married Bernhard Christoph Breitkopf (1695–1777),95 who built up its reputation as a world-class family publishing house. Several of the printing signs and symbols Müller listed are found in Bach’s music manuscripts and Bach documents, including the sign of the cross, the hand, and planetary signs. According to Müller, the cross symbol (+ † and X) is used to divide a section. Doctors and apothecaries used the sign X to mean talcum powder, and the sign + to mean vinegar or a crucible, while four dots on the four corners of the + indicate distilled vinegar. + is also used at the beginning of a funerary poem and sometimes at the end instead of a final line. Furthermore, the sign † is used both for exorcism and blessing. Authors also use † in manuscripts when listing questions, rules or exceptions, in the order ∗ † Δ ♀ ☽ ⨀.96 Müller writes that the ‘hand’ symbol is usually put in the margin of a book to alert the reader to a feature in the text. In 1743 it was used in calendars as an indication that the date was shown in the new rather than the old form, the hand indicating the beginning of the month.97 Planetary symbols to indicate the phases of the moon, as they do today, or the days of the week, were very common in calendars. Authors also used them to indicate additional sheets of paper, and lawyers were bound by law not to use any symbols other than planets, numbers and letters in legal documents.98 Planetary symbols were also used to indicate the elements in chemistry.99 Geßner’s manual was sold at the 1743 Easter Fair. No reader would have been surprised by these standard typographical symbols. When they are found in Bach’s music they should be understood primarily as everyday

94

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Johann Caspar Müller, Wohlmeynender Unterricht, bey Unterweisung eines Setzer und Drucker-Knabens. The undated title page, p. 145, implies that the book was not published until 1743. Müller’s text is on 145–366. Zedler, Lexicon, s.v. ‘Müller, Johann Caspar’. See Chapter 9, note 42. Geßner, Buchdruckerei, 395, §55. Ibid., 395 §56. The change over from the old Julian to the new Gregorian calendar took place at different times across Europe. In Leipzig, 18 February 1700 became 1 March 1700. Zedler, Lexicon, s.v. ‘Calender’. Geßner, Buchdruckerei, 396, §57. Symbols in calendars are given in plate VIII, after page 156. Walther, Briefe. Letter 9, particularly pages 76–9; and letter 15, pages 122–4.

Symmetry, proportion and parallels

characters, and not interpreted as if they held alchemical or esoteric significance. In view of the predilection for parallel techniques at this time, though, an intentional dual meaning cannot be ruled out.

Music–letter–number parallels Parallels methods were a source of invention to help composers and authors create dedicatory compositions; for a public occasion in honour of a nobleman, the name of the honoured personage and the date of the occasion would frequently be made plain. Sometimes evidence of these methods of invention would be hidden, or embedded in the structure of the music or poem. Number alphabets and number-letters could be applied in many different ways: in poetry, for example, there were not only the number alphabet parallels, but parallels that could be formed by the number of syllables or feet, the equivalent of the bar or phrase in music. One of the very few documented examples in music is a curious composition by Johann Christian Faber, Neue erfundene Composition. Faber composed this nine-movement piece in honour of the name day of Duke Ludwig of Braunschweig-Lüneburg on 25 August 1729. Similar to the acrostic for Duke Wilhelm Ernst of Weimar in 1713, each successive letter of Duke Ludwig’s name is represented in successive movements, although Faber then converted the letters into numbers through the milesian alphabet. Faber’s numbers–letters are then heard in the notes played by the trumpet. In the first movement, for example, the trumpet plays twenty notes, over the first of which is written ‘L=20’, in the second two hundred notes, over the first of which is written ‘U=200’, and so on.100 The method is unsubtle, but could have been ingenious had the music itself been of more remarkable quality. Converting letters to music was an age-old tradition, frequently described in books published in the seventeenth century. In Musurgia Universalis the celebrated Rome-based polymath Athanasius Kircher101 listed several different alphabets with which to translate letters into musical 100

101

W. Dehnhard, ‘Kritik der Zahlensymbolischen Deutung im Werk Johann Sebastian Bachs’, in Kongreßbericht Stuttgart 1985 (Kassel; Basel: Bärenreiter, 1985), 450. Also Tatlow, Bach and the Riddle, 105. Kircher’s fame was caused as much by his notorious and arrogant defiance of the censors’ authority as by his claim to universal knowledge and the wide circulation of his publications. See P. Findlen, Athanasius Kircher: The Last Man Who Knew Everything (New York; London: Routledge, 2004).

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notes, copying previous examples published by Daniel Schwenter.102 Kircher’s text in turn became the basis for many later published examples of musical alphabets (see Figure 2.5).103 The exploitation of the dual function of the letter name of a musical note and its pitch was an obvious parallelism, observed by many whose entire name could be represented by combinations of the letters of the musical scale or in an acrostic. The extension of the principle to the whole alphabet broadened its application, making it useful for spies to transmit encoded messages in a harmless-looking sheet of manuscript paper carried by an itinerant musician, or for ladies to exercise their intellects while improving their manuscript skills, and, more pertinently, for the composer to invent melodic ideas where a movement was based on a specific theme or dedicated to a specific person.104

Parallel meanings: numbers and symbols In Bach’s Lutheran community, numbers could signify many different things depending upon their context. Eclectic modes of interpretation included those practised originally by the Ancient Greeks, known to the church fathers or popular among medieval mystics. Smend complicated the process by using the words ‘cabbalism’ and ‘theological numbers’, and attempting to interpret the numbers he found in Bach’s music. Numerical interpretation has never been an exact science. In 1583 Petrus Bongus ascribed many different meanings to various numbers,105 and 150 years later the Bavarian theologian Joannes ab Unterberg updated that knowledge, in a tripartite volume on the history, philosophy and theology of numbers.106 In 1732 the paragrammatist Johann Friedrich Riederer devoted an entire book each to the significance of the numbers three and seven, containing vestiges of many cultural traditions.107 There was no single codification for the interpretation of numbers. 102

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Daniel Schwenter, Steganologia et steganographia nova (Nürnberg, 1620), 302; and Schwenter, Erquickstunden (Nürnberg, 1636), 239. For example in G. P. Harsdörffer, Mathematischen und Philosophischen Erquickstunden, vol. III (1653), p. 377; and G. Schott, Schola Steganographica (Nürnberg, 1665), 325. See Tatlow, Bach and the Riddle, 103–4. See §IV, Bach’s name in parallel forms, below. P. Bongus, De Mystica numerorum significatione (Bergamo, 1583). J. ab Unterberg, Tractatus Historicus, De Origine & antiquitate Numerorum, Tractatus Philsophicus, De Natura & Proportione Numerorum, Tractatus Theologicus, De Mystagogia, sive de Mysteriis Numerorum (Augsburg, 1734). Riederer, Gründliche Untersuchung; Riederer, Die bedenckliche und Geheimnüsreiche Zahl Drey (Nürnberg, 1732).

Symmetry, proportion and parallels

Zedler’s entry on the number 1000 (‘Tausend’), for example, shows that (1) the phrase ‘a large thousand’ (ein groß Tausend) signifies 1200 and not 1000; (2) in 1 Samuel 18:7 the phrase ‘ten thousand’ means a very large number rather than specifically 10,000; (3) in Genesis 24:6 the phrase ‘a thousand times a thousand’ means the greatest imaginable number; and (4) the phrase ‘many thousand pieces‘in the verse ‘Dein Wort ist mir lieber denn viel tausend Stück Goldes und Silbers’, Psalm 119:72, indicates the highest quality of perfection, ‘die Vollkommenheit der Sache’.108 The entry ‘Vier und Zwanzig Eltesten’ lists many different occurrences in the Bible of the numbers 12 and 24, including the twenty-four orders of musician in 1 Chronicles 24:9. The entry ‘centum, hundert’ (‘one hundred’) discusses the businessman’s use of increased sales in percentages, and ‘Dreyhundert’ (‘three hundred’), describes many scriptural uses, including Noah’s ark, which was 300 Ells long (Genesis 6:15), Joseph who gave his brother Benjamin 300 silver coins (Genesis 45:22), and Solomon who had 300 wives and 700 concubines (1 Kings 11:3). The article ‘Sechs hundert und sechs und sechzig’ covers seventeen columns on nine folio pages. Besides explaining the many numerical properties of the numbers 666 and 6, including defining it as the ‘Number of Man’ (‘Zahl des Menschen’), it points to the many interpretations of the biblical number ‘666’ from Revelation 13:18 and Jeremiah 50:8 referring to the apocalyptic beast. The majority of the article is a direct quotation from one source, a brand-new publication by Johann Georg Hagelgans,109 who embraced both the negative and the positive use of holy numbers: the devotional and inspirational use of biblical numbers in Sphaera Coelestis Mystica (1739), prefaced by 1 Corinthians 13:12: ‘Now we see but a poor reflection as in a mirror; then we shall see face to face’,110 and in Sphaera Infernalis Mystica (1740) an exposition on the number of the beast, 666 prefaced by the reassuring verse from John 1:5 ‘The Light shines in the Darkness and the Darkness has not overcome it.’111 Hagelgans’ systematic survey of significant biblical numbers is divided into three parts, with eleven chapters sandwiched between an introduction,

108 109

110 111

See Chapter Four for a discussion of the word ‘Vollkommenheit’. Sphaera Infernalis Mystica . . . Das ist: Höllisches Spinnenrad (Frankfurt am Mayn, 1740). Zedler reproduces pp. 19–23 and 193–215 literally. Sphaera Coelestis Mystica (Frankfurt, 1739). Sphaera Infernalis Mystica, 2, facing A2. ‘Das Licht scheinet in der Finsterniß und die Finsterniß habens nicht begriffen.’

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explaining the aim and use of divine arithmetic, and a defence of his opinions. In the chapter on the mysteries of the number 7 in the context of worship,112 he writes that once one has noticed the seven penitential, the seven prayerful and the seven praise psalms introduced into David’s Book of Psalms by the God-fearing Ancients, one’s respect and honour for this mysterious and holy number grows.113 The seven planets, seven metals and seven primary colours belong to the natural world and are a source of wonder in the visible world.114 The seven wise men of Greece, the seven wonders of the world and the seventy interpreters from Egypt, on the other hand, are all coincidental or formed by humans, and therefore according to Hagelgans cannot be classified as divine numbers.115 Hagelgans classifies numbers 1, 2, 3 and 7 as holy,116 numbers 4, 8, 12 and 24 as blessed,117 number 5 as half or imperfect,118 number 6 as human,119 numbers 7, 8 and 9 as end or balancing numbers,120 and number 10 as the most complete number. As he justifies his choice of 10 as the most complete he reveals more interpretations: §118 [Ten] is the most complete number, above all other, and in which all others are contained. It is the end and at the same time the beginning; a double number which is the most special and unique as it can be formed by all the other numbers in several different ways: through multiplication . . . 5  2=10, and through addition with the first four 1+2+3+4=10, with the two imperfect numbers 5 +5=10, with the angelic and human numbers 4+6=10, with the two most holy numbers 3+7=10, with the numbers of the bridegroom and bride 2 + 8=10, and with the first and last numbers 1+9=10. §119 The blind heathen also used this number for their two-faced God Janus, although we teach something better, seeing the origin or source from which its measure, number and density are constructed, finding in the Revelation to St John how God embraced all other possible numbers in this perfect circle.121

While not giving the number ten a specific interpretation, such magnificent praise raises it above all other numbers. Bach uses multiples of ten and one hundred consistently in his formation of parallel proportions.

112

113 116 118 119 121

Sphaera Coelistis Mystica, chapter 1, ‘Vom Geheimniß der Zahl VII in Beobachtung des Gottesdienstes’, 58–62. 114 115 Ibid., chapter 1, §66. Ibid., §67. Ibid., §68. 117 Ibid., ‘Heiligen Zahlen’, chapter 1, 19–62. Ibid.,‘Seeligen Zahlen’, chapter 2, 63–78. Ibid.,‘halben oder unvollkommen’, chapter 3, 79–82. 120 Ibid.,‘Menschlichen Zahl’, chapter 4, 83–5. Ibid.,‘Schluß-Zahlen’, chapter 5, 86–8. Ibid., ‘Allgemeinen Vollendungs-Zahl’, chapter 6, 89–92.

Symmetry, proportion and parallels

IV

Bach’s name in parallel forms

A recurrent feature of parallel techniques is exploitation of a proper name. Those performed on ‘Wjlhelm Ernst’ and ‘Pachelbelivs’, the paragrams on ‘Daum und Thym’ and ‘Skt Egidien’ and Kuhnau’s puzzle on ‘Steffani’ have all been mentioned. This practice dates back to the earliest classical times when the Greek, Hebrew and Roman alphabets could be read as numbers as well as letters, and authors exploited the names of heroes.122 The Bach family name lent itself very neatly to a variety of parallel devices, which have led to many intriguing and fanciful claims about Bach’s use of his name. Although it is difficult to discern whether a parallel conceit was planned or a simple coincidence of numbers or music, it is essential to review the evidence, not least because I claim that Bach’s name appears in the bar total or key pattern as the third characteristic of proportional parallelism, in all collections that he published or left in autograph fair copy. In 1732, under the entry ‘Bach, Johann Sebastian’, Walther reports how the Bach family name can be adapted to musical usage: The Bach family name is said to have originated in Hungary, and all those who have borne this name, so far as is known, are said to have devoted themselves to music; which perhaps springs from the fact that even the letters ‘B’ ‘A’ ‘C’ ‘H’ are melodic in their arrangement.123

Among the annotations Walther made to his personal copy of the 1732 dictionary is a note that it was Johann Nicolaus Bach (1669–1753) from Jena who had told him about this.124 Whatever the provenance, any member of the Bach family could have noticed the melodic parallel and used it.

B-A-C-H in melodies Although it was the Jena Bach who reported to Walther that musical notation spelt out the family name, we know from an account by Johann Nikolaus Forkel (1749–1818) that Johann Sebastian used the melodic form of B-A-C-H at least once: The last fugue but one has three themes; in the third, the composer reveals his name by B A C H. This fugue was, however, interrupted by the disorder in the author’s eyes, and as the operation did not succeed, was not finished.125 122 125

Tatlow, Bach and the Riddle, 37–9. Ibid., 466. See Chapter 9 §II.

123

NBR, Doc. 304.

124

Ibid., Doc. 305.

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Walther wrote that Johann Sebastian had published six partitas separately, giving the keys ‘B dur, C moll, A moll, D dur, G dur und E moll’.126 Devising a B-A-C-H signature in a large-scale key pattern is only a step away from the melodic B-A-C-H feature. The keys of the first three published partitas happen to be a permutation of the first three letters of the Bach family name, as Walther no doubt realised. It is commonly thought that the letter ‘H’ instead of ‘B’ was used universally in Bach’s time in Germany for the note B natural, but this was not the case,127 as Riepel illustrated by citing the use of B instead of H by Fux and Mizler,128 explaining that ABC was the old form, used by the Italians and French as well as some Germans. Later, when speaking of the use of ut re mi, Riepel comments that almost every music master has a different manner of teaching his students the note names.129 Because the letter B could read as both B and H, it gives an additional interpretation to the description in Walther: the four letters of the Bach family name could be equally well represented by three notes B/H-A-C.130 A century earlier Athanasius Kircher had used the letter ‘H’. Had Bach used Kircher’s Alphabetum Steganographicum musicum, or his Alphabetum Musicum, his full name would have been created the melodies shown in Figure 2.5. This begs the question of whether iconic themes, such as the opening of The Art of Fugue or the Ricercar à 3 of the Musical Offering, held any parallel meaning for Bach, and if so, whether being able to ‘decode’ the melody would add anything to our understanding of Bach’s music. Clarifying the ‘word’ might explain Bach’s starting point, the source of inspiration or Inventionsquelle.131

B-A-C-H in keys When Bach published CÜ II in 1735 he chose to position the French Overture after the Italian Concerto, rather than publish it as the seventh

126 127 128 129 130

131

Walther, Lexicon, s.v. ‘Bach, Johann Sebastian’. Geßner, Buchdruckerei, 142 shows that the music printing standard was for ‘B’ rather than ‘H’. J. Riepel, Grundregeln zur Tonordnung insgemein. (Frankfurt; Leipzig, 1755), 3. Riepel, Grundregeln, 11. Unfortunately Bach rarely wrote the key name so we cannot know when or whether he used ‘H’ or ‘B’ interchangeably for the keys of B major/minor. G. P. Harsdörffer, Poetischer Trichter. 3 vols. (Nürnberg, 1651–3), vol. III, 72.

Symmetry, proportion and parallels

Figure 2.5 ‘Johann Sebastian Bach’ in Kircher’s musical alphabets

Partita, or as the first work in CÜ II. He originally composed and revised the French Overture in C minor,132 but transposed it to B minor for the 1735 publication. This transposition created a large scale B-A-C-H signature across the two parts of these two keyboard publications (Table 2.1) and speaks of a changed plan from the B-A-C pattern in the 132

The manuscript of the C minor version in Anna Magdalena’s hand (P 226: 41–65) “Ouverture pour le clavecin par J. S. Bach” is extremely neat, suggesting that it was copied from a revised autograph source.

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Table 2.1 B/H-A-C key pattern across CÜ I and II Title

BWV

Keys

Bach allusion

Partita 1 Partita 2 Partita 3 Partita 4 Partita 5 Partita 6 Italian Concerto French Overture

825 826 827 828 829 830 971 831

B flat major C minor A minor D major G major E minor F major B minor

B C A G E F H

first collection, highlighting the new unity between the two collections, with all this implies for proportional parallelism. Transposing and inverting the B-A-C-H motif naturally gives many other possible ‘signatures’: at the fifth this would be F-E-G-F♯ and at the fourth E♭-D-F-E. An inverted F-E-G pattern can be seen in Table 2.1 column 5, with Partitas 5 and 6 and the Italian Concerto; the D major of Partita 4 standing outside this ‘self-referential ‘scheme. Although tonal transpositions and inversions would regularly occur in fugal treatment of the B-A-C-H theme, I wonder if the transposition of a name would have been as compelling a conceit to Bach and his contemporaries as the name in ‘normal’ order. A signature in its B-A-C form can be seen in the Six Solos for violin (BWV 1001–6) and in the Six Sonatas (BWV 1014–19), Table 5.4. The dual use of the musical letter ‘B’ facilitates the formation of a B-A-C signature in the keys of a collection. One could reasonably object that there are only seven or eight musical letters from which to choose, and that therefore early eighteenth-century composers writing a collection of six or eight works in different keys would naturally choose a combination of the keys A, B and C. Strangely enough, I have not found this signature combination in many other collections. The ordering of keys across CÜ I and II (Table 2.1) has recently been remarked upon.133 Bach’s contemporary Meynrad Spiess (1683–1761) included keys among his list of features to be ordered in a musical composition.134 Perhaps he too had noticed the pattern of keys in Bach’s collections.

133 134

Wolff, Essays, ‘The Clavier-Übung Series’, 189–205; Learned Musician, 378–9. M. Spiess, Tractatus Musicus Compositorio-Practicus (Augsburg, 1746), 134, col. 1.

Symmetry, proportion and parallels

B-A-C-H and other forms in number alphabets In his celebrated essay Bach bei seinem Namen gerufen, Friedrich Smend announced that he had found Bach’s signature embedded in music.135 With the numerical equivalents to ‘J. S. Bach ‘(41), ‘Bach’ (14) and ‘Johann Sebastian Bach’ (158) and using the simplest of all number alphabets, A=1 to Z=24, he noted the mirror image of 14 and 41 and isolated many occurrences of these numbers in Bach’s music.136 Although Smend’s lack of documentary evidence made his experimental results easy to discredit,137 he had discovered something very important about the creative possibilities of this time. Bach and his contemporaries could have used many different lusus ingenii and hybrid parallel techniques involving number alphabets and names. The name ‘Bach’ could be represented in the numbers suggested, but the variables were far greater than Smend had imagined. Bach signed his name in many different forms while thirty or more number alphabets and at least five different music alphabets were regularly used. And that is without allowing a composer to process the numbers using different parallel techniques. Translating a name to numbers through a number alphabet is an exact science, but working in reverse as Smend did, from numbers to their meaning, is far more hit and miss. In 1968 the compilers and editors, Werner Neumann and Hans-Joachim Schulze, of the first volume of Bach Dokumente grouped together all the surviving documents in Bach’s hand available at the time. In 2007 a supplementary fifth volume of more recently discovered documents was published. In BD I and V 185 documents are signed by Bach, in one of his many different signatures. Because the editors transcribed the exact signature form, it has been possible to make a statistical comparison of the signature forms Bach used.138 Even though far from complete, and ignoring conventions that may have motivated a particular signature type, Table 2.2 shows some important trends. When Bach signed a receipt he usually did so as ‘Joh: Seb: Bach’. By far his favourite form for title pages was ‘Johann Sebastian Bach’, with ‘J. S. Bach’ used less frequently and ‘Joh:

135

136 137 138

Smend, Johann Sebastian Bach bei seinem Namen gerufen (Kassel; Basel: Bärenreiter, 1950), reprinted in Bach-Studien: Gesammelte Reden und Aufsatze. Friedrich Smend zum 75. Geburtstag (Berlin, 1969). Smend, Johann Sebastian Bach: Kirchen-Kantaten, vol. III, 8. Tatlow, Bach and the Riddle, 6–36. W. Neumann, Johann Sebastian Bachs Unterschriften (Leipzig: Bach-Archiv, 1972), a facsimile collection of thirty-six of Bach’s signatures.

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Table 2.2 Statistical survey of signatures Bach used. Data from BD I and IV Form of Signature

I Letters

II Testimonial III Organ

Joh: Seb: Bach

1, 4, 5, 16, 20, 22, 38, 42, 43, 50

61, 62, 67, 69, 71, 73, 75, 79, 82

87

Joh: Sebast: Bach

27, 14, 18, 23, 32, 34, 10, 11, 27, 28, 35, 39,

57, 60, 63, 66, 68, 78, 81, A82a, A82b 80, A70

84, 85, 89

Johann Sebastian Bach

J. S. Bach Johann Seb(ast) Bach Joh. Sebastian Bach Joan(ne) Sebast: Bach Jean Sebastian Bach Bach J. S. B G. S. Bach Gio: Bast: Bach

36, 49

15, 17, 29, 30, 48, A13 12, 19, 31, 33, 40, 41, 54

86, A90a

65

91, 92, 93

V Receipts

VI Title pages

Totals

94, 95, 97, 98, 99, 100, 101, 102, 103, 105, 106, 107, 109, 112, 113, 114, 115, 117, 120, 124, 126, 127, 128, 129, 146 (4 ex), A111b, A111c, A112 A119a, A120a, A129a, A134 96, 110, 119, 123, 125, 130, 131, 132, 135, A111a, A133, A135a, A139

153, 157, 167

58

147, 161, 164

40

104, 108.122, 146 (1 ex)

152, 155, 159, 160, 164, 165, 169, 172, 175, 176 151, 154, 166, 174

156, 162, 168, 173,

38

158,

31

146 (23 ex)

74, 77 47

IV Legal

111, 121, 146 (2 ex) 90 (Joan) 146 (1 ex)

22 44

148 150, 177 155

118 170 BWV 71

6 2 2 2 2 2 1 1

Symmetry, proportion and parallels

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Table 2.3 Bach’s signature forms in three common number alphabets Signature form

Natural Order Alphabet

Trigonal Alphabet

Milesian Alphabet

Joh: Seb: Bach Joh: Sebast: Bach Johann Sebastian Bach J. S. Bach Bach Sebastian Bach J.S.B

31+25+14 31+63+14 58+86+14 9+18+14 14 86+14 9+18+2

186+189+46 186+551+46 369+688+46 45+171+46 46 688+46 45+171+3

67+97+14 67+288+14 148+338+14 9+90+14 14 338+14 9+90+2

70 108 158 41 14 100 29

421 783 1103 262 46 734 219

Sebast: Bach’ and ‘Joh: Seb: Bach’ in third equal place. When signing letters he seems to have used three forms fairly equally: ‘Johann Sebastian Bach’, ‘Joh Sebast Bach’ and ‘Joh Seb Bach’. Extant documents show that on the whole ‘Joh: Seb: Bach’ was Bach’s favourite signature,139 with regular, but significantly less frequent, use of ‘Joh: Sebast: Bach’, ‘Johann Sebastian Bach’ and ‘J. S. Bach’. Table 2.3 shows the numerical value of these four signature forms. I have added the forms ‘Bach’, because of the contemporary evidence that the surname ‘Bach’ was used in a musical alphabet, and ‘Sebastian Bach’ because tradition suggests that this was the name Bach went by. All six forms are given their numerical values according to the three most commonly used number alphabets in Bach’s time: the natural order,140 trigonal141 and milesian.142 The six signature forms generate eighteen possible numbers for Bach’s name. Although there is a high probability that composers in Bach’s time and location knew number alphabets and would have thought of using a signature as a parallel form, it is still a large jump to claim that a composer actually embedded his signature in a composition. Nevertheless, if one is intent on investigating the possible usage, the safest method is to note any recurring number in obvious musical units, and then assess its plausibility by weighing the result against external documentary evidence. Each occurence of a number I have tentatively isolated as an allusion to Bach’s name 139 140

141

142

I.e., Letters, Testimonials, Organ Testing, Legal Documents, Receipts and Title pages. Natural Order Alphabet: A=1, B=2, C=3, D=4, E=5,F=6, G=7, H=8, IJ=9, K=10, L=11, M=12, N=13, O=14, P=15, Q=16, R=17, S=18, T=19, UV=20, W=21, X=22, Y=23, Z=24. Trigonal Alphabet: A=1, B=3, C=6, D=10, E=15, F=21, G=28, H=36, IJ=45, K=55, L=66, M=78, N=91, O=105, P=120, Q=136, R=153, S=171, T=190, UV=210, W=231, X=253, Y=276, Z=300. Milesian Alphabet: A=1, B=2, C=3, D=4, E=5, F=6, G=7, H=8, IJ=9, K=10, L=20, M=30, N=40, O=50, P=60, Q=70, R=80, S=90, T=100, UV=200, W=300, X=400, Y=500, Z=600.

178 369 500 113 14 352 101

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will be discussed in Part Two. My observation of the strategic positioning of many proportional units based on the numbers 70, 158, 41, 14 and 29 appears to confirm Smend’s theory that Bach used the natural order alphabet. An uncanny recurrence of various permutations of the numbers 1, 2 and 3 in strategic large-scale units, or as the final bar total of complete collections, drew my attention, and, together with a later discovery of the parallel total 3120 : 3120 bars between his first four keyboard collections and the 1032 total of Aufrichtige Anleitung,143 forced me to consider the possibility that his use of the numbers 1, 2, 3 might have been intentional. Both 3120 and 1032 are permutations of the number-letters for B-A-C or 2-1-3, which raises the question of whether Bach might have intended it to refer to himself, or to the perfect number 6, with its 1+2+3=6 and 123=6.144 Permutation was a subject that fascinated mathematicians, philosophers and musicians. As Bach was able to generate and mentally retain endless possibilities to solve the technical challenges of his canons and fugues, I can see no reason why he would not have considered any combination of the numerals 2-1-3 as an allusion to his family name.

14-41 and 29 as family number names There is a neat symmetry in the numerical value of the initials of Bach’s name in the natural order alphabet Bach=14, J. S. Bach=41, and that of his first wife. This may be a simple numerical coincidence, but its recurrence in the names of their first- and second-born sons suggests deliberate design. Maria Barbara Bach, Johann Sebastian’s cousin and his first wife, retained her surname ‘Bach’ (=14) when they married. Her middle name Barbara (=41) created the same 41 : 14 as the value of her future husband. Her name as initials also contains a happy 1 : 1 symmetry: M.B.=14; Bach=14. Were the couple conscious of this numerical and harmonious match? Coincidentally, or deliberately, they chose names for their two eldest sons that also conform to this 41 : 14 pattern: their first-born son W. F. Bach=41; and their second son Carl Philipp Emanuel (Immanuel), using the initials given at his baptism,145 was also 41 – C. P. I. Bach=41. The pattern continues with parallels between the full initials of the father and 143 144 145

See Table 7.4. See Chapters 1 and 4 for ‘numerus perfectus’ and interpretations of the number 6. BD II, Doc. 67 ‘getauft den 10ten Martij Nahm[en] Carolus Philippus Immanuel’.

Symmetry, proportion and parallels

the two sons: J. S. B.=29, W. F. B.=29, and C. P. I. B.=29.146 Their daughters and younger sons fall outside this pattern. So does the name of Bach’s second wife, Anna Magdalena Wilcke (Wülcke), whose disappointing numbers A. M. W.=34, A. M. Wilcke (Wülcke)=72 (83), Magdalena=55 became an equally unsatisfactory A. M. B (15) and A. M. Bach (27) when they married on 3 December 1721, although had it been a serious issue, the harmonic perfection of 28 : 14 (Anna:Bach), and 27 : 27 (J. S. :A. M. Bach) would have more than compensated.147 Contrary to earlier Bach family traditions, Johann Sebastian Bach did not choose Johann as the name for either of his older sons. Although it is not possible to prove that they chose their sons’ names and godparents on account of their numerical value,148 the avoidance of ‘Johann’ and the recurring coincidence of 41 and 29 strongly suggests that Bach and his first wife had an eye on numerical unity within the male line.149 As if by design, Bach also became the fourteenth member of Mizler’s corresponding society.150

B-A-C and 2-1-3 The number letters of the word BACH in both the natural order and milesian alphabets are 2 1 3 8. In paragrams the numerical value of each letter was added to make a total for the whole word, so that Bach would become 14, as the sum of 2+1+3+8=14. Sometimes, however, the number letters were not added together, but remained separate, each number substituted for a letter in the solution word, such as in Kuhnau’s Steffani puzzle and in the algebraic problems Bach would have met at school.151 The coincidence of the letters B-A-C with the first three letters of the alphabet and the note-names of the first three notes of the musical scale would not have escaped the attention of any young, literate and numerate 146 147 148

149 150

151

JSB=9+18+2=29; WFB=21+6+2=29; CPIB=3+15+9+2=29. Anna=28, Magdalena=55, Wülcke=70. Anna Magdalena=83 and A. M. Wülcke=83. Although traditionally a child took the name of a godparent, one cannot exclude the possibility that a godparent was chosen for their name. BD II, Doc. 51 Friedemann’s godparents include Wilhelm Ferdinand von Lyncker, and Friedemann Meckbach. BD II, Doc. 67 C.P.E’s godparents included Adam Immanuel Weltig and Georg Philipp Telemann. There was no Carl. Their first-born, Catharina Dorothea, does not conform to the pattern. Musicalische Bibliothek, vol. IV (Leipzig, 1754), 107. In 1746 there was only one new member. Clearly he would not have been able to influence his position in the Eisenach Latin school register, BD IV, Image 20.14. Joh: Sebastian Bach; 15. Joh: Jacob Bach. Tatlow, Bach and the Riddle, 52–4.

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member of the Bach family. The further coincidence of Sebastian’s birthday would have been noticed by the bright schoolboy. He could not choose his birthday. It just happened to fall on the twenty-first day of the third month of the eighty-fifth year of the seventeenth century: 21385. This day and month was the official date of the spring solstice, although in reality the solstice fell days earlier for the first fourteen years of Bach’s life due to an error built into the Julian Calendar. The Protestant states corrected the error by losing 10 days in 1700, when the day after 18 February became 1 March, and not 19 February. The spring solstice finally coincided astronomically on Bach’s fifteenth birthday, 21 March 1700. Irrespective of the position of the sun and moon on 21 March, and whether he liked it or not, his birth date when written in the customary order Day-MonthYear152 21.3.85 translated into letters B-A-C-H-(E) and was numerically parallel to the numerical value of his surname, B-A-C-H=2-1-3-8. In its simplified form his birthday fell on 21.3, parallel to 2-1-3, B-A-C, and parallel to the musical notes 2-1-3, B-A-C.

Bach’s name in parallel imagery The name ‘Bach’ means ‘brook’ or ‘stream’ in German and this parallel was an obvious image to exploit in poetry. Johann Gottlob Kittel (1732–1809) (alias Micrander) composed the emblematic poem below when reviewing a concert given by Bach on the Silbermann organ in St Sophia’s church, Dresden on 14 September 1731. Ein angenehmer Bach kan zwar das Ohr ergötzen, Wenn er in Sträuchern hin durch hohe Felsen läufft; Allein, den Bach muß man gewiß weit höher schätzen, Der mit so hurtiger Hand gantz wunderbahrlich greifft. Man sagt: Daß wenn Orpheus die Laute sonst geschlagen, Hab alle Thiere er in Wäldern zu sich bracht;

152

A pleasant brook may well the ear’s delight inspire, As through the woods, between high cliffs, it finds its way; But surely one must rank that other Bach far higher, Who with his hurrying hand so wondrous sure doth play. ’Tis said, when Orpheus did his lyre strings awake, All creatures in the forest answered to the sound;

Bach used the order Day, Month, Year, e.g. 14 Jan 1714. BD I, 33.

Symmetry, proportion and parallels

Gewiß, man muß diß mehr von unserm Bache sagen, Weil Er, so bald er spielt, ja alles staunend macht.

But sure, ’twere better that such praise of Bach we spake, Since he, whene’er he plays, doth each and all astound.

In 1732 Ludwig Friedrich Hudemann published a poem dedicated to Bach in a collection of poems and translations. The poem is full of common musical imagery – Orpheus, his harp, Bach’s ability to sway the souls of the righteous, the choir of the Muses, the organ, the serpent’s tongue, Apollo, the laurel crown, marble edifice, living strings, and the perfection of Bach – as if Hudemann was designing an emblem for Bach.153 It is thought Hudemann wrote the poem in gratitude to Bach for a puzzle canon written into a now lost album during Hudemann’s visit to Leipzig in 1727. The pun on brook/Bach would easily have lent itself to being used in a personal seal, or as an emblematic dedication. Many emblems featuring a brook in either the image or the motto were engraved and circulated in published emblem books, but there is no evidence that Bach ever developed this image for his personal use. He preferred to use his initials, both in music and in the design of monograms. The first documented Bach monogram dates to 14 January 1714, on a wax seal used in a letter sent to August Becker in Halle, from Weimar.154 The second is also in a seal on a letter to Becker, dated 19 March 1714.155 A similar early monogram form, dated 1 May 1716, is found beside Bach’s signature on a report on the organ of Our Lady, Halle that he examined jointly with Johann Kuhnau and Christian Friedrich Rolle.156 All three examiners authorised their signature with a wax seal; Bach’s 1716 seal takes the form of three blooms over a knight’s helmet between the letters I, S and B.157 The more well-known seal that Bach used exclusively for the rest of his life first appears in a letter to the Erfurt town council, dated 15 March 1722.158 The initials J S B slope diagonally both forward and in mirror image, with a crown above. Many attempts have been made to interpret the

153

154 156 157 158

L. F. Hudemann, Proben einiger Gedichte und Poetischen Uebersetzungen (Hamburg: Kißner, 1732), 221. BD II, Doc. 325; NBR, Doc. 308. 155 BD I, Doc. 2. BD I, Doc. 4, note A. The wax imprint is damaged. BD I, Doc. 85, and NBR, Doc. 59. BD I, Doc. 85, note A, p. 160. BD IV, Image 250a, from Archiv der Liebfrauenkirche, Halle. Ibid. and BD I, Doc. 8; BD IV, Image 250b.

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emblematic imagery. Since Bach used this seal to authorise his most formal letters and also on some valuable personal property,159 we can assume there was no scurrilous double entendre in the imagery. The parallel meaning of the crown was no doubt known to himself, and quite possibly to those who had it engraved onto the now famous crystal goblet.160 This chapter has shown how parallelism and symmetry were at the heart of many commonly used artistic forms. The 1 : 1 proportion of symmetry was considered the most perfect, and therefore it would have been natural for a composer to use parallelisms in musical structures. Indeed the desire to recreate perfection, beauty and eurythmia may have motivated the growth and stimulated the popularity of hybrid parallel forms. The abundance of symmetrical forms, proportions and parallels in everyday life, however, was as a result of something that lay far deeper within the core values, the philosophy and theology of society. And this is the subject of the next chapter.

159

160

U. Wellner, ‘Ein unbekanntes Möbelstück aus dem Besitz Johann Sebastian Bachs’, BJ 95 (2009), 214–25. Engraving c. 1735. BD II, Doc. 375; NBR, Doc. 310.

3 Unity, proportions and universal Harmony

in Bach’s world

Hat jemals ein Tonkünstler die verstecktesten Geheimnisse der Harmonie in die künstliche Ausübung gebracht; so war es gewiß unser seeliger Bach. C. P. E. Bach and J. F. Agricola, 1750

Although much of great significance has been published about Bach’s faith and Lutheran music, little has been written about the theological and practical significance of proportions, the unity and Harmony.1 This chapter will explore these three fundamentally numerical concepts with a view to shedding light on Bach’s motivation for introducing proportional parallelism into his collections.2

I

Defining beliefs

Integral to Harmony is the 1 : 1 proportion of the unity and its origins stemming from the ancient teaching, or ‘Proportion-Lehre’, of the Greeks.3 Legend has it that Pythagoras (fl. 530 BCE) discovered and formulated the rules of Harmony and musical intervals when he heard the different pitches that sounded from hammers on metal as he walked past a smithy. With weights and lengths of chord he demonstrated that a ratio of 1 : 1 produced the interval of a unison, 1 : 2 an octave, 2 : 3 a fifth, 3 : 4 a fourth.4 The tale was reported as historical fact by Iamblichus (c. 250–325 CE)5 and repeated as such in European music theory books until the eighteenth century, including in books that Bach read.6 Mattheson outspokenly disputed its historical veracity.7 1 2

3 4

5 6

7

‘Harmony’ with a capital ‘H’ is used throughout as a translation of harmonia and Harmonie. Sources relevant to the doctrine of music have been assigned a short year/number reference (e.g. 1706-I) to the Appendix, where full bibliographic references and full text in parallel English– German translation are given. J. Mattheson, Orchestre 2, Register, 543, s.v. ‘Proportion-Lehre’; Buttstett, Ut, Mi, Sol, 75. The proportions 4 : 5 (major third) and 5 : 6 (minor third) became important in polyphonic music. Iamblichus, Life of Pythagoras, translated from the Greek by Thomas Taylor (London, 1818), 62. See Walther, Praecepta, vol. II, 21–35. Its inclusion in Boethius’ De Institutione Musica, book I, chapter 10, guaranteed its perpetuation. Mattheson, Orchestre 2, 309, 312.

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The proportions8 of musical pitches were thought to be fundamental to God’s created order. The so-called ‘universal harmony’ of existence could be seen in the macrocosm and microcosm of all creation.9 One such manifestation was the music of the spheres. The belief that each planet produced a different musical note as it rotated and that the distance between the planets was harmonically organised is frequently attributed to Pythagoras and his followers,10 although it was Plato (428/7–348/7 BCE) and Ptolemy (c. 85–c. 165 CE)11 who assigned specific pitches to the heavenly bodies.12 In 1599 Johannes Kepler (1571–1630) designated a speed to each planet – Saturn was assigned speed 3, Jupiter 4, Mars 8, Earth 10, Venus 12 and Mercury 16, and so Jupiter and Mars produced an octave (4 : 8=1 : 2), Mars and Venus a fifth (8 : 12=2 : 3) and so on13 – although he did not publish a fully developed theory of planetary harmony until twenty years later in Harmonices Mundi. The transmission and reception of Greek ideas in Europe is complicated by a conceptual contradiction between the Aristotelian, Ptolemaic and Neoplatonic traditions,14 causing an unresolvable debate over whether timeless mathematical laws governed nature, or conversely, whether humankind gradually discovered the laws. Various versions of these ideas were transmitted by Nicomachus (fl. c. 100 CE) in his mathematics and music treatises, which were then popularised by Boethius (c. 480–c. 525 CE). Boethius, whose writings were an essential part of the European university curriculum, divided music into three parts, musica mundana, musica humana and musical instrumentalis, all three of which were united by Harmony.15 ‘For Boethius, a faithful student of Platonic thought, it was

8

9 10

11 12

13 14

15

By using ‘proportion’ rather than ‘ratio’ I am following early eighteenth-century usage, when, although aware that a comparison of two terms was a ratio, theorists continued to use ‘proportion’. See Walther Praecepta, ‘Musica Poetica’, 10 (Benary, 76). Zedler, Lexicon, s.v. ‘Universalis Harmonia’. C. Riedweg, Pythagoras: His Life, Teaching and Influence, trans. Steven Rendall (Cornell University Press, 2005), 27–30, citing Nicomachus (c. 60–c. 120 CE) via Porphyry (fl. c. 300 CE). Zedler, Lexicon, s.v. ‘Corpora mundi totalia, Corpora celestia’. The Harmony of the World by Johannes Kepler, translated into English with an Introduction and Notes by E. J. Aiton, A. M. Dundan and J. V. Field. (American Philosophical Society, 1997), xix. Ptolemy’s pitches were in relation to the distance the bodies were from the Earth, the lowest note being assigned to the Moon, and the highest to Saturn. Ibid. Kepler described this in a letter to Herwart, 14 September 1599. G. Ilnitchi, ‘Musica Mundana, Aristotelian Natural Philosophy and Ptolomaic Astronomy’, Early Music History 21(2002), 37–74. Ibid., 40, ref. to Boethius, De institutione musica, I, 2, 187–9. Neither Walther, Lexicon nor Zedler, Lexicon lists the three classifications in their respecitive entries s.v. ‘Boethius’.

Unity, proportions and universal Harmony

number and proportion that were the “final” cause governing each of these three kinds of harmony.’16 Common to the four mathematical disciplines of the Quadrivium (arithmetic, astronomy, geometry and music) was the fundamental unifying principle that every area of creation reflected Harmony. This belief might well have fallen out of fashion but for a revival of interest in the late fifteenth, sixteenth and early seventeenth centuries, when Italian artists and their rich patrons fell under the spell of the Greeks, and intelligent and imaginative musicians across Europe, from Zarlino in Venice to Robert Fludd in Kent, reclaimed and adapted Boethian views.17 Harmonic proportions were once again hailed as the standard of perfection for all art forms, and proportions were the measurement by which beauty could be assessed objectively. Figure 3.1 shows a statement typifying the application of Harmony to the arts in sixteenth-century England, formulated by George Puttenham in his Arte of English Poesie to open the first chapter of Book Two, ‘Of Proportion Poetical’ Poeticall.18 Fundamental to the understanding of music in Bach’s time was proportional theory, demonstrating the significance and perfection of the six numbers of the senarius, because of its ratios 1 : 1, 1 : 2, 2 : 3, 3 : 4, 4 : 5 and 5 : 6, the unison and octave being the most pure.19 The word Harmony embraced both the philosophical non-sounding harmony of the spheres, or Universal Harmony, and the sounding harmonies of music. The overlap of meaning in the terms ‘unity’, ‘proportions’ and ‘harmony’, combined with the umbrella term ‘Musica’, creates a complex web of threads in the history of music which is virtually impossible to unravel. The task is complicated by conflicting opinions, the coexistence of old and new ideas, and the evolution of a concept, even within the writings of a single theorist. This overlapping can frequently be seen in early eighteenth-century reference works. The seven sections of Walther’s definition of ‘Musica’, for example, give first (section 1) a description of the nine muses and their poems, repeating the standard Greek view that everything in the universe works together in perfect Harmony: 16

17

18 19

T. Christensen, The Cambridge History of Western Music Theory (Cambridge University Press, 2002), 3. Writings on harmonia by Zarlino, Fludd and other theorists can be found in English translation in Joscelyn Godwin, Music, Mysticism and Magic: A Sourcebook (London; New York: Routledge & Kegan Paul, 1986). G. Puttenham, The Arte of Poesie (London: Richard Field, 1589), 53. See Chapter 1. Christensen, Cambridge History, 253–4, 276–8.

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Figure 3.1 Puttenham, The Arte of English Poesie (London, 1589), 53

Unity, proportions and universal Harmony

In these poems the Greeks undoubtedly wanted to convey that all movements of the heavens [planets], the position of the elements, the changes of the seasons, etc., in their order and beautiful proportion, produce nothing less than a well-ordered and intertwined Harmony.20

Sections two to six explain the different uses of the musical triad, while the seventh reads: And finally and above all it [Musica] is used for all that produces a Harmony, in particular for the order, construction and disposition, in short for the agreement of the whole with its parts, or the parts with themselves. And it is used in this sense by those who claim that everything is Music in the whole world, as has been seen above in section one.21

Walther is giving what he considers to be a rational and accurate explanation of the modern view of music. Although advanced mathematics and calculus were commonly used by this time, it was still the simplest proportions that described harmonic perfection, the ideal being the 1 : 1 of the unity.22 The word ‘Harmony’ also demonstrates the overlap between old and new. Walther gives four different definitions: ‘Harmonia (lat.), Harmonie (gall.)’ or Harmony formed as the result of combining different tones to make a beautiful and enjoyable consonance; ‘Harmonica, Harmonice (lat.)’ which is a science of the proportional measurement, order and magnitude of sound, embracing ‘Sonos, Intervalla, Systemata, Genera, Tonos, Tonorum commutationes’, and for which he cites as his authority Mattheson, Orchestre 3;23 ‘Harmonici’ which discusses the meaning of the harmonicists who allegedly give more authority to the Ear than to Reason; and finally the definition of the French, ‘harmonieux, -euse’. Zedler’s encyclopedia, on the other hand, includes fifteen entries for ‘Harmonia’ and its related forms, two of which – ‘Harmonia’ and ‘Harmonici’– were taken directly from Walther’s dictionary. The remaining thirteen entries include: ‘Harmonia or Armonia’ in anatomy; ‘Harmonia or Hermione’ the daughter of Mars and Venus; ‘Harmonia corporum Mundi totalium’ or ‘Harmonica Mundi’ or ‘Harmonie der Welt’, harmony of the world; ‘Harmonia praestabilita’, or Vorherbestimmte Harmonie, Harmonie Prästabilirte; ‘Harmonica Proportio, continua & discreta’, and ‘Harmonisch-proportionirte Größen’ or ‘Harmonische Proportion’, which is by far the longest entry of all, covering one-and-a-half columns. The single entry in Fritsch’s 20 23

Walther, Lexicon, s.v. ‘Musica’. Mattheson, Orchestre 3, 284.

21

Ibid.

22

Appendix, 1708-VI.

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German–English dictionary reads: ‘Harmonie oder übereinstimmung (die), harmony. Sie leben in guter harmonie mit einander, they agree pretty well together’.24 These lexicographical works give an insight into the breadth of definitions by authors living in the same region and time as Bach. What the words actually implied and how they were used, however, can only be discovered by analysing their meaning in context. The selected citations in this chapter illustrate the subtle complexities of Harmony, and the related concepts of proportion and unity. Bach knew or read all of the books cited.

II Confusion of Harmony proper and Harmony in music An important clue to the use and significance of the word ‘Harmony’ can be found in the publications covering the famous conflict between Mattheson and Buttstett, which began in 1713 with the publication of Johann Mattheson’s Orchestre 1. Believing that Mattheson’s views in Orchestre 1 ‘contravened the word of God’,25 Buttstett decided to put the record straight by publishing what he considered to be the correct biblical view of the matter.26 Infuriated, Mattheson responded in doublequick time with a complete scriptural defence of his position, turning the accusation on its head and charging his opponent with sinfulness and blasphemy, while ensuring maximum publicity by dedicating his response to thirteen of the most eminent contemporary musicians of the day, who had been invited to act as an impartial jury of his viewpoints.27 Although soundly defeated and publicly humiliated,28 Buttstett decided to respond one more time, in a single-sided Manifesto, Wieder das Beschützte Orchestre,29 dated September 1718, in which he tells his ‘loyal and respected readers’ that ‘nothing extra could be added to what he had written earlier’ (in 1716), his arguments remained ‘as clear as daylight’, ‘indisputable’, and his ‘conclusions rock-solid’. (See Figure 2.4.) 24 25 26 27

28

Fritsch, Lexicon, s.v. ‘Harmonie’. Buttstett, Ut, Mi, Sol, 3: ‘Es ist auch solches kühnes Unterfangen wieder Gottes Wort’. The title page reads: ‘im andern Theile aber das rechte Fundamentum Musices gezeiget’. The thirteen composers: Georg Bertouch, Johann Joseph Fux, Johann David Heinichen, Georg Friedrich Händel, Reinhard Keiser, Johann Philip Krieger, Johann Krieger, Johann Kuhnau, Christian Ritter, Johann Christoph Schmidt, Augustin Stricker, Georg Philipp Telemann, Johann Theile. Those who responded included Händel, Heinichen, Johann Krieger and Fux. 29 The 1718 Manifesto refers to at least one instance of public humiliation. See Figure 2.4.

Unity, proportions and universal Harmony

And to prove it one final time he would demonstrate it in the publication of ‘six sparkling new Masses . . . of the old kind’.30 The root of the Buttstett–Mattheson disagreement lay in their different understandings of Harmony. Their style of argument also differed greatly, Buttstett’s tending to mix moral, theological and musical thoughts while Mattheson would focus on each point at a time. For example, Buttstett wrote: We see once again that this governing principle is present [in the laws of] musical proportion and Harmony, and how the sounding Harmony falls in our ears . . . thus the Harmony of the universe falls into our souls, rules and drives them: Since our souls are and remain in pure Harmony now, they can always stand in union with the universe, indeed with the Creator Himself; for God is a God of order, and delights in it. But I always exclude the abusers; for as God takes no pleasure in those who abuse His word and His will, so the abusers of music cannot please God either.31

A year later Mattheson responded with a clarification of what he understood to be Buttstett’s erroneous use of the word Harmony, demonstrating the allimportant distinction between Harmony proper and Harmony in music: But Mr Organist, since you prattle on about distinctions and explanations, why don’t you distinguish primarily between what is properly called Harmony (Harmonia propriè sic dictam) and Harmony in music (Harmonia in Musicis)? All your images, your grand and mighty clavis B, the proportions of the mercy seat, of the incense altar etc., demonstrate a Harmony; but a silent Harmony is not true music. It may make a three- or six-fold species of musical Harmony; but so long as a thing does not [make a] sound, I cannot call it musical Harmony. We will with the help of God deal in more detail with Harmony in the third volume,32 and let it be seen how far the properties of this word relate to music. All the panes in the windows have a Harmony, but that does not mean that music is inside them, unless one mistakes the noise for music, when [for example] a cavalier is dubbed a knight and [then] smashes the windows.33

Mattheson was fully aware that Buttstett was describing the prevalent and widespread Lutheran view of Harmony which embraced both sounding

30

31 32 33

Only four of the six masses seem to have been published: Opera Prima Sacra, Bestehend in vier neu-componirten Missen (Erfurth: Buttstett, 1720). Copies have survived in the Wisentheid Library, Schönborn, and the Lenin Library, Moscow. I am grateful to Steffen Voss for alerting me to this. Appendix, 1716-I. This is evidence that in 1717 Mattheson already had plans for Orchestre 3. Appendix, 1717-I.

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and non-sounding proportions, a view that Bach too was familiar with. Mattheson nonetheless continued his attack, armed with biblical verses and logic, and in the process accusing Buttstett of distorting scripture. Paraphrasing God’s words to Moses in Exodus 25:17, Mattheson wrote: Moses was charged to make a mercy seat [atonement cover] two-and-a-half ells long and one and a half wide, therefore it was a harmonic construction, from which to take the triad and music. I have an ironing table in my laundry room with the same width and the same length, but one could beat or grab it from now until eternity before it would make a single note, let alone a musical concord.34

The mercy seat was kept inside the Temple’s innermost sanctuary, the Holy of Holies, and was associated with the presence of God: God had stipulated its dimensions. It was extremely precious, made of the finest wood overlaid with beaten gold, two Cherubim at each side, and was considered as a symbolic forerunner or type of Christ.35 Although the logic of Mattheson’s argument is inescapable, the parallel he makes between beating an ironing table and the mercy seat, if not blasphemous, would at the very least have been provocative.36 These examples may give the impression that Mattheson had little or no understanding of the spiritual significance of the unison or musical proportions, but that would be far from the truth. In the very next paragraph he makes what amounts to a creedal statement: There is no doubt whatsoever that the Lord God is pleased with proportions, and the universe demonstrates this, both in the microcosm and macrocosm, about which Robert Fludd, alias de Fluctibus, has written sufficiently. God is pleased with musical sounds and their proportions: I doubt that as little as I doubt Christ’s birth, because music is also His creation, indeed one of His best creations and gifts. but I [Mattheson] would have to be inhumanly gullible to believe that God had nothing beside the six Aretinian syllables in stock, and that He would have wanted to show our musical triad through the measurement of the mercy seat. Were one to claim that the mercy seat and other things in the Old Testament had been ordered because of music, no single mystical theologian would have ever thought of it. Can this prove that our (that is, our clumsy) music will last into eternity?37

34 35

36

37

Appendix, 1717-II. Zedler, Lexicon, s.v. ‘Gnaden-Stuhl’: ‘Dieser Gnaden-Stuhl ist ein Vorbild auf Christum gewesen. Rom 3,25, Ebr. 4,16.’ In Orchestre 2, 285 Mattheson accuses Buttstett of multiple counts of defamation and blasphemy (‘Vielfältige grobe und brutale Lästerungen und Calumnien’), directing his readers to pages ‘30, 54, 100, 134, etc.’ Appendix, 1717-III. Fritsch, Lexicon, s.v. ‘Stückwerck’ gives the English syonyms ‘imbecillity’ and ‘imperfection’.

Unity, proportions and universal Harmony

This statement goes a long way towards explaining why Mattheson was so frustrated with Buttstett. Buttstett believed from scripture that music composed on earth, using the hexachord,38 would survive into eternity. Mattheson did not. Although he believed profoundly in heavenly music, he did not believe that compositions written on earth would be heard in heaven, much less that this could be demonstrated from biblical verses. He was incensed by the illogicality of Buttstett’s demonstration: The mercy seat was one ell long and wide and two ells high: therefore it sounded an Octave . . . The opponent [Buttstett] states further, on p. 174, in case you don’t believe me, that one can demonstrate this with or without the monochord that half of the whole string sounds an octave, but that the mercy seat should also sound and mean an octave is just ridiculous. Let’s look at it logically. Major: Everything in duple proportion [2 : 1] sounds an octave, Minor: Moses’ mercy seat was proportioned 2 : 1, Ergo: We will make music in Heaven with the same sounds we use in the world. Quod erat probandum.

Mattheson continues mercilessly: Another of the same kind appears in §6 p. 174 . . . Major: God created and made the whole world in Harmony, Minor: But as we are assured in scriptures that heaven and earth will pass away, wherein no word is given that Harmony will also pass away; therefore he infers that by good consequence, Conclusio: Music will remain eternally.39

Reduced to this form, the illogicality of Buttstett’s arguments is as clear as Mattheson’s palpable delight in his own cleverness. And so it goes on, with Mattheson summarising Buttstett’s logic, that earthly sounds, including the symmetrical ut re mi fa sol la, will be used in heavenly harmony and music, and that it is ‘God himself who will compose the melody’.40 At which point Mattheson exclaims: ‘Ach! Thou great eternal composer, who created the entire universe with a single word, forgive poor sinners, and particularly the organist in Erfurt.’41 The conflict over Harmony went far deeper than the well-worn argument over sensus versus ratio, sounding music or rational proportions. At

38 39 41

The symmetry (1 : 1) of the hexachord may have helped form this view. 40 Appendix, 1717-IV. Appendix, 1716-III. Mattheson, Orchestre 2, 478. See Figure 3.2.

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Figure 3.2 Mattheson, Das Beschützte Orchestre (Hamburg, 1717), 478

Unity, proportions and universal Harmony

stake was whether the earthly efforts of the Christian composer, in our case Bach, would survive eternally, and how they might do so. Outliving Buttstett by almost three decades, Mattheson went on to devote an entire thesis to music in heaven in 1747.42 Using the same categories of evidence – argument, scriptures and church doctrine – as Werckmeister in 1691,43 Mattheson argues that heavenly music will be performed physically with physical instruments in eternity, writing: ‘This music [Heavenly music] can never age, but will always remain new, for this reason it is called the new song’,44 and: People who do not recognise, respect, seek or love such a precious foretaste of eternal life, why would they serve in the heavenly Jerusalem? . . . The more zealously they work against musical worship in this world . . . the more difficult it will be for them to be drawn to the pursuit of harmonious joy in eternity.45

Mattheson considers that ‘above all other Johann Christoph Ammon has shown, with a thorough and clear proof, that there is actually excellent music in eternal life’, including Ammon’s statement: ‘Given that all possible kinds of joy will, without question, be encountered in eternal life, should not then also fine music by all rights (indeed, with all its possible styles) be counted among them as the first of all?’46 This also shows that the debate about the kind of music played in heaven was still active in the late 1740s. That perfectly constructed and harmonically proportioned vocal and instrumental compositions would survive the Rapture and be played in the new heaven and new earth would have been a powerful motivating belief for the Lutheran composer. One wonders how many composers of this period thought like this. Was Bach’s student Kittel implying that Zelenka’s music would exist in heaven, or that there would be music in heaven, when he wrote: ‘To delight the soul in God’s honour, you [Zelenka] are able to write church music in the most stimulating manner, which is so touching that the reverent breast receives a foretaste of those heavenly pleasures’?47 The posthumous publication of two short treatises by the theologian Heinrich Georg Neuss (1654–1716) in Leipzig in 175448 demonstrates that 42

43 44 47

48

J. Mattheson, Behauptung der Himmlischen Musik aus der Gründen der Vernunft, KirchenLehre und heiligen Schrift (Hamburg, 1747), trans. J. L. Irwin, Foretastes of Heaven (Latham: Rowman & Littlefield, 2015). Werckmeister’s order is: Heiligen Schrift, Kirchen-Lehre und Music-Gründen. 45 46 Appendix, 1747-I. Appendix, 1747-II; Irwin, 137. Appendix, 1747-III; Irwin, 102. I am grateful to S. Paczkowski who alerted me to this source. See J. B. Stockigt, ‘The Court of Saxony-Dresden’, in Music at German Courts, 1715–1760 (Woodbridge: Boydell, 2011), 33. H. G. Neuss, Musica Parabolica oder Parabolische Music (Leipzig: J. S. Heinsius, 1754), 1–89, and Kurtzer Entwurf von der Music. Den Geist der Weißheit und Offenbahrung zur Erkenntniß Gottes und seiner geheimen Wahrheit zuvor (Leipzig: J. S. Heinsius, 1754), 90–124.

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belief in heavenly music was still active and valuable to musicians there, even after Bach’s death. Echoing sentiments by Werckmeister, Buttstett, Kittel and Mattheson, Neuss writes that music is a model and foretaste of eternal life and that music is the art of arts that will survive into eternity.49 This theological framework leads to some detailed applications for the good use and the abuse of music. For example, When the Holy Spirit himself participates in the music, the art takes on the correct heavenly Harmony and arouses a fervent devotion. However where the spirit of the world is at work [in the music], art lets itself be seen and arouses admiration. However the correct harmonic entry into the minds [of the people] is lacking; what remains is devotion, which should be the main purpose of music. A mind well ordered by the Holy Spirit recognises in itself, whether singer or musician, the spirit of the world or the spirit of God.50

Neuss applies this to practical performance, citing the ‘Chorus Symphoniacus’ and ‘Collegium Musicum’, stating that where one member is not inspired by the Holy Spirit the performance and Harmony of the entire ensemble is affected, which is an abuse of music.51 These beliefs may explain some of Bach’s seemingly stubborn demands in his dealings with his employers. How and why Neuss’ two short treatises came to be published in Leipzig in 1754, when their author had died forty years earlier in north Germany, is something of a mystery. A well-known theologically interested musician and author, such as Bokemeyer, Mattheson or Walther, might have been entrusted with the manuscripts when Neuss died in 1716. The Bokemeyer possibility is strong as he knew Neuss, and both were active in the Wolffenbüttel area, but Bokemeyer died in 1751 and his ties to Leipzig were not strong. Walther had died three years earlier in 1748, and so if he had been given Neuss’ works they would have passed to yet someone else before publication. Mattheson was still alive when publication took place, and had recently completed his own book on music in heaven,52 but he almost invariably published in Hamburg. Regardless of how the books came to be published and whether the two treatises were written by Neuss or not,53 their publication demonstrates that, as late as 1754, a reputable

49 52 53

50 51 Ibid., 92–3 . Appendix, 1754-I. Ibid., similar to 1691-IV 7 and 1691-V. J. Mattheson, Behauptung. In New Grove, s.v. ‘Neuss, Heinrich Georg’, Walter Blankenburg doubts Neuss’ authorship, whereas A Dictionary of Musicians (London, 1824), s.v. ‘Neusz, Heinrich Georg’, reads: ‘He also wrote the following works: Of the Use and Abuse of Music (1691), Musica Parabolica, a tract, and A Treatise on Music. The two latter were left in manuscript at his death.’

Unity, proportions and universal Harmony

Leipzig publishing house thought the key qualities of this doctrine of music were still of interest and worth printing.54

III Proportions and morality in a Thuringian doctrine of music Martin Luther (1483–1546) wrote about music several times, most importantly in two essays and in Encomion Musices.55 Thüringian-born music theorist Andreas Werckmeister had such a high regard for Luther’s works that he reproduced the full text of the two essays in his 1691 publication Der Edlen Music-Kunst. This musical manifesto contains Werckmeister’s definitive statement on music, based, as he claims, on scripture, church doctrine and the basics of music: The Noble Art of Music: its Greatness, Use and Abuse, published and explained from the Holy Scriptures, from some Old and Newly demonstrated pure Church Doctrines and from the basis of Music itself.56 It represents the kernel of what may be called a Thuringian doctrine of music. By studying what music theorists in the Thuringian region thought and wrote about Harmony, the unity and proportions, it may be possible to grasp how Bach thought. Thomas Christensen describes Werckmeister’s understanding of the ‘generative unity’: Like Mersenne, Werckmeister held that unity was the source of number and music, and an image of the divine creator. ‘If we compare the days of creation with music,’ he wrote, ‘we see that in the beginning God created heaven and earth in the first days. This beginning is the unity or unisonus out from which all consonances and dissonances flow. Indeed, God Himself is unity — a being without beginning or end’. Elsewhere he wrote: ‘Just as unity is compared to the one God, so is a Harmony originating in this unity and that contains in itself at once all the consonances in Harmony perfectly and complete.’57

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J. S. Heinsius collaborated with Zedler. Two essays published in Luther, Table Talk (Eisleben, 1566), 411. See Robin A. Leaver, Luther’s Liturgical Music: Principles and Implications (Grand Rapids, MI; Cambridge: Eerdmans, 2007), appendix 3, with parallel translations of two versions of Luther, Encomion musices (1538), 313–24. Werckmeister, Der Edlen Music-Kunst Würde, Gebrauch und Mißbrauch, So wohl Aus der Heiligen Schrifft Als auch aus etlich alten und neu-bewährten reinen Kirchen-Lehrern, und dann aus den Music-Gründen selbst eröffnet und vorgestellet. (Franckfurt; Leipzig: Calvisius, 1691). T. Christensen, Rameau and Musical Thought in the Enlightenment (Cambridge University Press, 1993), 84–90, esp. 88 for the generative unison.

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Behavioural application of the belief in Harmony In this search to understand Bach’s view of Harmony, it is significant that his close relative, Walther, was greatly influenced by Werckmeister, owning his complete works. The twelve chapters of Werckmeister’s Noble Art are preceded by a twenty-five-point dedicatory preface on the correct use of music, by his friend H. G. Neuss.58 Proportions and their significance are the main focus of the fourth chapter, where every aspect of music, i.e. Harmony, the senarius and septenarius and pitch,59 the bar, speed60 and range,61 is shown to be ordered, and to strive after the equality, 1 : 1.62 Werckmeister applies this principle to God, eternity and mankind; the well-proportioned human being rejoices whenever he hears music because it reflects both his own image and that of the wisdom of God.63 The same is not true of the human being of unsound (badly proportioned/ dissonant) mind and body. Repeating well-known scriptural references to God’s use of proportions in buildings, Werckmeister moves to the image that underpins his entire argument,64 that music is a mirror of divine creation and of the wisdom of God. This profound yet simple proportionally based metaphor was reused by generations of Lutheran music theorists, before and during Bach’s lifetime.65 The ‘mirror’ image is a recognisable parallel to the Pauline statement in 1 Cor 13:12 ‘Now we see but a poor reflection as in a mirror; then we shall see face to face’; and 2 Cor 3:18 ‘And we, who with unveiled faces all reflect the Lord’s glory, are being transformed into His likeness with ever-increasing glory, which comes from the Lord, who is the Spirit’.66 Music is the mirror, not the image.67 When man plays or hears music, the mirror of music actively reflects back God’s divine character through the ears to the soul. Music creates a self-perpetuating reflection of God, of His wisdom and of His

58

59 62 65 66

67

Neuss addresses Werckmeister as his most worthy Lord and Friend. Based in the Wolffenbüttel region for most of his professional life, Neuss moved to study theology at Erfurt University from 1677 to 1680 at the same time as the Bach family friend Johann Pachelbel was installed as organist at the Erfurt Predigerkirche. Neuss took singing lessons with Bokemeyer in Wolffenbüttel. 60 61 Appendix, 1691-IV 1. Appendix, 1691-IV 2. Appendix, 1691-IV 3. 63 64 Appendix, 1691-IV 4. Appendix, 1691-IV 5. Appendix, 1691-IV 6. Appendix, 1691-IV 6, 1708-III, 1754-II. In Calov’s translation (1681–2): ‘Wir sehen jetzt durch einen Spiegel in einem dunckeln Wort, denn aber von Angesicht zu Angesicht. Jetzt erkenne ichs Stückweise, denn aber werde ichs erkennen, gleichwie ich erkennet bin’ and ‘Nun aber spiegelt sich in uns allen des Herrn Klarheit mit auffgedecktem Angesicht, und wir werden verkläret im dasselbige Bild, von einer Klarheit zu der andern, als vom Geist des Herrn.’ A mirror image is by nature a 1 : 1 symmetry.

Unity, proportions and universal Harmony

creativity. Because it is harmonically proportioned, music also reflects back a picture of man, as he is harmonically proportioned, and thus it once more reminds man of God, since he is created in God’s image. It is a neverending process with many practical implications. Werckmeister concludes the chapter by explaining that the virtue of music is beyond comprehension; nevertheless, man must use music to glorify the almighty Creator and be careful not to misuse it.68 If music is the mirror that reflects back God’s image, Werckmeister is claiming that music can give great spiritual clarity and vision regarding eternal matters. This is a significant clue to Bach’s motivation for recreating the perfect proportions of Harmony in his compositions. Werckmeister’s style of writing is more suggestive of a pastor preaching to parishioners than of a scientist quantifying the study of music. His lack of classical references and his numerous paraphrases and citations of biblical verses give his writing a peculiar authority. For example, by stating that the musical triad, or trias harmonica, gives a beautiful image or parable of the Holy Trinity,69 Werckmeister puts Harmony and proportions at the centre, beginning and end of the universe with the Trinity, and the trias harmonica at the heart of the act of creation. He takes these implications to their logical conclusion, writing that the proportions in nature guide us to an orderly and intelligent existence, and that God also wishes to lead mankind to good things through music,70 a concept that Walther was to develop twenty years later.71 Werckmeister understood it to be the responsibility of the Christian musician to ensure that music fulfils this role, hoping that all musicians and Christians take heed and understand this about music.72 He places proportion and Harmony at the centre of a doctrine of music, the practical application of which was the standard for Lutheran musicians. Music was not a dilettante pastime. The Lutheran musician had a responsibility to use music well, for its divinely appointed purpose.73 It was a high calling. Werckmeister’s theoretical writings have earned him a mixed reputation among modern-day musicologists, with his fine work on temperament being counterbalanced by the judgement that ‘in many of his views he remained a mystic and decidedly medieval’.74 The latter is a grave misrepresentation of 68 69

70 73

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Appendix, 1691-IV 7. Appendix, 1687-II. Lippius is said to be the originator of this imagery: Synopsis Musicae Novae (Strasbourg, 1612), F4. 71 72 Appendix, 1687-IV. Appendix, 1708-II–IV. Appendix, 1687-IV. Appendix, 1723-III, where Bokemeyer applies the principles to church musicians, with a loose paraphrase of Titus 1:12–16. New Grove, s.v. ‘Werckmeister, Andreas’, by G. Buelow.

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Werckmeister’s theoretical writings, which were cited frequently in mainstream German-language music treatises until the 1750s.

Eternal implication of Harmony, the trias harmonica and its proportions One of Buttstett’s purposes in writing his 1716 monograph is stated in its subtitle, namely to explain ‘The true foundation of music, defending Guidonian solmization . . . and maintaining that one will make music in heaven with the very [same] sounds which we use here on earth.’75 Mattheson responded with charactertistic venom and clarity: Other parts [in Buttstett’s Ut Mi Sol] are sinful and blasphemous . . . such as when [he claims that] one’s compositions will and must be built solely on the six syllables of the tonsured Monk [Guido]. I will only pray: Father, forgive them, for they know not what they do.76

Behind both Buttstett’s argument and Mattheson’s rebuttals was a prevalent view of the proportions and significance of trias harmonica, the logic of which Buttstett had clarified in the preface to his first publication, Musicalische Clavier-Kunst und Vorraths-Kammer, citing Crüger, Praetorius and Werckmeister to show that God’s triune or three-in-one nature demonstrates perfect consonance, and that God’s divine nature, which exists from eternity and through all eternity, is the most perfect Harmony.77 The trias harmonica continued to be significant to musicians in Bach’s circles until at least the mid 1750s. Bach’s predecessor as Thomaskantor, Johann Kuhnau, had devoted a complete book to the subject, Disputatio de Triade Harmonica, which his widow intended to print posthumously in 1728,78 and which, in 1742, Mizler planned to translate into German.79 Perhaps more significantly, Bach’s eldest son Wilhelm Friedemann also allegedly wrote and was hoping to publish a treatise ‘with new discoveries on the subject’ as late as 1754.80

75 77

78 79

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76 Appendix, 1716-II. Appendix, 1717-V. J. H. Buttstett, Musicalische Clavier-Kunst und Vorraths-Kammer (Leipzig: Johann Herbord Kloss, 1713), preface. J. D. Heinichen, Der Generalbass in der Composition, 2nd edn (Dresden, 1728), final page. Fux, Gradus ad Parnassum, trans. Mizler (Leipzig, 1742), 87, note ‘a’. No published version in either Latin or German has survived. F. W. Marpurg, Historisch-Kritische Beyträge zur Aufnahme der Musik. 5 vols. (Berlin: Schütz, 1754–60), vol. I, 431 and 70–1; J. Adlung, Anleitung zu der musikalischen Gelahrtheit (Erfurt, 1758), 778.

Unity, proportions and universal Harmony

According to the widely held understanding of music history at this time, the Greeks and Jews had used only the quaternarius 1 : 1, 1 : 2, 2 : 3 and 3 : 4, i.e. the unison, the octave the fifth and the fourth in their music, which consisted solely of intervallic monody, and it was Guido who discovered the musical triad when his solmisation scheme caused the development of polyphony. This gave rise to the belief, logical within its own limits, that the Three-in-One God deliberately withheld knowledge of the triad from the heathen and the Jew, because they did not acknowledge the Trinity.81 The triad or trias harmonica and its proportions 4 : 5 : 6, i.e. the fifth, major third and minor third, had been Christianised to affirm God’s pleasure in Christian music, and to debase Jewish and heathen music. And because the triad was discovered as a result of Guido’s solmisation, solmisation itself became invested with quasi-holy properties, from which Buttstett argued that one would make music in heaven with the very sounds that we use here on earth.82 Some scholars realised at the time that this thesis was both anti-Semitic and historically flawed.83

Spiritual and moral obligations of music because of its Harmony Bach was surrounded by these ideas, as one can see by the social contacts he had with many of the music theorists. For example the Erfurt-based composer and organist Johann Pachelbel taught Bach’s eldest brother. Had Bach’s parents lived, it is likely that Buttstett, Pachelbel’s successor at the Predigerkirche in Erfurt, would have been their first choice as music teacher for their youngest son, Johann Sebastian. Walther, who was the same age as Bach and his close relative, was both a student of Buttstett and an enthusiastic scholar of music theory. Buttstett too was distantly related through marriage to both Bach and Walther, through the Lämmerhirt family.84 Although Bach was never taught by Buttstett, we can be sure that Bach and Walther would have read and discussed the content of the 1713–18 Mattheson–Buttstett battle, given their familial associations with one of its protagonists.85 81

82

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Buttstett, Musicalische Clavier-Kunst, preface; citing Werckmeister, Musicae Mathematicae, 146–8. Appendix, 1716-II. Bach too may have sympathised with this view. See D. Ledbetter, Bach’s Well-Tempered Clavier (Yale University Press, 2002), 120–5. Adlung, Anleitung, §44, 162–3, referring to Walther, Lexicon, s.v. ‘Bagnoli’ and Bagnoli’s battle in Ragionamento in difesa delle osservationi (Rome, 1713). Buttstett married Martha Lämmerhirt, a relative of the mothers of Bach and Walther; see Chapter 1. D. Ledbetter, in Bach’s Well-Tempered Clavier (New Haven: Yale University Press, 2002), 125 suggests more strongly that Bach might have expressed solidarity with Buttstett.

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A greater influence on Walther’s thoughts and writings was the work of Andreas Werckmeister. Statements such as ‘music is a foretaste of heavenly Harmony’86 were intricately bound to the understanding that the unity of the 1 : 1 unison lay at the heart of God’s creation: ‘God Himself has made nature through His omniscient counsel so that everything might strive to achieve unity (1 : 1) and therein take pleasure’.87 Werckmeister understood that every aspect of musical order strove after the equality of 1 : 1,88 that the 1 : 1 proportion of Harmony could also be seen in God, in eternity and in mankind, and that this caused human beings to rejoice whenever they heard music, because Harmony reflected both their own image and the image of the wisdom of God.89 The word streben in his phrase ‘For we now see, hear and perceive everywhere that God Himself created nature through His omniscient counsel, so that everything might strive to achieve unity [1 : 1] and therein take pleasure’90 was forceful. It meant ‘to use all endeavours to get it, to bestir yourself mightily, to use all your effort to acquire it’.91 Werckmeister was describing an active belief that motivated and necessitated a practical response from musicians and listeners. And the cyclical mirror image92 leads to the behavioural application: ‘We [Christian musicians] must be content to know how we should use and employ it [music] to the glory of the almighty Creator, and guard ourselves against every possible misuse of it.’93 This belief was widespread, at least in the region of Thuringia, where Bach grew up and was educated. It is implied in the opening definition of Walther’s 1708 treatise,94 and in his statement that to produce a good Harmony it must not only be ‘composed after the artistic rules, but above all and primarily when it is used in virtuous and God-pleasing practices’.95 Using music in virtuous and God-pleasing exercises would produce Harmony, and achieving Harmony in music-making and composition was itself a spiritual exercise, about which Walther wrote: Even the blind heathen had noticed these qualities about Harmony . . . How much more therefore should we Christians use this noble gift of God correctly, so that God might take pleasure in His handiwork; for music not only shows man his own image (i.e. that he is harmonically proportioned), it [music] also confronts God with His own divine wisdom in which He [God] rejoices.96 86 89 91 92 95

87 88 Appendix, 1691-I. Appendix, 1687-I. Appendix, 1691-IV 4. 90 Appendix, 1691-I, 1691-IV 6. Appendix, 1687-I. Fritsch, Lexicon, s.v. ‘streben, to strive, strain or labour for a thing’, col. 1889. 93 94 Appendix, 1691-IV 8, 1708-III. Appendix, 1691-IV 7. Appendix, 1708-I. 96 Appendix, 1708-II. Appendix, 1708-III.

Unity, proportions and universal Harmony

For Walther, belief in Harmony demanded moral, behavioural and theological responses. As Bach had been raised within a family with similar theological and philosophical values, it is likely that he too thought of Harmony in this way, and that how he chose to use music was a matter of great spiritual importance. Bach, Walther and Buttstett, as already stated, came from Thuringia, the cradle of Lutheranism. Mattheson, on the other hand, was a north German, married to an Englishwoman and influenced by the thinking of leading British intellectuals. Nonetheless, there was a common core of agreement in their philosophy of proportions and Harmony: all of them believed that God is pleased with proportions, that 1 : 1 and 1 : 2 in Harmony pleased God. Mattheson called this ‘proper’ Harmony.97 And they all believed that God is pleased with musical sounds, that the perfectly proportioned intervals that create Harmony are pleasing to God. Mattheson called this Harmony in music.98 Whereas Mattheson made a distinction between sounding and non-sounding Harmony, Werckmeister and Buttstett understood these sounding and non-sounding aspects of Harmony to be an integrated whole, and they believed their view to be the correct scriptural interpretation of Harmony. They also believed that wellproportioned music composed on earth would last into eternity. Modern-thinking and highly respected Lutheran musicians working in the Thuringian region in the 1700s held these views, some of which also appear beyond denominational and political borders. In Vienna, Capellmeister Johann Joseph Fux (1660–1771) emphasised the centrality of the proportions 1 : 1 and 1 : 2 in his famous Latin Gradus ad Parnassum, citing the same Aristotelian motto as Walther and others – that the closer a proportion is to the unity or equality, the more perfect it is99 – a motto that Mizler in his 1742 German translation of Fux’s treatise called edifying and devotional.100 His choice of the word devotional (erbaulich) is a significant confirmation of the theological understanding of proportions and their position in the doctrine of music at the time. In summary, Bach lived and worked in the same theological climate as Werckmeister, Buttstett, Walther and Neuss. Their common core belief embraced the understanding that harmonically proportioned music 97 99

100

98 Appendix, 1717-I. Ibid. Appendix, 1708-VI. As part of Mattheson’s published letter exchanges with leading composers on the subject of Buttstett’s Ut, Mi, Sol, Kuhnau wrote to Mattheson on 8 December 1717 demonstrating the principle literally in tuning and temperament. Critica Musica, OrchesterKanzeley (Hamburg, 1725), vol. VII, 229–39 (No. 10). Appendix, 1742-I. Bach owned a copy of the Mizler-Fux translation. NBA Supplement (2011), 60.

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reflected the image of God,101 was a foretaste of heavenly Harmony and eternity and demanded a godly and correct response, to glorify God and to delight one’s neighbour.102 Proportions were the fundamental, unseen, yet measurable component that lay behind every aspect of this belief, which actively motivated and necessitated a practical response from both musician and listener. It was a belief with a long history; it had motivated the ‘heathen’ Greeks to claim that music held godly and virtuous properties – which gave Walther the opportunity to use the Pauline ‘how much more’ construction, and persuade the modern Christian to use this noble gift of God even better.103 Although originally describing the physical properties of music, the word Harmony became an important theological and philosophical concept in Bach’s time, while also retaining its physical sense of perfect proportioning. In spite of their many disagreements, Mattheson and Buttstett both agreed that God was pleased with perfect proportions,104 and that music, because of its harmonic proportions, would be performed in heaven on physical instruments.105 Buttstett also believed that music composed on earth would be played in eternity, because of the perfection of its harmonic proportions. Werckmeister and Walther exhorted musicians to strive to achieve proportion and to practise virtue and godliness to achieve good harmony, so that God might take pleasure in it.106 Did Bach believe this too? Did he work and strive to achieve proportion in his compositions so they would please God, and even last into eternity? What a powerful motivation for a musician! Introducing perfect proportions across a composition or a collection, whether for church use, public consumption or private delight, would have been a logical response with profound implications. Mattheson, as has been seen, took issue with Buttstett’s interpretation of Harmony, accusing him of confusing proper Harmony with Harmony in music.107 But for Buttstett and many composers in Bach’s circle the two meanings were still intertwined.

101 103

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102 Appendix, 1691-IV, 7. Appendix, 1691-I, 1701-I. Appendix, 1708-III. Resonating with a German version of the Greek pollo mallon (πολλῷ μᾶλλον) construction frequently used by Jesus in the gospels, e.g. Matt 6:30, 7:11, 10:25, 18:13, and parallel passages, and by Paul in his epistles: Romans 5:9,10, 15, 17; 1 Cor 12:22; 2 Cor 3:9,11. Appendix, 1717-III. Appendix, 1747-III. See also D. Yearsley, Bach and the Meanings of Counterpoint (Cambridge University Press, 2002), 18–39. 107 Appendix, 1687-I, 1708-II. Appendix, 1717-I.

Unity, proportions and universal Harmony

IV

Bach and Harmony

What Bach meant when he used the word Harmony and how it motivated his compositional practice now become complex and significant issues. Did he strive for 1 : 1 unity in his compositions and in his life? Are the 1 : 1 and 1 : 2 parallel proportions in his revised and published collections evidence of this belief? Did he introduce proportional parallelism into his publications because he believed that the Harmony of the 1 : 1 and 1 : 2 proportions would ensure that perfected compositions would last for eternity? In light of the prevalent theology of music and Harmony, several contemporary Bach documents deserve renewed consideration. Resigning from his Mühlhausen post on 25 June 1708, Bach wrote: I should always have liked to work toward the goal, namely, a well-regulated church music to the glory of God and your will, and would have helped out as much as possible with the church music that is growing up in almost every township, and often better than the [Mühlhausen version of] Harmony fashioned here.108

What did he mean? If he believed as Walther did that good Harmony will result not only when it is composed after the artistic rules, but primarily when it is used in virtuous and God-pleasing practices,109 Bach may have been implying that the practices in Mühlhausen had not been entirely virtuous or God-pleasing. If so, his sentence contains a hefty innuendo that the authorities would not have missed. In the 1730s Bach was actively lobbying the Leipzig authorities for better musicians for church services,110 while perfecting works for publication in his own private compositional practice. Was this also motivated by a particular belief in Harmony? Bach’s adapted version of Niedt’s treatise which survives in a copy made in 1788 by a student, used the word Harmony when focusing on the definition of figured bass or thorough-bass. The thorough-bass is the most perfect foundation of music. It is played with both hands on a keyboard instrument in such a way that the left hand plays the written notes, while the right hand strikes consonances and dissonances so that this results in a full-sounding Harmony to the honour of God and the permissible delight of the soul.111

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109 NBR, Doc. 32, BD I, Doc. 1. Appendix, 1708-II. BD I, Doc. 22, e.g. 23 August 1730 ‘Kurtzer, jedoch höchstnötiger Entwurff einer wohlbestallten Kirchen Music’. NBA Supplement (2011), 3–38. Bach’s editorial omissions from Niedt’s text are discussed in Niedt, The Musical Guide, trans. Pamela L. Poulin and Irmgard C. Taylor (Oxford: Clarendon Press, 1989), 28–9, and Pamela L. Poulin, ed., Johann Sebastian Bach: Precepts and Principles for Playing the Thorough-Bass or Accompanying in Four Parts. Leipzig, 1738 (Oxford: Clarendon Press, 1994), 10–11.

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The reason why Bach and Niedt considered the thorough-bass to be the ‘most perfect’ (‘vollkomm[en]ste’) foundation of music lies in their understanding of Harmony.112 The word ‘vollkommen’ itself has very many philosophical and theological implications stemming from God’s absolute perfection.113 Modern musicians tend to contrast harmony with counterpoint, but for Niedt and his readers, ‘a true counterpoint is produced when the thorough-bass is played’.114 This understanding of Harmony has logical consequences: The ultimate end or final goal of all music, including the thorough-bass shall be nothing but for the honour of God and the renewal of the soul. Where these factors are not taken into consideration, there is no true music; rather, a devilish bawling and droning.115

This has been repeated many times as if it were Bach’s original, but it was in fact a recycled version of the prevalent doctrine of music.116 This is what Bach chose to teach to his students. Niedt, on whom he leant heavily, was far more expansive on the subject of the consequences of absence of Harmony,117 writing four lengthy sentences and tying himself deeply into a view of Satanic music that Bach clearly felt it best to avoid. Edited translations of Bach documents have unwittingly contributed to our limited understanding of Harmony. When Forkel published his Bach biography in 1802, he wove together information given to him by C. P. E. Bach and others, and arranged it into numbered sections without titles. The biography was translated into English and published in The Bach Reader in 1945. Unsatisfied with Forkel’s untitled sections, the editors invented headings, naming the fifth, ‘Bach’s Harmony’.118 Unfortunately this misleading title was also used in the New Bach Reader in 1998,119 perpetuating the misunderstanding that Bach’s sons were referring to their father’s musical techniques.

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113 115 116 117 118

119

Even theorists with different philosophical and theological beliefs considered it to be fundamental. See Heinichen, Generalbass, Einleitung, 1; translation in Buelow, Thorough Bass Accompaniment According to Johann David Heinichen, rev. edn (Ann Arbor: UMI, 1986), appendix B, 309. 114 Zedler, Lexicon, s.v. ‘Vollkommenheit’. Niedt, Musical Guide, 237. Poulin, Precepts and Principles, 29. For example Appendix, 1700-I, 1691-IV 7, 1691-I and 1754-II. Niedt, Musical Guide, 29–30. Hans T. David and Arthur Mendel, eds. The Bach Reader. A Life of Johann Sebastian Bach in Letters and Documents (New York; London: W. W. Norton, 1945), 317. NBR, 441.

Unity, proportions and universal Harmony

How Bach’s sons used the term may shed light on their father’s understanding of the concept. A famous phrase in the 1754 obituary in the New Bach Reader translation reads: If ever a composer showed polyphony (‘Vollstimmigkeit’) in its greatest strength it was certainly our late lamented Bach. If ever a musician employed the most hidden secrets of Harmony (‘Harmonie’) with the most skilled artistry, it was certainly our Bach.120

Using the English words ‘polyphony’ and ‘harmony’ for the German ‘Vollstimmigkeit’ and ‘Harmonie’, the NBR translation suggests that the authors of the obituary were contrasting Bach’s use of counterpoint and harmony. But I suspect this is a distortion. According to Fritsch’s German– English dictionary, the word ‘Vollstimmigkeit’ meant ‘harmony and unanimity’, ‘unity or one accord’; whereas both the words ‘vielstimmig’ and ‘vollstimmig’ meant ‘unity’ and ‘harmony’, and only ‘vielstimmige Musik’ meant specifically ‘with many voices’, or ‘polyphony’.121 Rather than praising Bach’s incomparable techniques of counterpoint and harmony, the obituary is praising the unity and proportional ordering of his compositional writing, which displays the unseen mysteries of Harmony in its fullest sense: If ever a composer showed unity [1 : 1] in its greatest strength it was certainly our late lamented Bach. If ever a musician brought the most hidden secrets of Harmony [in its fullest sense] into artistic practice, it was certainly our Bach.122

Retranslated thus, the phrase can be understood as a valuable testimony to Bach’s use of proportional parallelism. There are other examples. When C. P. E. Bach reported on Bach as a critic of others’ compositions he stated that Bach was apparently ‘very severe as regards harmony (quoad Harmoniam) but otherwise he valued everything that was really good and gave praise where praise was due even if it contained human weakness’.123 The description ‘very severe as regards harmony’ may lead a modern reader to understand it as referring to four-part progressions. The word Harmonia at this time implied so much more and C. P. E. Bach’s report probably meant: ‘When criticising works he [Bach] was very severe as far as the proportional unity/spiritual perfection [of the works] was concerned, but otherwise he appreciated all that was really good and gave approbation even

120 121 122

NBR, 305. Fritsch, Lexicon, s.v. ‘Vollstimmige music, eine’ and s.v. ‘Vielstimmige music’. 123 Appendix, 1750/4-I. NBR, Doc. 395; BD III, Doc. 803.

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when humanity shone through.’ In this translation one can appreciate the contrast between ‘humanity’ [Menschligkeit] and the spiritual implications of the phrase quoad Harmoniam. Reporting on Bach as a teacher C. P. E. Bach again used the phrase quoad Harmoniam. Having explained how his father’s students learned techniques of writing: four-part thorough-bass, four-part chorales and fugues, the discussion can now be seen to broaden, to embrace Bach’s view of the spiritual elements of musical composition, Mattheson’s ‘so-called proper Harmony’, writing: ‘without doubt the realisation of the thorough bass and an introduction to chorales is the best method of learning composition, [quoad Harmoniam] as far as Harmonia is concerned’.124 At the end of his letter C. P. E. Bach wrote that ‘Everyone found conversation (Umgang) with him [J. S. Bach] pleasant and frequently very edifying (erbaulich)’.125 He gives no examples of the edifying erbaulich content of his father’s conversation, but perhaps Bach spoke to visitors and acquaintances about the position of music and the significance of proportions in God’s world, as Werckmeister did: Whenever I [Werckmeister] am asked by various friends how such Harmony is formed, I find myself constrained to serve my neighbour with the gift God has given me; thus I could not refrain from explaining the advantages of the construction of this Harmony alone, but also the fundamentals of composition through mathematical demonstrations, in order to honour God and to be useful to my neighbour.126

Werckmeister’s conversation was erbaulich because of the devotional significance of Harmony.127 He was not giving a free music theory lesson to his friends, but rather building them up in the faith through the musical gift and knowledge he had been given. This is an example of the kind of action required of the Christian musician, described by many including Werckmeister, Walther and Bokemeyer.128 There is evidence of Bach’s theological understanding of music and Harmony in the title pages of his collections. The short verse on the title page of his Orgelbüchlein (BWV 599–644) is a perfect encapsulation of the prevailing doctrine of music:129 ‘Dem höchsten allein zu Ehren Dem nächsten draus sich zu belehren’ [To Honour/Worship/Praise the Highest [God] to inform thereby my neighbour]130 The same motivation can be 124 125 128 130

BD III, Doc. 803. NBR, Doc. 385 reads ‘as far as harmony is concerned’. 126 127 BD III, Doc. 803. Appendix, 1701-I. Appendix, 1754-I. 129 Appendix, 1691-IV 8, 1708-II, 1708-V, 1723-II. Appendix, 1700-I, 1708-IV. NBR, Doc. 69.

Unity, proportions and universal Harmony

seen in the title pages of the Clavier Übung collections Clavir Übung . . . Denen Liebhabern zur Gemüths Ergoetzung verfertiget [Keyboard Practice, composed for music lovers, to refresh their spirits]. Although honouring God is not spelt out, it is implicit in the words Gemüths Ergoetzung,131 both here and in Bach’s own teaching document.132 The title also implies that the word Übung contains an element of spiritual refreshment. Walther’s use of the phrase ‘tugendsamen und Gott wohlgefälligen Übungen’133 in his description of Harmony lends a whole new dimension to ‘Übung’, suggesting that Bach intended far more than technical keyboard training exercises when he chose the word.134 Music lovers or practitioners purchasing these keyboard collections would have understood this, knowing that what they were buying would help them engage in a worthy and uplifting spiritual exercise. Bach intended his Clavier Übung to move man to greater devotion to God, and to lead others to God-pleasing practices.135 Designing the bar structure in layers of parallel proportions would create in these collections a perfect mirror, reflecting God, so that the virtuous practitioner would experience a foretaste of eternity. In common with many composers from this region and beyond, Bach created collections of six compositions. Was this motivated by their common understanding that six, the first numerus perfectus and the senarius, contained all of Harmony?136 How and if Bach’s compositions demonstrate Harmony and perfection of proportions now becomes a burning question. Bach set himself some almost impossible challenges that would push the rules of music to the limits. He excelled in writing fugues and complex puzzle canons. And he gave the title Trias Harmonica to one of canons. If the theory of proportional parallelism is correct, he went a step further in using music correctly when he created Harmony itself with the layers of perfect proportions in his collections. By not using music correctly the composer would be guilty of disobeying God’s word and God’s will.137 Conversely by obedience, one was delighting God, and leading one’s neighbour to virtuous and God-pleasing practices.138 Were 131 132

133 134

135 136 137

Fritsch, Lexicon, s.v. ‘Ergetzung [sic] (die) das ergetzten, delight, delighting, joy, rejoicing.’ Bach, Vorschriften und Grundsätze probably copied in 1738 by C. F. Richter with title page and corrections by Carl August Thieme (1721–95). Appendix, 1708-II. In Bach: Goldberg Variations (Cambridge University Press, 2001), 3–4, Peter Williams ventures a similar opinion, although without referring to contemporary sources that Bach would have known. Appendix, 1708-V, 1708-II. Appendix, 1691-IV 1. Numerus perfectus is defined in Chapter 1. 138 Appendix, 1717-I, 1754-I. Appendix, 1687-IV, 1708-II.

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the revisions Bach made to create these parallel proportions motivated by his profound belief in a divinely proportioned universe? Did he believe that the perfect proportions of the triad reflected the triune nature of God, giving Him pleasure?139 I suspect he did.

Significance of proportional parallelism The idea of Bach spending time to create perfect proportions in his collections through the number of bars, particularly when the resulting Harmony would not be heard, runs counter to modern thinking. Although it makes no sense that perfection in a sounding art form could be based on something unheard, the evidence above shows that Bach may indeed have been strongly motivated to create silent perfection through compositional proportions, because he would have understood the layers of proportion in his collections as Mattheson’s Harmony proper, and not as Harmony in music. Sources show that in Bach’s time and place, the proportions 1 : 1 and 1 : 2 were still considered the ideal of perfection. And if Bach believed in Harmony as many of his contemporaries did, he would have introduced the parallel proportions to ensure that his revised and published compositions would last not only for posterity, but for eternity. Furthermore because proportions were the objective measure of beauty, their correct use guaranteed artistic success.140 The period between 1700 and 1770 was a turbulent time for German musicians. Developments in science and philosophy were challenging what had seemed for generations to be the gospel truth about the divine position of proportions in music, with all that implies for the status, calling and practice of the musician. As science played an increasingly important part in the understanding of astronomy, scepticism undermined the foundations of belief in the Harmony of the spheres. An indication of this process can be found in Zedler’s 1733 article ‘Corpora mundi totalia’, which after detailed descriptions of the Harmony of the spheres, gives a scientific explanation of the foundation of the universe from chaos.141 At the end the author writes: ‘In a word, it is speculation, which every one is free to believe.’142 Harmonic proportion as the objective measure of beauty was also being questioned in architecture and in the visual arts. Matters seem to have been fairly stable in Leipzig when Walther defined eurythmia in 1732, 139 141 142

140 Appendix, 1687-II, 1687-III. Appendix, 1754-I. Zedler, Lexicon, s.v. ‘Corpora mundi totalia’. Ibid., ‘Mit einem Wort: es sind Muthmassungen, die einen jeden, zu glauben, frey stehen.’

Unity, proportions and universal Harmony

but by 1743 a change can be detected in Zedler’s entry ‘Beauty in Architecture’, in which the following significant qualification was appended to the proportional definition of beauty: ‘what some find beautiful others do not’.143 It would take Lutheran society until the late eighteenth century before all vestiges of the old proportional world view disappeared: in Britain it happened much earlier. In 1757, for example, the Irish scholar Edmund Burke (1729–97) was able to ridicule what was still almost sacred in Leipzig: Each mind perceives a different beauty . . . To seek the real beauty or real deformity is as fruitless an inquiry as to pretend to ascertain the real sweet or real bitter . . . I know that it has been said long since, and echoed backward and forward from one writer to another a thousand times, that the proportions of a building have been taken from those of the human body. To make this forced analogy complete, they represent a man with his arms raised and extended at full length, and they describe a sort of square, as it is formed by passing lines along the extremities of this strange figure. But it appears very clearly to me that the human figure never supplied the architect with any of his ideas. For in the first place, men are very rarely seen in this strange posture . . . and certainly nothing could be more unaccountably whimsical, than for an architect to model his performance by the human figure, since no two things can have less resemblance or analogy than a man, and a house or temple.144

In music treatises of the first half of the eighteenth century, the lack of any mention of God, particularly in the customary devotional introduction, is indicative of these changes. Although the ‘modern’ theorist could not avoid mentioning musical proportions or the triad, it was possible to bypass discussion of their integration with the scriptures and church doctrine. It would be too simplistic, however, to imagine that the absence of God from music treatises indicates that the author was agnostic or even atheistic. We know that belief in the centrality of harmonic proportions was still strong and active, but fashions were changing and, regardless of one’s theological persuasion, it became acceptable, and was fast becoming the ideal, to discuss music as a scientific entity apart from God. By the 1720s the word Harmony had several different meanings; and to these the modern understanding, as a technical description of four-part chords learnt at school, was slowly added.

143 144

Zedler, Lexicon, s.v. ‘Schönheit in der Baukunst’. Edmund Burke, Enquiry into the Origin of Our Ideas of the Sublime and Beautiful (1757; 9th edn, 1782), 175 and 181, in Wittkower, Archtectural Principles, 5th edn (Chichester: Academy Editions, 1998).

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In how many other regions of Europe, and for how long, this hangover from Greek, Judaeo-Christian and Renaissance thought remained active needs to be investigated. In the 1650s Athanasius Kircher spread a similar philosophy through Jesuit channels,145 and the Vienna-based Catholic theorist Johann Joseph Fux repeated it in the 1720s. By the early nineteenth century it seems that the word Harmony had begun to lose its spiritual implications. New time- and location-specific sources will be needed to ascertain how the word was understood at different times, across different confessional and political borders, and also by later Lutherans in the Leipzig area. Bach would have known something of Christian Wolff’s understanding of the word Harmony through the concept of predestined Harmony (vorherbestimmte Harmonie). It was one of the chief causes of Wolff’s dismissal on 8 November 1723 from his Halle professorship, when a royal decree banished him from the city within 24 hours and from Prussian territory within 48 hours, on pain of death. The affair caused a public outcry,146 and as Bach lived only 45 kilometres from the scene of the scandal,147 he would have heard all about it.148 The scandal may even momentarily have struck a personal chord for Bach, as one of Wolff’s main opponents, arguing that his proof of predestined Harmony was based on false principles,149 was Johann Gottfried Walther (d. 1727),150 the namesake of his cousin. The importance of Wolffian philosophy to our understanding of Bach and his compositional motivation must not be underestimated.151 Lorenz Mizler, Bach’s student and younger colleague, acknowledged his philosophical allegiance to Wolff in the seventh of twelve statutes of his corresponding society:

145

146

147 148

149

150 151

See P. Findlen, Athanasius Kircher: The Last Man Who Knew Everything (New York; London: Routledge, 2004). Zedler, Lexicon, s.v. ‘Wolf [sic] (Christian, Reichs–, Frey– und Edler Herr von)’. In a ceremony as public as his earlier dismissal, Wolff was reinstated by the Holy Roman Emperor in 1744, the first and only academic ever to be accorded this honour. 45 kilometres on modern roads. Cöthen was even closer, just 35 kilometres north of Halle. The family moved to Leipzig from Cöthen on 22 May 1723. Bach’s formal official installation at St Thomas School was on 1 June. J. G. Walther, Eleatische Gräber (Magdeburg: Seidel, 1724), 50; Zedler, Lexicon, s.v. ‘Vorherbestimmte Harmonie’. Zedler, Lexicon, s.v. ‘Walther, Johann Gottfried, ein Magister’. L. Felbick, Lorenz Christoph Mizler de Kolof: Schüler Bachs und pythagoreischer Apostel der Wolffischen Philosophie (Hildesheim: Olms, 2011).

Unity, proportions and universal Harmony

VII. In preparing their articles [for the journal] Members should observe the writing style of the Leipzig Deutsche Gesellschaft and the teaching and principles of Wolf’s [sic] philosophy, because while both are rational, the latter are, above others, the most useful for music.152

In a footnote to this statute, Mizler promised to publish a demonstration of the usefulness of Wolffian philosophy to music. There is no evidence that he fulfilled this promise,153 but six months later he wrote: But where in Wolfian [sic] philosophy does it deny that God is the originator of Harmony? Who has demonstrated the proof of the essence of God, the structure of the universe and all that’s in it, and also Harmony (I am talking about the course of nature) better than Wolf? [sic].154

After a period of deliberation, and understanding the stipulation of the seventh statute, Bach chose to become a member of Mizler’s corresponding society in 1747. Nonetheless, it was before he knew Mizler, and before the scandal of Wolff’s dismissal, that Bach had learned how to use the word ‘Harmony’. To use music correctly was a spiritual exercise. Music and its harmonious perfect proportions pleased God. They reflected God’s wisdom and filled man with delight. Bach knew that if his published works were perfectly proportioned, his harmonious music would continue to please God and to fill man with delight far beyond his own lifetime: they might even be available in heaven. This chapter has shown the many theological implications behind the concepts of the unity, proportions and Harmony, the spiritual value of which led to correct usage of music, and accepted codes of behaviour. Bach’s life choices can now be understood as motivated by an active desire to use music correctly and to avoid abusing it at all costs. His beliefs did not make him perfect, but they would have guided and influenced his actions, and may even account for his stubborn behaviour when individuals or authorities thwarted his God-given calling. The next chapter will demonstrate the prevalence of numbers and ordering in compositional planning and how they may have influenced Bach to make significant musical choices. 152 153

154

Mizler, Musicalische Bibliothek, vol. I, part IV (April 1738), 75. Ibid., 75: ‘Den Nutzten der Wolfischen Weltweisheit in der Musik werde ich in einer besondern Schrift: de usu ac præstantia philosophiæ Wolfianæ in musica, zeigen.’ The title is adaptated from his nineteen-side tract published two years earlier: De Usu Atque Praestantia Philosophiae In Theologia, Jurisprudentia, Medicina breviter disserit. Mizler, Musicalische Bibliothek, vol. 1, part IV (April 1738), 68.

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4 Bars, compositional planning and proportional

parallelism

Totius Musicae anima Tactus est. J. G. Walther, 1708

Using sources that Bach knew or could have read, this chapter demonstrates how he and his contemporaries thought about planning compositions, that the bar was used to measure their length and that proportions were the norm for compositional ordering. Every element of the technique of proportional parallelism can be found in treatises of his time.

I

Compositional numbers, proportions and planning

Musical numbers Walther gave four definitions for musical numbers in his dictionary: Numeri radicales Consonatiarum & Dissonantiarum, which are the root numbers that form musical consonances and dissonances, i.e. 1, 2, 3, 4, 5, 6, 8, 9, 10, 15, 16, 24, 25, 80, 81, 125, 128; Numeri radicales Harmonici, 1, 2, 3, 4, 5, 6, 8, which are harmonic because a proportion formed by any two of them makes a harmonic interval. These are also known as the senarius and septenarius,1 although Walther avoids these rather antiquated terms. He gives three meanings for numeri musici; the mnemonic melody referred to by Virgil, ‘numeros memini, si verba tenerem’, the numbers used in figured bass and numeri musici as an alternative term for numeri harmonici.2 The senarius had great significance for the Lutheran musician – it contains all the perfect consonances, and was called the Mundus numerus by Lippius, because ‘on the sixth day God created for his pleasure man as the climax of his creation, and it was good’.3 This concise philosophical and theological explanation of the value to music of the harmonic numbers is amplified and expanded in many treatises that Bach read. With no justification for its inclusion Walther followed the definitions of numerus musicus with the mathematical term numerus perfectus: 1

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3

2 Defined in Chapter 1, §II. Zedler’s Lexicon repeats Walther’s definitions literally. C. Matthäi, Kurtzer, doch ausfürhlicher Bericht von der Modis Musicis (Königsberg, 1652), 15.

Bars, planning and proportional parallelism

Table 4.1 Symmetry of the hexachord Hexachordum

Ut

Re

Mi

Fa

Sol

La

Naturale Durum Molle

C G F

D A G

E B A

F C B♭

G D C

A E D

Intervals

Tone

Tone

Tone

Tone

Semitone

Table 4.2 Symmetry of semitones in B-A-C-H B♭ Semitone

A 3 Semitones

C

H (B ♮) Semitone

‘Numerus perfectus’ (lat.) is in mathematics e.g. the number 6; because it is made up of its aliquot parts; dividing it into two parts makes 3, then into three parts makes 2, finally into six parts makes 1. If you add these together you also get 6 (1+2 +3). This kind of number is very rare, for from 1 to 10 there is only this number 6; in 10–100 there is only the number 28; in 100–1000 only 496; and in 100–10,000 only 8128. For further reading see Conrad Matthäi Bericht von den Modis musicis, p. 15, where the motivated reader will be referred to the thirty-sixth proposition of the ninth book of Euclid.4

Walther does not explain its application to music or its significance in music or composition. His readers would have known that the number six was integral both to music, through the fundamental and perfect proportions of the senarius, and to the code of behaviour it represented in Lutheran circles. The fashion for collections of six works at this time may have been motivated by the belief that the number 6 was both perfect and central to God’s created Harmony, which lead man to great pleasure.5 The number six and perfect proportions were also a central feature of the hexachord that Buttstett defended so staunchly. The six Guidonian intervals, Ut, re, mi, fa, sol, la were still in use and praised by conservatives in Bach’s time. Table 4.1 shows the symmetry of the hexachord, with two tones surrounding the central semitone between mi and fa, which expressed in semitones is 2 : 2 : 1 : 2 : 2. Table 4.2 shows the intervallic expression of the name ‘B-A-C-H’, which, like the hexachord, is also symmetrical: 1 : 3 : 1. This symmetry

4 5

Walther, Lexicon, s.v. ‘Numerus perfectus’. Appendix, 1652-I, 1687-I, 1687-III, 1691-VIII, 1708-II, 1708-III.

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may suggest yet another reason for the familial predilection for melodic sequences on the Bach surname.6 Musical numbers appear in descriptions of compositional stuctures. The term progressio arithmetica, for example, goes beyond standard pitch formation to cover a technique of assessing the proportions used in the construction of a composition. Theorists a generation younger than Bach used musical numbers in a compositional method that empowered the amateur to compose music by numbers without knowing the rules of counterpoint. Two were published in 1757, by C. P. E. Bach and by Johann Philipp Kirnberger (1721–83), who was proud to be a student of J. S. Bach, boasting elsewhere that his methods continued his master’s teaching traditions.7 Kirnberger claims that ‘Anyone who is familiar only with dice and numbers and can write down music notes is capable of composing as many of the aforesaid little pieces as he desires,’8 and the title of C. P. E. Bach’s publication promises a ‘Method for making six bars of double counterpoint at the octave without knowing the rules’.9 The idea caught on and was freely imitated and adapted by others. Two French authors developed a system requiring a nine-sided top, De Lange in his Le Toton Harmonique and the anonymous author of Ludus Melothedicus.10 Similar publications claiming to be by Haydn and Mozart were published as late as the 1790s.11 The playfulness of these composing-by-number methods is strangely at odds with the impression we have of the serious master–pupil apprenticeship, and also of the later cult of the inspired composer-genius. When J. S. Bach taught his sons double counterpoint12 – and if he taught Kirnberger to compose Minuets and Polonaises – it would surely have been by the rule-bound method, rather than by random numbers. However, it is not beyond the bounds of possibility that the master of permutation himself would have had some fun with his most advanced students, and may even have suggested the dice-throwing method to demonstrate the formulaic 6 8 9

10

11

12

7 NBR, Doc. 304. BD III, Doc. 867. NBR, Doc. 314. J. P. Kirnberger, Der allezeit fertige Menuetten– och Polonoisenkomponist (Berlin, 1757). ‘Einfall, einen doppelten Contrapunct in der Octave von sechs Tacten zu machen, ohne die Regeln davon zu wissen, vom Hrn. Carl Philipp Eman. Bach, Königl. Preuß. Kammermusicus’, in F. W. Marpurg’s Historisch-Kritische Beyträge zur Aufnahme der Musik, vol. III (Berlin, 1757), 167–81. H. F. de Lange, Le Toton harmonique, ou Nouveau jeu de hazard (Paris: Chevardière, 176[?]); Anon., Le jeu de dez harmonique, ou Ludus melothedicus (Paris, 1757). Anon. [M. Stadler], Gioco filarmonico o sia maneria facile per comporre un infinito numero de minuetti e trio, and Musikalisches Würffelspiel (Simrock, 1792). NBA Supplement, ed. P. Wollny (2011), 41–44.

Bars, planning and proportional parallelism

nature of some compositional techniques. But I doubt if Bach ever needed to use it himself: even at the end of his life, his capacity to generate permutations of every shape or form appears to have been inexhaustible.

Golden sections and the Fibonacci sequences The golden section must be mentioned here as many readers will assume it played a part in the numerical and proportional ordering of musical compositions in Bach’s time.13 There have been several attempts in recent years to demonstrate Bach’s use of this proportion, but historical evidence undermines the results. Although the numerical expression of the golden section had been discovered by Kepler by the 1650s, and although Bach may have read about Kepler’s discovery14 as well as about an experiment using it to help position lute frets,15 there seems to have been no general interest in the proportion in Bach’s time, either for its aesthetic properties or as a means of compositional invention. The situation is similar for the Fibonacci series, an approximate numerical expression of the golden section originally devised by Leonardo da Pisa in 1202. There is no evidence that additive series held any interest for either mathematicians or musicians in Bach’s time, even though anyone with basic numeracy skills could have formed them. Had Walther considered either the golden section or the Fibonacci series important or useful for music, he would have included them in his dictionary. But he did not. It was the numerus perfectus that he chose to define, referring to an example in a contemporary music treatise, and to its original definition in Euclid.

Compositional planning Mattheson and Meinrad Spiess (1683–1761) both give clear recommendations that musical compositions should be planned. In 1739 Mattheson wrote: 13

14 15

R. Tatlow, ‘The Use and Abuse of Fibonacci Numbers and the Golden Section in Musicology Today’, Understanding Bach 1 (2006), 69–85. Ibid., 75, note 25. M. Mersenne, Harmonie Universelle: The Books on Instruments, trans. R. E. Chapman (The Hague: M. Nijhoff, 1957): Proposition XVI, 283: ‘To determine if the twelve frets of a lute can be marked by the segments of a line cut in mean and extreme ratio’. ‘Salinas has taken into his head a new method of dividing the neck of stringed instruments by means of a line cut proportionally. But I find that he is mistaken in many things and that this section cannot serve his plan . . . ’.

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What is first required for the disposition is an elegant ordering of the parts and particulars in the melody or in an entire melodic work [in einem gantzen melodischen Wercke], almost in the way one orders and designs a building, and makes a plan or sketch to show where a room, a parlour, a chamber, etc. should be placed.16

Mattheson’s principle of compositional planning covers both the smallerscale melody and the larger-scale melodic work; its architectural image implies specific dimensions. For practical reasons, his illustrations of order and planning are limited to small-scale details in a melody. Nonetheless, the words ‘in an entire melodic work’ make it clear that the principle of measured planning includes the larger scale. This is important evidence to support Bach’s practice of proportional parallelism in structures of every size. In 1746 Meinrad Spiess also recommended compositional planning, in a publication that, in view of their common membership of the Mizler society, Bach would have read carefully. Defining the Dispositio as ‘a well-devised division of a musical work’ (‘eine wohl ausgesonnene Eintheilung eines Musicalischen Wercks’), Spiess recommends ordering both the general and specific details of a composition. General disposition is when, for example, the setting of the whole text of an opera, etc. is read through, weighed up, studied, and a specific Modus Musicus, specific instruments, emotional expressions, etc., are chosen for each Aria, following the example of an architect, who makes a sketch or plan to show where the reception room, where the store, chamber, room, kitchen, etc. should be placed. In brief: [General Disposition] is when the composer gets his head around all the threads of his projected musical composition and forms it into a perfect system.17

His example of general ordering includes the allocation of key, instrumentation and mood for opera arias in response to its libretto. His example of specific ordering includes the sectionalisation in ascending order of a well-invented theme, fugue, aria, etc., and, significantly for proportional parallelism, deciding the length of the piece, which itself should be divided into well-proportioned sections.18 Architects of the period specified dimensions in their ground plans,19 and Mattheson’s and Spiess’ architectural images imply that the composer would similarly specify the measurements of a composition. 16

17 19

Mattheson, Kern Melodischer Wissenschaft (Hamburg: Herold, 1737), 128; and Capellmeister, 235. 18 M. Spiess, Tractatus Musicus Compositorio-Practicus (Augsburg, 1746), 134. Ibid. For example, L. C. Sturm, Vollständige Anweisung Allerhand Oeffentlich Zucht- und LiebesGebäude (Augsburg, 1720), also citing architectural texts by Nicolai Goldmann.

Bars, planning and proportional parallelism

Mattheson cites the practice of Agostino Steffani (1654–1728) as a role model of successful compositional planning: The world-famous Steffani once said to me that before he ever put pen to paper he kept the text of the opera or work by him for a very long time and came to a highly detailed understanding with himself as to how and in what form would be the best way to organise the work. Thereafter he set his movements [Sätze] to paper.20

This is an important testimony to the contemporary practice of precompositional ordering of a texted composition. Mattheson follows the description with a subjective judgement on the practice: ‘It is a good way, although I guess that nowadays when everything has to be done in a rush few will be found who care to use such things,’21 implying that only the diligent composer would use the method. Numerical evidence in all of Bach’s vocal works demonstrates that, by ordering features of his compositions that were specified in the poetic text, he, like Steffani and Spiess, focused first on ordering the free-texted arias and tutti choruses. We know that the concept of a compositional ground plan was familiar to Bach and his colleagues because of a comment ‘und einen andern Grundplan’ (‘and a different ground plan‘) written on the reverse of the final sheet of his early version of The Art of Fugue, P 200,22 which suggests not only that the writer was familiar with the ground-plan concept, but also that both a primary and an alternative ground plan for The Art of Fugue existed at the time, or was known to have existed.

Numerical ordering It would be ideal to know how Bach calculated and annotated his numerical ground plans, and why these plans have not survived. A composer making and revising a detailed numerical plan of the kind described by Mattheson and Spiess would need a method of documentation. If Bach revised the structures of his collections over lengthy periods of time, as numerical evidence suggests, he must either have had an outstanding memory for figures, and/or a relatively long-lasting method of recording the bar totals of movements, works and collections. If he kept files or booklets for numerical workings they have long since been destroyed. Used-up sketch books would not have been considered worth keeping, and any rough paper that had outlived its original purpose would have been recycled for everyday domestic purposes. A few papers with jottings 20

Mattheson, Capellmeister, 240.

21

Ibid.

22

D-B Mus. ms. Bach P 200.

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have survived from Bach’s household, one of which cannot be deciphered.23 It is also possible that Bach economised by using an erasable skin palimpsest, or chalk and slate, instead of paper when he planned the numerical dispositions and revisions of his compositions and collections. Occasionally he recorded the bar total in a composing score (e.g. in the ‘Confiteor’ of the B-minor Mass, P 180) and when he was copying parts (e.g. throughout the Missa, D-D1 Mus. 2405-D-21).24 This practice raises the possibility that he recorded compositional figures on the outermost edges of his scores. Since the ragged extremities were frequently trimmed in the binding process, however, any marginal jottings would long have been lost. Were any still remaining today, the marginalia would have been noted eagerly by editors of Friedrich Smend’s generation and reported by the few scholars still permitted to see Bach’s original autograph scores. The recommendations formulated by Mattheson and Spiess were a crystallisation of current knowledge based on past and present compositional practices. As such they are a valuable indication of the working method of a contemporary composer like Bach. Making a general and specific plan, with dimensions, would have been second nature to Bach. Because compositional ordering was normal, the lack of surviving numerical plans in his hand does not prove that such plans never existed. A great deal of important numerical and aesthetic evidence about compositional constructions and ordering has been lost, both through recycled workings and, more recently, as a result of modern English translations. Key words such as Verhältnis are commonly translated as ‘relation’ or ‘relationship’,25 whereas dictionaries from Bach’s time show that Verhältnis was primarily a mathematical term, used by music theorists of the period, and even in later periods, to mean ‘proportion’.26 For 23

24

25

26

See NBA KB I/35, 176 for an example of note-taking from the Bach household, perhaps Bach’s writing, in ink on the reverse of the printed title page of a lost New Year cantata for Fürst Leopold von Anhalt and Friederike Henriette (BWV Anh.I.8). Throughout BWV 1014–1019a, St 162, Johann Heinrich Bach included the bar total at the end of every movement in the harpsichord part. For example, in E. Harriss, Vollkommene Capellmeister (Ann Arbor: UMI, 1981), 478; E. Lippman, Musical Aesthetics: A Historical Reader (New York: Pendragon Press, 1986), vol. I, 136, ‘Mattheson’s Verhalt as Relation in BWV 248/52’; and in N. K. Baker and T. Christensen, Aesthetics and the Art of Musical Composition in the German Enlightenment (Cambridge University Press, 1995), 37–41, citing Sulzer, Allgemeine Theorie der schönen Künste. Conversely, the English word ‘relation’ however is not always a translation of ‘Verhältniß’. Non-standardisation of spelling means that Zedler lists ‘Verhältnis’, whereas Mattheson prefers ‘Verhältniß’. Zedler, Lexicon, s.v.’Verhältnis, Gleichmaß, Ebenmaß’, refers the reader to vol. 29, 889, s.v. ‘Proportio’. Both Fritsch and Walther define ‘Proportio’ and ‘Proportion’, confirming the

Bars, planning and proportional parallelism

example, Harriss’ translation of Mattheson’s phrase Verhältniß, Gleichförmigkeit und Übereinstimmung as ‘relation, uniformity and agreement’ misses the numerical and aesthetic implications of Mattheson’s original. The words Gleichförmigkeit and Übereinstimmung also held numerical implications, both meaning ‘uniformity’ and ‘unison’,27 which could be expressed by the 1 : 1 proportion. The following translation reveals more accurately what Mattheson had to say about the practice of compositional planning: Whoever wishes to make full use of the aforementioned method, regardless of his compositional skill, should outline his complete project on a sheet of paper, sketch it roughly, and then set it into order before he proceeds to the elaboration. In my opinion this is the absolute best way to organise a work so that each part demonstrates a true proportion, uniformity and unison (Verhältniß, Gleichförmigkeit und Übereinstimmung): for nothing in the world is more pleasing to the ear than this.28

Zedler’s dictionary defines ‘proportion’ as the agreement/conformity of two or more ratios.29 The word Glied has also been mistranslated. It referred specifically to the two parts of a ratio or proportion,30 a meaning that continued in music for at least a further seventy years.31 Additionally the word was used in an architectural context to mean the smaller parts of which the whole was constructed, for example, divided into large, medium (no less than one sixth of the whole) and small (no larger than one twelfth of the whole) parts.32 Thus Mattheson’s phrase ‘Den Verhalt aller Theile, Glieder und Gliedmassen wohl beobachten’,33 misleadingly translated by Harriss as ‘Observe well the relationship of all parts, members and limbs’,34 would be better represented in English as ‘Observe well the proportion of all sections, parts and terms’, thus bringing into focus the numerical element of compositional planning.

27

28 29

30 32 34

numerical meaning, although neither includes an entry for the German synonyms ‘Verhalt’ or ‘Verhältnis’; D. G. Türk, Anleitung zu Temperaturberechnungen (Halle and Leipzig: Schwickert, 1806), §5, 3 and §7, 4. Fritsch, Lexicon, s.v. ‘Gleichförmigkeit (die) a conformity, a uniformity’; ‘Die ubereinstimmung zweyer music-noten, the unison of two notes in musick.’ Mattheson, Capellmeister, 240. Zedler, Lexicon, s.v. ‘Proportion, die Größ-Vergleichung’. ‘Die Aehnligkeit zwey oder auch mehrer Verhältnisse.’ 31 Ibid., s.v. ‘Glied’. Türk, Temperaturberechnungen, §5, 3 and §7, 4. 33 Zedler, Lexicon, s.v. ‘Glied’. Mattheson, Capellmeister, 141. Harriss, Vollkommene Capellmeister, 313.

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In the preceding paragraph Mattheson had explained his reasons for recommending 1 : 1 proportioning: not simply because it would sound good, but because the result would be longer-lasting: Moreover if Gleichförmigkeit in all things contributes a great deal so that it is not only pleasant to the human senses, but also thereby becomes more lasting, as is well known to good architects, then it is easy to guess why some things lose little or nothing of their inner goodness [Güte] and stability [Feste] with age,35 even though they may receive some external knocks; whereas others, however much they shine and boast soon find their cradle to be their grave. This depends largely on good or bad disposition.36

Mattheson’s choice of the words Gleichförmigkeit, Güte and Feste alludes to the spiritual qualities of the unity. Not only was the unity pleasant to the human senses, the 1 : 1 of the unison had inner strength and lasting value.37 The term numerus musicus also covers the numerical ordering of compositions. Included in a list of eight qualities, Mattheson claims that numerus musicus helps to maintain the flow of a piece of music, first by paying careful attention to the uniformity [Gleichförmigkeit], or 1 : 1, of the metres or rhythms, and secondly by maintaining ‘exactly the geometrical proportion [Verhalt] of similar movements, namely the numerus musicus, i.e., the melodic number measurement’.38 Traditionally this has been understood to refer to the balance of beats within bars, i.e. that each 44 bar has four crochet beats, but in the very next paragraph, in a commentary on his fifth rule of loveliness or charm, ‘Observe well the proportion of all parts, sections, and sections of the proportion,’39 Mattheson makes it clear that he had the balance of a much larger-scale unit in mind. The fifth rule of loveliness consists in the precise observation of the correct proportion [Verhalt] of all parts of a melody with one another. Our previous concern related only to the proportion [Verhalt] of intervals, which must be distinguished well from this last, where the sections [Theile] themselves are compared. This current rule aims not only to show for example that the second part of an Aria is bound to or has an understanding, so to speak, with the first, but also that the smaller sub-divisions also exhibit their essential uniformity [Gleichförmigkeit] . . . No one need to be so rigorous as to take up a compass and ruler; however, both great dissimilarity and loathsome proportion [Verhalt]

35

36 38

Fritsch, Lexicon, s.v. ‘Güte’ and s.v. ‘Feste’ show the spiritual implications of these words, missing in the English ‘goodness’ and ‘stability’. 37 Mattheson, Capellmeister, 240. Appendix, 1687-I, 1687-III, 1691-IV 4, 1708-VI. 39 Mattheson, Capellmeister, 141. Ibid.

Bars, planning and proportional parallelism between sections [Theile] are just as loathsome to loveliness . . . as a large head and short legs to the beauty of a body.40

This description is about the proportional ordering of all parts of a melody and all parts of a large-scale composition, exactly as one finds in the parallel layers of proportion in Bach’s works. Mattheson emphasises that he is not speaking about proportional ordering within musical intervals, lest his point be misunderstood.41 Mattheson illustrates his point with a small-scale numerus musicus across an aria, for practical reasons of space. The 1 : 1 proportion above all other proportions is implied by the words ‘Gleichförmigkeit’ and ‘unison’. Statements such as ‘each part is ordered so that each has a true proportion, uniformity and unison’ and ‘a pleasing ordering of all the parts and conditions of a melody or of an entire melodic work in the manner in which a building is designed’ are fairly accurate descriptions of the kind of proportional planning Bach employed, and that was defined as a numerus musicus. The term numerus musicus might also cover Walther’s 1732 definition of eurythmia, because in music eurythmia is created with numbers: Eurythmia: Decoration and Beauty, which in music arises from numbers, specifically when a melody is organised according to its numerical content [‘nach dem Numero’], which is particularly necessary to be observed in French Pièces.42

Among the French-inspired music popular at the time in the Leipzig area were dance movements, such as the Gavotte and Bourrée, that Walther and many other theorists, including Niedt and Mattheson, defined by their bar totals. For example, Walther’s definitions of Gavotte and Menuet read: ‘Gavotte is a dance in simple time with two reprises, the first of which has four bars and the second eight,’43 and ‘Menuet is a French dance. The melody of this dance has two reprises, each of which is played twice. Each reprise has four or eight bars (tact), or at least, with a few rare exceptions, no uneven number of bars (tact).’44 Walther is describing the smallest-scale layer of proportional parallelism here, with the number of bars creating a perfect 1 : 2 or 1 : 1 across a movement, 4 : 8 bars and 8 : 8 bars. A comparable term is used by Heinrich Bokemeyer in an essay on the melodic art describing the importance of the numerus poeticus, or the number of syllables, feet, lines and strophes, when setting texts to 40 41 43

Ibid., 156–7. Originally in Kern Melodischer Wissenschaft, 55. 42 Mattheson, Capellmeister, 156. Walther, Lexicon, s.v. ‘Eurythmia’. 44 Walther, Lexicon, s.v. ‘Gavotta’. Ibid., s.v. ‘Menuet’.

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music.45 Counting these units in a poem, to create uniformity and 1 : 1, is the same process that Mattheson describes for the composer who wants to create unity with the parts and sections across a musical work. Bach probably thought of proportional parallelism as a numerus musicus, as eurythmia, and as expressing Gleichförmigkeit and Übereinstimmung. As has been seen in Chapter 3, Mattheson’s motivation for recommending proportions in composition was that ‘nothing in the world is more beautiful to the ear’, even though large-scale proportions across a complete work would not be audibly detectable. In seeming contradiction to his stance, Mattheson profoundly believed that non-sounding proportions were pleasing to God, and he realised that many musicians of the time believed that non-sounding proportions had an integral role in composition. Even though his writings are marked by his mission to stamp out the old rational view of silent proportions, his recommendations for proportional planning were useful guidelines for all composers, regardless of which party they supported in the sounding/non-sounding Harmony debate. The true proportion, unison and unity that Mattheson recommends concur with the order found throughout Bach’s collections in their revised and published forms. The recurring architectural images, numerical terms, and descriptions of proportional construction in treatises of this period combine to give a pretty good description of Bach’s use of proportional parallelism.

II Units of measurement for compositional planning If a composer in Bach’s time drew either a general or a specific ground plan ‘so that each part of a composition demonstrates a true proportion, uniformity and unison’, he would need to be able to count a feature in the score with which to form the proportions. With Spiess’ general planning the composer could use a larger-scale unit and form a 1 : 1 proportion or unison between the dimensions of six movements in a work, 3 : 3, or six works in a collection, 3 : 3, just as an architect could decide to design a 1 : 1 proportion between the area of six rooms in a building, or six buildings in a complex. Bach regularly formed layers of proportion with such units across 45

Mattheson, Critica Musica, vol. II (Hamburg: Wiering, 1725), 310, § XV; see also D. G. Morhof, Unterricht von der Teutschen Sprache und Poesie (Lübeck; Franckfurt, 1700), 496, chapter six, ‘Von dem Numero Poetico’, where he specifies the number of syllables, feet, lines and strophes.

Bars, planning and proportional parallelism

and within his collections.46 Smaller units of measurement would have been used to draw up a well-proportioned specific plan, in the same way that the architect decided on the dimensions of each room in the building. At this layer of construction the composer had to decide how long each section, movement and work should be. This required a measurable unit.

The bar Over the chequered history of number symbolism in musicology, a variety of smaller units, such as bars, sections, breves, minims, notes, words, letters and repetitions of notes, phrases and words, have provided data for the analysis of musical scores. Those looking for symbolism have also taken the numbers as the basis of interpretations, some enthusiastically pursuing their goal ‘with more vigour than discretion . . . sometimes to the point of absurdity’.47 No such implications resonate from the descriptions of compositional planning cited above. The numerical ordering described by Mattheson and Spiess has proportion and not number as its goal. The numbers themselves are on the whole irrelevant. If there is any symbolism in compositional planning, it lies in the use of the unison, the 1 : 1 proportion. Bach used the number of bars to form layers of perfect proportions between movements and between works, within and between his collections. He did this at the revision stages of his compositions, taking already composed movements and works and revising and expanding them into perfectly proportioned collections. The bar is the most obvious small unit for this process, and the most time-efficient for the busy composer, because he already had this figure to hand when he was designing the layout of his manuscripts. The German word ‘Tact/Takt’ requires careful translation because it had several different meanings in Bach’s time. In modern English the musical term ‘bar’ (also known in America as ‘measure’) indicates only the area that lies between two vertical bar lines. In modern German and in Scandinavian languages the word has several meanings, including the measurement of time (i.e. the time-signature, Taktart), the duration of musical notes (Takt can mean the semibreve or whole note), and the pulse shown 46

47

For example Tables 5.1 and 5.2, in which Bach forms 1 : 1 and 1 : 2 proportions between the number of collections (1 : 1), solos (2 : 1), sonatas (2 : 1), movements (2 : 1 and 1 : 1) and sections in a movement (1 : 1). Malcolm Boyd, Bach, The Master Musicians (London; Melbourne: Dent, 1983), 223.

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by the hand (tactus). In Bach’s time the word Tact encompassed all of these meanings as well as some richer ambiguities. In 1708 J. G. Walther devoted an entire chapter to the subject, beginning with the statement: ‘Shown by the hand or only in the mind, the Tact is a regular motion with which sound, along with time, is measured. For in the same way that long, heavy or liquid objects are measured by ells, weight or capacity, sound or pitches are measured by the bar.’48 He continues that the Tact is proportioned into equal and unequal parts,49 stating that some unequal proportions can be rejected because of their vexatiousness (Verdrüßlichkeit) and troublesomeness (Mühe),50 and ending the chapter with the phrase Totius Musicae anima Tactus est, i.e. ‘the bar is the soul of all music’.51 Twenty-four years later his definition was much the same.52 There is no doubt that Walther and his contemporaries understood the Tact to be a unit of measurement, although the specific meaning is frequently only clear from the context. When Mattheson wrote ‘Soll der Täcte Anzahl einen Verhalt haben’53, for example, he did not mean that the number of bars in a movement should be in proportion, as he clarifies later. He meant that the number of pulses (tact) within each bar should be kept in proportion. Walther, on the other hand, defined dance movements using ‘tact’ to mean the unit between two barlines when he defined the Gavotte,54 as seen above. In 1710 Friedrich Erhardt Niedt (1674–1717) also used the bar in this way, in descriptions of the structure of various musical movements: ‘In simple time Ritornelli seldom reach eight bars, but in triple time there may be twelve or even sixteen bars,’55 and for the Rondeau he writes: ‘Some set the first reprise in seven, ten or twelve, but the second in fourteen, twenty, and twenty-five bars, maybe even twice as many.’56 Bach owned a copy of Niedt’s treatise, adapting it for his own use and purposes when he taught.57 In 1721 Mattheson thought sufficiently highly of Niedt’s treatise to publish a second edition, ‘improved, expanded and with most pertinent details’.

48

49 51 53 54 55

56 57

Walther, Praecepta, 55 (Benary, 28). I am grateful to Dominik Sackmann, for alerting me to the importance of this statement. 50 Walther, Praecepta, 61 (Benary, 30). Walther, Praecepta, 69 (Benary, 33). 52 Walther, Praecepta, 72 (Benary, 33). Walther, Lexicon, s.v. ‘Tact’. Mattheson, Capellmeister, 141; Harriss, Vollkommene Capellmeister, 313. Walther, Lexicon, s.v. ‘Gavotta’ Friedrich Erhardt Niedt, The Musical Guide, trans. P. L. Poulin and I. C. Taylor (Oxford: Clarendon Press, 1989), 143–4. Ibid., 144. F. E. Niedt, Musicalische Handleitung oder Gründlicher Unterricht (Hamburg, 1710).

Bars, planning and proportional parallelism

Mattheson’s idea of ‘improvements’ can be judged by his comment following Niedt’s description of the Sarabande. Niedt defined the length of the Sarabande, writing ‘§8 A Sarabande (which must have eight bars in each reprise) can be constructed from this Courante bass’. Taking four times as much column space as Niedt, Mattheson added: It is not an iron-clad rule that the Sarabande must have eight bars in each reprise. As long as the reprise does not have an uneven number of bars there is no restriction as to length. An inexperienced person might see a Sarabande which happens to have eight bars and then conclude that it is a necessary characteristic for all Sarabandes to have eight bars.58

commenting after Niedt’s sixteen-bar example: I cannot help mentioning that the arithmetical progression (progressio arithmetica) is not quite right in this Treasure Trove of Sarabandes. It would not be enough to have the correct number of bars; the cadences and Clausulae must occur at the right time as well, or else everything is lopsided. Here the phrase ending should rightly occur in the fourth bar, but in both reprises it occurs in the fifth bar, and this is just as objectionable as if the piece had an uneven number of bars. It follows from this that the last phrases in both reprises would have only three bars each. It seems to me that the division of the eight bars is bad if one part has five and the other part three. This also results in a nasty and confused symmetry for the ear.59

For Mattheson, the success of the regularity of four-bar phrases in a sixteen-bar section is because of their progressio arithmetica, in this case 4+4+4+4 bars. This audible 1 : 1 : 1 : 1 naturally pleased Mattheson, the advocate of heard proportions. It also shows that his praiseworthy progressio arithmetica was formed by bars. The parallel proportions in Bach’s collections are also examples of progressio arithmetica formed by the number of bars, even though they are too large to be heard. A numerus musicus characterised by a 1 : 1 or 1 : 2 division, and typical of French dance forms, appears in Bach’s suite movements, where it is not uncommon to find a strict binary form with a literal 1 : 1 form, e.g. 32-bar movements with a double-bar repeat midway, after bar 16.60 The parallel layers of perfect proportion, 1 : 1 and 1 : 2, that I have discovered on a larger scale in Bach’s publications are a sophisticated version of this simple foreground division within a suite movement. I am sure that had 58 59 60

Niedt, Musical Guide, 171. Ibid., 146, note (t) ‘Progressio arithmetica’, and 147 ‘Die Zahl der Täcte’. For example, Goldberg Variations. Suite movements in the French Overture (BWV 831).

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proportional parallelism been formulated as a theoretical concept in Bach’s time, it would have been classified as a numerus musicus.

Measuring time and the bar A report concerning the compositional use of the bar for timing a church cantata was published in Mizler’s journal Musicalische Bibliothek. It appears in a summary of the activities of the corresponding society from 1746 to 1752, in which Mizler listed the seven musicians who had joined since 1746, Johann Sebastian Bach, having become the fourteenth member in June 1747.61 Communication between society members, all of whom were men, was carried out by written correspondence.62 As the account describes, Bach sent a canon (BWV 1076) for the members to study and to discuss. In the same parcel was a discussion paper on church cantatas, giving guidelines on how to assess the duration of a cantata using the number of bars and minutes. Figure 4.1 shows that this was reported, without a paragraph break, immediately after the report of Bach’s canon BWV 1076: In the fifth parcel of the Society the late Capellmeister Bach contributed a six-part threefold circle fugue. (See table IV. Figure 16.) Also, texts of church cantatas were commented on. We want to bring before you now, for the use of the church composer and poet, the essence of how to make music on spiritual poems. 1: A church cantata must not last too long, so that the final goal of music, to promote worship, and the chief goal, to be taught and strengthened in the fear of God and Christian teaching, is not hindered or the service unnecessarily prolonged. In winter it should be somewhat shorter than in summer, because both performers and listeners alike will be prevented from giving their attention to the service on account of the extreme cold. From experience one can determine the length; i.e., a cantata of 350 bars (Takt) of varying time signatures (Mensur) will take approximately 25 minutes to perform, which in winter is long enough, whereas in summer one can add 8 to 10 minutes and thus form a cantata of roughly 400 bars (Täkte). It is not the intention that a composer should bind himself more to the timing than to the music, and to producing a movement in beautiful order.63

In this description the word Takt can be understood in several ways. If the composer were to convert the cantata to the number of semibreve 61 62

63

L. Mizler, Musicalische Bibliothek, vol. IV, part I (Leipzig 1754), 107. See Chapter 2 §IV above. The postal service across the Holy Roman Empire was run by the princes of Thurn und Taxis. See Zedler, Lexicon, s.v. ‘Post-Ordnung’ for rules and operational conditions for residents of Leipzig. Mizler, Musicalische Bibliothek, vol. IV, part 1 (1754), 108.

Bars, planning and proportional parallelism

Figure 4.1 L. Mizler, Musicalische Bibliothek, vol. IV, Part 1 (Leipzig, 1754), 108

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pulses (Takt=semibreve), regardless of time-signature or metre, the total number of bars would be different to the total found were he to count the number of pulses in each bar (Takt=tactus) or the number of units lying literally between bar lines (Takt). Since bars of any metre are counted in this equation, the word Takt here must mean the unit lying between two bar lines, i.e. ‘measure’ or ‘bar’. A careful reader will notice that the arithmetic does not work. If 350 bars are performed in 25 minutes, the equation is 1 minute per 14 bars, and so 490 bars rather than 400 bars would be performed in 35 minutes. The error may have resulted from misreading a handwritten 9 for a zero. The report assumes that the composer would know how many bars he had composed, and unquestioningly disregard the metre and speed of individual movements. The method cannot be accurate, given that a bar in 3 8 Presto could take an eighth of the time of a bar in . The guideline was little more than a revised version of Michael Praetorius’ statement published in 1619, which, due to changes in notation of the bar line and to musical styles of the church cantata, had become hopelessly inaccurate by the 1740s: I [Praetorius] should also like to mention here that I have indicated the number of tempora [breves] contained in each composition at the end of the thoroughbass part, even after each section or part of a work, for it is necessary to take into account how many tempora [breves] can be played in a quarter of an hour at a moderate tact [tempo]. That is 80 tempora in half of a quarter of an hour, 160 tempora in a full quarter of an hour, 320 tempora in half an hour and 640 in a whole hour. Thus one can judge more accurately how long a particular song or concerto might last, so that the sermon is not delayed and can begin at the proper time, and other parts of the liturgy can also be arranged accordingly.64

Praetorius’ purpose in noting the number of tempora or bars beside the bass part at the end of each song or section was to enable the composer to estimate the length of a piece. The quarter-of-an-hour unit used to measure time corresponds to the usual measure of an hourglass or Sanduhr, which was still a well-known standard a century later in Leipzig when the following description was published: Sand-Uhr, Stunden Glas: One can make these clocks so that they run for a whole hour, half an hour, a quarter of an hour or half of a quarter of an hour, and so show the hour and its parts.65

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65

Michael Praetorius, Syntagma musicum, vol. III (Wolffenbüttel, 1619), 87–8. Translation based on J. T. Kite-Powell, Syntagma Musicum III (Oxford University Press, 2004), 100. Zedler, Lexicon, s.v. ‘Sand-Uhr, Stunden-Glas’.

Bars, planning and proportional parallelism

Hourglasses were regularly installed in pulpits throughout northern Europe until as late as the 1800s.66 Although by Bach’s time the clock and pocket watch were fairly common, Praetorius’ hourglass units of fifteen minutes would have been understood with no difficulty. If Bach did make a note of the timing of his cantatas, the annotations have not survived on the scores or in any of his letters. Timings have survived in the scores of several of his contemporaries,67 and Johann Adolph Scheibe (1708–76) left the following description of how he used timings: Sometimes when shipping one of my compositions to be performed at a remote location, and so as to prevent as far as possible all disarray and misunderstanding of its character, I have noted the duration of its movements with the pocket watch when I went through it myself on the keyboard. Giving my correspondent written details of how many minutes or also seconds each large or small movement requires to capture a correct and expressively unifying performance, I asked him to see that these movements are [performed] exactly in this prescribed timing.68

Scheibe’s purpose in recording clock time was to ensure that a stranger could reproduce the correct character of the piece in performance, whereas the Bach/Mizler guideline was for the composer’s own benefit, to ensure that the sermon could begin on time. Published in 1619, Praetorius’ description suggests that the practice of measuring a musical unit against time dates to well before the seventeenth century. The theorists leave no doubt that the bar would have been the obvious choice were a composer trying to measure a musical work, and for a composer making a compositional ground plan in order to introduce a perfect proportion in every part.69 Mizler’s bar–minute–cantata report appears in the summary of the society’s activities from 1746 to 1752, Bach having become a member in June 1747. In the flush of a new member’s enthusiasm and in view of his vast experience of cantata composition, it is highly likely that he would have made some amendments or contributions to the discussion document. Appearing immediately after the report of Bach’s death the positioning of the cantata equation implies a more significant connection – that Bach was not only actively involved in its revision, but that he may have been the original contributor responsible for its formulation. If it was Bach

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67

68 69

Many original examples survive today, e.g. in Slottskyrkan, Stockholm and in Skokloster’s Kyrka, where a 60-minute timer integral to the pulpit was installed in 1674. Johann David Heinichen, Selected Music for Vespers, ed. M. Williams (Middleton, WI: A-R Editions, 2010), critical report, 347–8. J. A. Scheibe, Ueber die Musikalische Composition (Leipzig, 1773), 299–300. Mattheson, Capellmeister, 240.

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who updated Praetorius’ guidelines for the ‘modern’ cantata composer, the bar–minute equation would be an invaluable statement about his working method. As it is, it shows that Bach and his contemporaries had to manipulate the number of bars in their cantata compositions in order to stay within the time limits set by the liturgy. And it shows that changes in time signature were disregarded when counting the number of bars in a composition, as they are today. The bar was the single fixed unit in a score with which to order the music beautifully and to create proportional order across a work.

III

Measuring the score

Composer and copyist used the bar and the stave when ordering and planning the layout of a page or score. Paper was expensive and economy was desirable even when it was not a necessity. A plan of the score and the layout of each page had to be made before the rastrum (multi-nibbed stave pen) and ink touched paper. First it was necessary to decide how many interleaved sheets were required for the entire composition, and how they would be folded so that the score followed sequentially. The next task was to rule the requisite number of staves onto the plain sheet of paper with a rastrum of the appropriate width.70 It was then a matter of keeping an eye on the plan to ensure that the allocated number of bars per page was followed.71 Student composers learned their craft through the everyday task of transcribing scores. The importance to Bach of learning through copying is illustrated in the famous account of his illicit moonlight transcriptions of precious compositions owned by his older brother when Sebastian was a boy,72 and also, and more reliably documented, in the meticulous copies of works by other composers that he transcribed as an adult.73 Copying errors cost time and money. Knowing the number of bars in a movement or a section helped create the best possible layout of the copied page, and was also a way of checking that the copy was identical in length to the original. Copyists frequently kept track of the number of bars at the end of a movement. Bach’s annotations occasionally survive in his scores – some were caused by copying, but others are not so simple to explain. In 70 71 72 73

Zedler, Lexicon, s.v. ‘Rastrum’. For example in his presentation copy of the Brandenburg Concertos, Am. B. 78. BD III, Doc. 666, 81; NBR, Doc. 306, 299. K. Beißwenger, Johann Sebastian Bachs Notenbibliothek (Kassel; Basel: Bärenreiter, 1992).

Bars, planning and proportional parallelism

the autograph score of the 1733 Missa of the B Minor Mass (P 180) Bach wrote the number 94 by bar 94, the last bar of page 72, and 100 at the end of the first stave of page 73, which is bar 100. He copied out the ‘Quoniam’ movement many times when he made the instrumental and vocal parts for the Missa (D-Dl Mus. 2405-D-21). The alto voice is silent throughout the 127-bar long ‘Quoniam’, which Bach indicated by writing the figure 127 above rest symbols that amount to 127 whole bars. It was standard practice, and is yet another indication that Bach both knew and recorded the exact length of the movement in terms of the number of bars. But it does not explain his annotation of the bar numbers 94 and 100 on the score of this movement, nor his annotation of cumulative bar numbers elsewhere. The bar numbers recorded on pages 72 and 73 may have been a checkpoint during the copying process, because we know he copied these parts, but if this was the only reason, why did he not write cumulative bar numbers more frequently for the many other movements that he copied? Fifteen years later in the autograph score of the ‘Confiteor’ of the Symbolum Nicenum of the B-minor Mass, he wrote the numbers 61, 100 and 141 at the foot of each of pages 137, 138 and 139, corresponding to the final bars on those pages. The ‘Confiteor’ is in Bach’s composing hand, the corrections showing that he was either composing directly into the score, or making a new adaptation from a pre-existing composition.74 Unfortunately no surviving autograph parts have survived to confirm whether or not these cumulative bar numbers could have been Bach’s copying checkpoint, written after the movement was composed. It has recently been suggested that Bach wrote these numbers to keep an eye on the formal proportions of the performance length.75 Proportional parallelism suggests more specifically that Bach wrote the numbers to help him achieve a predetermined bar total towards creating larger-scale non-sounding proportions in the work as a whole.76

Measurements for fair copies and printing The music engraver also used the number of bars to ensure a perfect layout. His fee was based on a fixed sum for each engraved plate, with a 74 75 76

G. B. Stauffer, Bach: The Mass in B Minor (Yale University Press, 2003), 134–5. P. Wollny, ‘Beobachtungen am Autograph der h-Moll-Messe’, BJ (2009), 144, note 32. Tatlow, ‘Parallel Proportions, Numerical Structures and Harmonie in Bach’s Autograph Score’, in Exploring Bach’s B Minor Mass, ed. Yo Tomita, Robin A. Leaver and Jan Smazcny, (Cambridge University Press, 2013),142–62.

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different sum charged for the number of pages actually pulled and printed from the plate.77 Andrew Talle has recently discovered that these charging practices prevailed in Leipzig,78 where Bach could choose from many different engravers and printers.79 Counting the words in a book or bars in a composition in order to calculate the layout of the page to be printed or engraved was an obvious technique, yet it was sufficiently important for the procedure to be described in detail in a manual by Johann Caspar Müller (d. 1717) (see Figure 4.2): Ausrechnen, compter le Manuscrit [To calculate, Count the manuscript] Most people consider calculating a manuscript to be a peculiar art, especially as it [a manuscript] can be written in so many different ways, sometimes narrow, sometimes wide and sometimes close to the margins. The greatest requirement for the task is caution. The first lesson before you begin calculating is to read the manuscript through very carefully and check for the leaves and pages that look different to the majority, as they will require a different calculation. When this is done, look for a line in the manuscript that is typical of the majority, and set it in the format to be used, and then count the syllables or, if you want to be more exact, the letters that have been used, and make a note of this. Then begin by setting one line at a time from the beginning until an even line is reached, which frequently happens in the 2nd, 3rd or 4th line. Mark this place [on the manuscript] with red ink, to show how wide each [printed] line is. Now he [the typesetter] knows how many written lines make a printed line, and in this way it is possible to count without worry, although he must always make a mark [Strich] on the manuscript where the even number of lines will appear. If he comes to a passage that is written larger or smaller he should not count the lines but rather the syllables or letters. He must indicate all columns accurately otherwise the pagination will not work properly, and when you have done that, do not rely upon your own judgement, but count all the columns once more with great focus and concentration and then it will not be so easy to make a mistake. Remember the publisher must be paid for this trouble and labour as it is painstaking and tedious work.80

77

78

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80

D. Hunter, ‘The Printing of Opera and Song Books in England, 1703–1726’, Notes 46 (1989), 328–51, and 48 (1991) 647–85. A. Talle, ‘A New Look at Sperontes’ Singende Muse an der Pleisse’, unpublished paper, American Bach Society biennial meeting, Madison, WI, May 2010. Das jetzt lebende und jetzt florirende Leipzig (Leipzig: Boëtius, 1736) lists fifteen book printers (Buchdrucker), eight engravers (Kupffer-Stecher), nine printers from copper plates, and 3 print-makers (Schrifft-Giesser), although not all worked with music engraving. C. F. Gessner, Der in der Buchdruckerei wohl unterrichtete Lehr-Junge (Leipzig: an der OsterMesse, 1743), 161–2. Gessner’s book includes the posthumous publication of J. C. Müller, Wohlmeynender Unterricht on 145–366, and tables reproduced from M. D. Fertel, La Science pratique de l’Imprimerie (Saint-Omer, 1723).

Bars, planning and proportional parallelism

Bach would have worked in this manner when preparing a composition for the engraver.81 The layout of both his fair copies and engravings suggests that he knew how many bars he had composed, how many bars were on a single page, and how many bars he still needed, and that he had a well-ordered large-scale plan. There is also very clear evidence to suggest that he used the layout flexibility to his advantage as he refined a musical plan, for example in the adaptation of BWV 1049/1 to BWV 1057/1, and in his revisions to Clavier Übung III, even while it was at the engraver’s. Another feature that might suggest a reason for Bachboth s cumulative bar numbers in the score of the B Minor Mass, P 180, is that both ‘Quoniam’ and ‘Confiteor’ run directly into the following ‘movement’ without any double bar or change of time signature. Something similar happens twice more in the Missa, where the ‘Gloria’ runs into the ‘Et in terra’ without a double bar line, and the ‘Domine Deus’ into the ‘Qui Tollis’. In these latter instances there is a change of time signature between the successive movements, the time signatures at the beginning of ‘Et in terra’ and ‘Qui Tollis’ acting as a bar line in the middle of bar 100 and bar 95 respectively.82 But in neither case does Bach make a note of the cumulative bar total at the end of any page, although he also copied the parts for these movements. The bar numbers in the scores of the ‘Quoniam’ and ‘Confiteor’ therefore may have been a guide to help him as he made minor compositional adjustments. This seems reasonable for the ‘Confiteor’ as it is a compositional score, but it does not account for the annotated bar numbers in the ‘Quoniam’. The possibility remains that he recorded bar numbers such as these to guide him as he extended the movement to a predetermined length to create a large-scale proportional unit, and therefore they might be evidence of Bach achieving proportional parallelism. Bach’s scores show that he owned and maintained several different widths of rastrum for ruling manuscript paper. The spaces between the five nibs of the rastrum determined how many staves and then how many bars would fit onto a sheet of paper. Bach rarely left any paper blank and frequently filled up spaces at the end of a sheet with slimmer staves for movements requiring fewer instruments. Practical finances determined the wisdom of counting the number of bars in published music. Calculating the number of staves and bars per engraved plate was the equivalent of the book printer’s calculation of syllables and lines to guide the size of font and 81

82

C. Wolff, ‘Die Rastrierungen in den Originalhandschriften Joh. Seb. Bachs’, Festschrift für Friedrich Smend (Berlin: Merseburger, 1963), 80–92. P 180, 27 and 60 in the original pagination.

123

124

foundations

Figure 4.2 Müller, Wohlmeynender Unterricht (Leipzig, 1743), 172–3

Bars, planning and proportional parallelism

Figure 4.2 (cont.)

125

126

foundations

the correct setting of a text. We know that printers in Leipzig charged the composer per plate and per sheet, and that therefore the layout and format and number of bars on every sheet of engraved collections will have been carefully planned and calculated. This can be seen from the regularity of the number of bars per sheet in each of the partitas in Bach’s CÜ I (BWV 825–30). Unfortunately accounts or detailed documents that might reveal Bach’s relationship with his engravers have not survived, although Gregory Butler’s painstaking reconstruction of the printing procedure for several of Bach’s publications has gone a long way to fill the gaps of knowledge.83 Bach provided a fair autograph score for the engraver to use as a model. Either a freehand engraving was transcribed directly onto the copper plate, or the model autograph score was rendered transparent by soaking it in oil and then traced around by a non-musician.84 In either case Bach would have calculated the number of bars very carefully to ensure a perfect layout for each plate. He knew not only how many bars he had composed, but also how many bars were to be published. Theorists encouraged the composer to make proportioned plans of different parts of a composition, i.e. to introduce the correct progressio arithmetica to parts and to the whole. The bar was used to measure the length of a composition and its sections, and to assess the progressio arithmetica. The bar would have been an obvious means of introducing proportions into the plans of a composition. Mattheson and Scheibe were motivated to reproduce the ideal of beautiful order, unity and proportion by the aural effect. Many others were motivated to reproduce the ideal because it fitted their view of God, creation and the universe. Beautiful order and proportion in musical structures were recreated for many different reasons. Parallel techniques, symmetrical organisation and proportions were all commonplace in everyday life and in all academic disciplines in Bach’s time and location. Although Bach and theorists of his time did not define the practice of proportional parallelism, it would have been a self-evident application of their beliefs.85 Walther wrote that eurythmia in music is achieved when a melody is well constructed numerically.86 Theorists including Mattheson, Walther and Niedt discuss the technical nuts and bolts of eurythmia in music as 83 84

85

86

G. Butler, Clavierübung III: The Making of a Print (Durham, NC: Duke University Press, 1990). G. Butler, ‘Sources 2. Printed editions’, in J. S. Bach, ed. Malcolm Boyd, Oxford Composer Companions (Oxford University Press, 1999). That is not to say that all composers of the period used proportional parallelism, or that they would have formed proportions in the same manner. Walther, Lexicon, s.v. ‘Eurythmia’.

Bars, planning and proportional parallelism

progressio arithmetica and numeri musici. The ideal numerical construction is 1 : 1 because ‘the closer a proportion is to the unity or equality, the more perfect it is’.87 Mattheson encouraged composers to aim for Gleichförmigkeit, symmetry, proportion and unison when drawing up a plan for a complete composition.88 Part Two will show that all of Bach’s publications and fair autograph scores display such eurythmia and symmetry, using the bar totals to introduce large- and small-scale 1 : 1 and 1 : 2 proportions between sections, movements and works in collections. In accordance with the prevalent philosophical and theological ideal, Bach’s proportions are all very close to the unity. We have it on Forkel’s authority that Bach knew about ordering compositions proportionally as early as 1713,89 when he transcribed and arranged a group of Italian concertos for keyboard.90 Forkel claimed that much of his source material came directly from Bach’s two elder sons’ reports, and therefore his accounts, however anecdotal, must be taken seriously. This particular one strongly suggests that the numerical proportions of a composition were an integral part of Bach’s learning process,91 and that Bach studied these as he made the concerto transcriptions, BWV 972–82, which survive in a fair copy by J. B. Bach, P 280.92 Although Bach left almost no working documents to explain how he ordered large-scale works numerically or otherwise, the evidence that there was ‘another ground plan’ for the Art of Fugue bears witness to a longforgotten conversation or instruction, with its architectural language, that Bach or one of his sons had with the engravers during the publication process.93 Walther stated that ‘Totius Musicae anima Tactus est’,94 ‘the bar is the soul of all music’, just months before his cousin Johann Sebastian Bach moved to Weimar. It was in the handwritten dedication copy of Praecepta der Musicalischen Composition, for the young prince Johann Ernst of SaxeWeimar (1696–1715) on his name day, 13 March 1708.95 At this stage both Bach and Walther were idealistic, newly wed 23-year-olds at the beginning of what they hoped would be illustrious careers. It seems reasonable

87 90 91

92 95

88 89 Appendix, 1708-VI. Mattheson, Capellmeister, 240. NBR, 441; BD VII, 36. See Chapter 10, §II. The meaning of the word ‘Verhältnis’ changed little in Leipzig between Zedler’s definition, s.v. ‘Proportio’ in his vol. XXIX in 1741 and Forkel’s use in 1802; and as can be seen by comparing Zedler’s definition with J. C. Adelung, Grammatisch-kritisches Wörterbuch der hochdeutschen Mundart, 2nd edn (Leipzig, 1793–1801), s.v. ‘Das Verhältniß’. 93 94 See Chapter 10, §I. See Chapter 9, §II. Walther, Praecepta, 72 (Benary, 33). Weimar, Herzogin Anna Amalia Bibliothek/Hs Q 341 c.

127

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therefore that they would have met frequently now that they lived in the same town, and that their conversations would include discussions of their most recent projects as well as future aspirations. Did Bach agree with Walther’s statement that the bar or tactus ‘is ‘the soul of all music’, and what exactly did they understand by ‘the soul of all music’? A year earlier in his influential poetry publication, Hunold had stated that ‘Invention is the Haupt Stücke’ in all poetry, ‘invention is the Soul, disposition the Body, and verse and rhyme merely decorative Clothing’.96 Had Walther pursued this soul–body–clothing analogy, using the common rhetorical divisions Inventio (Erfindung), Dispositio (Einrichtung) and Decoratio (Zierde),97 what would he have considered to be the disposition/body and the decoration/clothing of music, when the soul, or the invention, was the bar? Proportional parallelism uses this soul of all music, the bar, to order the parts of a composition, the body, into proportions. A composer using proportional parallelism would have been dealing with elements fundamental to music, the soul and body in the Walther–Hunold–Mattheson analogy. Although we cannot know if Bach and Walther thought in these concepts, the imagery shows that in the early eighteenth century the elements of proportional parallelism were bound to the core and essence of music. Frequently repeated accounts about Bach’s relationship to music theory touch on the subject of mathematics.98 In 1739 Scheibe wrote: Let any one ask a great Bach, who has perfect command of all artifices of art, and whose astounding works one cannot see or hear without surprise, whether in the attainment of this great skill and dexterity, he even once thought of the mathematical relations of the tones, and whether he once consulted mathematics in the construction of so many musical artifices.99

A sentence towards the end of the obituary by Johann Friedrich Agricola (1720–74) and C. P. E Bach reads: ‘To be sure, our late-departed Bach did not enter into deep theoretical considerations of music.’100 Reports of this nature have been used to emphasise that Bach had no interest in music theory, and implicitly no interest in numbers. However, Bach’s lack of involvement with music theory, and any dislike of dry mathematical

96

97 98 99 100

Christian Friedrich Hunold, Die allerneueste Art zur Reinen und galanten Poesie zu gelangen (Hamburg: Liebernickel, 1707), 540. Mattheson, Capellmeister, 235. J. Mattheson, Grundlage einer Ehrenpforte (Hamburg, 1740), 231; BD II, Doc. 470. J. A. Scheibe, Der Critische Musicus (Hamburg: 1739), vol. III, 355. BD II, Doc. 468. Mizler, Musicalische Bibliothek, vol. 4 (1754), 173; NBR, Doc. 306, 307

Bars, planning and proportional parallelism

instruction about intervals and their proportions would not have prevented him from using the bar numbers associated with proportional parallelism. The bar numbers used to facilitate compositional ordering were neither speculative nor theoretical; they were practical tools. And as has been shown, and can be read in the Appendix, Bach had every spiritual motivation to strive to create layers of aesthetically pleasing proportions within the structures of his compositions. Such perfectly proportioned artworks were pleasing to God, delightful to man, and enduring.101 The evidence in Part One proves that an ordering technique using 1 : 1 and 1 : 2 proportions would have been a natural development of current practices in compositional planning, in line with the prevalent ideals of beauty and perfection. For many composers in the Thuringian area the technique would have had additional spiritual implications. Proportion and symmetry in visual, literary and musical forms would have been second nature. Bach would have understood emblematic parallels whether or not they interested him. Bach knew that his surname could be used in music to create useful melodic material, and he knew that his name could be converted to numbers. His use of the word ‘Harmony’ held theological implications, as it did for Werckmeister, Buttstett, Walther and Neuss. Bach knew how many bars he composed, and he used this knowledge to help him create parallel layers of proportional order in his scores and collections. Part Two will give the data and source evidence to support these claims.

101

Appendix, 1687-III, 1708-IV, 1717-IV.

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part ii

Demonstrations

5 Three collections for strings

Six Sonatas and Partitas for Solo Violin (BWV 1001–6) Six Sonatas for Violin and Harpsichord (BWV 1014–19) Six Suites for Solo Cello (BWV 1007–12) Numerus perfectus (lat.) ist bey den Mathematicis z.E. die Zahl 6; weil sie aus allen ihren partibus aliquotis wiederum entstehet und gemacht wird; theilet man sie nehmlich erstlich in zwey Theile, kommen 3; hernach in 3 Theile, kommen 2; endlich in sechs Theile, kommet 1. Diese Theile nun wieder zusammen gethan, kommt sie selber, d.i. 6 wieder heraus, als: 1. 2. 3. = 6. Dieser Zahl-Art sind sehr wenige; denn in 10 ist nur dieser 6; In 100 ist 28; in 1000 ist 496; in 10000 ist nur 8128. J. G. Walther, 1732

Grouped together in this chapter are three collections for string instruments, each containing six works. Although some movements and works in these collections may date from as early as his Weimar days (1708–17), it was in Cöthen (1717–23) that Bach began to revise, polish and form them into perfectly proportioned collections.

I

Libro Primo: a perfect violin collection

Bach’s collection of three sonatas and three partitas for solo violin is a textbook case of proportional parallelism. The autograph fair copy of the score, P 967,1 demonstrates the theory’s three characteristics with utmost clarity: many layers of 1 : 1 and 1 : 2 proportion coexist within its 2400-bar structure, and the keys of four solos form an allusion to Bach’s name in the pattern B-A-C.

1

D-B Mus. ms. Bach P 967.

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Bach named the violin sonatas and partitas Sei Solo [sic] a Violino senza Basso accompagnato – Libro Primo; I will use the title ‘Six Solos’. The neatness of Bach’s autograph score leaves no doubt that he was copying from a now lost original, rather than composing directly onto the page.2 He wrote the title page in Italian, concluding it with a signature and date, Joh: Seb: Bach ao. 1720, numbering the forty-one sides consecutively on alternate recto pages, from 2 to 22. He did not publish the collection, but at the time such a polished, paginated autograph manuscript with title page and signature was the composer’s equivalent of a publication and could generate income. It could be lent for a fee to interested parties, or a sponsor could pay the composer to make a copy. The Six Solos attracted at least two commissions. In 1726 Johann Peter Kellner (1705–72) copied an early fivesolo version of the collection;3 and sometime between 1727 and 1731, Bach’s second wife, Anna Magdalena, transcribed the Six Solos and the Cello Suites, P 268 / P 269,4 for Georg Heinrich Ludwig Schwanberg (1696–1774), who himself made a single title page for the set of two collections.5 No accounts survive to indicate the fee paid to Bach by either Schwanberg or Kellner.6

1 A round bar total, usually a multiple of 10, 100 or 1000 The bar totals in Bach’s polished works are almost always a multiple of 10, frequently 100 and sometimes 1000. Table 5.1 shows that Bach’s score of the Six Solos has exactly 2400 bars. This becomes 2408 bars when the da capo bars are included, and 3453 bars when all repeats are observed. Of the thirty-two movements in this collection, twenty-one have repeats and one a da capo. The da capo in the ‘Gavotte en Rondeau’ (BWV 1006/3) may be evidence of how Bach manipulated the score to achieve his perfect numerical plan. The ‘Gavotte en Rondeau’ movement covers page 21, with thirteen systems and two bars written on a partial fourteenth. The first eight bars, 2 3

4 5

6

NBA KB VI/1, 7. Kellner (1705–72) dated his copy 3 July 1725. D B Mus. ms. Bach P 804/121–45. NBA KB source D; sources B, P 268, and C, P 267, are not discussed as they add nothing to the numerical observations. D-B Mus. ms. Bach P 268, P 269. H.-J. Schulze, Studien zur Bach-Überlieferung im 18. Jahrhundert (Leipzig; Dresden: Peters Edition, 1984), 95–101. There are two commonly used variants of his surname: Schwanberg (BD II, 239, the form he used to sign his name), and Schwanenberger (BD II, 224 and 248). Private account records from this period are rare, but occasionally turn up, e.g. Andrew Talle, ‘Die kleine Wirthschafft Rechnung von Carl August Hartung’, BJ (2011), 51–80.

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135

Table 5.1 Numerical structure of the Six Solos, Sonatas and Partitas, P 967 BWV Key 1001/1 1001/2 1001/3 1001/4 1002/1 1002/2 1002/3 1002/4 1002/5 1002/6 1002/7 1002/8 1003/1 1003/2 1003/3 1003/4 1004/1 1004/2 1004/3 1004/4 1004/5 1005/1 1005/2 1005/3 1005/4 1006/1 1006/2 1006/3 1006/4 1006/5 1006/6 1006/7

Work

Movement

G minor Sonata 1 Adagio Fuga Allegro Siciliana Presto B minor Partita 1 Allemanda Double Corrente Double Presto Sarabande Double Tempo di Borea Double A minor Sonata 2 Grave Fuga Andante Allegro D minor Partita 2 Allemanda Corrente Sarabanda Giga Ciaccona C major Sonata 3 Adagio Fuga Largo Allegro assai E major Partita 3 Preludio Loure Gavotte en Rondeau Menuet I Menuet II Bourée Gigue

Bar totals Movements Solos

Bars 22 94 20 136 24 24 80 80 32 32 68 68 23 289 26 58 32 54 29 40 257 47 354 21 102 138 24 92 34 32 36 32

2:1 22 94 20 136 24 24 80 80 32 32 68 68 23 289 26 58

B-A-C

2:1 272

B

408

A

396

32 54 29 40 257 47 354 21 102

412

C

138 24 92 34 32 36 32

524

388

2400 1600 : 800 B-A-C 1600 : 800 32

5:3 4:2

with a double bar line and repeat indication, are followed by eighty-four bars, at the end of which is a double bar after bar 92, and the instruction ‘da capo’. Had Bach omitted the da capo indication and written out the final eight bars, the movement would have had 100 bars (108 with repeats)

D

Repeats 22 94 20 272 48 48 160 160 64 64 136 136 23 289 52 116 64 108 52 [sic!] 80 257 47 354 21 204 138 48 8 108 68 64 72 64

2408 3453

136

demonstrations

instead of 92 bars.7 This would have destroyed the perfect numerical plan, although the 2408-bar total had biblical resonances.8 Even though she had no space limitations on the page Anna Magdalena reproduced Bach’s exact layout for this movement when she made the copy for Schwanberg.9

2 Perfect proportions at two or more layers of the structure The second characteristic of Bach’s revised collections is the presence of layers of parallel proportion. These will now be described in ascending order of magnitude. They exist simultaneously in the structure and unite the collection with a non-sounding eurythmia.

Proportions between movements of a work Table 5.2 shows the perfect 1 : 1, 1 : 2 and 2 : 3 proportions formed in the first work of the collection, the G-minor Sonata (BWV 1001). The opening Adagio has twenty-two written bars and no repeat. The following movement ‘Fuga’ has ninety-four bars with no repeats. The third movement, ‘Siciliana’, has twenty bars, ending with a double bar in the middle of the eighth stave. Either to avoid wasting space, or as a visual indication that the performer should proceed directly, Bach began the fourth and final movement ‘Presto’ on the same stave immediately after the double bar line of the ‘Siciliano’. The ‘Presto’ has 136 bars, in two sections with a double bar and repeat after bar 54, and a repeat after bar 136. Since both sections are repeated, the violinist plays 272 bars. There are 136 bars in the first three movements and 136 bars in the fourth, forming a 1 : 1 proportion in 3 : 1 movements. The proportions across this first solo become 1 : 2 in 3 : 1 movements when the repeats are observed. These proportions cannot be heard in real time as the speed and the pulse are different in the four movements; they are what Mattheson termed 7

8

9

NBA KB VI/1, 115. Even though Bach wrote 92 bars, 100 bars are given in NBA and BWV2a. Cumulative bar totals at a da capo indication can be found throughout St 162 (BWV 1014–19), copied by J. H. Bach and J. S. Bach. Bach’s interest in eschatology is suggested by a marginal annotation in his Bible on Daniel 12:12, where the year 2408 is underlined. See Leaver, J. S. Bach and Scripture: Glosses on the Calov Bible (St Louis: Concordia, 1985), 113, reproduction on 115. This parallel allusion may have been pleasing, but clearly Bach chose not to make it integral to his plan. It is a rare sample of how Bach wrote large numbers: as 2408 and not 2,408. Bach also retained the same layout when he transcribed it for lute in 1736/7 (BWV 1006a). NBA KB V/10, 161–71.

D

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137

Table 5.2 Proportioned pair: G-minor Sonata and B-minor Partita, P 967 BWV Movements Bars 1001/1 1001/2 1001/3 1001/4

Adagio Fuga Siciliana Presto

Totals

2:3

1:1

22 22 94 94 20 20 136 136

Bars*

22 94 20 136

272 272

136 : 136 2:1

1002/1 1002/2 1002/3 1002/4 1002/5 1002/6 1002/7

Allemanda Double Corrente Double Sarabande Double Tempo di Borea 1002/8 Double Totals

24 24 80 80 32 32 68

24 24 80 80 32 32 68

68

68

408

22 94 20 272

80

24 80

80 32

80 32

32

32

68 68 68

408 272 : 136 204 : 204 136 : 136

680 272 : 408

272 136 : 272 2:1

24 24

1:2 22 94 20

1:1

24

68

22 94 20 272

408 408 1:1

24 24 80 80 32 32

1:2

48 48 160 160 64 64

48 48 160 160 64 64 136

48

48

136

136

816

816 544 : 272 408 : 408 272 : 272

48 160

48 160

160 64

160 64

64

64

136 136 136

1224 408 : 816

harmonia propriè.10 That a composer as great as Bach created inaudible proportions runs counter to both our twenty-first century idea of Bach the virtuoso performer and to our modern cognitive bias. However, the early eighteenth-century view of music was different. Non-sounding Harmony of this kind was self-evident to Bach and his contemporaries. The first Partita in the collection, the Partita in B minor (BWV 1002), has eight movements, structured as four movements each with a Double of exactly the same length and form as its corresponding movement. All eight movements are repeated. The Allemande and its Double have twenty-four bars each, both of which are divided into two twelve-bar sections, to form a 1 : 1 proportion of 12 : 12 bars. The eighty-bar Corrente and its Double are also divided into two parts, with the division at bar 32, thus creating a 2 : 3 proportion with 32 : 48 bars. The thirty-two bar Sarabande and its Double are divided at bar 8, thus forming a 1 : 3 proportion with 8 : 24 bars. The

Appendix, 1717-I.

1:1

48 48 160 160 64 64 136

* including repeats

10

1:1

136

138

demonstrations

Table 5.3 Proportion in Partita 3 in E major, P 967 BWV

Movements

Bars

1006/1 1006/2 1006/3 1006/4 1006/5 1006/6 1006/7

Preludio Loure Gavotte en Rondeau Menuet I Menuet II Bourée Gigue

138 24 92 34 32 36 32

138 24

388

194 : 194

Totals

1:1

Repeats

92 34 32 36 32

138 48 116 68 64 72 64 570

Tempo di Borea and its Double are divided into two sections of 20 and 48 bars. As every section of every movement in this Partita is repeated, the layers of proportion remain identical whether or not the repeats are observed. Table 5.2 shows several of the many different 1 : 1 and 2 : 1 proportions in this B-minor Partita. The first six movements (three movements and their respective Doubles) have 272 bars, and the final two movements, Tempo di Borea and its Double, 136 bars, thus forming an overall 2 : 1 proportion, with and without repeats. Note that Bach made the first six and the final two movements a multiple of 136 bars, exactly as he structured the G-minor Sonata. Several obvious 1 : 1 proportions are formed between parent movements and their Doubles, both with and without repeats. The numerical precision between the structures of the G-minor Sonata and B-minor Partita, caused by their common base of 136 bars, must have been planned in advance, either together or after the structure of one was established. Evidence from Kellner’s copy of the solos strongly suggests that Bach planned the B-minor Partita after he had completed the G-minor Sonata.11 The sixth solo, the Partita in E major (BWV 1006) is the only other work in this collection to have a proportion between movements. Table 5.3 shows that the 194 written bars of the three outer movements form a 1 : 1 proportion with 194 written bars of the remaining four movements – a symmetrical ‘proportion in figure’,12 typical of Bach’s ordering. As numerous combinations of seven random numbers between 24 and 138 can create a 1 : 1 proportion, this result with 194 : 194 bars could easily be dismissed as arithmetical coincidence. However, as 1 : 1 and 1 : 2 11

See Table 5.14.

12

See Figure 2.2.

Three collections for strings

proportions formed in this way are seen repeatedly in Bach’s scores, this proportion may also have been planned. Bach’s lute transcription of the E-major Partita (BWV 1006a), c. 1736/7, has an additional bar at the end of the Preludio,13 bringing the 34 movement to a close with a full dotted minim in bar 139. The space and regularity of this final phrase gives the impression that the earlier violin version is missing a concluding bar, ending as it does on the third beat of bar 138, and disturbing the progressio arithmetica. Single-bar adjustments of this type are typical of Bach’s revision process, and, as Eppstein observed,14 frequently made to the final work of a collection. The absence of final bar 139 in his violin version from 1720 might indicate that Bach shortened it in the interests of creating a perfectly proportioned structure across the collection of Six Solos.15

Proportions between works in a collection Due to the common denominator of 136 bars between the first sonata and the first partita, a proportion between the two was bound to occur. Table 5.2 shows the double 2 : 3 and 1 : 2 proportions formed respectively by the 272 written bars and four movements of the G-minor Sonata and 408 written bars and eight movements of the B-minor Partita. When the repeats are observed the bar count changes to 408 and 816 bars, forming a further double 1 : 2 proportion in 4 : 8 movements in 408 : 816 bars. The precision of these figures is striking. Just one more bar or phrase in any of the twelve movements and this double proportion would be lost. It is a perfect example of eurythmia between movements, illustrating Mattheson’s fifth rule of loveliness ‘to observe well the proportion of all parts, terms and divisions’.16 As he revised his material to create a proportioned collection of six, Bach must have begun by organising the numerical unity between the newly composed B-minor Partita and the G-minor Sonata.

13

14

15

16

NBA KB V/10, 161–71. Autograph. Musashino Music School, Tokyo: J-Tma Littera rara, vols. II–XIV. H. Eppstein, ‘Fragen der Ordnungsprinzipien in Bachs Köthener und Leipziger Instrumentalsammlungen’, in Leipziger Beiträge zur Bach Forschung, ed. U. Leisinger. (Hildesheim: Olms, 2002), 131–5. Bach’s reuse of the 138-bar version in his 1731 transcription for organ from BWV 29/1, Sinfonia, P 166, may seem to contradict this, until one realises that BWV 29 too is a revised work, with a dated autograph score, several layers of proportion in its written 572 bars (138 : 138 and 286 : 286), and exactly 700 bars with repeats. Mattheson, Capellmeister, part II, chapter 5, §52, 141.

139

140

demonstrations

Table 5.4 Two-violin collections. Double 2 : 1 proportions 1600 : 800 bars, 4 : 2 solos, B-A-C key pattern Six Solos for Violin, BWV 1001–6 BWV Key

P 967

1001 1002 1003 1004 1005 1006

Sonata 1 Partita 1 Sonata 2 Partita 2 Sonata 3 Partita 3

Totals

G minor B minor A minor D minor C major E major

Bars 272 408 396 412 524 388

Six Sonatas. BWV 1014–19

2:1 272 408 396

B-A-C BWV Key 408 396

412 524

524 388

1014 1015 1016 1017 1018 1019

B minor A major E major C minor F minor G major

2400 1600 : 800 1328

P 229 Sonata 1 Sonata 2 Sonata 3 Sonata 4 Sonata 5 Sonata 6

Bars 328 419 397 477 403 376

2:1 328 419

B-A-C 328 419

397 477

477 403

376

2400 1600 : 800

Proportions across the collection as a whole The next layer of proportion is a large-scale double 2 : 1 proportion coexisting across the collection as a whole. Table 5.4 shows that four of the Six Solos have exactly 1600 bars and the remaining two have 800 bars, i.e. 4 : 2 solos in 1600 : 800 bars. The formation of a proportion with non-consecutive sections was described by Puttenham as a ‘proportion by situation’. The signatorial B-A-C is formed consecutively in the 1600-bar block by the keys of three of the four solos, which create the potentially self-referential bar totol of 1328 bars (A-C-B-H). The probability of six terms between 272 and 524 falling randomly into a perfect double 2 : 1 proportion is minimal. Bach must have planned it.

Proportions between two collections The largest-scale proportion to be seen in Bach’s publications is that between two or more related collections. Two collections form large-scale proportions with the Six Solos. The first is the Six Sonatas for violin and harpsichord (BWV 1014-1019) in its third and final version, copied by Johann Christoph Altnickol (1720-59), P 229. Table 5.8 shows that it has exactly 2400 bars, and an overall double 2 : 1 proportion across the collection identical to that seen across the Six Solos. Many scholars have assumed that the collection of six solo Cello Suites was intended as Bach’s Libro Secondo to complement the Six Solos collection for which Bach inscribed Libro Primo on the title page. Anna Magdalena Bach did indeed copy both the Cello Suites and the Six Solos for violin together, with Schwanberg’s title page for them, assigning them as ‘Pars 1’

Three collections for strings

and ‘Pars 2’. The numerical results suggest that the Cello Suites may also have been related to the Six Solos with a 3 : 2 : 1 proportion in 2400 : 1600 : 800 bars, Table 5.16. However, as the Six Sonatas are such an exact numerical and structural parallel to the Six Solos, I suggest that Bach intended the Six Sonatas for violin and harpsichord to be the primary matching collection, with the Cello Suites as a possible Libro Terzo.

3

A recognisable signature formed by the key patterns or bar totals

The third characteristic in Bach’s revised collections is the presence of a selfreferential allusion either in the total number of bars or in the overall key pattern. In both the Six Solos and the Six Sonatas the signature is formed by the key patterns rather than by emblematic numbers. In each case the B-A-C pattern17 can be clearly seen when the 1600 bars of the 2 : 1 proportion are grouped together, rather than in the final order of the collections. It has been suggested that Bach deliberately used forty-one sides of music for the Six Solos as an allusion to the numerical value of one of his signature forms; ‘J. S. Bach’. However, had Bach intended this, he would surely have numbered each side of music,18 yet he did not. The parallel nonetheless exists.

Evidence of construction The three largest movements of the Six Solos, the Ciaccona from the D-minor Partita and the second movement fugues from the A-minor and C-major Sonatas, form a 900-bar unit or ‘building block’. Given the similar rational blocks in other Bachian collections it is very likely that Bach used this figure to help him expand the smaller unrevised five-solo collection into the larger-scale perfectly proportioned six-solo construction. The Ciaccona appears after the Giga, traditionally the final movement of a partita, as the fifth movement in an otherwise ordinary four-movement partita. Spitta wrote of this anachronism: [The chaconne] is longer than all the rest of the suite put together, and must not be considered as the last movement of it, but as an appended piece; the suite proper concludes with the gigue.19 17

18 19

Contrary to modern German practice, the pitch B♮ was named both ‘B’ and ‘H’ in Bach’s time. See p. 62 above. As he did in the Missa of the B Minor Mass in 1733, P 180. P. Spitta, Johann Sebastian Bach: His Works and Influence on the Music of Germany (1685–1750), trans. A. C. Bell and J. A. Fuller-Maitland. 3 vols. (London, 1884; reprint edn New York, 1951), vol. II, 95.

141

142

demonstrations

Table 5.5 Three massive movements form a 900-bar block: Evidence of construction? BWV

A minor

Bars

BWV

D minor

Bars

BWV

C major

Bars

1003/1 1003/2 1003/3 1003/4

Grave Fuga Andante Allegro

23 289 26 58

1004/1 1004/2 1004/3 1004/4 1004/5

Allemanda Corrente Sarabanda Giga Ciaccona

32 54 29 40 257

1005/1 1005/2 1005/3 1005/4

Adagio Fuga Largo Allegro assai

47 354 21 102

Total

Fuga

289

Ciaccona

257

Fuga

354

Total

900

The 900-bar block and the overall construction of the Six Solos gives an additional explanation for the positioning and length of the Ciaccona in the D-minor Partita. Table 5.5 shows the disproportion between the 257 bars of the Ciaccona and the 155 bars of the remaining four movements in the Dminor Partita. The same imbalance exists in the A-minor and C-major Sonatas, where enormous fugues dwarf the remaining movements. The Aminor Fuga has no fewer than 289 bars and the C-major Fuga 354 bars, each more than twice the length of the sum of its companion movements. There are no repeats in any of these three fugal movements. Violinist and audience cannot fail to notice their majestic dimensions, whether they are performed alone in the context of the individual sonata or partita, or as part of the whole collection. Their extraordinary length, the extensive changes Bach made as he expanded them, and their combined round total suggest that Bach used this 900-bar unit as he constructed the six-solo collection.

Kellner’s copy, P 804: an early version of the collections? A copy of five of the violin solos, with a title page dated 3 June 1726 and signed by Johann Peter Kellner, P 804,20 raises many questions about the evolution and chronological development of the Six Solos. Hausswald and Gerber, in their 1958 NBA edition of the collection consider that Kellner prepared his copy from a now-lost intermediary source, probably from five individual solos.21 More recently Russell Stinson has cast doubts over the authenticity of the five-solo collection,22 based on differences between 20 22

21 D-B Mus. ms. Bach P 804, fascicle 22. NBA KB VI/1, 34. R. Stinson, The Bach Manuscripts of Johann Peter Kellner and his Circle (Durham, NC: Duke University Press, 1989), 55–70.

Three collections for strings

P 967 and P 804, and because of Kellner’s reliability as a copyist, where ‘in certain instances he [Kellner] appears to replace readings with material of his own composition, obviously in hopes of arriving at a better text’,23 and ‘Kellner’s possible reasons for making these cuts [to the D-minor Chaconne] are, of course, not nearly as important as the realization that this variant, obviously corrupt, cannot be authentic Bach’.24 The nature of the differences is such, though, that most scholars still accept that the fugues in Kellner’s copy are Bach’s early versions.25 Compared with Bach’s autograph, P 967, Kellner’s copy is indisputably incomplete, missing the Allemande and Courante from Partita 2 and containing movements in which ‘bars are completely missing’.26 Turning this assumption on its head, the absence of the Allemande and Courante may be evidence rather that Bach had not completed these movements, and added them when he later revised the work. If one sees P 967 as an expansion of P 804, there is plentiful evidence, including the numerical, to suggest that Kellner had based his copy on a collection that Bach was in the process of compiling and revising. In his final version, P 967, Bach had expanded the G-minor Sonata by eight bars, adding seven bars to the Fuga and one bar to the Presto; and the E-major Partita by 124 bars, adding four new movements. He added material to the D-minor Partita and to all the fugal movements, including the Ciaccona,27and he reordered the solos adding the B-minor Partita (BWV 1002) between the G-minor and A-minor Sonatas. In both P 804 and P 967 the A-minor Sonata (BWV 1003) has exactly the same number of bars. Table 5.6 shows the numerical structure of Kellner’s copy, P 804. The first striking feature is the 1 : 1 proportion between the 264 bars of both the G-minor Sonata and the E-major Partita, a characteristic of Bach’s works in the construction rather than the final stages. Another striking feature is the almost perfect 1 : 1 proportion between the 790 bars in the four fugal movements and the remaining 787 (790) bars. The 1577-bar total is remarkably close to the self-referential figure 1580 (1577),28 thus very 23 24 25 26 27

Ibid., 57; referring to Kellner’s copies of other Bach works. Stinson, Kellner and his Circle, 65. Ibid., 65, referring to the G-minor and C-major fugues only; and NBA KB VI/1, 35. NBA KB VI/1, 20 (source D) and 34–5 in the detailed description of the sources. Sonata 1: 7 whole bars added to (34b–42) Fuga; 1 bar added to Presto; Sonata 3: 13 bars (187b– 200), 15 bars (256–70), 11 bars (276–88), 66 bars of recapitulation indicated with . Partita 1 (BWV 1006), Gavotte en Rondeau follows same pattern as P 967. Partita 2, Ciaccona: 94 bars added with interpolations at bars 21–4, 89–120, 126–40, 151, 177–216 and 241–4. In Kellner’s copy bars 85–6 cover 4 bars as the note values are semiquavers, not demisemiquavers. ‘Johann Sebastian Bach’ is 158 in the A=1 to Z=24 alphabet.

D

28

D

143

144

demonstrations

Table 5.6 Implicit 1 : 1 structure of a collection of Five Solos for violin, P 804 Key

P 804

Movement

G minor

Sonata 1

Adagio Fuga Siciliana Presto Grave Fuga Andante Allegro Adagio Fuga Largo Allegro assai [Preludio] Gavotte en Rondeau Menuet I Sarabande Giga Ciaccona

A minor

C major

Sonata 2

Sonata 3

E major

Partita 1[3]

D minor

Partita 2

Totals

5 Solos

18 movements

Bars 22 87 20 135 23 289 26 58 47 251 21 102 138 92 34 29 40 163 1577

Fugues

1 : 1 22

87

Bars 264

87 20 135 23

289

396 289

26 58 47 251

421 251

21 102 138 92 34 29 40

264

232

163

163

790

787 : 790

1577

nearly fulfilling two characteristics of proportional parallelism, and making the implied self-referential 790 : 790 structure too significant to ignore. Not only is it formed with four fugal movements, three of which would later create the larger 900-bar block in P 967, but the 790-bar total was a unit Bach was to choose for a 790 : 1580 construction in his greatest fugal collection, The Art of Fugue.29 The almost 1 : 1 proportion in P 804 may have no significance beyond indicating the point Bach had reached when he left the draft manuscript from which Kellner made his copy. In view of the later structure of P 967, 1600 : 800, it may be better to understand the 790 : 790 of P 804 as a step towards 800 : 800 bars. Although the score from which Kellner made his copy has not survived, the numerical structure of his version suggests that the original model was a now lost early or interim version of the collection, rather than five single sonatas which Kellner randomly grouped together. If Kellner’s copy is accepted as an early 18-movement five-solo collection, it would be

29

See Chapter 9, §II.

Three collections for strings

145

Table 5.7 Revised order, nomenclature and bar structure in the Six Solos, P 804 to P 967 J. S. Bach’s autograph score, Libro Primo, P 967

Kellner’s copy: Early version Order in P 804

– Bars

Sonata 1 (G minor) [Missing] Sonata 2 (A minor) A Sonata 3 (C major) C

264 0 396 421

+/ +8 +408 – +103

Subtotal Partita 1 (D minor) Partita 2 (E major)

272 408 396 524

2:1 272 408 396 524

B-A-C Reordered B A C

2:1

Sonata 1 (G minor) Partita 1 (B minor) Sonata 2 (A minor) Partita 2 (D minor)

272 408 396

Sonata 3 (C major) Partita 3 (E major)

524

388

1600 264 232

+148 +156

Subtotal Totals

Bars

412 388

412 388

412

800 1577

+823

2400 1600 : 800

instructive to recreate Bach’s revision method and trace how, with minimal alterations, he formed the perfectly proportioned six-solo collection. Table 5.7 shows that Bach disguised the structure of the earlier five-solo collection copied by Kellner, when he made his fair autograph copy of the Six Solos, P 967. Kellner’s copy placed the three sonatas first, G minor, A minor and C major, followed by the two partitas, in D-minor and E major. By making a few revisions (Table 5.7, col. 4) and adding a new solo between the first and second sonatas (Table 5.7, row 4) in the key of B minor, Bach was able to form a 1600-bar unit with a self-referential B-A-C pattern in the keys. Generating the unit of 800 bars required more major surgery on the Partitas in D-minor and E major. In summary, Bach’s collection of Six Solos, P 967, provides a perfect illustration of proportional parallelism: its 2400 bar total is a multiple of 100, there is an obvious reference to Bach’s name in the keys, and many layers of perfect proportions coexist in its structure. As has been seen, an even larger-scale layer of proportion can be formed between two collections. The title Libro Primo on the cover of P 967 implies that Bach envisaged a parallel collection or subsequent book to the Six Solos. Because a title page unites the solo cello and violin works, it is generally thought that the sister collection to the Six Solos was intended to be the Cello Suites. However, the numerical structures reveal a more intimate connection between the violin solos and the collection of the Six Sonatas for violin and harpsichord (BWV 1014–19).

1600 : 800

146

demonstrations

II Libro Secondo? Six Sonatas for Violin and Harpsichord Table 5.8 shows the numerical structure of Altnickol’s copy, P 229,30 of the Six Sonatas for violin and harpsichord (BWV 1014–19), with its 2400 bars, in which four Sonatas have 1600 bars and two have 800 bars, i.e. a double 2 : 1 proportion identical to that found in the Six Solos, strongly suggesting that Bach designed and intended the parallel between the two. Bach probably composed the Six Sonatas during his Cöthen period, 1717–23, although no original manuscript copy of the collection from that time has survived. The collection went through several developmental phases before he decided on the final version; revisions and changes made largely to the sixth sonata. The problems associated with the sixth sonata in this collection are well documented.31Adapting or composing the final work in a collection was one of Bach’s well-tried and tested methods of fine-tuning a numerical plan. Altnickol’s copy, P 229, Source A in the NBA edition, is universally considered to be Bach’s final version,32 and it is Altnickol’s copy that demonstrates the three characteristics of proportional parallelism, with a perfectly proportioned structure, two layers of which correspond exactly to that of the Six Solos. Altnickol could not have made this copy before 1747.33 Table 5.8 shows the multiples of 10 and 100 in the overall bar totals: 1790 written bars and 2400 bars when the repeats are included. This version of the collection has two layers of perfect proportion: the double 2 : 1 proportion seen in Table 5.8 with 4 : 2 Sonatas in 1600 : 800 bars, and the triple 1 : 1 : 1 proportion formed with the Six Solos, with 1 : 1 collections in 6 : 6 works, both with 2400 : 2400 bars. The earliest surviving score of the collection is a copy of the harpsichord part dating from c. 1725,34 St 162,35 largely in the hand of Johann Heinrich Bach.36 It contains all six sonatas37 and has a title page in Italian: Sei Sounate [sic] à Cembalo certato è Violino Solo, col Basso per Viola da Gamba accompagnata se piace Composte da Giov: Sebast: Bach. The bar total is given in eighteenth-century script at the end of each movement and at each double bar in this score.38 The violin part that originally belonged to the 1725 harpsichord part is missing, and has been replaced by a copy of the first four sonatas made by Schwanberg c. 1727–8.

30 33 35 37 38

31 32 D-B Mus. ms. Bach P 229. NBA KB VI/1, 141–2 and 200–12. NBA KB VI/1, 137. 34 Schulze, Bach-Überlieferung, 117. Schulze, Bach-Überlieferung, 115. 36 D-B Mus. ms. Bach St 162. NBA KB VI/1, 139, source E. Schulze, Bach-Überlieferung, 116. The scribe of the cumulative bar totals has not been identified.

Three collections for strings

147

Table 5.8 Bar structure of the Six Sonatas, BWV 1014–19 BWV

Key

Work

Movement

1014/1 1014/2 1014/3 1014/4 1015/1 1015/2 1015/3 1015/4 1016/1 1016/2 1016/3 1016/4 1017/1 1017/2 1017/3 1017/4 1018/1 1018/2 1018/3 1018/4 1019/1 1019/2 1019/3 1019/4 1019/5

B minor

Sonata 1

Adagio Allegro Andante Allegro Dolce Allegro Andante un poco Presto [Adagio] [Allegro] Adagio ma non tanto Allegro Largo Allegro Adagio Allegro

Totals

A major

Sonata 2

E major

Sonata 3

C minor

Sonata 4

F minor

Sonata 5

G major

Sonata 6

Allegro Adagio Vivace Allegro Largo Allegro Adagio Allegro 25 movements

Bars 36 101 29 61 38 92 29 115 34 144 65 119 36 109 60 118 108 60 27 148 69 21 62 21 88 1790

B-A-C

}

B

31

36 141 29 122 38 122 29 230 34 144 65 154 72 109 60 236 108 120 27 148 91 21 124 21 119

610

2400

40 61 A 30 115

C

Bars

35 36

118 60

22 62

Table 5.9 shows the changes Bach made to create the 1600-bar block and to form the B-A-C key signature. By the time Johann Heinrich Bach made his copy of the collection (BWV 1014–1019a), Sonatas 3 and 5 already had exactly 800 bars, and Sonatas 1, 2 and 4 were already in B minor, A major and C minor. This suggests that Bach had begun to revise the structure to make it parallel to the Six Solos, but had not finished the revisions. At this stage there was no overall proportion. Table 5.9 shows the 2540 bars in St 162, with 1740 bars in four sonatas and 800 bars in the remaining two, counting the repeats and da capos. Bach chose to keep five of the sonatas identical in length and to make radical changes only to the sixth in the collection. Table 5.10 shows the six movements and 516 bars originally in the G-major sonata. To make the collection conform

2:1 328

419

397

477

403

376

1600 : 800

148

demonstrations

Table 5.9 Early version of Six Sonatas St 162 compared to final version, P 229 BWV

Key

St 162

1014 1015 1016 1017 1018 1019a

B minor A major E major C minor F minor G major

Sonata 1 Sonata 2 Sonata 3 Sonata 4 Sonata 5 Sonata 6

Totals

Bars B A

Block

328 419 397 477 403 516

C

BWV

397 403 1019

2540

+/

P 229

– – – – –

328 419 397 477 403 376

140

800

2400

2:1 328 419 397 477 403 376 1600 : 800

Table 5.10 Changes to Sonata 6 to create 5 movements in 376 bars Final five-movement version, P 229

Early six-movement version, St 162 Bars

}

Bars

Changes

P 229

1 Presto 2 Largo 3 Cembalo solo 4 Adagio 5 Violin solo 6 Presto ab initio

69 21 116 17 32 69

22

32 22

91 21 232 17 64 91

Same Same Replaced Replaced Replaced Omitted

91 21 124 21 119 –

Totals

324

192

516

116

376

to a double 2 : 1 proportion with 1600 : 800 bars in 4 : 2 Sonatas, Bach needed to shed 140 bars. Such a radical cut is extremely rare in Bach’s revisions – he almost always increased the length of his structures. Rather than making time-consuming revisions, he chose in this case to retain the first two movements, and replace the third, fourth and fifth movements so that it became a five-movement sonata with 376 bars. Table 5.11 shows the many structural proportions and parallels this revision created between the Six Solos and the Six Sonatas. Included in the comparison is the Italian title page in Johann Heinrich Bach’s hand in St 162, which is similar in form and wording to Johann Sebastian Bach’s own Italian title page for the Six Solos. Altnickol’s copy, P 229, lacks an original title page.39 39

NBA KB VI/1, 137. The German title page in a later hand reads: ‘Sechs Trios fürs Clavier und die Violine Hm–Ad–Ed–Cm–Fm–Gd von Johann Sebastian Bach’.

Three collections for strings

Table 5.11 Parallels between two violin collections. P 967 and P 229 Six Solos P 967

Proportions

Six Sonatas P 229

2400 bars 1600 : 800 bars 4 : 2 works B-A-C in 1600-bar block Italian title page Solo

1:1 2:1 2:1

2400 bars 1600 : 800 bars 4 : 2 works B-A-C in 1600-bar block Italian title page (St 162) Duo

1:1 1:2

The case of the Six Sonatas demonstrates how the theory of proportional parallelism can corroborate the status of a Bachian collection even when it lacks an autograph fair copy or a version published by Bach. The precision of the numerical structure in Altnickol’s copy, P 229, confirms the diplomatic source evidence that shows P 229 to be Bach’s latest version of the Six Sonatas. The numerical parallels add the further insight that Bach intended these two collections to be a complementary pair. On account of its perfected numerical structure and the documented source evidence, P 229 should be afforded the same status as one of Bach’s revised autograph scores. Bach named the Six Solos ‘Libro Primo’. Had he dictated the title page missing from Altnickol’s copy, it seems highly likely that it would have included the assignation ‘Libro Secondo’. Without deliberate design, the bar totals of any six works within a range of 272 and 524 bars in any musical collection are highly unlikely to form an exact double 2 : 1 proportion. It is even less likely that two large collections by the same composer would have an identical number of bars,40 let alone identical bar totals and proportions, each forming an exact double 2 : 1. These results surely demonstrate Bach’s compositional design. The structure of yet another collection for a solo stringed instrument, the six Cello Suites, also appears to be numerically related.

III

Libro Terzo? Six Suites for Cello

Bach’s autograph score of the six Cello Suites (BWV 1007–12) has not survived. The primary copy on which modern editions are based, P 269,41 was prepared by Anna Magdalena Bach for Georg Heinrich Ludwig 40 41

The results are remarkable, even though one set includes repeats and the other does not. D-B Mus. ms. Bach P 269.

149

150

demonstrations

Schwanberg (1696–1774).42 The watermarks indicate that the batch of paper she used was the same as her husband used between autumn 1727 and winter 1731.43 It is thought that Bach compiled the collection in Cöthen before 1720, and that he may have composed some of the suites when he lived in Weimar.44 In this section the numerical structure and the characteristics of proportional parallelism will help ascertain the extent to which Bach had revised and perfected the collection of cello suites to a publication-ready state when Anna Magdalena made the copy. Anna Magdalena’s copy of the Six Solos, P 268, and her copy of the Cello Suites, P 269, were originally a single two-part set. A comparison between P 268, and Bach’s autograph manuscript, P 967, shows how carefully Anna Magdalena emulated her original model when she copied the violin solos. Following the same line, scholars have therefore surmised that her copy of the Cello Suites ought to be relatively true to Bach’s lost original, yet found it wanting.45 Schulze cites her erroneous misnaming of the Allemande (BWV 1011/2) as Courante, and the unusual comment La Fin. des Suixttes, as examples that must have deviated from Bach’s original, a trait of her copying that caused Bach to check her work.46 Other anachronistic features in her score that modern editors assume to be copying errors include (1) clear repeat indications in movements traditionally not repeated, (2) the inaccurate flow of slurs, and (3) her omission of the literal da capo indication after Bourée 2 in the fourth suite, interpreting her Verte as an indication to turn back to Bourée 1.47 Bach’s assignation ‘Libro Primo’ in the title page of the Six Solos implies that it was to be the first part of a comprehensive project.48 Anna Magdalena’s copies of the solo collections for violin and cello, P 268 and P 269, were given a united title page by Schwanberg, who used the words ‘Pars 1’ and ‘Pars 2’, which has since been interpreted to mean that Bach intended the two solo collections to belong together. The precision of the numerical correlation between the final version of the Six Sonatas, P 229, and the Six Solos, seen above, strongly suggests that Bach saw the Six Sonatas as part of a large-scale two-part set. The following discussion of the numerical structure of the Cello Suites will shed light on the extent to which this collection too may have been revised to integrate a third collection into the string collections project.

42 44

45 48

43 Schulze, Bach-Überlieferung, 96–101. Ibid., 97. J. Butt, ‘Cello Suites’, in J. S. Bach, ed. Malcolm Boyd. Oxford Composer Companions (Oxford University Press, 1999). 46 47 NBA KB VI/2, 27. Schulze, Bach-Überlieferung, 97 and 100. NBA KB VI/2, 77.

NBA KB VI/2, 18.

Three collections for strings

Evidence from the score Table 5.12 shows the numerical structure of the six Cello Suites P 269, with 1975 written bars and 140 bars of da capo, which brings the total to 2115 bars, and 4000 bars when all the repeats and da capo indications are included. The shaded column shows a clear double 2 : 1 proportion within the 2115 bars, with 4 : 2 Suites in 1410 : 705 bars. The pattern of the keys, D-C-E♭, is in the same intervallic relationship as the self-referential B-A-C, although a minor third higher; some may wish to see this as a signatorial reference. But it is when all the repeats that Anna Magdalena included are counted that the total becomes 4000 bars and the collection seen to be in perfect numerical relationship with the two violin collections. The 4000 bars can be seen only when Anna Magdalena’s repeat instructions are followed precisely, including the curious repeats she marked for the preludes of suites 2, 3, 4 and 5, even though they make little musical or editorial sense. Repeats in the movements marked with a da capo are not observed, as seems to have been customary; and the dal segno indication of Gavotte 1 (BWV 1012/5) is followed literally, so that the opening 4-bar refrain is repeated every time it is performed (i.e. 8 + 16 + 8 + 16 + 8 bars), hence 56 and not 48 bars.49 In addition to the possible selfreference in the key relationships, the G-major Suite has 410 performed bars, which may be an allusion to Bach’s name. There are also several layers of perfect proportion in the structure which, combined with the double 2 : 1 structure in 1410 : 705 bars, suggest that P 269 was a faithful copy of Bach’s lost original, and that the original had been numerically revised. Table 5.13 shows the proportional planning within the D-major Suite (BWV 1012). It has a 1 : 1 : 1 structure in 3 : 2 : 2 movements in blocks of 200, and a 1 : 1 proportion in the first three movements, 144 : 144 bars. This numerical ordering demonstrates that Bach understood Mattheson’s fifth rule of charm, ‘the precise observation of the correct proportion of all parts of a melody with one another’.50 Its many units of multiples of 200 bars strongly indicate compositional revision. Unfortunately no early version of the cello collection has survived. However, traces of evidence in the numerical structure suggest an earlier plan, and

49

50

Many modern scores adopt a rational layout of this Gavotte, disguising the performance implication by removing the four-bar refrain indicated by Anna Magdalena’s (presumably also Bach’s original) dal segno symbol. Mattheson, Capellmeister, 155.

151

152

demonstrations

Table 5.12 Bar structure of Cello Suites: 1975, 2115 and 4000 bars BWV Key 1007/1 1007/2 1007/3 1007/4 1007/5 1007/6 1007/5 1007/7 1008/1 1008/2 1008/3 1008/4 1008/5 1008/6 1008/5 1008/7 1009/1 1009/2 1009/3 1009/4 1009/5 1009/6 1009/5 1009/7 1010/1 1010/2 1010/3 1010/4 1010/5 1010/6 1010/5 1010/7 1011/1 1011/2 1011/3 1011/4 1011/5 1011/6 1011/5 1011/7 1012/1 1012/2

Suite Movement

Bars

Prélude Allemande Courante Sarabande Menuet 1 Menuet 2 Menuet 1 Gigue Prélude Allemande Courante Sarabande Menuet 1 Menuet 2 Menuet 1 Gigue Prélude Allemande Courante Sarabande Bourée 1 Bourée 2 Bourée 1 Gigue Prélude Allemande Courante Sarabande Bourée 1 Bourée 2 [Bourée 1 Gigue Prélude Allemande Courante Sarabande Gavotte 1 Gavotte 2 Gavotte 1 Gigue Prélude Allemande

42 32 42 16 24 24

G major 1

D

D minor 2

D

C major 3

D

E♭ major 4

D]

C minor 5

D

D major 6

D

Bars

2:1

238

238

295

295

408

408

24 34 63 24 32 28 24 24 24 76 88 24 84 24 28 24 28 108 91 40 64 32 48 12

329

[48] 42 223 36 24 20 36 22

469

36 72 104 20

376

469

Bars*

42 64 84 32 48 48 24 68 126 [AMB] 48 64 56 48 48 24 152 176 [AMB] 48 168 48 56 48 28 216 329 182 [AMB] 80 128 64 96 24 48 84 446 [AMB] 72 48 40 72 44 36 144 376 104 40

Totals D-C-Eb 410

566

D

788

C

706

E♭

902

C

628

D

Three collections for strings

153

Table 5.12 (cont.) BWV Key

Suite Movement

1012/3 1012/4 1012/5 1012/6 1012/5 1012/7

Courante Sarabande Gavotte 1 Gavotte 2 Gavotte 1 Gigue

D

Totals

Bars

D

Bars

2:1

72 32 28 20/4

Bars*

Totals D-C-Eb

144 64 56 56 28 136

28 68

1971/5 140[88] 2115 1410 : 705 4000

4000

* including repeats

Table 5.13 Evidence of proportional planning in BWV 1012 Including Anna Magdalena’s repeat indications, P 269 BWV

Movement

Bars

1012/1 1012/2 1012/3 1012/4 1012/5 1012/6 1012/7

Prélude Allemande Courante Sarabande Gavotte 1 Gavotte 2 Gigue

104 40 144 64 56 56 136

104 40

136

56 136

600

200 : 200 : 200

200 : 400

Totals

1:1:1

1:2 104 40

144 56

104 40 144 64

64

144

56 56

imply that the 4000-bar version was an intermediate solution before Bach had time to create a more perfect parallel to the Six Solos and the Six Sonatas.

(a)

1:1

A 4000–bar structure and many layers of perfect proportion

The bar totals of the six suites do not fall into large-scale proportion, either in the configuration 3 : 3 or 4 : 2 suites. However, Table 5.14 shows that when the collection is viewed by movement, the bar totals form a largescale double 1 : 1 proportion with 4 : 4 movements and 2000 : 2000 bars. The Gigue movements have exactly 800 bars. and these form a second layer of proportion with the 1200 bars of Courantes, Menuets/Gavottes/Bourées

144 : 144

154

demonstrations

Table 5.14 A double 1 : 1 proportion in 4000 bars formed between movements Including Anna Magdalena’s repeat indications, P 269 Movements in BWV 1007–12

Bars

1:1

2:3

1. 2. 3. 4. 5. 6.

Préludes Allemandes Courantes Sarabandes Menuets/Gavottes/Bourées 1 Menuets/Gavottes/Bourées 2 Da Capo of Menuets/Gavottes/Bourées 1 7. Gigues

1076 352 636 304 376 268 188 800

1076 352

Totals

4000

2000 : 2000

636

636

376

376

304 268 188 800

188 800 800 : 1200

Table 5.15 Large-scale 3 : 2 proportion with 2400 : 1600 bars across movements Including Anna Magdalena’s repeat indications, P 269 BWV 1007 1008 1009 1010 1011 1012

Prélude Allemande Courante Sarabande Men/1 Men/2 42 126 176 182 446 104

64 48 48 80 72 40

84 64 168 128 48 144

32 56 48 64 40 64

48 48 56 96 72 56

48 48 48 24 44 56

Totals 1076

352

636

304

376

268

D 24 24 28 48 36 28

Gigue Bars

Totals

68 152 216 84 144 136

(368) (440) (612) (524) (456) 2400 1600

188 800

4000

1 and their repeat after Menuets/Gavottes/Bourées 2. Further parallel layers of proportion can be found within movement types.

(b) Layers of proportion within 4000 bars: 1600 : 2400. Table 5.15 shows a second large-scale proportion in the 4000 bars: 2400 bars in the shaded area and 1600 bars formed by the 1076 bars of Préludes and the 524 bars of the sixth suite (BWV 1012), excluding the 104 bars of Prélude already counted. Bach must have adapted the preludes and the sixth suite to achieve this exact total. Of all the movements in this

Three collections for strings

Table 5.16 Compositional blocks and proportions within the Cello Suites 2400 : 1600 bars Including Anna Magdalena’s repeat indications, P 269 BWV 1007/1 1008/1 1009/1 1010/1 1011/1 1012/1–7 Totals

Bars 42 126 176 182 446 628 1600

1:3 42 126 176 182 446 628

BWV 1007/2–7 1008/2–7 1009/2–7 1010/2–7 1011/2–7

400 : 1200

Bars 368 440 612 524 456

1:1 368 612 524 456 980 : 980

2400

collection, it is the opening preludes that display the greatest compositional diversity and thus offered Bach the greatest freedom as he strove to reach a specific bar total.51 Table 5.16 shows this more clearly, with the Préludes in Suites 1–5 and the 628 bars of Suite 6 making 1600 bars, which contain another layer of double proportion with 3 : 3 groups in 400 : 1200 bars. The next column shows how movements 2–7 of Suites 1–5 have 2400 bars, and a double 1 : 1 proportion with 980 : 980 bars. These two large-scale 2 : 3 proportions in 1600 : 2400 bars, several smaller layers of proportion, and an implied signature in both the keys and as the total of the G-major Suite (BWV 1007), suggest that this collection too had been numerically perfected. If these results show that Bach found a way of making the collection perfectly proportioned, even if it meant introducing repeats in preludes where none are expected, Anna Magdalena’s reputation as an inaccurate copyist needs to be reviewed.

Evidence of an early 1800-bar structure The collection has 1975 bars when the repeats are not observed: 1375 bars in Suites 1, 3, 5 and 6 (214, 380, 433 and 348 bars) and 600 bars in the D-minor and E flat-major Suites forming a building block typical of Bach’s numerical construction. This 600-bar block suggests that Bach may have originally planned an 1800-bar construction, with a double 1 : 2 proportion in 2 : 4 suites and 600 : 1200 bars. Such a structure would have formed a 51

J. Butt, ‘Cello Suites’.

155

156

demonstrations

Table 5.17 Speculative reconstruction exchanging BWV 1011/1 with a 48-bar Prelude Bars counted as written, i.e. without repeat or da capo indications BWV

Prélude Allemande Courante Sarabande Men/1 Men/2 Gigue Bars

1007 1008 1009 1010 1011 1012

42 63 88 91 48* 104

Totals 436

32 24 24 40 36 20

42 32 84 64 24 72

16 28 24 32 20 32

24 24 28 48 36 28

24 24 24 12 22 24

34 76 108 42 72 68

176

318

152

188

130

400

214 271 380 329 258* 348

2:1 214 271 380 329 258 348

1800 1200 : 600

3 : 4 proportion in 1800 : 2400 bars with the Six Solos, and 1 : 1 in 6 : 6 Solos : Suites. Table 5.17 shows that a 2 : 1 proportion is formed when the extensive 223-bar C-minor Prélude (BWV 1011/1) is replaced by a prelude with 48 bars. Although hypothetical, the possibility warrants further investigation. The 223-bar version of the Prélude from the Suite in C minor (BWV 1011) has survived in both P 269, and in an autograph transcription for lute (BWV 995) with a dedication to ‘Monsieur Schouster’.52 The watermarks and writing indicate that the lute transcription was made at exactly the same time as P 269, between autumn 1727 and winter 1731. Schulze suggests that Bach made the dedicated transcription spontaneously, intending to have a second fair copy made by someone, such as Anna Magdalena, before handing it over to the sponsor.53 If this was the case, it is highly likely that his wife would have had both the cello version and Bach’s lute transcription to hand when she made P 269. The C-minor Prélude of the fifth suite is more than twice the length of any of the other preludes in the collection. This discrepancy suggests that it did not originally belong to the collection, and was probably the means by which Bach generated the perfect 1600 : 2400 structure described above. Had the length of the C-minor Prélude been 48 and not 223 bars, as in Table 5.17, the 1800-bar collection would have an exact double 2 : 1 proportion with 4 : 2 suites in 1200 : 600 bars, matching the double 2 : 1 proportion in the Six Solos and in the Six Sonatas. Furthermore, Table 5.18 52 53

Bibliothèque Royale, Bruxelles. Ms II.4085 (Fétis Nr. 2910). Schulze, Bach-Überlieferung, 101.

Three collections for strings

Table 5.18 Perfect proportions in P 269 with a hypothetical 48-bar Prelude in BWV 1011 Bars counted as written, i.e. without repeat or da capo indications Movements 1. 2. 3. 4. 5. 6. 7.

Préludes* Allemandes Courantes Sarabandes Menuets/Gavottes/Bourées 1 Menuets/Gavottes/Bourées 2 Gigues

Totals

Bars 436* 176 318 152 188 130 400 1800

1:2

2:3

3:4

436* 176

436* 176 318 152

318 152

130

130

188

188

400

400

400 : 800

400 : 600

600 : 800

* indicates the hypothetical structure with a 48-bar prelude for the C minor suite

shows that it would have been proportioned movement-wise 1 : 2 : 3, with 400 bars of Gigues, 600 bars of Courantes, Sarabandes, and the second Menuets/Gavottes/Bourées, and 800 bars of Préludes, Allemandes and the first Menuets/Gavottes/Bourées, with 1 : 2, 2 : 3 and 3 : 4 proportions formed between the groups of movements. It must be emphasised that this is a hypothetical reconstruction and that no 48-bar cello Prélude in C minor has survived, although a copy of an undated 48-bar Prélude in E flat major for lute (BWV 998) from the 1730s has.54 Had BWV 998 originally been for cello in minor mode, it would have fitted perfectly into the implied 1800-bar plan. If Bach intended it to be copied into P 269, Anna Magdalena did not fulfil his primary wishes. It is not difficult to appreciate how a distracted copyist, however experienced, might have confused an instruction about two different lute preludes.55 If Bach checked Anna Magdalena’s work,56 and if he noticed the error, he let it stand. I suspect that this plausible and simple 1800-bar structure may have been the original plan for the Cello Suites, and that when the error had been noticed, practical expediency caused the last-minute introduction of repeat marks to the Préludes to create a perfectly proportioned collection for Schwanberg. 54 55

56

Ueno Gakuen College, Tokyo (J-Tuu). No callmark. Lute solo (BWV 998), copyist J. S. Bach. Bach himself seems to have done the same in 1739 when he made the error in P 28, the fresh score of the St John Passion. See Chapter 12. Schulze, Bach-Überlieferung, 97.

157

158

demonstrations

The perfection of the 2400 : 2400 parallel between the Six Solos and the Six Sonatas suggests furthermore that, although the collection of Cello Suites in its 4000-bar version of P 269 had been perfected, Bach may have wished to revise its alternative, written total of 1975 bars by adding a further 425 bars. To do this, he would probably have expanded several of the freely structured prelude movements to create a simpler double 2 : 1 structure in 1600 : 800 bars and 4 : 2 movements, relating it more perfectly to the two violin collections, just as he expanded the early fugal movements in the Six Solos. I suggest therefore that, because of the perfect numerical parallel between the Solos and Sonatas, and the title-page association between the Solos and the Suites, Bach’s 4000-bar solution was an intermediate one for the Cello Suites, left in the hope of a final revision that never materialised. Although Bach composed other works for stringed instruments, some of which have survived in his handwriting, none besides these three were compiled and left as best fair copy collections. Proportional parallelism demonstrates the intentional perfection of the structure of each collection, despite the proposed interim solution of the Cello Suites. Furthermore, the numerical evidence confirms that the copies by Altnickol, P 229, and Anna Magdalena, P 269, represent Bach’s wishes faithfully, and that, aside from surface blemishes in the orthography, they bear the same numerical characteristics as an autograph manuscript, or publication overseen by Bach. The clues to Bach’s handiwork, implied in the constructional order of Kellner’s copy of the Five Solos, also show that P 804 is far more than a random collection of five works for solo violin. There will always be those who desire an explanation or interpretation of the specific numbers that recur in these three related collections: 400, 800, 900, 1600, 2400 and 4000.57 Although a parallel meaning could be found for every number in these collections, it would be inconsequential compared with the eternal significance of the Harmony in Bach’s exquisitely executed layers of 1 : 1 and 2 : 1 proportions.

57

See J. ab Unterberg, Tractatus Historicus . . . Tractatus Philosophicus . . . Tractatus Theologicus De Mystagogia, sive de Mysteriis Numerorum (Augsburg: Klugheimer, 1734) for a contemporary interpretation of numbers.

6 Four in two collections for keyboard

Well-Tempered Clavier Book One (BWV 846–69) Inventions and Sinfonias (BWV 772–801) Clavier Übung Part I (BWV 825–30) Clavier Übung Part II (BWV 831 & BWV 971) Wann ich dann von unterschiedlichen Freunden, wie solche harmonia einzurichten sey, bin ersuchet worden, und ich meinem Nechsten mit der Gabe so mir Gott gegeben hat, zu dienen mich schuldig befinde: so habe nicht allein die Vortheile zum Bau diese harmoniae, sondern auch die Grundsätze zur Composition insgemein durch Mathematische demonstrationes, Gott zu ehren, und meinem Nechsten zum Nutz heraus zu geben nicht unterlassen können. A. Werckmeister, 1701

The subject of this chapter is four collections for keyboard instruments. The first two have their origins in Cöthen or possibly earlier, and were revised and polished around the time the Bach family moved to Leipzig in 1723. The second two collections were born, revised and published amidst the intensity of Bach’s first twelve years in Leipzig.

I

Ingenious keyboard instruction – the first 3120

In 1722 Bach made a neat hand copy, P 415,1 of what would become the first book of the forty-eight preludes and fugues. Its ornate title page reads: [Das Wohltemperirte Clavier] The Well-Tempered Clavier, or preludes and fugues through all the tones and semitones, both as regards the tertia major or Ut Re Mi and as concerns the tertia minor or Re Mi Fa. For the use and profit of the musical 1

D-B Mus. ms. Bach P 415.

159

160

demonstrations

youth desirous of learning as well as for the pastime of those already skilled in this study … Anno 1722.

The Well-Tempered Clavier, Book 1 (hereafter WTC I) has 2088 bars in forty-eight movements: twenty-four preludes and twenty-four fugues ordered systematically with one major and one minor prelude-and-fugue pair for each semitone of the diatonic scale in ascending key order beginning with C major. Bach numbered the movements sequentially, Praeludium 1, Fuga 1, Praeludium 2 Fuga 2 and so on. The single repeat indication in the collection is at the end of Prelude 24 in B minor, where the 47 written bars are performed as 94 bars. This gives an alternative total of 2135 bars, a figure that could be a parallel allusion to Bach’s name: 2-1-3 as B-A-C. Table 6.1 shows the bar total for each movement of the work in the order they appear in Bach’s autograph score, P 415, giving the cumulative total for the preludes, for the fugues, and for each prelude-and-fugue pair. The shaded columns show the symmetrically arranged 1 : 1 proportion within this overall total, and how each group of 1044 bars divides into further layers of perfect proportion. The symmetrical arrangement of the 1 : 1 proportion in 1044 : 1044 bars may have been designed, although with twenty-four terms the probability of a 1 : 1 proportion forming naturally is fairly high. Table 6.1 also shows the large-scale double proportion between the 696 bars of preludes and fugues in the keys of C♯, E♭ and A♭ major and the remaining 1392 bars, with 1 : 2 in the 696 : 1392 bars, and 1 : 3 in the 3 : 9 prelude-and-fugue pairs. There is also a block of 500 bars formed by the prelude-and-fugue pairs in the keys of B, A and C major, which may also have been a deliberate allusion to his name. Bach’s handwritten figure 27 at the end of the 27-bar Fugue in C major (BWV 846) shows that he was aware of the number of bars in this manuscript. The collection went through various stages of revision, beginning life as a group of preludes, some of which can be found in the 1720 ClavierBüchlein for Wilhelm Friedemann, Bach’s eldest son. Wilhelm Friedemann was born in 1710, and was a Weimar boy until shortly after his seventh birthday, when the family uprooted to Cöthen. He needed excellent musical training if he was to follow in his father’s footsteps as a virtuoso keyboard player and composer. Perhaps conscious of his own lack of paternal instruction at this age,2 and unsure how many years he had left 2

Johann Sebastian was a day short of nine years and eleven months when his fifty-year-old father died. Wilhelm Friedemann was nine years and ten months when the Clavier-Büchlein was begun.

Table 6.1 Structure of WTC I. Autograph score. P 415 BWV Key

Title

846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869

Praeludium Praeludium Praeludium Praeludium Praeludium Praeludium Praeludium Praeludium Praeludium Praeludium Praeludium Praeludium Praeludium Praeludium Praeludium Praeludium Praeludium Praeludium Praeludium Praeludium Praeludium Praeludium Praeludium Praeludium

Totals

C major C minor C♯ major C♯ minor D major D minor E♭ major E♭ minor E major E minor F major F minor F♯ major F♯ minor G major G minor A♭ major G♯ minor A major A minor B♭ major B♭ minor B major B minor

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Bars

Title

35 38 104 39 35 26 70 40 24 41 18 22 30 24 19 19 44 29 24 28 20 24 19 47

Fuga 1 Fuga 2 Fuga 3 Fuga 4 Fuga 5 Fuga 6 Fuga 7 Fuga 8 Fuga 9 Fuga 10 Fuga 11 Fuga 12 Fuga 13 Fuga 14 Fuga 15 Fuga 16 Fuga 17 Fuga 18 Fuga 19 Fuga 20 Fuga 21 Fuga 22 Fuga 23 Fuga 24

819

Bars

Total

27 31 55 115 27 44 37 87 29 42 72 58 35 40 86 34 35 41 54 87 48 75 34 76

62 69 159 154 62 70 107 127 53 83 90 80 65 64 105 53 79 70 78 115 68 99 53 123

1269

2088

1:1 62 69 159 154 62

1:1

1:1

2:1

62

131

69 159

131 313

154 62 70 107 127 53 83 90

80

B-A-C-H

132 70 107 127 53

234 136

83 90

170

80 65 64 105 53 79 70 78

115 68 99 53 123 1044 : 1044

65 64 105 53 79

129 158 149

70 78

193

193

115 68

167

53 123

176

99

522 : 522

522 : 522

1392 : 696

176 500

162

demonstrations

to train his own generation of Bach musicians, Johann Sebastian decided to create a special book of keyboard music for his 9-year-old son, writing on the cover: Clavier-Büchlein vor Wilhelm Friedemann Bach angefangen in Cöthen den 22. Januari Ao. 1720.3 The Clavier-Büchlein (US-NH Deposit 31) contains meaty material for a child, and one can easily imagine the pedagogical rigour that accompanied the examples. The original paper has uniform watermarks, and as none of the entries are dated it is difficult to state with any accuracy when they were written into the book – the handwriting suggests it was added to regularly until about 1723.4 Wilhelm Friedemann had the 148-page book rebound in Halle in 1750, and consequently its original order is disguised.5 The preludes, copied on consecutive pages (29–55) by father and son, seem to date from between 1721 and early 1722,6 just a few months before Bach extended and arranged them in a different order in his autograph copy, P 415.7 The lack of fugues and the extent of Bach’s revisions to the preludes between the early 1720 versions and his P 415, dated 1722, suggest that he did not start out with a plan for a collection of twenty-four prelude-and-fugue pairs,8 although copies of intermediate versions show how rapidly the conception of a collection of twenty-four preludes and fugues grew.9 Bernhard Christian Kayser (1705–58),10 one of Bach’s pupils, copied out the collection c. 1723, P 401, in a transitional version between the preludes in Friedemann’s ClavierBüchlein and Bach’s final polished version in P 415. Kayser’s manuscript included two movements not in WTC I (BWV 881/2 and the first fourteen bars of BWV 923), but otherwise the length of the preludes and fugues was identical to Bach’s final version, P 415, with the exception of two movements, the C-minor Prelude (BWV 847) and the B-flat major Fugue (BWV 867), both of which are one bar shorter than in P 415. Table 6.2 compares 3

4

5

6

7 9 10

US-NH Deposit 31, description in G. Herz, Bach Sources in America (Kassel: Bärenreiter, 1984), 87–100; facsimile images, 347–9. D. Schulenberg, The Keyboard Music of J. S. Bach, 2nd edn (New York; Oxford: Routledge, 2006), 162. NBA KB V/5. The Clavier-Büchlein is made up of a gathering of 9 quaternios, each consisting of four folios placed inside one another, and one binio, with 2 folios, one placed inside the other. Herz, Bach Sources in America, 88. D. Ledbetter, Bach’s Well-Tempered Clavier: The 48 Preludes and Fugues (New Haven: Yale University Press, 2002), 4, asks if there was originally a series of educational preludes without fugues. 8 NBA KB V/6.1, source A. Schulenberg, Keyboard Music, 200. Ibid., 30, source B0.1. F. Konswitschny. Formerly known as Anonymous 5. In 2003 Andrew Talle identified the scribe as Bernhard Christian Kayser. See Talle, ‘Nürnberg, Darmstadt, Köthen – Neuerkenntnisse zur BachÜberlieferung in der ersten Hälfte des 18. Jahrhunderts’, BJ 89 (2003), 134–72.

Four in two collections for keyboard

163

Table 6.2 Preludes, bar additions and order: Clavier-Büchlein, P 401 and P 415 Clavier-Büchlein

P 401 Kayser

Key

Order Bars 1/ Title

C major C minor C♯ major C♯ minor D minor D major Eb major Eb minor E minor E major F major F minor F♯ major F♯ minor

1 2 later later 3 4 later

Totals

5 6 7 later – –

24 27 104 39 15 18* – 35* 23 24 13* 18* – –

+11 +10 – – +11 +17 +70 +5 +18 – +5 +4 +30 +24

Praeludium Praeludium Praeludium Praeludium Praeludium Praeludium Praeludium Praeludium Praeludium Praeludium Praeludium Praeludium Praeludium Praeludium

Bars 1 2 3 4 5 6 7 8 9 10 11 12 13 14

35 37 104 39 26 35 35 70 70 40 41 24 18 22 30 24

1:1

P 415 1:1:1 35

35 40 41 24

545 105 : 105

18 22 30

1/ BWV

Blocks 35 37 104 39

26 35 70 70 40 41 24 18 22 30 24

70 : 70 : 70 330

215

the order and bar lengths of these three versions: the eleven preludes in Wilhelm Friedemann’s Clavier-Büchlein, their form in Kayser’s copy, P 401, and Bach’s fair copy, P 415. Bach retained the original length of only three of the preludes, extending the remainder in order to create a perfectly proportioned plan. Four of the preludes, marked *, were incomplete in the ClavierBüchlein. Additional bars are shown in the þ/ columns. The first fourteen preludes in Kayser’s copy, P 401, are proportionally ordered. There is a 1 : 1 proportion in 105 : 105 bars, which includes a 1 : 2 proportion in 35 : 70 bars, and a triple 1 : 1 : 1 proportion based on 70 bars. The fourteen preludes also fall into two rational blocks of 330 and 215 bars. Table 6.2 shows that at this intermediate stage, the D-minor and E-minor Preludes were positioned before the D-major and E-major Preludes, and that the C-minor Prelude had just 37 bars, rather than 38 bars in Bach’s revised version. Creating proportions and proportioned consecutive blocks as he developed a collection seems to have been typical of Bach’s expansion technique. The surviving material is unfortunately too patchy to reconstruct his procedure in detail. When he introduced the fugues to the collection in P 415, the proportions in the preludes based on 35 and 70 bars were not affected. Continuing

+1

846 847 848 849 851 850 852 853 855 854 856 857 858 859

164

demonstrations

to create consecutive blocks, he transformed the 545 bars in the fourteen preludes (P 401) into 1350 bars of fifteen prelude-and-fugue pairs, with a block of 810 bars in prelude-and-fugue pairs 1–8, and 540 bars in pairs 9–15. These large numbers would become integral to his large-scale proportional plan for the collection, shown in Table 6.5. Although Kayser’s intermediate version, P 401, contains the same preludes and fugues as Bach’s P 415, it lacks the perfection of Bach’s final numerical plan because in P 401 both the C-minor Prelude and the B-flat major Fugue are one bar shorter. When he came to devise the title page of WTC I he chose to incorporate Guidonian solmisation syllables Ut re mi and re mi fa which may indicate his solidarity with Buttstett’s views of eternal Harmony.11 While Bach was revising and refining WTC I, he was also working on a collection of two- and three-part keyboard works, completing a signed and dated fair copy, P 610, in 1723:12 Aufrichtige Anleitung, (Sincere/Frank/Honest Introduction) wherein the lovers of the clavier, and especially those desirous of learning, are shown a clear way not only (1) to learn to play clearly in two voices but also, after further progress, (2) to deal correctly with three obbligato parts; furthermore, at the same time not only to have good inventiones but to develop the same well and, above all, to arrive at a singing style in playing and at the same time to acquire a strong foretaste of composition.13

Table 6.3 shows that Aufrichtige Anleitung (AA) (BWV 772–801) has 1032 bars in fifteen two-part Inventions followed by fifteen three-part Sinfonias ordered systematically according to key.14 There are no ambiguous features to complicate the counting. As in WTC I, there is a single repeat indication in the collection. In Invention 6 (BWV 777) the 62 written bars become 124 performed bars if the repeat is observed, and the bar total of the Inventions is increased from 488 to 550 bars. However, the perfected numerical construction, with its layers of parallel proportions across both the WTC I and AA, is based on the number of written bars. The shaded columns of Table 6.3 show the many layers of proportion formed within the 1032 bars of the collection: a consecutive 1 : 1 proportion with 516 bars in the twelve outer movements and 516 bars in the central eighteen movements; a symmetrical double 1 : 1 proportion in a dovetail pattern in the central eighteen 11 12 14

Chapter 2; and D. Ledbetter, Bach’s Well-tempered Clavier (Yale University Press, 2002), 120–5. 13 D-B Mus. ms. Bach P 610, NBA KB V/3, 13–23, source A. NBR, Doc. 92. Schulenberg, Keyboard Music, 185–98. For the smaller-scale levels of construction of each Invention, see B. Haas and V. Diederen, Die zweistimmigen Inventionen von Johann Sebastian Bach (Hildesheim; Zürich; New York: Georg Olms Verlag, 2008), vol. II.

Four in two collections for keyboard

165

Table 6.3 The perfect proportioning of Aufrichtige Anleitung, P 610 BWV Key

Title

772 773 774 775 776 777 778 779 780 781 782 783 784 785 786

C major C minor D major D minor E♭ major E major E minor F major F minor G major G minor A major A minor B♭ major B minor

Inventio Inventio Inventio Inventio Inventio Inventio Inventio Inventio Inventio Inventio Inventio Inventio Inventio Inventio Inventio

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

787 788 789 790 791 792 793 794 795 796 797 798 799 800 801

C major C minor D major D minor E♭ major E major E minor F major F minor G major G minor A major A minor B♭ major B minor

Sinfonia Sinfonia Sinfonia Sinfonia Sinfonia Sinfonia Sinfonia Sinfonia Sinfonia Sinfonia Sinfonia Sinfonia Sinfonia Sinfonia Sinfonia

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Totals

Bars 22 27 59 52 32 62 23 34 34 32 23 21 25 20 22 [488] 21 32 25 23 38 41 44 23 35 33 72 31 64 24 38

1:1

1:1

1:1

1:1

1:1

22 27 59 52 32 62

22 27

22 27 59

52

52 32 62

23 34 34 32 23 21 25 20 22 21 32 25 23 38 41 44 23 35

23 34

23 34 34 34

32

32 23

23

25

25

21

21

20

20 22 22

21

21 32 32

25

25 23

23

38

38 41 41

44

44 23 35

23 35

33 72 31 64 24 38

[544] 516 : 516 258 : 258 129 : 129 129 : 129

movements with 9 : 9 movements in 258 : 258 bars; two further 1 : 1 proportions formed by each of these nine movements; a 1 : 1 proportion between the outer twelve movements: 258 : 258 bars, and a further 1 : 1 proportion formed from one of these groups with seven movements in 129 : 129 bars. The final five-movement group of 258 bars does not form a perfect proportion. Thirty terms in a range of 21 to 72 are bound to create some proportions naturally, but the perfectly symmetrical layout of the large-scale double

33 72 31 64 24 38

31 64 24 38

258 : 258 129 : 129

166

demonstrations

proportion across AA, with its 1 : 1 in 516 : 516 bars and 2 : 3 in 12 : 18 movements, as well as its many smaller layers of proportion, must have been planned. As with WTC I, the numerical structure of the finished, perfected collection of Inventions and Sinfonias in P 610 was the result of various stages of revision, which will now be traced from the first versions in Wilhelm Friedemann’s Clavier-Büchlein,15 through an intermediate stage in a copy by Kayser, P 219,16 to Bach’s 1723 autograph fair copy, P 610.

An early unproportioned and incomplete version Father and son copied twenty-nine Praeambulas and Fantasias onto pages 74–103 and 118–144 of the Clavier-Büchlein, leaving pages 56–73 free after the eleven preludes for WTC I discussed above. The handwriting, which has been dated to the period 1722–3, and corrections indicate that some of the Praeambulas and Fantasias were copied from an original that is now lost and some were newly composed,17 Friedemann copying five and Johann Sebastian twenty-four. There are some omissions in the manuscript: the last 13 bars of the D-major Fantasia 14 and the whole of the C-minor Fantasia 15 are missing, as are the last two leaves of Friedemann’s book. Although it is generally accepted that the bars were missing rather than that the final two movements were unfinished,18 one cannot rule out the possibility that Bach left the final two works incomplete in order to facilitate the creation of large-scale numerical perfection across the work, and to instruct his son in the art of building a well-proportioned collection. Table 6.4 shows the numerical structure and order of the collection as copied into Wilhelm Friedemann’s Clavier-Büchlein, with its 482 bars of Praeambulas and 499 bars of Fantasias. The collection in this form is not perfectly proportioned.

A 1000-bar plan in Kayser’s copy, P 219 It was Bach’s student Bernhard Christian Kayser who again made a copy of the collection from a now lost source. Kayser’s version, P 219, represents 15 17

18

16 NBA KB V/3, 23–5, source B. NBA KB V/3, 25–7, source C. Ibid., 24. The Praeambulas in G, F and C minor and E and E-flat major are all composing scores. NBA KB V/3, 24. The editors assume the final C minor Fantasia was originally there, but has since been lost.

Four in two collections for keyboard

167

Table 6.4 Earlier names and orders. Clavier-Büchlein, 1722/3 and Kayser’s copy P 219 Clavier-Büchlein für Wilhelm Friedemann Key

Title

C major D minor E minor F major G major A minor B minor B♭ major A major G minor F minor E major E♭ major D major C minor C major D minor E minor F major G major A minor B minor B♭ major A major G minor F minor E major E♭ major D major Total C minor

Praeambulum Praeambulum Praeambulum Praeambulum Praeambulum Praeambulum Praeambulum Praeambulum Praeambulum Praeambulum Praeambulum Praeambulum Praeambulum Praeambulum Praeambulum Fantasia 1 Fantasia 2 Fantasia 3 Fantasia 4 Fantasia 5 Fantasia 6 Fantasia 7 Fantasia 8 Fantasia 9 Fantasia 10 Fantasia 11 Fantasia 12 Fantasia 13 Fantasia 14 Fantasia 15

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Bernhard Christian Kayser, P 219

Copyist

Bars 1/ Key

Title

Bars

JSB JSB WFB WFB WFB WFB WFB JSB JSB JSB JSB JSB JSB JSB JSB JSB JSB JSB JSB JSB JSB JSB JSB JSB JSB JSB JSB JSB JSB

22 52 21 34 32 21 22 20 21 23 34 62 32 59 27 21 23 44 23 33 64 38 24 31 72 35 41 38 12 981 –

+13

C major C major D minor D minor E minor E minor F major F major G major G major A minor A minor B minor B minor B♭ major B♭ major A major A major G minor G minor F minor F minor E major E major E♭ major E♭ major D major D major C minor

Inventio 1 Sinfonia 1 Inventio 2 Sinfonia 2 Inventio 3 Sinfonia 3 Inventio 4 Sinfonia 4 Inventio 5 Sinfonia 5 Inventio 6 Sinfonia 6 Inventio 7 Sinfonia 7 Inventio 8 Sinfonia 8 Inventio 9 Sinfonia 9 Inventio 10 Sinfonia 10 Inventio 11 Sinfonia 11 Inventio 12 Sinfonia 12 Inventio 13 Sinfonia 13 Inventio 14 Sinfonia 14 Inventio 15

[32]

C minor

Sinfonia 15

22 22 21 21 52 52 23 23 23 23 44 44 34 34 23 23 32 32 33 33 25 25 64 64 22 22 38 38 20 20 24 24 21 31 23 72 34 35 62 41 32 38 59 25 27 1000 500 : [32]

+2

+4

the collection’s developmental state between the Clavier-Büchlein in 1722 and Bach’s fair copy, P 610,19 and gives clues to Bach’s constructional method. In P 219 Kayser named the two-part movements ‘Inventio’ and the three-part ‘Sinfonia’, and each Sinfonia is placed immediately after its corresponding Invention, in the order of keys used for the 19

NBA KB V/3, 13–23.

1:1

21 31 23 72 34 35 62 41 32 38 59 25 27 500

168

demonstrations

Praeambulas in Wilhelm Friedemann’s Clavier-Büchlein. Table 6.4, column 4, shows the revisions Bach made to three of the movements at this stage, with extensions to the two-part movements in E minor and A minor by two and four bars, and adding thirteen bars to the three-part movement in D major. As a result of these adjustments two consecutive blocks of 500 bars and a perfect 1 : 1 proportion are formed, see Table 6.4 shaded column, with Invention and Sinfonia pairs 1–8 making a block of 500 bars and Invention and Sinfonia pairs 9–14 a second block of 500 bars, together creating a rational construction of 1000 consecutive bars. The Cminor Sinfonia stands outside the numerical plan, and it is interesting to note that the C-minor Fantasia would also have been the final work in Wilhelm Friedemann’s collection, but that it was either lost or deliberately not included. In the Clavier-Büchlein the fourteen consecutive three-part movements had a total of 499 bars. Perhaps it was this proximity to the round number 500 bars that suggested the 500 : 500 proportion and that motivated the reordering? Or it may have been the 500-bar block that created the B-A-C key pattern in WTC I, seen in Table 6.1, that gave Bach the idea. Consecutive blocks united by a common bar total are characteristic of Bach’s construction method and typical of the majority of his revisions, the constructional scaffolding disappearing when the composer made his final copy, P 610, reordering and, in this case, renumbering the thirty movements.

The final plan That a symmetrical 1 : 1 proportion can be found in the 2088 bars of the Well-Tempered Clavier (Table 6.1), and a consecutive 1 : 1 across the 1032 bars of Aufrichtige Anleitung (Table 6.3), is hardly evidence of conscious compositional planning. But when the two collections are viewed as a single set, a magnificent large-scale structure appears that must have been designed. Table 6.6 shows how the two keyboard collections intertwine to create two new perfectly proportioned throughnumbered collections – four collections coexisting within two. With the numeration Bach assigned for the prelude-and-fugue pairs and Invention and Sinfonia pairs in P 610 and P 219, consecutive movements form a perfect 2 : 1 proportion, with 2080 bars in 1–24 (Preludes and Fugues 1–8, Inventions and Sinfonias 9–15, and Preludes and Fugues 16–24), and 1040 bars in 1–15 (Inventions and Sinfonias 1–8, Preludes and Fugues 9–15). The shaded column shows the symmetrical ordering of this numerical design.

Four in two collections for keyboard

169

Table 6.5 Two additional collections of 24 and 15 works in 2080 : 1040 bars Two-collection set Preludes and Fugues 1–8 Preludes and Fugues 9–15 Preludes and Fugues 16–24 Inventions and Sinfonias 1–8 Inventions and Sinfonias 9–15 Totals

Bars 810 540 738 500 532

2:1 810 540 738 500

Collection of 24

Collection of 15

Preludes and Fugues 1–8 Inventions and Inventions and Sinfonias 9–15 Sinfonias 1–8 Preludes and Fugues 16–24 Preludes and Fugues 9–15

532

3120 2080 : 1040

2080

Table 6.7 shows a possible reconstruction of the compositional chronology to suggest an order in which this double collection evolved. Three of the sources can be dated fairly reliably: (i) Wilhelm Friedemann’s Clavier-Büchlein, although individual entries are not dated; (ii) Bach’s autograph of WTC I, P 415, (1722) and (iii) his autograph of AA, P 610 (1723). In 1720/1 there is no evidence of a plan beyond a small collection of preludes in different keys. Before he completed P 415, he had the idea of making a complementary collection with 15 two-part Praeambulas and 15 three-part Fantasias, aiming for a simple consecutive 500 : 500-bar construction, using the final C-minor Fantasia/Sinfonia to fine-tune the plan. A potential set of fifteen preludes and fugues in the same keys as the fifteen Inventions and Sinfonias could easily have formed a perfectly parallel structure,20 but no such manuscript has survived. It has been suggested that the blank pages 56–73 were reserved so that Wilhelm Friedemann could copy the remaining WTC I preludes – fifteen preludes would have fitted very conveniently onto the blank pages – but he never completed the exercise. By 1722 his father had transformed them into 2088 bars of twenty-four preludes with corresponding fugues, which, with the final length of the new C-minor Fantasia/Sinfonia, perfected the numerical plan with its large-scale 1040 : 2080 structure, formed by the constructional blocks of 810 and 540 consecutive bars in the Preludes and Fugues. It also included the consecutive 500-bar blocks in the Inventions and Sinfonias. There may be many reasons why Wilhelm Friedemann did not complete the blank pages, 56–73, in his book. Perhaps the joy had gone out of the 20

The Preludes and Fugues in the fifteen keys in Kayser’s version have 1216 bars, and 1218 in Bach’s autograph, P 415, which, with the 1032 bars of fifteen Invention and Sinfonia pairs in P 610, makes a total of 2250 bars.

1040

170

demonstrations

Table 6.6 Perfect 2 : 1 proportion and ‘Proportion by situation’ Key

Title

C major C minor C♯ major C♯ minor D major D minor E♭ major E♭ minor E major E minor F major F minor F♯ major F♯ minor G major G minor A♭ major G♯ minor A major A minor B♭ major B♭ minor B major B minor C major D minor E minor F major G major A minor B minor B♭ major A major G minor F minor E major E♭ major D major C minor

Praeludium and Fuga 1 Praeludium and Fuga 2 Praeludium and Fuga 3 Praeludium and Fuga 4 Praeludium and Fuga 5 Praeludium and Fuga 6 Praeludium and Fuga 7 Praeludium and Fuga 8 Praeludium and Fuga 9 Praeludium and Fuga 10 Praeludium and Fuga 11 Praeludium and Fuga 12 Praeludium and Fuga 13 Praeludium and Fuga 14 Praeludium and Fuga 15 Praeludium and Fuga 16 Praeludium and Fuga 17 Praeludium and Fuga 18 Praeludium and Fuga 19 Praeludium and Fuga 20 Praeludium and Fuga 21 Praeludium and Fuga 22 Praeludium and Fuga 23 Praeludium and Fuga 24 Inventio and Sinfonia 1 Inventio and Sinfonia 2 Inventio and Sinfonia 3 Inventio and Sinfonia 4 Inventio and Sinfonia 5 Inventio and Sinfonia 6 Inventio and Sinfonia 7 Inventio and Sinfonia 8 Inventio and Sinfonia 9 Inventio and Sinfonia 10 Inventio and Sinfonia 11 Inventio and Sinfonia 12 Inventio and Sinfonia 13 Inventio and Sinfonia 14 Inventio and Sinfonia 15

Totals

Bars 62 69 159 154 62 70 107 127 53 83 90 80 65 64 105 53 79 70 78 115 68 99 53 123 43 75 67 57 65 89 60 44 52 95 69 103 70 84 59 3120

2:1 62 69 159 154 62 70 107 127 53 83 90 80 65 64 105 53 79 70 78 115 68 99 53 123 43 75 67 57 65 89 60 44 52 95 69 103 70 84 59 2080 : 1040

Four in two collections for keyboard

171

Table 6.7 A chronological overview. WTC I and Aufrichtige Anleitung 22.i.1720 1720/1 1722 1722 1722 xii.1722 7.ii.1723 1723 19.iv.1723

Clavier-Büchlein for Wilhelm Friedemann begun Early version of seven preludes in Clavier-Büchlein Title-page date of Well-Tempered Clavier, P 415 Praeambulas and Fantasias in Clavier-Büchlein. Implicit 500þ500þ32 structure Lost source Y, Inventions and Sinfonias interleaved key order of Clavier-Büchlein Application sent to Leipzig Test for cantorate in Leipzig Title-page date of Aufrichtige Anleitung, P 610 Final contract with Leipzig

compositional exercise when he knew that his father had already developed it way beyond their original conception. And although the original simpler versions of the remaining preludes would have fitted in the allocated pages, the full-length preludes would not, and so the pages were left blank, and later filled with other material. There was also the unsettling news at this time of a possible move to Leipzig,21 which meant the Praeambulas and Fantasias had to be polished and completed quickly, and copied again with additional bars and revisions onto an interim and now lost copy. Bach then had to make his own reordered fair copy, P 610, if he was to present it at his Leipzig audition and interview on 7 February 1723. All this in addition to the new church cantatas he had to find time to compose. Clearly Bach needed all the manual assistance he could get. Bach’s teenage student Kayser was on hand with quill poised. He made copies of both WTC I,22 P 401, and AA, P 219, creating a clean version that may have helped Bach to check through his own work before his trip to Leipzig. It has been suggested that many of Kayser’s additions, particularly the ornaments, originate from Bach’s teaching.23 It is not beyond the bounds of possibility that Bach instructed Kayser to copy these two collections as an exercise in observing and learning how to create a numerically proportioned structure. The lost source from which Kayser copied the two- and three-part collection would have demonstrated the consecutive blocks of 500 bars

21

22

23

Wolff, Learned Musician, 227; the timing of the composition and wording of the matching title pages suggests that Bach composed the keyboard set of two collections to support his application for the post of Thomaskantor. NBA KB V/3, 32; source B 3: D-B Mus. ms. Bach P 401, with a title page by J. Chr. Oley; Andrew Talle, ‘Nürnberg, Darmstadt, Köthen’, BJ (2003), 155–68. Kayser was formerly known as Anonymous V. NBA KB V/3, 68 and 81.

172

demonstrations

which were integral to the large-scale proportion uniting the two keyboard collections. Whether under Bach’s instruction or not, Kayser added two bars to his copy of the twenty-four preludes and fugues, rendering it numerically identical to P 610. Perhaps he realised that with his copy of the Inventions and Sinfonias, P 219, he held the structural and proportional key to the matching pair.24 Bach had created a large 3120-bar set from two discrete collections. The choice of the number 3120 may have been motivated by its reference to his surname B-A-C, or as a reflection of the first numerus perfectus, 6, with its component parts 1, 2 and 3. Both are parallel allusions typical of the period, and neither excludes the other. Had the data used in this demonstration contradicted the diplomatic source evidence, and had such a large-scale construction happened just once, the satisfying bar total, the large-scale 2 : 1 proportion, the smallerscale 1 : 1 proportions and the blocks of 500 bars could all be written off as coincidence. But the sources and the figures correspond perfectly. The documented changes indicate how Bach transformed the two collections into a perfectly harmonious whole. The layers of perfect proportion across the two collections are an even stronger indication that Bach was actively expressing his profound belief in the centrality of music in God’s created order through this collection.25 And magnifying the effect further, Bach created an even larger-scale unity, 1 : 1, between this first and his next keyboard collections, Clavier Übung, Parts I and II.

II Edifying clavier exercises – the second 3120 Bach’s first keyboard collection was published in 1731 under the title Clavir Übung Theil 1, Opus 1 (hereafter CÜ I).26 It comprised six partitas, five of which had been published earlier as individual units: Partita 1 in 1726 (BWV 825), Partitas 2 and 3 in 1727 (BWV 826–7), Partita 4 in 1728 (BWV 828) and Partita 5 in 1730 (BWV 829).27 In spite of a public announcement in 1730 advertising a seventh Partita, the collection was published as a whole with only six Partitas, the sixth Partita never being sold separately.28 In 1735 Bach published a second keyboard collection, the

24 26 28

25 D-B Mus. ms. Bach P 219. NBA KB Source C, c. 1724. See Chapter 3 and the Appendix. 27 Schulenberg, Keyboard Music, 321–46. NBA KB V/1. BD II, Doc. 277. Leipzig, 1 May 1730: ‘The Fifth part of Bach’s Clavier Übung is now ready and with the remaining two the whole work will be completed for the up-coming Michaelmas Fair.’

Four in two collections for keyboard

Table 6.8 Symmetrical 1 : 2, 2 : 3 and B-A-C-H signature. CÜ I & CÜ II (1735) BWV

Partita

Bars

825 826/1 826/2–6 827 828 829 830 971/1–2 971/3 831

1 in B♭ major 2 in C minor 2 in C minor 3 in A minor 4 in D major 5 in G major 6 in E minor Italian Concerto Italian Concerto French Overture

249 90 TS 288 342 422 391 396 241 210 491

Totals

3120

1:2

Key

249 90

B♭ C 288 342 422 391 396 241

210 491 1040 : 2080

A

Bars 249

90 288 342 422 391 396 241 210 491

B (H) B-A-C-H

Bars

2088

1032

second part or Zweyter Theil der Clavier Übung, (hereafter CÜ II), which consists of just two works: a three-movement Italian Concerto (BWV 971) and an eleven-movement French Overture (BWV 831).29 The omission of any reference to its opus in the title suggests that Bach intended it to be associated with CÜ I. The numerical construction confirms this idea. Together the forty-one movements of CÜ I and the fourteen movements of CÜ II have 3120 bars. Table 6.8 shows how these 3120 bars form a symmetrically arranged large-scale 1 : 2 proportion with 1040 : 2080 bars in a 2 : 3 proportion formed by three continuous sections in publication order, dividing the second Partita and the Italian Concerto into two parts. A permutated B-A-C-H pattern can be seen in the keys of four of the eight works. Furthermore, six sections have 2088 bars and four 1032 bars, exactly parallel to the 2088 bars of WTC I and 1032 bars of AA. Table 6.9 illustrates the layers of large-scale structural parallels between the two parts of the Clavier Übung and Bach’s first pair of keyboard collections. When he published CÜ II in 1735, Bach united, for the second time, two contrasting keyboard collections into a set with 3120 bars, thereby creating a mega double 1 : 1 construction from 1 : 1 sets made up of 2 : 2 keyboard collections in 3120 : 3120 bars, with each set having the same large-scale 1 : 2 proportion in 1040 : 2080 bars. There are,

29

No copies have survived of the sixth and seventh and it is therefore assumed that neither was published individually. NBA KB V/2.

173

174

demonstrations

Table 6.9 Proportional integration of two sets of two keyboard collections 1722/3 & 1726–35 AA WTC I CÜ I Sinfonia BWV 826/1 CÜ II CÜ I all but BWV 826/1 CÜ I CÜ II

1:1

1:1

1032 1032 2088 [French/Italian]

1:1

1:2 1:1 1040 : 2080

1:1 1040

1:1 2080

2088 90

[French/Italian]

942 2088

2178 942

Totals

3120 : 3120

1040 : 2080

1040

2080

1032 : 1032 2088 : 2088 3120 : 3120 1040 : 1040 2080 : 2080

however, fewer smaller-scale layers of proportion within the CÜ I and II pair. This is a natural consequence of the fact that Bach could not, without enormous expense, adjust the structures of the first five partitas which had already been printed and sold individually. The barring in the engraving of CÜ I and CÜ II is very clear, and the 3120 bars are those written rather than repeated. The only notational anomaly that affects the numerical result is the ‘Sinfonia’ of the C-minor Partita, BWV 826/1, where at bar 29 there is the dual count of a time signature as bar line, a TS feature.30 Instead of a bar line there is simply a new time signature where the movement changes from c to 34 , rendering its length both 90 and 91 bars. There is a similar case in bar 163 of the French Overture, but since it affects the bar total only when the movement is repeated it is irrelevant to the 3120-bar structure. The spelling of the title words Clavier Übung is inconsistent in the various published partitas. The first title page used in 1726 for Partita 1 (BWV 826) uses the form ‘Clavier’. The same plate was reused for the title page of the fifth partita in 1730, with a judicious change of the numeral I to V. The title pages for the individually published partitas 2, 3 and 4, however, use the form ‘Clavir’, without an ‘e’. When Bach had a new plate engraved for the title page of the complete collection, Opus 1, he chose the form ‘Clavir Übung’, perhaps because of its satisfying numerical value, 123,31 parallel both to his own name, as 3 x 41, and as a B-A-C/2-1-3 number, and to the overall bar total of 3120.32 The 1032-bar total of the 30 32

Explained in Chapter 1. See Chapter 2.

31

CLAVIR: 3+11+1+20+9+17=61 UBUNG: 20+2+20+13+7=62.

Four in two collections for keyboard

175

Table 6.10 Partitas in A and E minor. Autograph, P 225, and Print, BWV 827, 830 A-minor Partita, 1725

E-minor Partita, 1725–30 1/

Movement P 225

Title

Prelude Allemande Corrente Sarabande Menuetto Scherzo Gigue

118 16 } 56 } 28 } 40 } — 50 }

Fantasia +2

Totals

308

Burlesca +32 +34

CÜ I

Movement

120 16 } 56 } 28 } 40 } 32 } 50 }

Prelude 105 Allemande 20 } Corrente 116 } Air — Sarabande 36 } Tempo di Gavotta 32 } Gigue 52 }

342

361

P 225

Title

1/

CÜ I

Toccata

+3

+ 32

108 20 116 32 36 32 52

+ 35

396

first two partitas has the same 2-1-3 allusion. Evidence from the early versions of the partitas and the numerical structure suggests how Bach worked to create this perfectly proportioned plan.

Early versions of works in the collection The earliest copy of the A-minor Partita (BWV 827) can be found in Anna Magdalena’s second Clavierbüchlein (P 225),33 dated 1725, written carefully by Bach onto the first seventeen pages of his wife’s new leatherbound book. When preparing this partita for publication Bach renamed the first movement ‘Fantasia’, inserting two new bars between bars 117 and 118 of the original, and adding a 32-bar Scherzo between the Menuetto and Gigue, Table 6.10, shaded column +/, thus transforming its six movements in 308 bars into seven movements and 342 bars. He also wrote the E-minor Partita (BWV 830) on pages 18–41 of the 1725 music book, immediately after the A-minor Partita. When he prepared this partita for publication he changed the title of the first movement from ‘Prelude’ to ‘Toccata’, and increased its length by inserting two bars between bars 73 and 74, adding a bar between the final and penultimate bars, and a new 32-bar ‘Air’, Table 6.10, shaded column +/. Two movements of the E-minor Partita were reused from earlier compositions: 116 bars came from the recently revised Sonata for violin and harpsichord (BWV 1019a/3), St 162 (Table 5.9), which he renamed ‘Corrente’, and 32 bars from BWV 1019a/5, which 33

D-B Mus. ms Bach P 225.

176

demonstrations

Table 6.11 1 : 2 proportion in Partitas in A and E minor. Autograph, P 225, 1725 pp. 1–41

Prelude

Allemande

Corrente

Sarabande

Menuetto

A minor E minor

118 105

16 20

56 116

28 36

40 32

Totals

36

223

172

64

72

Gigue

Totals

1:2

50 52

(308) (361)

446

[669]

223

(446)

669

102

he transcribed for keyboard and set as a ‘Tempo di Gavotta’. Bach’s neat handwriting and attention to detail as he copied these two partitas onto the first forty-one sides of his wife’s new book reflect the care he took over their composition.34 They were not just beautiful to behold, they were carefully constructed as a perfectly proportioned pair. The 223 bars of the first movements form a 1 : 2 proportion with the 446 bars of the remaining movements (see Table 6.11). Anna Magdalena’s book began with a perfect presentation set of two partitas, proportioned 1 : 2, in keys a perfect fifth or 2 : 3 apart. Nonetheless, when Bach grafted these movements into his published collection he destroyed this perfection and unity by increasing their length by 69 bars. One can understand the additional bars and the two extra movements as improvements motivated by musical considerations. However, I suspect this was matched by his motivation to create a new perfect numerical structure on a larger scale. There are clues in the evolving numerical structure of CÜ I to suggest that Bach always intended the published keyboard collection to complement his first unpublished set of keyboard works from 1722/3. Table 6.12 shows that the first two published partitas, including their repeats, have 1032 bars, the same total as the two-part Inventions and Sinfonias. The parallel implies that Bach may have planned to add a further 2088 bars, to create a collection with 3120, parallel to the 1032 and 2088 bars of his earlier set. The perfected A- and E-minor Partitas (P 225) have 1115 bars including repeats. Had Bach used these towards the projected total of 2088 bars, he would have had only 973 bars for the final partitas. There is no source evidence to suggest that he had composed the French Overture before 1730. However, if he had, and if by then he had planned to 34

Kobayashi dates the handwriting of the E-minor Partita in P 225 to between 1725 and 1730. Notenschrift, NBA 9/2 (1989) 208. It was possibly C. P. E. Bach who paginated the two partitas much later.

Four in two collections for keyboard

177

Table 6.12 Evolving plan, including repeats, to mirror AA and WTC I? BWV

Date

Score

Work

825 826 827a 830a 831a

1726 1727 1725 c. 1725 pre-1728

Print Print P 225 P 225 pre-P 226

Partita 1 in B♭ major Partita 2 in C minor Partita 3 in A minor Partita 6 in E minor ‘French’ Partita in C minor

Totals

Bars

Bars

477 555

1032

477 555 498 617 982

498 617 982

2097

1032 : 2088

include this eleven-movement ‘partita’ in the collection, its 982 repeated bars (excluding the D of Gavotte/Passepied/Bourée) could easily have been adjusted by nine bars to 973 bars to make a five-partita set of 3120 bars. But this did not happen, and it is in any case unlikely that the French Overture had eleven movements by this time. The reconstruction in Table 6.12 suggests that the hypothetical 1032 : 2088 scheme would have been too limiting and musically restricting. By using the number of written rather than repeated bars, Bach could increase the scale of his collection and still use the good idea of the 3120, 1040 : 2080 construction, with 1032 and 2088 visible in two parts parallel to the 1723 keyboard pair. (see Table 6.8).

Hints of the construction procedure The two works in CÜ II were composed significantly earlier than their 1735 publication date might suggest. Anna Magdalena made a very neat copy of the French Overture in C minor,35 BWV 831a, P 226,36 for which Bach wrote the title, ‘Ouverture pour le Clavecin a 2 Clav. composée par J. S. Bach’. Based on the handwriting and watermarks, the copy can be dated to c. 1732–5 or possibly to the middle of 1733.37 It is possible that a shorter, early version of the French Overture could have been the advertised seventh Partita.38 The Italian Concerto, BWV 971, was composed even earlier than the French Overture.39 Two manuscript copies based on a pre-publication version have survived. The first was made by Johann Christoph Oley (1738–89) before 1762, and has the title Concerto en 35 37 38 39

3120 [19]

36 NBA KB V/2, 14; source 2 B. D-B Mus. ms. Bach P 226 fascicle 9, 41–65. NBA KB V/2, 15 and 48. Kobayashi, Notenschrift, 208. BD II, Doc. 276, Leipzig, 1 May 1730. K. Beißwenger, ‘An Early Version of the First Movement of the Italian Concerto BWV 971’, in Bach Studies 2, ed. D. Melamed (Cambridge University Press, 1995), 1–19.

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demonstrations

F dur.40 Its bar structure is identical to the published version, with a first movement of 192 written bars. A second copy was made by Leonhard Scholz (1720–98) and represents an even earlier version of the concerto. The layout of the first movement is unique: it is written with a D indication after bar 163.41 This is a striking parallel to the 163 bars of the first movement of the French Overture, which would become its companion in CÜ II. When Bach prepared the Italian Concerto for publication, however, he wrote out the da capo section in full, making a first movement with 192 bars. This 192 bars was essential to form the 1040 : 2080 proportion shown in Table 6.8. Perhaps it was this numerical coincidence that gave Bach the idea of including the Concerto in the Clavier Übung collection, and expanding the collection beyond partitas? The 1 : 1 proportion in 163 : 163 bars also suggests that he had some concrete means of recalling the length of works he had composed earlier. The key of the Italian Concerto may also have played a part in its inclusion in the Clavier Übung series. Christoph Wolff has pointed out a logical expanding major-minor key pattern across CÜ I: We do not know why the planned seventh Partita was not published. At any rate, according to Bach’s well-ordered tonal plan, it must have been intended to be set in F major . . .[Bach] did not use an ascendingly ordered succession of keys as he had in the Well-Tempered Clavier and the Inventions and Sinfonias; instead he chose a sequence based on gradually expanding upward and downward intervals . . . Without the seventh Partita, the consistent logic of the original plan was, of course, destroyed. Yet the end result forms a hardly less logical order: one piece in the major mode, followed by two in minor for the second half, for a total of three pieces in major and three in minor modes.42

The numerical evidence shows that Bach designed the two parts of the Clavier Übung as a unit, and therefore if Wolff’s observation reflects Bach’s conscious patterning, Bach did indeed continue the logic of the key pattern. The already composed Italian Concerto with its fitting 163-bar first movement was in F major. The minor-mode French Overture continued the major–minor patterning. Bach decided to transpose it to B minor, which lay centrally between the E and F of the penultimate works in the set, and also completed the B-A-C-H signature across the set.

40 41

42

NBA KB V/2, 14; Oley’s copy is source A: Boston Public Library Ms M 200.12(2). D LEb Rar Ib, 58, formerly D Gb Ms.Scholz 5.2.3, reads ‘Da Capo all Segno’, and D LEb Rar Ib, 59, formerly D Gb Ms.Scholz 5.2.4 reads ‘Da Capo d’al Segno’: image in Beißwenger, ‘Italian Concerto’, 2–3. Wolff, ‘The Clavier-Übung Series’, Essays, 189–90.

Four in two collections for keyboard

Table 6.13 A 1700-bar block, without repeats, suggesting early ordering BWV

Date

Score

Work

Movements

828 829 830 831

1728 1730 1731 173?

Print Print Print P 226

Partita 4 in D major Partita 5 in G major Partita 6 in E minor French Overture in C minor

7 7 7 11

422 391 396 491

32

1700

Totals

Bars

At what point and for how long Bach planned a seven-partita collection is not known – the rumour may have been nothing more than a simple advertising ploy or mistake. At what point he devised the structure of this two-collection set to make it a precise parallel to his first keyboard set is also unclear. A block of 1700 written bars suggests a possible compositional timeline. If the 1700-bar block shown in Table 6.13 is evidence of Bach’s organisational planning it could help reconstruct the order in which Bach worked. By 1727 he had published the first, second and third partitas and probably also composed the Italian Concerto. This gave him 1420 bars. With hindsight it is easy to see that all he needed to reach the desired total of 3120 was an additional 1700 bars. However, although theoretically possible, it seems highly unlikely that as early as 1727 Bach would have decided to include a concerto in a collection of partitas. It is more likely that the 1700-bar block dates to early 1731 or late 1730, when he was preparing the sixth partita for publication. Having a draft of the French Overture to hand, and the Italian Concerto on his desk, he saw how he could create a perfect set of two complementary collections of 3120 bars each. The 1700-bar block may have acted as a structural guide as he made minimal additions to Partita 6 before publication in 1731 of CÜ I as a set of six, while he calculated the number of bars needed to revise and graft the French Overture into the structure. An earlier version of the French Overture may well have been the advertised seventh Partita, but Bach changed his plan. The final touch to his perfect scheme was to create the B-A-C-H key pattern by transposing the French Overture to B minor, some time after mid-173343 and probably shortly before its publication as part of CÜ II in 1735. The intentionality of Bach’s design is further suggested in a 1032 and 2088 structure, parallel to WTC I and AA, formed by the unconventional 43

The estimated date of Anna Magdalena’s copy in P 226 based on her handwriting and the watermarks of the paper, NBA KB VIII/1, 71f.

179

180

demonstrations

Table 6.14 A striking 1 : 1 proportion suggesting a large-scale working plan BWV

Collection

Work

Bars

829 830 971 831

CÜ CÜ CÜ CÜ CÜ CÜ

Partita in G major Partita in E minor Italian Concerto French Overture German Organ Mass Goldberg Variations

687 680 451 982 1840 960

687 680 451 982

5600

2800 : 2800

988

I/5 I/6 II/1 II/2 III IV

Totals

1:1

1840 960

C minor Sinfonia of the second partita. Its opening dotted section sets the expectation of a typical French overture, but within seven bars something quite different happens, and again at bar 29, when it unexpectedly changes to 34 metre, almost but not quite in the style of an Italian Sinfonia.44 The proportional integration can be seen in Table 6.9, where its 90 bars (counted as TS) combine with the 942 bars of the Italian Concerto and French Overture of the second part of Clavier Übung to make a total of 1032 bars. The first part of Clavier Übung, without the C minor Sinfonia, has 2088 bars. Table 6.14 shows a further remarkable numerical feature of the completed two-collection set – the bar total of the final four works, when counted at the repeat, form an exact block of 2800 bars. The constructional significance of this 2800-bar block becomes apparent when one sees the 2800-bar block Bach had formed by 1741 with the third and fourth parts of the Clavier Übung series. The distinct blocks of 2800 bars and 1700 bars suggest that while Bach was constructing his collections he was aware of both the written and repeated bar totals. Changes to bars, movements and key transposition are a normal part of compositional revision procedure. Regrouping works into a collection to create a new artistic constellation is part of normal planning procedure. Usually such revisions and regrouping are necessary because compositions are in a rough and ready state. This was not the case for Bach when he constructed the first two parts of his Clavier Übung series. Neither technical nor musical reasons can explain his extension to the A-minor and E-minor Partitas: they were already excellent. Nor was there a practical or acoustical reason why Bach should transpose the French Overture from C minor to B minor. It too was already excellent in its original key. 44

Schulenberg, Keyboard Music, 327.

Four in two collections for keyboard

The changes were motivated by Bach’s desire to bring his first published two-set collection into harmonious order. Its layers of larger and smallerscale proportions demonstrate empirically its numerical kinship and unity with his earlier unpublished two-set collection. The words Zweyter Theil and his omission of Opus 2 on the title page confirm his intention. His two publications created a unity with harmonious proportions that would never be heard,45 but which Bach hoped would delight his neighbour and lead to greater devotion to God.

45

Appendix, 1701-I, 1708-V.

181

7 Two further collections for keyboard

Clavier Übung Part III (BWV 669–89, 552, 802–5) Clavier Übung Part IV (BWV 988) Fourteen Canons (BWV 1087) Nun frage ich alle Musikverständige, und unter denselben alle gründlich geschickte Organisten, ob alles dieses ohne Regeln der Composition zu bewerkstelligen möglich sey? Ob zum tüchtigen Clavier-und Orgelspielen nicht eben soviel Erfahrung und Wissenschaft erfordert werde, als zur Composition selbst? Ob eine solche musikalische Uebung, in welcher man theils eigene, theils fremde Gedanken, richtig, deutlich, ordentlich, zusammenhangend, und rührend ausdrucken soll, ohne gelehrtes Nachsinnen glücklich von statten gehen könne?1 J. A. Birnbaum, 1739

Grouped together in this chapter are two keyboard collections exploring different musical forms and united by the common title Clavier Übung. The first, for organ, is part three of the Clavier Übung series, sometimes known as the German Organ Mass. The second, for ‘Clavicimbal’ with two manuals, is commonly known as the Goldberg Variations although there is little justification for its nickname.

I

Edifying clavier exercises of a third kind

On 10 January 1739, Johann Elias Bach wrote enthusiastically to a colleague: It happens that my honoured Cousin will bring out some clavier pieces that are mostly for organists and are exceedingly well composed, and they will doubtless be ready for the coming Easter Fair and make some 80 folios.2 1

182

2

J. A. Birnbaum, Vertheidigung (March, 1739) in J. A. Scheibe, Der Critische Musicus, 976–7. NBR, Doc. 205; BD II, Doc. 434. In a letter to Cantor Johann Wilhelm Koch in Ronneberg.

Two further collections for keyboard

In spite of the sales pitch, it was not until September 1739 that the last pieces were engraved and the collection ready to purchase.3 The title page reads: Third Part of Clavier Übung, consisting of various preludes on the catechism and other hymns for the organ. For music lovers and especially for connoisseurs of such work, to refresh their spirits, composed by Johann Sebastian Bach . . . Published by the Author.4

The delay was primarily due to a major structural change in the work when the fifteen-movement collection grew into twenty-seven movements. Using evidence from the prints that discloses details of the original engraving plates, Gregory Butler reconstructed the order in which Bach compiled and expanded the collection, showing that, even after engraving had begun, Bach made substantial revisions to the collection’s content and form. This chapter will test the numerical construction of the fifteen-movement collection first submitted to the engravers, as well as the structure of the final twenty-seven-movement publication, looking for evidence of the three characteristics of proportional parallelism.5 The numerical results give a unique insight into Bach’s revision procedure, as he transformed what would have been a perfectly proportioned collection of fifteen movements into one nearly twice as long.

Bach’s first plans for Clavier Übung Part III (CÜ III) Bach took at least three years to prepare CÜ III. Several movements date from as early as 1736,6 while the four Duetti were not ready until as late as July or August 1739.7 The size and spacing of the music and erasures on the engraved pages enabled Butler to demonstrate that Bach radically changed the shape and content of the collection after the engraving procedure had begun. The manuscript versions of the collection Bach submitted to the engraver to use as a template8 have not survived, but there may have been a second original copy of the early fifteen-movement 3

4 5

6 8

G. Butler, Bach’s Clavier-Übung III. The Making of a Print (Durham, NC; London: Duke University Press, 1990), 85. NBR, Doc. 206, BD I, Doc. 167. Facsimile of title page: NBR, 203. NBA KB IV/4, 33. Tessmer questions the status of the supposedly early versions of BWV 676 and 683. Although some of the thirty-six or more surviving manuscript sources of Clavier Übung III (CÜ III) may contain working versions of movements that predate the 1739 publication, examination of these sources is beyond the scope of this chapter. 7 Butler, Bach’s Clavier-Übung III, 16. Ibid., 20. Ibid., 51. Called a Stich- or Abklatschvorlage.

183

184

demonstrations

collection among Bach’s papers.9 The published title page makes no mention of the opening prelude, the four duets and the closing fugue, which implies both that this freer material was not in the original submission, and that the title page was engraved some time before the collection was expanded.10 The evidence based on the engraving, points to two distinct Vorlagen representing different layers of compositional activity. The earliest was a fair autograph score of the Missa settings (BWV 669–77), and the pedaliter chorales, BWV 678, 680, 682, 684, 686 and 687. This was the collection first submitted to the engravers. On the basis of internal musical evidence, these movements break down further into two clearly distinguishable strata—a Missa layer and a catechism layer.11 Butler was first alerted to Bach’s changed plan by the erasure and correction of page numbers in the 1739 print. This erasure of original pagination cannot be attributed simply to errors on the part of the engraver responsible for the engraving. This is not an isolated instance, but occurs in two widely separated settings in which the difference in pagination between the original and present page numbers is the same. Furthermore, in the second instance, the revised pagination carries on for four pages in succession. Clearly, the engravers, as was their habit, were simply copying blindly and unquestioningly the pagination they found on the fair copy they were reproducing.12

The plates show evidence of the original page numbers 13, 31, 32, 33 and 34 over which the numbers 22, 40, 41, 42 and 43 were re-engraved.13 Four engravers were responsible for producing the final print: Balthasar Schmid in Nuremberg (the title page and thirty-four of the seventy-seven pages of musical text),14 Johann Gottfried Krügner in Leipzig, Krügner’s senior assistant (probably Rosine Dorothee Krügner, née Boëtius) and another Krügner assistant.15 Bach was experienced in the engraving and publication process by 1739: he knew first hand what would be involved, and that accuracy was paramount because preparing the copper plates was a very expensive procedure. When he submitted his first fair copy manuscript to the engravers, we can be fairly certain that he thought the collection was finished, and therefore revised and numerically perfect. As the autograph manuscript of this first version has not survived, and because the 9

10 14

Ibid., 50, citing Klotz in NBA KB IV/2, 53. A manuscript collection of chorale settings, originally a draft copy in St Thomas’s, then belonging to Schicht, then to Spitta, and finally deposited as Sp 1483 in the Berlin Hochschule für Musik, but then lost in 1945. 11 12 13 Butler, Bach’s Clavier-Übung III, 44. Ibid., 83. Ibid., 41. Ibid., 40. 15 Ibid., 21. Ibid., 31.

Two further collections for keyboard

Table 7.1 Fifteen mass and catechism movements sent to the engravers first BWV

Chorale setting

Bars

669 670 671 672 673 674 675 676 677 678 680 682 684 686 688

Kyrie, Gott Vater in Ewigkeit Christe, aller Welt Trost Kyrie, Gott heiliger Geist Kyrie, Gott Vater in Ewigkeit Christe, aller Welt Trost Kyrie, Gott heiliger Geist Allein Gott in der Höh sey Ehr Allein Gott in der Höh sey Ehr Fughetta on Allein Gott in der Höh sey Ehr Dies sind die heiligen Zehen Geboth Wir glauben all an einen Gott Vater unser im Himmelreich Christ, unser Herr, zum Jordan kam Aus tiefer Noth schrey ich zu dir Jesus Christus, unser Heyland

42 61 60 32 30 34 48 126 20 60 100 91 64 54 118

54

108

118

940

470 : 470

1157

Totals

1:1

Alt

42 61 60 32

84 122 120

30 34 48 126 20 60 100 91 64

additional material and consequent compressed layout resulted in so many erasures and revisions in the 1739 publication, it is impossible to reconstruct the exact content, length and structure of the originally submitted version. However, it is possible to test its numerical construction from the length of these fifteen movements in the 1739 publication. Table 7.1 shows that these fifteen movements are perfectly proportioned. The modern BWV number and the title stipulated in the publication are given for easy reference together with the number of bars for each movement, with the four stile antico movements (BWV 669, 670, 671 and 686) counted both at the breve, and at the semibreve. At the breve these movements have a perfect numerical structure, with Table 7.1 showing one of several constellations in which the fifteen movements in 940 bars form a 1 : 1 proportion, with 470 : 470 bars. With the alternative count the published version of the fifteen movements is 1157 bars, just 43 bars short of 1200 bars. Fifteen movements in approximately 1200 bars would create a logical parallel with the 1200 bars of his fifteen Leipzig chorale preludes that he was working on at this time.16 This parallel of a collection for organ 16

See Table 11.2.

185

186

demonstrations

consisting of fifteen movements in just short of 1200 bars suggests that the autograph score Bach first sent to the engravers may have been a 1200-bar, fifteen-movement collection. Several scholars have associated the Leipzig Chorale Preludes and CÜ III on musical grounds,17 but in the absence of an original score, in spite of the new numerical evidence, the association must remain speculative. Besides, Bach changed his plan: a different, even greater, parallel had caught his imagination.

The structure of Bach’s 1739 publication Over the next few months Bach sent twelve additional movements to the engravers to be interleaved between the fifteen already being engraved. Six of these were chorale settings and six were prelude-and-fugue movements, creating in all a twenty-seven movement collection. Table 7.2 shows the content and numerical structure of these additional movements in the order in which they appear in the final publication. There are exactly 900 bars forming a double 1 : 1 and 1 : 2 proportion, with 6 : 6 movements in 300 : 600 bars. The groups of 300 and 600 bars might even contain clues to the order in which Bach revised and compiled the expansion. We know that the duets were the last to be sent to the engravers,18 and thus it follows that if Bach used Duetto I (BWV 803) in the formation of the 300-bar block, its length would have been fixed before he even began to compose it. He would have had more flexibility for the lengths of the remaining three Duetti. The 33-bar da capo repeat in Duetto II (BWV 804) creates an alternative total of 933 or 931 bars in the twelve movements, depending upon whether the TS feature in the E-flat ‘St. Anne’ Fuga (BWV 552/2) is taken into consideration. Many perfect proportions were formed when these additional twelve movements were grafted onto the original fifteen-movement structure. Table 7.3 shows the 27 movements in the order in which they appear in the published collection: 27 movements in 1840 bars or alternatively 2090, counting the four stile antico movements (BWV 669, 670, 671, 686) at the semibreve and including the repeat in the second duet, or 2088 bars counting the two TS bars in the E-flat Fuga (BWV 552/2).

17

18

R. Stinson, J. S. Bach’s Great Eighteen Organ Chorales (Oxford University Press, 2001), 30: ‘Bach probably regarded the two [CÜ III and the Great Eighteen] from a musical perspective as complementary collections.’ Butler, Bach’s Clavier-Übung III, 20.

Table 7.2 The additional twelve movements sent to the engravers BWV

Setting

Bars

552/1 552/2 679 681 683 685 687 689 802 803 804 805

Praeludium Fuga Fughetta Dies sind die heiligen Zehen Geboth Fughetta Wir gläuben all an einen Gott Vater unser im Himmelreich Christ, unser Herr, zum Jordan kam Aus tieffer Noth schrey ich zu dir Fuga on Jesus Christus, unser Heyland Duetto I Duetto II Duetto III Duetto IV

205 117 35 15 24 27 74 67 73 116 39 108

Totals

900

1:2 205 117

+/

Alt

[ 2

115 TS]

+33

149

35 15 24 27 74 67 73 116 39 108 300 : 600

931/933

Table 7.3 Dual bar structure of CÜ III: 1840 bars alternatively 2088/90 bars Theme Mass Mass Mass Mass Mass Mass Mass Mass Mass Decalogue Decalogue Creed Creed Prayer Prayer Baptism Baptism Penitence Penitence Communion Communion

Totals

BWV

Movement

552/1 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 802 803 804 805 552/2

Praeludium Kyrie, Gott Vater in Ewigkeit Christe, aller Welt Trost Kyrie, Gott heiliger Geist Kyrie, Gott Vater in Ewigkeit Christe, aller Welt Trost Kyrie, Gott heiliger Geist Allein Gott in der Höh sey Ehr Allein Gott in der Höh sey Ehr Fughetta: Allein Gott in der Höh sey Ehr Dies sind die heiligen Zehen Geboth Fughetta: Dies sind die heiligen Zehen Geboth Wir glauben all an einen Gott Fughetta: Wir glauben all an einen Gott Vater unser im Himmelreich Vater unser im Himmelreich Christ, unser Herr, zum Jordan kam Christ, unser Herr, zum Jordan kam Aus tieffer Noth schrey ich zu dir Aus tieffer Noth schrey ich zu dir Jesus Christus, unser Heyland Fuga: Jesus Christus, unser Heyland Duetto I Duetto II Duetto III Duetto IV Fuga

Bars 205 42 61 60 32 30 34 48 126 20 60 35 100 15 91 24 64 27 54 74 118 67 73 116 39 108 117 1840

Alt 84 122 120

108

149

115 TS 2088/2090

188

demonstrations

Table 7.4 Perfect proportioning within twelve consecutive groups Consecutive groups

BWV

Theme

1. Prelude 2. Kyrie Christe Kyrie 3. Kyrie Christe Kyrie 4. Allein Gott in der Höh 5. Dies sind die heiligen zehen Geboth 6. Wir glauben all an einen Gott 7. Vater unser im Himmelreich 8. Christ unser Herr zum Jordan kam 9. Aus tiefer Noth schrey ich zu dir 10. Jesus Christus, unser Heyland 11. Duetti I–IV 12. Fuga

552/1 669–71 672–74 675–77 678–79 680–1 682–3 684–5 686–7 688–9 802–5 552/2

– Mass Mass Mass Decalogue Creed Prayer Baptism Penitence Communion – –

Bar totals and proportions Section totals and proportions

Bars 205 163 96 194 95 115 115 91 128 185 336 117

1:1 205 163 96 194 95 115 115 91 128 185 336 117

Alt bars 205 326 96 194 95 115 115 91 182 185 369 115 TS

1840 920 : 920 2088 12

4:8

12

1:2 205 326 96 194 95 115 115 91 182 185 369 115 TS 696 : 1392 4:8

Bach’s titles and the consecutive positioning of the 27 movements suggest that he saw the latter as twelve groups of compositions: the opening prelude, two Kyrie–Christe–Kyrie mass settings, seven groups of chorale or catechism settings, a group of four duets, and the final fugue. Table 7.4 shows the structure of CÜ III when viewed in these twelve consecutive groups. The 1840 bars and the twelve groups fall into a 1 : 2 and 1 : 1 proportion with 4 : 8 groups in 920 : 920 bars; and a more symmetrically arranged double 1 : 2 proportion appears with the alternative bar total of 2088 bars, with 4 : 8 groups in 696 : 1392 bars. This structure and its bar totals mirror the 1392 : 696 proportion in the 2088 bars of Bach’s first collection of preludes and fugues, WTC I,19 although lacking the B-A-C allusion in the keys. Bach was working on fugal techniques and compiling his second book of keyboard preludes and fugues, WTC II, at this time, no doubt comparing the second book to his first, which suggests that he could have designed this extra triple proportion between the WTC I and CÜ III collections, with 1 : 1 and 2088 : 2088 bars falling into 1 : 2 with 696 : 1392 bars. Many smaller-scale layers of proportion can be formed within the structure of CÜ III. Some are a natural result of numbers being grouped

19

See Table 6.1.

Two further collections for keyboard

189

Table 7.5 Examples of perfect proportioning in consecutive movements BWV Consecutive settings

Date

680 681 682 683

mid-1730s 100 100 late 1738 15 15 mid-1730s 91 late 1738 24

Wir glauben all Fughetta: Wir glauben all Vater unser im Himmelreich Vater unser im Himmelreich

Totals

Bars

1:2

BWV Date 802 803 91 804 24 805

mid-1739 mid-1739 mid-1739 mid-1739

Duetti Bars I II III IV

230 115 : 115

together, while others speak of Bach’s method of constructing a collection. For example, the double 1 : 1 proportion shown in Table 7.5 between the chorale pairs ‘Wir gläuben all an einen Gott’ (BWV 680–1) and ‘Vater unser im Himmelreich’ (BWV 682–3) with 2 : 2 settings in 115 : 115 bars is clearly no coincidence. Evidence from engraving erasures shows that Bach composed and added the second of each pair later, when he knew the exact length of the first in each pair.20 This made it easy for him to ensure that each additional setting would form proportions in every part. Table 7.5 shows another example suggestive of intentional proportional planning: the double 1 : 1 and 1 : 2 proportions formed between the four Duetti composed and compiled together as a group. The first and third have 112 bars, the second and fourth have 224 bars. The 33-bar da capo repeat in Duetto II is not part of this symmetry. Butler suggests that the four duets BWV 802–5 were conceived as two prelude-and-fugue pairs, and reflect the influence of Bach’s contemporaneous work on WTC II.21 The 1 : 2 proportion in Table 7.5 formed genre-wise with two preludes in 112 bars and two fugues in 224 bars adds numerical support for Butler’s observation. The numerical evidence has suggested several parallels that may have been in Bach’s mind during the various stages of the collection’s evolution. Earliest of all, there seems to have been a collection of fifteen Mass and Catechism settings with 1200 perfectly proportioned bars. These pieces would have made a perfect parallel to the collection of fifteen Chorale Preludes in 1200 bars (BWV 651–65, Table 11.2). Bach then expanded CÜ III by adding six chorale settings and six preludes and fugues in order to create a perfect organ collection of twenty-seven movements. Its 2088 bars

20

Butler, Bach’s Clavier-Übung III, 83–4.

21

Ibid., 18.

1:2

73 73 116 116 39 39 108 108 336 112 : 224

190

demonstrations

in twelve groups of movements and a 1 : 2 proportion 696 : 1392 bars parallel the 2088 bars of WTC I, with its twenty-four pairs of preludes and fugues, and its 1 : 2 proportion in 696 : 1392 bars. Its alternative bar count of 1840 bars could be used to advantage at a later stage if the need arose. Expanding this published collection from fifteen movements in c. 1200 bars to its final perfectly proportioned published version with twenty-seven movements in 1840/2088/90 bars must have cost Bach time, money and effort. Clearly he prized the new plan for this third part of his Clavier Übung series highly. As the project’s prime sponsor, Bach was free to decide whether and how to compose a fourth part, and what kind of composition it should be. Everything was set for him either to publish WTC I with its 2088 bars as a numerical parallel to CÜ III, or to publish a second collection for organ, thus creating a contrasting set in his CÜ series, for keyboard with pedal, to balance the first set of two collections for keybord without pedal. Instead he decided upon a set of keyboard variations, framed by an aria and interspersed with nine canons, for this fourth part of the Clavier Übung series. On the surface the aria with variations had little or no connection with the previous collections in the series, and this opened up many unforeseen and exciting possibilities for new parallel relationships.

II The final Clavier Übung (CÜ IV) – an aria and variations with canons Bach’s Aria and Thirty Variations for Keyboard (BWV 988), the Goldberg Variations, was probably printed in 1741 and first sold in Leipzig at either the 1741 Michaelmas Fair or the 1742 Easter Fair.22 Its thirty-two paginated sides, enclosed in a double wrapper, were engraved by Balthasar Schmid of Nuremberg. On the front of the wrapper is an elaborate title page that reads: [Clavier Übung]. Keyboard practice, consisting of an Aria with Divers Variations, for the Harpsichord with 2 Manuals. Composed for Music lovers to Refresh their spirits by Johann Sebastian Bach.23

The title does not specify that it is the fourth part of the Clavier Übung series, but because it shares the title Clavier Übung and subtitle ‘Denen Liebhabern zur Gemüths-Ergetzung’, and as it was the fourth collection that Bach published in the series, and the words ‘Part IV’ were written into 22

Wolff, Essays, 208.

23

BD I, Doc 172. NBR, Doc 255.

Two further collections for keyboard

a very early copy of the print,24 there is every reason to think that Bach himself regarded it as part four.25 The name ‘Goldberg’ is mentioned neither on the title page nor in Bach’s obituary.26 It was Forkel who first introduced the myth that the variations were written for the insomniac Count Keyserlingk (1696–1764) to be played by his young house musician Johann Gottlieb Goldberg (1727–56).27 The only part of the story that can be substantiated is Bach’s meeting with Count Keyserlingk in November 1741 in Dresden, probably coinciding with a visit to his eldest son Wilhelm Friedemann. The formal regularity of the Goldberg Variations is crystal clear at a glance. There are thirty-two movements (Aria, thirty variations and Aria da capo), all but one (Variation 16) of which has the same binary division at the half-way point marked by a double-bar and a repeat. This visual regularity has encouraged the search for a deeper logic within the structure. Peter Williams sees two patterns with many ‘threes’ and many ‘twos’.28 Although this cannot be disputed, it raises the perennial question of whether these patterns are analytical coincidence or evidence of Bach’s deliberate design.29 In this section the structure will be considered in terms of proportional parallelism. One could be forgiven for assuming that a composer planning a thirty-two-movement work engraved on thirty-two pages would allocate thirty-two bars to each movement, and make a total of 1024 bars. But this was not Bach’s way. Table 7.6 shows that the collection has 960 bars divided by a double 1 : 1 proportion, 16 : 16 movements and 480 : 480 bars formed by consecutive movements. With the exception of Variation 16,30 every movement is either 16 or 32 bars in length, and every section of every movement is repeated, making the performed version literally double the number of bars. There are two notational 24 25

26 27

28 29

30

NBA KB V/2, 103, source C 11. From the circle of J. C. Kittel, Bach’s last pupil. Wolff sees the omission as a result of new publishing conditions, in which Schmid, who had been involved with parts 2 and 3, now took on a larger role. NBA KB V/2, 109; Wolff, Essays, 208. Peter Williams, Bach: The Goldberg Variations (Cambridge University Press, 2001), 5. Ibid., 4, referring to J. N. Forkel, Über Johann Sebastian Bachs Leben, Kunst und Kunstwerke, (Leipzig, 1802), 51–2. Williams, Goldberg Variations, 39–45. For examples of interpretation-based solutions see V. Dequevauviller, La Clavier Übung de Bach: Essai de reconstitution (Paris: Association pour la Connaissance de la Musique Ancienne, 2001), and W. Schenkman, ‘Tatlow’s Bach and Bach’s Signatures in the Goldberg Variations’, Bach 34/2 (2003), 63–106. BWV (1990) gives 96 bars for Variation 16, including its repeat. BWV2a 1998 has an obvious error, giving the written bar total as 47.

191

192

demonstrations

Table 7.6 Consecutive double 1 : 1 proportions across the Goldberg Variations collection Variatio Time Attribution

Bars

1:1

1:1

1:1

8

3 4 3 4 2 4 12 8 3 8 3 4 3 8 6 8 3 4

9

c

Canone alla Terza à 1 Clav

16

16

16

10

¢

Fughetta à 1 Clav

32

32

32

Aria 1 2 3 4 5 6 7

11 12 13 14 15

12 16 3 4 3 4 3 4 2 4

32

32

32

à 1 Clav

32

32

32

à 1 Clav

32

32

32

Canone all Unisuono à 1 Clav

16

16

16

à 1 Clav

32

32

32

à 2 Clav

32

32

32

Canone alla Seconda à 1 Clav

32

32

32

à 1 o vero 2 Clav

32

32

32

à 2 Clav

32

32

32

à 2 Clav

32

32

32

Canone alla Quarta

32

32

32

à 2 Clav

32

32

32

à 2 Clav

32

32

32

32

32

Canone alla Quinta à 1 Clav

32

Ouverture à 1 Clav

48

48

48

17

c 38 3 4

à 2 Clav

32

32

32

18

¢

Canone alla Sexta à 1 Clav

32

32

32

à 1 Clav

32

32

32

à 2 Clav

32

32

32

16

20

3 8 3 4

21

c

Canone alla settima

16

16

16

22

¢

à 1 Clav alla breve*

16

16

16

à 2 Clav

32

32

32

Canone all Ottava à 1 Clav

32

32

32

à 2 Clav

32

32

32

à 2 Clav

32

32

32

Canone alla Nona à 2 Clav

32

32

32

à 2 Clav

32

32

32

à 1 o vero 2 Clav

32

32

32

à 1 Clav Quodlibet

16

16

16

32

32

32

19

29

3 4 9 8 3 4 18 16 6 8 3 4 3 4

30

c

Aria

3 4

23 24 25 26 27 28

Totals

32 movements

Double 1 : 1 proportions

960

480 : 480

240 : 240

240 : 240

16 : 16

8:8

8:8

Two further collections for keyboard

features that throw an element of ambiguity over the otherwise clear-cut numerical structure: the ‘Da Capo al Fine’ indication after the thirtieth variation and the ‘alla breve’ qualification of Variation 22. The spacesaving convention of the da capo indication allowed the thirty-two movements to fit satisfactorily onto thirty-two pages, and to create a perfect parallel between its thirty-two pages and thirty-two movements. Table 7.6 shows that the final aria is included as the thirty-second movement in this double 1 : 1 scheme. There are three movements in cut common time in the collection: variations 10, 18 and 22. All three have 32 written bars, but for Variation 22 alone Bach added the qualification ‘alla breve’, the pulse felt at the breve rather than at the semi-breve, thus allowing the dual possibility of counting this movement as 16 ‘bars’ rather than 32 bars. Had there been an error in the engraving process and the ‘alla breve’ indication omitted from Variations 10 and 18, Bach could have corrected the omission in his personal, post-publication copy,31 but he did not.32 When Variation 22 is counted literally as written ‘at the breve’, i.e. as 16 and not 32 bars, the perfection of the numerical plan becomes apparent. My demonstration is based on this bar count, rather than on the alternatives of 944 bars (without the Aria da capo) or 976 bars (with Variation 22 as 32 bars and including the Aria da capo). The consecutive double 1 : 1 proportions, with 16 : 16 movements in 480 : 480 bars, each of which falls again into a consecutive double proportion with 8 : 8 movements in 240 : 240 bars, can be seen in Table 7.6.

Physical evidence to support this numerical design. Each movement in this work is a multiple of 16 bars, and consequently many symmetrical patterns and multiples of 80 (165) can be formed. Bach created this regular structure, but such regularity makes it difficult to discern which of the many numerical correlations are evidence of Bach’s construction. Below are four that suggest deliberate planning.

31 32

Wolff, ‘The Handexemplar of the Goldberg Variations’, Essays, 162–77. NBA KB V/2, 94–6. Bach did however amend the missing double bar line and repeat marks at bar 18 of Variation 16, clarifying an ambiguity which could potentially have affected the bar count.

193

194

demonstrations

(a) Variation 16 Ouverture marks the beginning of the second half The Ouverture stands out visually and stylistically for several reasons. It is the only movement with a specific title (‘Ouverture’), as well as the common assignation ‘Variatio’; the word ‘Ouverture’ is written by the side of the stave rather than above or below, where the word ‘Variatio’ always appears. As a result the stave has to begin with a hefty indent, the only movement in the entire publication to have this layout. It also stands out as the only French overture in the collection, and the only movement in which the binary division and repeat are not at the midway point. These features have been noticed before, and caused Werner Breig to write that Variation 16 ‘provides a decisive caesura in the middle of the work’.33 Williams claims further that Bach intentionally placed a French overture not only in this collection but at the centre of each of his four Clavier Übung publications: The symmetry is there to be seen on paper and is probably more theoretical than practical: it need not mean that if one timed a performance of all the music, those pieces would hit the halfway point. But note that if this organization around a kind of musical pivot is not accidental — and it is hard to see quite how it could be— several things would follow.34

The numerical structure adds a further observation to the positioning of Variation 16. It is at this point that the second consecutive group of 480 bars begins. Bach created his Variation 16 to highlight the numerical bipartite division of the 32 movements – its indentation, irregular length and title Ouverture acting as a signpost of the work’s structural division for the copyist and performer.

(b) The nine canons Bach designated nine of the thirty variations ‘Canone’. Table 7.7 shows that every third variation is a canon until the thirtieth, which instead of being termed ‘Canone’ has the title ‘Quodlibet’. The nine canons are arranged systematically: Variation 3 at the unison, Variation 6 at the second, Variation 9 at the third and so on until Variation 27 at the ninth. Butt comments:

33

34

W. Breig ‘Bachs Goldberg-Variationen als zyklisches Werk’, Archiv für Musikwissenschaft 32 (1975), 243–71; Wolff, Essays, 168. Williams, Goldberg Variations, 30–1 lists four consequences.

Two further collections for keyboard

Table 7.7 A consecutive double 2 : 1 proportion with 160 : 80 bars in 6 : 3 canons Variation

Time

6

12 8 3 8

9

c

3

3 4 2 4

12 15 18 21

¢ c 9 8 6 8

24 27 9 Variations

Attribution

Bars

2:1

Canone all Unisuono à 1 Clav

16

16

Canone alla Seconda à 1 Clav

32

32

Canone alla Terza à 1 Clav

16

16

Canone alla Quarta

32

32

Canone alla Quinta à 1 Clav Canone alla Sexta à 1 Clav Canone alla Settima

32 32 16

32 32

Canone all Ottava à 1 Clav

32

32

Canone alla Nona a 2 Clav

32

32

240

160 : 80

9 Canons

16

As far as the canons are concerned the cycle may be said to ‘overshoot’, since those at the octave and the 9th are analogous to the opening canons at the unison and at the second.35

Bach must have been aware of this quasi-duplication, yet he pursued the logic. Table 7.8 shows the consecutive double 2 : 1 proportion formed by the 240 bars with 6 : 3 canons in 160 : 80 bars. This patterning was only possible because Bach included three movements with sixteen bars. The title and regular positioning of the nine canons are plain for every performer to see. By stretching a mesh of 240 bars of canon evenly across the work’s 240 : 240 : 240 : 240 bars, Bach created a further level of numerical and structural unity across the collection. This perfect proportioning suggests that the nine canons were fundamental to Bach’s numerical construction of the collection.

(c)

3

The fourteen movements in 4 time 3

Table 7.8 shows that seven of the fourteen movements in 4 time appear in the first half, i.e. Aria–Variation 15, and seven in the second. All move3 ments in 4 time have 32 bars, and therefore form a double 1 : 1 proportion 3 with 7 : 7 movements with 224 : 224 bars. The equal distribution of the 4 movements across the whole again suggests conscious planning. Some may 35

J. Butt, ‘Goldberg Variations’, in J. S. Bach, ed. Malcolm Boyd, Oxford Composer Companions (Oxford University Press, 1999).

195

196

demonstrations

Table 7.8 Proportioning within time and keyboard attributions Variatio

3 4

Bars

Aria

3 4

32

32

1

32

5

32 7

32

32

2

32

8

32

32

3

16

32

32

4

32

32

32

6

32

32

32

9

16

32

32

10

32

32

32 15

32

32

32 16

32 32

1 5 8 12 13 14 17 20 23 25 28 29 Aria 14

3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4

1:1

à 1 Clav Bars à 2 Clav Bars 1 o 2 Clav Bars

None Bars

32+32

Aria

32

32

32

12

32

11

32

32

21

16

13

32

32

Aria

32

14

32

32

17

32

32

20

32

32

23

32

32

48

25

32

32

32 18

32

26

32

32

32 19

32

27

32

32

32

32 22

16

28

32

32

32

32 24

32

32

32 30

16

448 224 : 224 14

400

1 : 1 proportion

32

1:1

29

32

32 112

12

384

14 in 400 bars

2

64

14 in 448 bars

224 : 224 1:1

4 in 112

3

wish to claim that the fourteen movements in 4 time also act as an allusion to Bach’s name.36

(d) A 1 o vero 2 clav – for one or two manuals Another feature of the score that may have aided Bach’s construction of the collection is the manuals required, which are specified for all but four movements.37 Williams considers this highly unusual: The two directions a 1 Clav (‘for one manual’) and a 1 o vero 2 Clav (‘for one or two manuals’), are, I think, unique, and though so worded as to be obvious antitheses to a 2 Clav (long used by organists for lines of a chorale), they are really rather strange. No one needed to say a piece was ‘for one manual’ and would do so only for special reasons, such as (a) wishing to give every variation its own rubric or (b) using 1 Clav to mean ‘any or all sets of strings’ and 2 Clav ‘two separate 8’ sets.38 36 38

D

37 See Chapter 2. Aria and its , Variation 12 and 21. Williams, Goldberg Variations, 50–1.

Two further collections for keyboard

This unique feature may have been introduced deliberately to alert the performer to a parallelism. There are no remarkable numerical characteristics in the movements labelled 2 Clav, a 1 o vero 2 Clav. Table 7.8 shows, however, that the fourteen movements specified for one keyboard form a unit of 400 bars. Bach did not change these specifications in his personal copy of the collection.39 Distinguishing fourteen variations, not once but 3 twice, first with 4 time and then with the unusual a 1 Clav assignation, suggests intentional planning to incorporate the number 14. There is no correlation between the value of the title words40 and the number of bars in the musical structure. Nor is there convincing documentary or numerical evidence that the word ‘Goldberg’ was an inspiration point.41 In the 1970s Werner Breig suggested that Bach had an earlier plan for a cyclical collection of just twenty-four variations built around the first eight canons and framed by the Aria and its da capo.42 Unfortunately there is no way of testing Breig’s hypothesis without knowing the exact length of the speculative early variations.43 Bach’s fourth collection in the Clavier Übung series is a casebook example of symmetrical ordering. Its 960 bars were organised in the simplest way, through consecutive movements, to form two layers of double 1 : 1 proportions. The regularity of the structure highlights the difficulties of discerning compositional intent in parallel techniques. Its 3 fourteen variations in 4 time, and fourteen variations for one manual, may well have been a device alluding to Bach as author. His choice of a physical 1-3-2 (1 work with 32 movements on 32 pages) may also have been intended as a permutation of his name, 2-1-3.

III

CÜ III and IV and parallel collections

Bach published no more collections in the Clavier Übung series. This raises questions such as whether he felt the series was complete, whether he had plans to add to it, and if so, what those plans were. It also raises the question 39 40 41

42 43

NBA KB V/2, 94–6. Numerical values: Aria=28, Variatio=90, Canone=49 and ouverture=137. Contrary to the claims of V. Dequevauviller in ‘Des Concertos Brandebourgeois aux Variations Goldberg’, Revue de musicologie 86/2 (2000), 277–88. Breig, ‘Bach’s Goldberg-Variationen’, 260–1. The version of the Aria that Anna Magdalena copied in c. 1740 into her 1725 Clavierbüchlein, D-B Mus. ms Bach P 225, 76–7, c. 1740 has the same number of bars and is in the same key as its counterpart in the printed collection.

197

198

demonstrations

Table 7.9 A double 1 : 1 within CÜ III and IV possibly planned in 1742 Group

Title and BWV numbers

1 2–3 4 5–9 10–11 12 I II

Prelude (BWV 552/1) 2 Kyrie-Christe-Kyrie settings (BWV 669–74) 2 settings of Allein Gott in der Höh sei Ehr (BWV 675–6) 12 catechism settings (BWV 678–87) 2 settings of Jesus Christus (BWV 688–9) 4 Duetti (BWV 802–5) Fuga (BWV 552/2) Aria and Variations 1–15 (BWV 988) Variations 16–30 Aria da Capo (BWV 988)

Totals

Bars 205 259 194 544 521 117 480 480 2800

1:1 205 259 194 544 521 117 480 480 1400 : 1400

of unity within the series. Apart from the title words Clavier Uebung, the four collections appear to have little in common. Numerical parallels between several of his revised and completed collections, however, suggest relationships that may have been designed, and they may even show that Bach had an overarching scheme for all the collections he revised. Table 7.9 shows some of the parallels suggested by he joint bar total of CÜ III and IV. Together these two parts of the Clavier Übung create together a set with 2800 bars, 1840 bars published in 1739 and 960 bars in 1742. Ordered consecutively, both CÜ III and IV are divided by a double 1 : 1 proportion,44 thus the larger set of two also creates a double 1 : 1 proportion, with 1400 : 1400 bars in 4 : 4 consecutive sections. Furthermore, as the number 2800 is the second numerus perfectus, 28, multiplied by 100, as well as the B-A-C-H number 14 multiplied by 200,45 one cannot rule out the possibility that Bach aimed for this number resonating with 14s. Coexisting with the first overarching numerical scheme for the Clavier Übung series, is a possible scheme created in conjunction with the publication of the Schübler Chorales in 1747, see Table 8.9. Bach’s ongoing preparation of The Art of Fugue, with its implied 2370-bar structure, may also have suggested a new idea for a complementary collection with the Schübler Chorales and CÜ III in its alternative bar count of 2090 bars: see Chapters 9 and 11 below, and Table 11.7.46 And 44 45

46

See Tables 7.4 and 7.6. 2800 is 200 x 14, thus potentially related to ‘14=Bach’, and 3120 a permutation of 2-1-3 (B-A-C). See Tables 9.10, 9.11 and 11.7.

Two further collections for keyboard

the figures suggest that Bach had yet a third plan for his four-part Clavier Übung series, although this plan was never realised in print. It was to include an addendum to CÜ IV to unite all four parts of the published Clavier Übung into one numerically perfect whole. The plan needed just 70 bars.

IV

Canons on the ground

Although Bach had published a great set of perfectly proportioned variations on the ‘Goldberg’ Aria, including nine canons united by variation form, he continued to improve the concept. Using the bass notes of the Aria he decided to generate further permutations and write a set of perpetual canons: a form that was a perpetual reminder of the eternal and never-ending origin of music.47 The canons (BWV 1087), discovered in Bach’s own copy of the original print, Paris Ms. 17669,48 had all been composed by or before 1748.49 Canon 11 (BWV 1077), was written before 15 October 1747, when Bach copied it into an album owned by theology student Johann Gottlieb Fulde; and Canon 13, Canon Triplex à 6 voci (BWV 1076), was engraved around 1747 and features in Haußman’s portrait of Bach, painted in 1746, although whether the picture shows Bach with the print or the manuscript of the canon has not yet been established.50 Table 7.10 shows that together the fourteen canons have either 73 or 70 bars. They are all puzzle canons, in abbreviated notation that requires solving before being performed. Two notational ambiguities make the exact length impossible to ascertain, hence the alternative bar count shown in Table 7.10. The first ambiguity is an extra upbeat or half bar in canons 2, 3, 4 and 6; the second is the pulse in Canon 14, which has a clear 2 4 time signature even though there are bar lines after every fourth crotchet 2 4 beat – giving a total of 8 bars in the 4 instruction, or 4½ bars in 4 time 2 including the extra upbeat.51 When Canon 14 is counted as 4 and upbeats 47 48

49 50

51

Appendix, 1723-II. F-BN Paris Ms. 17669. BWV 1087 covers the complete set of fourteen canons. Schmieder compiled the catalogue in 1950 before Alain’s discovery, which caused canons 11 and 13 each to have an additional BWV number. Canons 11 and 13 had been known since Bach’s time, and in 1950 were assigned the catalogue numbers BWV 1077 and 1076. When the set of fourteen canons was discovered in 1974, it was assigned the number BWV 1087; thus canons 11 and 13 each have two catalogue numbers. Y. Kobayashi, ‘Zur Chronologie der Spätwerke’, BJ 74 (1988), 60. Wolff, Essays, 414, postscript. Kobayashi, ‘Zur Chronologie der Spätwerke’, 55, cited in E. Crean, ‘The Fourteen Canons, BWV 1087’, Understanding Bach 5, 67–75. 2 BWV2a erroneously gives C instead of 4 for the time signature of Canon 14.

199

200

demonstrations

Table 7.10 Structure and proportion in abbreviated notation of fourteen canons (BWV 1087) Canon

Bars

Precise bars

1 2 3 4 5 6 7 8 9 10 11 12 13 14

5 4 4 4 5 4 5 5 5 10 5 5 3 9

5 4 4½ 4½ 5 4½ 5 5 5 10 5 5 3 4½

Totals

73

70

1:1 5 4 4½ 4½ 5 4½ 5 5 5 10 5 5 3 4½ 35 : 35

disregarded the fourteen canons have 73 bars, whereas when canon 14 is 4 counted as 4 the alternative total is 70 bars. The fourteen figures in 70 bars form a 1 : 1 proportion.

Background story In 1974 Bach’s personal copy of the Goldberg Variations (CÜ IV) was discovered by Olivier Alain. The copy was significant not only because it contained the composer’s handwritten corrections and improvements, but because tucked inside the back cover was a sheet of manuscript on which Bach had written these fourteen hitherto unknown canons.52 At the time Christoph Wolff considered it ‘the most important Bach source that has come to light in a generation’.53 We do not know Bach’s intended purpose for the extra fourteen canons, nor whether he wished them to be incorporated into a revised version of the Goldberg publication. Perhaps the theological significance of perpetual canon had something to do with it. In 1723 52

53

Verschiedene Canones über die ersten acht fundamental-Noten vorheriger Aria von J. S. Bach, BWV 1087, F Pn Ms. 17669 at the Bibliothèque Nationale, Paris. Wolff, Essays, 163, originally published in JAMS 29 (1976), 224–41.

Two further collections for keyboard

Bokemeyer encapsulated this view, writing that the perpetual canon ‘is the most perfect model of all artistic work because its united beginning and the end are a reminder of the eternal origin of the Harmony of eternity.’54 Wolff considered it ‘obvious that the fourteen canons form the hitherto unknown but direct and logical link between the Goldberg Variations and the Musical Offering’.55 Numerically there is some support for Wolff’s claim. Taking canon as the common genre, the nine canons in CÜ IV, Table 7.7, have 240 bars, and all the canons and ricercars in the Musical Offering have 660 bars, Table 9.2, which together create a rational total of 900 bars. The 70 bars of the fourteen canons in BWV 1087 would then create a block of 970 bars of canon in these two collections, although there are no obvious large-scale parallels with this and other canonic collections created or revised at the time. There are, however, other plausible explanations. Although it is not possible to be sure whether Bach designed the 3 fourteen movements in 4 time and the fourteen movements for one manual in the Goldberg Variations, the number fourteen in BWV 1087 is an established fact, because Bach numbered the canons sequentially from 1 to 14. It could be argued that there are actually fifteen canons,56 as Bach ascribed the number 10 to two parts of Canon 10, and that Bach’s ingenious addition of ‘etc.’ implies that he could easily have continued with many more. Wolff ventures to suggest that Bach’s choice of fourteen, rather than any other number, had a self-referential motive: The fact that the total of numbered canons comes to fourteen is not without significance. This number represents Bach’s name (BACH=2+1+3+8=14) . . . there can be no doubt that Bach chose this number deliberately, for the canons could have been counted in other ways, which would have led to a different total. Moreover, at the end of the last canon appears the abbreviation “etc.”, which shows clearly that the composer could have continued with further canons had he wanted to.57

Had Bach intended to publish a new edition of CÜ IV including the fourteen canons, the collection would have had 1030 bars in all, including 960 bars of Goldberg Variations and 70 of canons, and a guaranteed 1 : 1 proportion across the whole collection. Although the additional 70 bars would have destroyed the 1400 : 1400 proportion between CÜ III and CÜ IV (Table 7.9) in 1742, Table 7. 11 explains how the new total formed by CÜ IV (the Goldberg Variations) and its supplementary fourteen

54 57

Appendix, 1723-II. Wolff, Essays, 168.

55

Wolff, Essays, 168.

56

Williams, Goldberg Variations, 32.

201

202

demonstrations

Table 7.11 Bach’s evolving plan for the Clavier Übung series? Date 1722 1723 1731 1735 1739 1748?

Bars Well-Tempered Clavier Book 1 Inventions and Sinfonias, Aufrichtige Anleitung Clavier Übung Part I Clavier Übung Part II Clavier Übung Part III Clavier Übung Part IV and 14 canons (BWV 1087)

Totals

2088 1032 2178 942 2090 1030

1:

1:

1

2088 1032 2178 942 2090 1030 3120 : 3120 : 3120

canons creates a far more unifying total of 3120 bars, weaving together six major keyboard collections. The first 3120 structure was created in 1723, around the time of his arrival in Leipzig, and the second appeared when publication of CÜ I and II was complete in 1735. The third parallel was never fulfilled in print, because Bach’s autograph fair copy of the fourteen canons remained tucked inside his own printed copy of CÜ IV and lay forgotten for 200 years. The perfection of these three large-scale proportions with their 3120 bars demonstrates a numerical unity across the keyboard collections. Six parts form a large-scale 1 : 1 : 1 proportion, using a total made up of the B-A-C integers 1, 2 and 3. The sum and product of the integers 1, 2 and 3 prove the number 6 to be perfect. Hypotheses based upon sound source evidence can generate stimulating ideas and open new avenues of inquiry, but it is a dangerous pursuit.58 Aware of this, I have tried at all times to keep an open mind to new possibilities while respecting the confines of available documentary evidence. The figures in this chapter and throughout the book are based on the bar structures of Bach’s manuscripts and original prints, and checked against the latest scholarly NBA editions and BWV catalogues. If these parallel proportions are Bach’s numbers, they demonstrate a dramatically new image of Bach the composer. Each of the four parts of the Clavier Übung has the phrase ‘zur Gemüths Ergetzung verfertiget’ engraved on the title page, a phrase that in Williams’s words: ‘suggests that any such volume of music was not to be taken as the vainglorious produce of some showy performer but was, indeed, a pious 58

See Dequevauviller, La Clavier Übung de Bach, 105, where the result is found by adding together thirteen Bach collections, and mixing the bar totals from Bach’s published and unpublished collections with collections not compiled by Bach but by modern editors.

Two further collections for keyboard

offering’.59 The philosophy behind the wording of the title pages would also have motivated the numerical structure of the four Clavier Übung collections, with its perfection on the grandest possible scale. Bach’s active efforts to create their larger and smaller parallel proportions attest to his desire to reach beyond worldly visibility to the unseen realm where timebound Harmony meets eternity.

59

Williams, Goldberg Variations, 3–4.

203

8 Two small late collections

Canonic Variations on ‘Vom Himmel hoch’ (BWV 769) Six ‘Schübler’ Chorales (BWV 645–50) Unser seel. Bach ließ sich zwar nicht in tiefe theoretische Betrachtungen der Musik ein, war aber desto stärcker in der Ausübung. Zur Societät hat er den Choral geliefert: Vom Himmel hoch da komm’ ich her. vollständig ausgearbeitet, der hernach in Kupfer gestochen worden. C. P. E. Bach and F. W. Marpurg, 1754

This chapter will consider two unusually short, published keyboard collections related by the chorale. In the final ten years of his life Bach prepared four collections for publication that feature canonic works: The Art of Fugue, the Goldberg Variations, the Musical Offering, and his shortest collection and the subject of the first part of this chapter, the Canonic Variations based on the chorale ‘Vom Himmel hoch’. The second part of this chapter will focus on a short collection of six chorales for organ, known today as the ‘Schübler Chorales’. Bach worked with chorales throughout his life, spinning improvisations on them for church services and setting them for voices and instruments in his cantatas and passions.

I A grandfatherly miniature – variations on ‘Vom Himmel hoch’ The compositional history and intentions of the Canonic Variations have been the subject of speculation and discussion since 1754, when C. P. E. Bach and J. F. Agricola wrote that Bach submitted the chorale Vom Himmel hoch da komm’ ich her to the Mizler society ‘completely worked out, which afterwards was engraved in copper’.1 In the 1960s a 204

1

NBR, Doc. 306, 307. BD III, Doc. 666, 89.

Two small late collections

heated debate arose2 over whether Bach’s final version was the surviving undated manuscript copy (P 271, 22v–25v, 100–6)3 or the undated fivevariation engraving by Balthasar Schmid. It was not until three decades later that new documentary evidence resolved the issue once and for all.4 By isolating and interpreting many details in the print, and comparing them with Bach’s manuscript, Gregory Butler proved that there could be no black and white answer to the question: Variations I–III in the engraving are earlier than their later manuscript equivalent, Variation V was probably entered at about the same time in both manuscript and engraving, and the manuscript of Variation IV slightly predates its engraved counterpart.5 Although today we think of the collection with five variations, the work went through several stages before it reached this form. The engraving bears witness to three: (a) a three-variation set with title page,6 (b) the composition and addition of Variation V,7 and (c) the composition and addition of Variation IV, which completed the fivevariation set in time for publication and sale at the Leipzig Michaelmas fair in September 1747.8 Bach’s manuscript implies two further stages: (d) a four-variation set (Variations I, II, V and III) copied at one sitting, which has a Schlußzeichen after Variation III marking the end, and (e) the later addition of Variation IV after the Schlußzeichen, to complete a set of five variations.9 The numerical structures of these developmental stages will now be examined to see which of the versions might have been considered ‘completely worked out’.

A plan for an engraved set of three variations with title page? Based on evidence in Schmid’s engraving, the physical layout suggests that it may originally have been a three-variation set proportioned 1 : 2 : 3 with one title page (page 1), two pages of music (pages 2 and 3) and three variations across the two pages. Table 8.1 shows that the three movements of this three-variation set have a total of sixty-eight bars. Contrary to the 2

3 4

5 8

Walter Emery, ‘A Note on the History of Bach’s Canonic Variations’, Musical Times 104/1439 (January 1963), 32–3; and H. Klotz, ‘Über Johann Sebastian Bachs Kanonwerk “Vom Himmel hoch, da komm ich her”’, Die Musikforschung 19/3 (1966), 297 and 303. D-B Mus. Ms. Bach P 271. G. Butler, ‘J. S. Bach’s Einige Canonische Veraenderungen: The View from the Original Print’, in Bach’s Clavier-Übung III (Durham, NC; London: Duke University Press, 1990), 91–116, and G. Butler, ‘J. S. Bachs Kanonische Veränderungen über “Vom Himmel hoch” (BWV 769). Ein Schlußstrick unter die Debatte um die Frage der “Fassung letzter Hand”’, BJ 86 (2000), 9–34. 6 7 Ibid., 34. Ibid., 14, and Butler, Bach’s Clavier-Ubung III, 104–6. Ibid., 22. 9 Ibid., 25. Ibid., 26–7.

205

206

demonstrations

Table 8.1 Proportions in what may have been an early plan for a three-variation set Page/bars

Bars

Words

Value

Title page, XXVIII Variatio 1 all’Ottava Variatio 2 alla Quinta Variatio 3 alla Settima

1 2/1–18 2/1–14a; 3/14b–23 3/1–27

18 23 27

Vom Himmel hoch

46 57 33

Total: Pages and words

3

Total: Bars and word value

3 68

1:1

1:2

3:3 136

68 : 136

norms for a published and perfected Bachian collection,10 no perfect proportions can be formed between the movements of this possible set of three. There is however an unusual 2 : 1 proportion that Bach may have introduced deliberately. The numerical value of the first three words of the chorale melody ‘Vom Himmel hoch’, 136, creates a 2 : 1 proportion with its 68 bars; its three words and three variations create an additional 1 : 1 proportion. If the resulting double word-bar parallel is evidence of Bach’s planning, it is an example of Bach using the numerical value of these three words in a tried and tested parallel method of compositional invention described and used by poets in Bach’s circle, including Menantes and Picander.11 The words on the carefully engraved title page provide further evidence of the same kind. Table 8.2 shows the numerical value of the title page, line by line. There are many recurring groups of 280: both line 1 and line 11 have a total of 280, and lines 3 and 9 together make a third 280, while lines 2 and 4b–8 have a total of 560 (i.e. 2
280). These results strongly suggest that someone crafted the title page with a view to creating a parallel conceit. Adjustments to the spelling forms and essential key words suggest how this was done.12 The keywords ‘Weynacht-Lied’ (122) and ‘Johann Sebastian Bach’ (158) may have been the invention point for the symmetrical patterning based on the figure 280. Finding a title with a parallel value was probably the next step. The title words ‘Einige canonische 10

11

12

The norm, according to proportional parallelism, is the presence of two or more layers of proportion. Christian Friedrich Hunold, Die allerneueste Art zur Reinen und galanten Poesie zu gelangen (Hamburg: Liebernickel, 1707), 542; Picander, Ernst-Schertzhaffte und Satyrische Gedichte, vol. III (Leipzig, 1732, 27). See Chapter 2. The use of ‘vor’ rather than ‘für’ in line 6, and ‘2’, not ‘zwey’, are examples of a Riederer-like exploitation of German orthography.

Table 8.2 Numerical value of title page showing personalised numbers: 280, 1400, 2138 Line

Words

Value

1 2 3 4a 4b 5 6 7 8 9 10 11 12

Einige canonische Veraenderungen über das Weynacht-Lied Vom Himmel hoch da komm ich her vor die Orgel mit 2 Clavieren und dem Pedal von Johann Sebastian Bach Königl. Pohl. und Chur. Saechs[s]. Hoff Compositeur Capellm. u. Direct. Chor. Mus Lips. Nürnberg in Verlegung Balth: Schmids

48þ87þ145 44þ23 93þ29 46þ57þ33 5 48þ20þ30 51þ18þ54þ40þ2þ84 37þ21þ36 47 57þ87þ14 64þ48þ37þ48þ71þ34þ146 58þ20þ57þ42þ50þ53 94þ22þ105þ41þ72

Totals

JSB numbers 280 67 122 136 5 98 249 94 47 158 430/448 280 334

280 67 122 136 5 98 249 94 47 158 430/448 280

2300/18

1400

2:1:1:1

Block

280 67 122 136 5 98 249 94 47 158 430/448 280 334 560 : 280 : 280 : 280

900/918

208

demonstrations

Veraenderungen’ was a clever choice, not only because its total is 280, but also because of the parallel allusion in the word ‘einig’ (discussed below). Manipulating the biographical words in line 11 will have helped achieve the third 280. Abbreviations of Bach’s professional credentials are never standardised in his title pages, and almost always difficult to decipher. Unusually on this title page the orthography, and therefore their numerical value, is crystal clear. The title page also includes the catalogue number, N. XXVIII. Butler has demonstrated that Schmid’s sequences are an unreliable guide to a work’s publication date. Would it not be in character for the composer, whose surname had a value of 14 and who allegedly waited to join the Mizler society until the fourteenth place was available,13 to wait again until this ‘Einige’ set of variations could have the publication number 28 with many 280s in its title? The number 280 is both a multiple of 28, the second numerus perfectus, and forms a perfect 2 : 1 proportion with the 14 of ‘Bach’. These parallel allusions to the family surname support Butler’s suggestion that the early three-set collection may have been composed as a present to celebrate the birth and baptism of the first Bach grandchild, Johann August.14 Had it been designed solely and specifically for Johann August, however, one would expect to find a numerical allusion to the dedicatee, in this case 143.15 This absence, combined with the generic 280s of the title page, implies that, although the birth of Johann August may have been the catalyst for the composition and engraving of the variations, Bach did not intend them as a personalised gift to his first grandson. It was perhaps his gift as grandfather to the as-yet unknown generation of Bach musicians, of whom Johann August was the representative. There is a further numerical parallel in the collection through the number of notes in the chorale melody. ‘Vom Himmel hoch’ in its plainest form has 33 notes. Due to a passing note in bar 15, the chorale melody in Variation 1 has 34 notes, while Variations 2 and 3 have 33 and 36 notes respectively. Bach may have introduced the passing note in the first variation to create an additional 1 : 2 proportion with the 68 bars,

13

14

15

F. Smend, J. S. Bach Bei Seinem Namen Gerufen (Kassel; Basel: Bärenreiter, 1950), 27 claims that Bach could have become the twelfth member, but waited to become the fourteenth. Butler, Bach’s Clavier-Übung III, 104. Butler posits that Bach’s experience of the Prussian occupation of Leipzig, on 30 November 1745, and the peace accord signed at Dresden on Christmas Day 1745, may have influenced Bach’s choice of the Christmas chorale Vom Himmel hoch and motivated him to write the variations. The numerical value of Johann (58) August (85) = 143. His name was recorded in the now lost baptismal record as Johann (58) Adam (18) = 76. BD II, Doc. 540.

Two small late collections

i.e. 34 : 68 notes:bars, and 68 : 136 bars:title numbers. If this was intentional he did not pursue the conceit to its logical end, which he could have done by giving the chorale melodies of Variations 2 and 3 68 notes, thus creating a perfect 2 : 1 proportion with the 34 notes of the first variation. No bound copy of a three-variation set with title page has survived, but its structure was not destroyed by later additions, and its four sides could easily have been pulled and separated from the final five-variation engraving. It is therefore not beyond the realm of possibility that the 1754 ‘completely worked out’ collection was the three-variation version. This version with its title page fulfils two of the three characteristics of proportional parallelism. It has several layers of proportion: 34 notes in the chorale melody of the first variation, 68 bars in the three variations, 136 in the title words ‘Vom Himmel hoch’, three words, three variations. And it has an allusion to Bach’s name, in the title page numbers. The bar total of the collection, however, is not at any stage a multiple of 10 or 100. The implications of this missing characteristic will be discussed below. A clear Endzeichen in the autograph score P 271 after Variation III on the verso of leaf 24 indicates that at some point in its compilation the work ended after this variation. But this simple observation is confused because by then the manuscript was in its four-variation form in the order I, II, V, III, Endzeichen. It would have been technically possible to pull and bind a four-variation collection from the engraved plates, although, because Variations II and V are on the same sheet, the order would have been I, II, III, and V.16 No manuscript or engraved copy of the collection in this constellation has survived, nor does its numerical structure, with 124 bars (18+23+56+27) and lack of proportions recommend it. Further ideas that suggest Bach’s purpose for the Endzeichen after Variation III will be discussed below.

A perfect plan for a set of five variations? Table 8.3 shows that the five-variation collection in both the manuscript and the engraving has 166 bars and five movements. Once more the bar total is not a multiple of 10 or 100, but the collection does display the expected double proportion between movements: 1 : 1 and 2 : 3 with 83 bars in two variations and 83 bars in the remaining three. 16

Whereas in the engraving Variations II and III are on the same sheet.

209

210

demonstrations

Table 8.3 Order, symmetry and proportion in the engraving and autograph score, P 271 Ordering in 1747 print Variatio 1 all’Ottava 2 alla Quinta 3 alla Settima 4 all’Ottava 5 alla Sesta, etc Totals

Ordering in Bach’s autograph

Bars 1 : 1 Bars Variatio 18 18 18 1 all’Ottava 23 23 23 2 alla Quinta 27 27 27 3 alla Sesta, etc 42 42 42 4 alla Settima 56 56 5 all’Ottava 166 83 : 83 110 Totals

Ordering in incipit

1: 1

Bars 1 : 1 Bars Incipit Value 1 : 1 18 18 18 Von 23 23 23 Himel 56 56 hoch 27 27 27 da 42 42 42 kom 166 83 : 83 110

47 45 33 5 36 166

47 45 33 5 36 83 : 83

5 variations and 5 words in the incipit 166 bars and 166 is the numerical value of the incipit 83 : 83 proportion between the bar total. 83 : 83 proportion in the value of the incipit

5: 5 166 : 166 83 : 83 : 83 : 83

In the manuscript version there is a symmetrically arranged ‘proportion by situation’ with a 6 : 5 proportion in the 60 bars of the outer two variations, and the 50 bars of the second and fourth around the central movement. In both manuscript and print four of the movements have 110 bars, a noteworthy number as it is integral to the structure of the Musical Offering.17 Table 8.3 shows that the 110 bars are arranged symmetrically in the manuscript score, and consecutively in the print. The words ‘Von [sic] Himel [sic] hoch da kom ich her’, in Luther’s antiquated spelling, are written above the first variation in both manuscript and print, contrasting with the more modern spelling of the engraved title page. This orthographic inconsistency in such prominent title words is striking, and typical of the ploys used to alert a reader to the presence of a parallel conceit. Table 8.3 shows that the value of the first five words ‘Von Himel hoch da kom’ forms a perfect 1 : 1 proportion with the number of bars in the final five-variation collection, 166 : 166. Furthermore, the five words mirror exactly the proportion within the bar structure: the 2 : 3 words having a value of 83 : 83, just as the 2 : 3 movements have 83 : 83 bars. Thus the words create several new layers of proportions with the structure of the collection: 5 words : 5 variations; 166 bars : 166 words, 2 : 3 words with value 83 proportioned with 2 : 3 variations in

17

Table 9.2: structure of the canons is 110 : 110. Table 9.3: ‘canon’=44, ‘sonata’=66.

Two small late collections

83 bars. Although the five-word incipit is grammatically incomplete, the numerical correspondences between it and the bar structure of the collection must be noted. The numerical value of Luther’s spelling was beyond Bach’s control, but parallel devices using the first lines of hymns were common and well known.18 To achieve the number–word–bar correspondence based on ‘Von Himel hoch da kom’, Bach must have manipulated the number of bars in Variations IV and V before he asked Schmid to engrave the spelling above the first variation. Butler suggests that Luther’s spelling was made redundant by the subsequent title page.19 The numerical evidence suggests the contrary: that regardless of the order of the engraving, the dual orthography was intentional, serving to alert an eighteenth-century reader to the presence of lusus ingenii in the collection.20 The reader not only had to solve the enigmatic notation of the first three engraved variations but also to seek a solution to the structure of the collections of five – and possibly three – variations. Over the years scholars have found other allusions to Bach’s name in this collection; in the melody of Variations IV and V,21 in the notes B-AC-H at the end of Variation IV;22 in a self-referential number in the 41 bars (J. S. Bach) of the first two movements that lie side-by-side in both printed and written scores, and in a referential allusion in the total number of bars,23 which Friedrich Smend claimed stood for Bach, i.e. because 83
1
2=166, then 8, 3, 1, 2 (BACH=2, 1, 3, 8), strongly implying that Bach chose the number deliberately. Table 8.2, columns 4 and 5, show two other instances in the title page, although I am not persuaded that they were intentional. The Bach numbers 2 1 3 8 appear in permutation as 2318 in the alternative numerical value of the perfectly proportioned title page, together with further potential allusions to Bach’s name, the most persuasive of which is the cumulative total of the main words, 1400, containing three sets of 280 formed by key words. However, without further evidence of Schmid’s method of constructing a title page, these numerical correlations must remain simple observations.

18 19

20 21 23

See Chapter 2, for Gessner’s description of the acrostic in well-known hymns. Butler, Bach’s Clavier-Übung III, 105. Butler assumes that the title page would have been engraved after the entry indicators. See Chapter 2 for discussion of lusus ingenii. 22 Klotz, ‘Über Johann Sebastian Bachs Kanonwerk’, 303. NBA KB IV/2, 86. Unpublished letter to Jansen, 25 April 1943.

211

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demonstrations

Various plans for a perfected set? The three-, four- and five-variation versions of the Canonic Variations demonstrate two characteristics of proportional parallelism, but none has a bar total that is a multiple of ten or a hundred. In the few published collections where this is the case, the complete structural plan is revealed when two companion collections, associated by a common title or compositional time-line, are seen together.24 This begs the question of Bach’s larger design for the Canonic Variations as part of a companion set. Bach scholars have associated the Canonic Variations with several different compositions. For example, the similarity between the eight fundamental tones of the Goldberg Variations and the melody ‘Vom Himmel hoch’ was one of several factors that led Wolff to claim that ‘the idea to elaborate the Christmas cantus firmus originated as an afterthought in connection with the fourteen canons’.25 And Peter Williams noted some formal associations with the Schübler Chorale collection,26 writing In their form, the nature and ingenuity of their counterpoint, their complexity of notation, the association of their texts with Advent and Christmas, and above their musical language, the Canonic Variations are an obvious contrast to the Schübler Chorales. Perhaps Schübler had originally been intended for the publisher?

These source-based observations can be tested using the principles of proportional parallelism.

(a) Was there a companion pair for the three-variation collection? The fourteen canons and seventy-two bars of BWV 1087, based on the eight fundamental tones of the Goldberg Variations are not related numerically to the 166 bars and five movements of the engraved copy of the Canonic Variations, but there is a striking numerical coincidence between the canons and the three-variation canonic set. Table 8.4 shows that the 72 bars of canons and the 68 bars of variations contain between them 140 bars, forming a parallel to the 280 value of the Canonic Variations title page, and to the 280 bars of the six Schübler Chorales. This exact 1 : 2 proportion with 140 : 280 bars would be typical of 24

25

26

For example, the CÜ I and II pair (3120 bars), and the Easter and Ascension Oratorio pair (1400 bars). C. Wolff, ‘Bach’s Personal Copy of the Schübler Chorales’, Essays, 177; Butler, ‘J. S. Bachs Einige Kanonische Veraenderungen’, 15. P. Williams, The Organ Music of J. S. Bach, 2nd edn (Cambridge University Press, 2003), 518.

Two small late collections

Table 8.4 Multiples of 280 bars from collections completed in 1740s Companion Collections?

Bars

1:2

Variations on ‘Vom Himmel hoch’ BWV 769, c. 1747? Canons on Goldberg Ground BWV 1087, c. 1747? Schübler Chorales BWV 645–50, c. 1748?

68 72 280

Totals

420

140 : 280

1400

280 : 280 : 280 : 560

Title-page values of ‘Vom Himmel hoch’ BWV 769

68 72 280

Bach’s construction technique. If the proportion is his design, it implies that these three small sets were planned as companion pieces, probably while he was working on the three-variation set in early 1747. Furthermore, had Bach decided to sell the three-variation set separately, even after publication of the five-variation set, then the 140 : 280 plan within the three collections (Table 8.4) could have been devised later too, even after 1747.

(b)

Was there a companion pair for the four-variation collection?

Table 8.5 shows that the bar total of the hypothetical four-variation collection is 124 bars, and that of the four duets in canonic style added at the last minute to Clavier Übung III is 336 bars. Together therefore these eight movements have 460 bars, and form a triple 1 : 1 proportion: 4 Variations : 4 Duets, combining to make 2 : 2 Duets and Variations with 230 : 230 bars. There is however no documentary evidence to suggest that Bach made such an association between these canonic movements, and so, in spite of the parallel proportions, I am not convinced this result represents Bach’s planning. The companion parallel I am more persuaded by, on historical and chronological evidence, is formed with the 124 bars of the Six Canones Diversi (fascicle III D of the Musical Offering), shown in Table 8.5. Like the duets from CÜ III, the Canones Diversi were added almost as an afterthought to the engraved collection as Bach was compiling the Musical Offering, which was composed at much the same time as the Canonic Variations. The striking 1 : 1 proportion with 124 : 124 bars and its corresponding timescale and genre is sufficiently persuasive to consider it valid evidence of deliberate compositional design. The Musical Offering could be purchased in individual sections and these six canons could have been drawn from the engraved plates separately, since they were printed on

213

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demonstrations

Table 8.5 Possible compositional companions for a speculative four-variation plan BWV

Bars

769/1 769/2 769/5 769/3

18 23 56 27

Totals

124

BWV

Bars

Bars

1:1

BWV

Movement

802 803 804 805

73 116 39 108

91 139 95 135

91 139

336

460

95 135

1079/4a 1079/4b 1079/4c 1079/4d

Canon 1 Canon 2 Canon 3 Canon 4

à2 à2 à2 à2

18 8 4 8

230 : 230

1079/4e

Canon 5 à 2

8

8

1079/4f

Fuga canonica

78

78

Four Canonic Variations c. 1747. Four Duets c. 1739

Four Canonic Variations, c. 1747. Six Canons from Musical Offering, c. 1747

Bars

124

1:1 18 23 56 27

18 8 4 8

124 : 124

the two inner sides of a folded folio sheet, fascicle III D.27 It would also have been possible to purchase the four Canonic Variations as a group, if the two independent sheets of Variation 4 were removed. Attractive as the 124 : 124 parallel is, it is not a multiple of 10, the first characteristic of proportional parallelism. However, were the 72 bars of the Goldberg canons brought into the numerical plan, it would result in a collection of 24 movements in 320 bars: 6 canons, 4 Canonic Variations and 14 Goldberg canons in 124+124+72 bars respectively. With the exception of the 14 devised but not engraved Goldberg canons, this collection could have been generated from existing engraved plates to create a new 320-bar block. The miniature Schübler publication could also have been added to make a pleasing collection of 30 movements in 600 bars. The possibilities are endless, but in the absence of hard evidence, such as a bound exemplar or copy in these combinations, they must remain speculative.

(c) Was there a companion pair for the five-variation collection? When Bach revised his plan to make a set of five variations, he must have had a reason for going against his normal practice of making the total a multiple of 10 or 100. Although I have not isolated a companion piece for the five-variation set, numerical evidence suggests that it may have been part of a new large-scale plan of collections for organ, collected in P 271,28 27 28

Introduction to the facsimile (Leipzig: Peters, 1977), 12. See R. A. Leaver, ‘Ms Bach P 271: A Unified Collection of Chorale-Based Pieces for Organ?’ Bach Notes 1 (Spring 2004), 1–4.

Two small late collections

Table 8.6 A collection for organ in P 271? P 271 Fascicle Fascicle Fascicle Fascicle Fascicle Fascicle Totals

1 2 2 2 2 2

1v–20r 20v–22r 22v–25v 25v 26

Compositions

BWV

Copyist

Bars

Trio Sonatas 15 Organ Chorales 2 Organ Chorales Canonic Variations Fragment Lost

525–30 651–65 666–7 769a 668

Bach Bach Altnickol Bach Anon ?

1560 1200

Bars

64 166

2760

230

the first two fascicles of which were bound together during Bach’s lifetime.29 Table 8.6 shows that the first work in P 271 is a fair copy of the Six Trio Sonatas, BWV 525–30, with 1560 bars, and the second the fifteen chorale preludes (BWV 651–65), with 1200 bars. This creates a total of 2760 bars or 230
12. Bach then left some pages blank, and late in 1747 filled the remaining pages with the 166 bars of Canonic Variations. Later still his son-in-law Altnickol added two further chorale preludes (64 bars: BWV 666–7) to the blank pages directly after Bach’s fifteen and before the Canonic Variations. Unfortunately, we do not know whether Altnickol did this with Bach’s authorisation.30 Table 8.6 shows that Alnickol’s addition of 64 bars creates a consecutive block of 230 bars with the 166 bars of Canonic Variations (22v–25v). This new block of 230 bars is potentially significant as it is numerically related to the 2370 bars of the first two works in P 271. The bar total of Clavier Übung III, published a few years earlier, is also a multiple of 230 x 8 (1840), thus creating a 12 : 8 or 3 : 2 relationship with the organ works in P 271. Might the mini 230-bar building block at the end of P 271 indicate that Bach had plans for yet another organ collection of mixed genre? Given the numerical value of the Canonic Variations’ title page, 2300, Table 8.2, and the coincidence of 460 bars and 230 : 230 of the hypothelical Duet-Variation collection, it seems that in the 1740s Bach was deliberately using the number 230 in his parallel structures.31

29 30 31

R. Stinson, J. S. Bach’s Great Eighteen Organ Chorales (Oxford University Press, 2001), 30. Y. Kobayashi, ‘Zur Chronologie der Spätwerke’, BJ 74 (1988), 56–7. It was written after 1746–7. I doubt that the number 230 held any direct symbolic meaning. Around this time Bach copied the numbers 1260, 1290, 1335 and 1941 in the margins of his Calov commentary beside Daniel 12:7–12. He did not copy the number 2300 when it occured several chapters earlier.

215

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demonstrations

Parallel meanings of the title ‘Einige canonische Veraenderungen’? David Yearsley has pointed out the similarity between the title of Telemann’s Etliche contrapunctische Veränderungen über die telemannische Sonatina and that of Bach’s Canonic Variations.32 The numerical structure of the title page, shown in Table 8.2, suggests that the choice of title, wording and spelling was deliberate, whether influenced by Telemann or not. Bach’s title is often translated as ‘Some Canonic Variations on the Christmas hymn “Vom Himmel hoch da komm ich her”’.33 Entries in Fritsch’s German–English dictionary (Leipzig, 1716) show that the word ‘Einig’ had many more implications than the all-purpose ‘Some’.34 1. eins mit einem seyn, to be of one and the same mind with one, to agree with him. ‘Einig mit einander leben, to live peaceably and unanimously together, to agree well together. 2. Einig, eintzig . . . only, sole. ‘Das ist einig, eintzig, einiglich oder eintziglich mein Verlangen’, ‘that is the only thing I desire; that’s my only desire, or that’s only my desire’. 3. ‘Einig, oder etlich‘, wobey es ja oder gewiß ist was man redet, ‘some or some one’. ‘Ich hatte einig geld bey mir’ ‘I had some money about me’. Hence Bach’s title could be translated as: 1. ‘Unified Canonic Variations’, as in ‘agree well together’, 2. ‘Sole Canonic Variations’, and 3. ‘Some Canonic Variations’. Telemann’s publication of the contrapuntal variations rules out the second meaning, but the first fits well, embracing the goals of musical composition ‘to agree well together’ and the ‘Übereinstimmung’ and eurythmia of universal harmony.35 I suspect that Bach chose the word ‘einige’ in the title because of its parallel allusion to unity and agreement, as well as for its numerical value, with its allusive 280. The translation ‘Some Unified Canonic Variations’ would capture the duality of the German more fully. In summary, in the 1990s Butler’s masterful detective work released the collection from the long shadow cast by its description in Bach’s obituary. Proportional parallelism has now shed new light on the compositional evolution, corroborating many of Butler’s observations. Heading the collection is the title page with its exquisitely crafted symmetry around the number 280. The three-variation miniature with title page can now be seen as a worked-out combination of proportion poetical and musical, its ‘Bach’ 32 33

34

D. Yearsley, Bach and the Meaning of Counterpoint (Cambridge University Press, 2002), 124 G. Butler, ‘Canonic Variations on Vom Himmel hoch’, in J. S. Bach, ed. Boyd, Oxford Composer Companions (Oxford University Press, 1999). 35 Fritsch, Lexicon, s.v. ‘Einig’. Zedler, Lexicon, s.v. ‘Eurythmia’.

Two small late collections

numbers perhaps implying that it was dedicated to future Bach generations. The 1 : 1 parallel between the four-variation collection and fascicle 3D of the Musical Offering suggests a plausible explanation for the Endzeichen in P 271, and the expected 1 : 1 parallel within the bar structure of the final five-variation publication confirms that it is perfectly proportioned, even though its bar total raises a question mark over an intended companion piece. But above all the fluid perfection of the proportions and parallels points beyond itself to the reality of a glorious age when unity and agreement of Harmony were the highest goal of creativity.

II

A perfect chorale project published by Schübler

The compositional purpose of the Schübler Chorales has been the subject of schlarly debate and speculation.36 The collection is not in Bach’s late style, it shows no signs of revision, and asking why Bach went to the trouble and expense of paying for the publication of note-for-note transcriptions,37 some scholars have even wondered if it was published without Bach’s authorisation.38 Some have suggested that the collection was published in response to J. A. Scheibe’s public criticism of Bach’s music as over-elaborate and ‘schwülstig’,39 the more popular and approachable style of the six short chorale settings being the musical counterpart of Birnbaum’s written response to Scheibe’s criticism.40 But if Bach had really wanted to prove that he could write in a less complicated style, surely he would not have continued with his larger, elaborate publishing projects in the late 1740s? And is it likely that he would change his lifelong method of composing in his last years simply to answer a petty, albeit stinging, public criticism? A demonstration of the numerical construction within the Schübler Chorales will offer new ideas as to why Bach had the collection published. Some time around 1748, the craftsman to whom Bach entrusted the Musical Offering project, Johann Georg Schübler, engraved the set of six chorale preludes for organ. The title page gives no clue to its pedagogic or musical intent, stating simply that the chorales are of various kinds and 36 38 40

37 NBA KB IV/I, 127–72. D. L. Humphreys, ’Schübler Chorales’, in J. S. Bach, ed. Boyd. 39 NBA KB IV/I, 166. NBR, Doc. 343: BD II, Doc. 400. J. A. Birnbaum, Vertheidigung (Leipzig. March, 1739), in J. A. Scheibe, Der Critische Musicus, vol. 4 (Hamburg, 1739; 1745), 976–7.

217

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demonstrations

to be played on an organ with two manuals and pedal.41 Although no manuscript copy of the collection has survived, we do have Bach’s handwritten corrections in a copy of the printed version,42 as well as several copies of the original publication.

The numerical structure The six chorales have no ambiguous notational features. Table 8.7 shows their numerical structure, the original sources, and the variations that affect the bar count. There is a da capo indication in BWV 649 and BWV 650, and a sectional repeat indication in BWV 645 and BWV 647. The consistent application of these variables creates three different bar totals: 255 written bars, excluding the repeats and the da capos; 280 bars, which include the da capos but exclude repeats, and 317 bars when both the da capos and repeats are counted. The 280-bar total, formed without repeats by including the two sections written with a da capo indication, is typical of a polished Bachian collection: it is a multiple of 10, contains several layers of proportion, and its total is probably a self-referential number. Table 8.7 shows the movements in publication order, with modern BWV numbers, the text incipit of the melody, and the layout of each chorale with the da capo sections indicated separately, to reveal a structure in eight sections. These sections in 280 bars fall into a double 1 : 1 proportion with 4 : 4 sections in 140 : 140 bars, and 140 bars forming a further layer of proportion. More striking, though, is the 2 : 2 : 1 proportion formed by the 66 bars of BWV 650 and the 33 bars of BWV 646, the proportional building blocks of 100 bars, and the block of 166 bars, parallel to the bar total of the Canonic Variations. The chorales are keyboard arrangements of cantata movements that would not have reached a domestic market had they not been published in this form. Five of the movements can be traced to known cantatas.43 BWV 10/5 was the basis for BWV 648,44 and BWV 6/3 for BWV 649.45 As 41 42 43

44 45

NBR, Doc. 245, Image, 227; see Table 8.8 below. C. Wolff, ‘Bach’s Personal Copy of the Schübler Chorales’, 178–86, footnote 3, p. 415. Cantata 140 survives only in fifteen original parts, Thomana 140, ‘Wachet auf’, copyists J. S. Bach, J. G. Haupt, J. L Krebs; Cantata 93 in eleven original and three new parts, Thomana 93, Fascicle 1, ‘Wer nur den lieben Gott läßt walten’ (BWV 93), copyists J. G. Haupt, J. S. Bach; and Cantata 137 also only in fifteen original parts, Thomana 137, ‘Lobe den Herrn’ (BWV 137), copyists J. S. Bach, J. A. Kuhnau, A. M. Bach, J. C. Bach. Library of Congress, Washington: ML 30 8b B 2 M 4 (Whittall Collection). P 44, Fascicle 2.

Two small late collections

219

Table 8.7 Original sources, bar structure and proportional divisions 1/ Bars

BWV Melody

Original bars

645 646 647

BWV 140/4 74 – Unknown – ? BWV 93/4 50 –

53 33 34

BWV 10/5 35 – BWV 6/3 100 41

35 46

648 649

Wachet auf rufft uns Wo soll ich fliehen hin Wer nur den lieben Gott Meine Seele erhebt Ach bleib bey uns

650

Kommst du nun, Jesu BWV 137/2 66 –

D

}

2:2:1

21

53

1:1 53 53 53 33 34 34

33 16

46 13

54 12

Totals

1:1

13 54 12

54

13 13 54 54 12

34 35 46 13 12

[255] 280 [317] 66 : 66 : 33 100 : 100 166 140 : 140

the source for the second chorale setting ‘Wo soll ich fliehen hin’ is unknown, it is quite probable that Bach manipulated its total to create the 33 bars that form the 1 : 2 proportion with 66 bars of BWV 650. Bach made minimal alterations to the lengths of the settings when he made the transcriptions. His judicious use of notation, though, helped clarify the proportions. For example, the original length of ‘Wer nur den lieben Gott läßt walten’, BWV 93/4, is 50 bars, which he reduced by 16 bars in BWV 647 when he introduced a repeat. Similarly the original length of ‘Ach bleib bey uns’ (BWV 6/3) is 100 written bars, which Bach first truncated to 59 bars, and then to 46 written bars in BWV 649 by using a da capo, 46 D 13 bars. The selection of chorales and their proportional ordering would probably have happened simultaneously. Because the 35 bars of the original cantata movement (BWV 10/5) are unchanged in its transcription in BWV 648, and because 35 bars is exactly one eighth of the final length of the collection that would have eight sections, it seems likely that the setting of ‘Meine Seele erhebt den Herrn’ was the starting point for Bach’s numerical plan. The lack of an original source for ‘Wo soll ich fliehen hin’ suggests further that this setting in BWV 646 was arranged specially for the collection, with its length predetermined by the numerical structure.

Layers of meaning in the physical score Lacking any indication of its purpose or intended readership, the title page of the Schübler Chorales contrasts with the title pages of the Clavier Übung

220

demonstrations

series, with their phrase ‘Denen Liebhabern zur Gemüths Ergoetzung verfertiget’ (‘composed for music lovers, to refresh their spirits’). This omission is perplexing. Perhaps it indicates that there was a ready-made market for smaller-scale, and thus cheaper, publications of this kind?46 The title-page description of the six chorales as ‘von verschiedener Art’ (‘of various kinds’) can be interpreted in many ways, one of which may be a theological or liturgical thread motivating Bach’s choice of chorales. Although the chorales belong to different periods in the church calendar, one can sense patterns of unity and diversity in the theological content of their texts. Four are for Sundays after Trinity.47 The fifth, ‘Meine Seele erhebt den Herren’, is a chorale specific for the Visitation of Mary,48 and the sixth, ‘Ach bleib, bey uns Herr Jesu Christ’, was prescribed for the second day of Easter.49 It is difficult to believe that Bach disregarded their texts when he made the selection of six. The design of the title page may also hold a layer of meaning. Tables 8.2 and 8.3 above show what appears to be a deliberate parallel device in the letter-word values of ‘Vom Himmel hoch’ and the title page of the Canonic Variations. Table 8.8 shows what appears to be a deliberately constructed parallel proportion within the wording and orthography of the engraved title page of the Schübler Chorales. The first seven lines have a numerical value of exactly 1000, within which is both a 1 : 1 proportion with 500 : 500 in 3 : 4 lines and 2 : 3 in a different combination of 3 : 4 lines. Line 10, coincidentally or by design, provides a parallel between some of Bach’s credentials and the numerical structure of the collection. Lines 9, 11 and 12, however, do not seem to be part of a carefully designed parallel.50 We do not know who devised and designed the numerical parallels or whether its parallel association to the bar structure of the six chorales 46

47

48 49

50

See H.-J. Schulze, “Die 6 Choräle kosten nichts” – Zur Bewertung des Originaldrucks der “Schübler-Choräle”, BJ 94 (2008), 301–4. ‘Wer nur den lieben Gott läßt walten’ for Trinity 5 (in BWV 93 on 9 July 1724);‘Wo soll ich fliehen hin’ for Trinity 11 (BWV 199 on 12 August 1714 and on 8 August 1723, and used during communion); ‘Kommst du nun, Jesu, vom Himmel herunter’ for Trinity 12 (BWV 137 on 19 August 1725, although with the text ‘Lobet den Herren’); ‘Wachet auf, ruft uns die Stimme’ for Trinity 27 (BWV 140 on 25 November 1731); Schulze, ‘Die 6 Choräle’, 242; G. Stiller, Johann Sebastian Bach and Liturgical Life in Leipzig (St Louis: Concordia, 1984), 247. Ibid., set by Bach in BWV 10 for 2 July 1724. Stiller, Johann Sebastian Bach, 240, 247. Set by Bach in BWV 6 for 2 April 1725. It was also listed in both Leipzig and Dresden schedules appearing under the general heading ‘Hymns Concerning the Word of God and the Christian Church’. The values of lines 11 and 12 are 586 and 1051 respectively, and the value of line 9 is ambiguous, 443, 438, 461 or 466 depending upon the unclear ö in ‘Königl.’ and the value of ß in ‘Saechß’.

Two small late collections

221

Table 8.8 Perfectly proportioned lines of the title page Line Title words 1 2 3 4 5 6 7

SECHS CHORALE von verschiedener Art auf einer Orgel mit 2 Clavieren und Pedal vorzuspielen verfertiget von

Numerical value

Value

52+59 47+129+37 27+49 54 40+2+84+37+36 171 129+47

111 213 76 54 199 171 176 1000

8 10 9

Johann Sebastian Bach 58+86+14 Capellm: u: Direct: Chor: Mus:Lips: 58+20+57+42+50+53 Königl. Pohln: und Chur Sachs Hoff. Compositeur

158 280 438

1:1 111 213

111 213 76 76 54 54 199 199 171 171 176 176 500 : 500 400 : 600

158 280 438 438 : 438

11

In Verlegung Joh: Georg Schüblers zu Zella am Thüringer Walde

576

was intentional. The design nonetheless creates Harmony and unity within the publication. Another feature that may hold some clue to Bach’s intentions for the collection is the binding of his personal copy (the Handexemplar).51 On his father’s death in 1750, C. P. E. Bach inherited Bach’s personal copies of both the Schübler Chorales and Clavier Übung III, and we know from a letter written by C. P. E. to Forkel that by 26 August 1774 the two collections had been bound together, and, from other sources, that they remained so at least until 1847.52 The surviving back flyleaf of the binding bears a Berlin watermark and, according to Wolff, ‘appears to stem from the second half of the eighteenth century . . . From this watermark we can conclude that C. P. E. Bach had the two prints of organ chorales stemming from his father’s estate bound together during his years in Berlin.’53 Did C. P. E. Bach bind these two together specifically because they, rather than any of the other organ collections that he inherited, reflected his father’s purpose to create a relationship between the two works? The figures suggest he might have. Table 8.9 shows how the 280 bars of the Schübler Chorales combine with the alternative count of 2090 bars of Clavier Übung

51 53

Wolff, ’Bach’s Personal Copy of the Schübler Chorales’, 178–86. Ibid., 182.

52

Ibid., 181.

2:3

222

demonstrations

Table 8.9 Bach’s binding suggesting a known association between the collections Date

Collection

Bars

1:1

1739 Clavier Übung III 2090 bars 1748/9 Schübler Chorales 280 bars NB: Above two bound together by C. P. E. Bach 1748/9 Art of Fugue 790 : 1580 (-41) bars

2090 280

Totals

2370 : 2370

2370

III to form a large collection of 2370 bars,54 and a perfect 1 : 1 proportion with the implicit bar total of the Art of Fugue,55 a collection that was in the workshops of the Schübler firm at this period. Genre-wise, CÜ III, with its many chorale preludes, is the most obvious companion piece to the Schübler Chorales. Perfectly structured when it was published in 1739, there was no reason for further augmentation or improvement, but Bach was an inveterate reviser of his own work, constantly generating new ideas and plans. Throughout much of the 1740s he was working on the engraving and revisions of The Art of Fugue. He completed the autograph fair copy around 1742 and between 1742 and 1746 he was both overseeing its engraving and expanding its structure. It is thought that in 1748–9 he was working on the quadruple fugue, which breaks off after 239 bars, at around the same time that he decided to have the Schübler Chorales engraved. Since it was C. P. E. Bach who bound together his father’s personal copies of CÜ III and the Schübler Chorales, and his cousin Johann Heinrich Bach, possibly with other Bach family members, who oversaw the posthumous publication of The Art of Fugue, it seems plausible that Bach himself designed the parallel proportions to unify these final published collections. The usual explanation for Bach’s decision to publish such a basic collection of chorales is biographical; that he occupied himself with collecting together and tidying up his earliest work at the end of his life because his health was failing, and his stamina to create on a more ambitious scale waning. A further explanation is suggested by its numerical

54 55

See Chapter 7, §I. In spite of the unfinished nature of The Art of Fugue, its 1 : 2 structure 790 : 1580 is strongly implied. See Chapter 9, §II.

Two small late collections

structure, and the spiritual reasons behind that structure which may have motivated Bach. This small chorale collection may have been devised because it held an important place in the construction of a new and meaningful large-scale whole. The role of the chorales, and possibly their texts, is understood more fully when considered within the broader context of CÜ III and its chorale settings. They bear witness to Bach’s constant purpose as a composer, to create a microcosmic reflection of the macrocosmic unity and harmonic perfection of God’s created order.

223

9 Two large late collections

Musical Offering (BWV 1079) The Art of Fugue (BWV 1080) Vorige angeführte Rationes mögen genung seyn zu behaupten daß wir die Soni, so hier in der Welt gebräuchlich sind und welche Guido Aretinus mit ut, re, mi, fa, sol, la, benahmset hat, dereinst bey der Himmlischen Harmonie und Music auch gebrauchen werden: Die Melodie wird aber Gott componiren. J. H. Buttstett, 1716 (Appendix 1716-III)

Bach was in his early sixties when he composed and revised The Art of Fugue and the Musical Offering. He knew that time and good health were finite resources – to administer these wisely would have been a high priority. Choosing to create layers of unheard proportion may seem an unwise investment today. However, the perfect numerical organisation of his final collections intimates strongly that this was one of Bach’s priorities in the 1740s, when the invisible wall between earthly and heavenly Harmony seems to have been thinner.

I

Musical Offering: a royal treasure hunt

A trip to Potsdam and a meeting on 7 May 1747 with the flute-playing King Frederick the Great (Friedrich II of Prussia) resulted in one of Johann Sebastian Bach’s most curious publications, Musicalisches Opfer (hereafter the Musical Offering). Working out the potential of a theme ‘so exceedingly beautiful’,1 Bach mixed genres, various score formats,

1

224

‘So ausbündig schön’, in a report by the Berlinische Nachrichten von Staats- und gelehrten Sachen, 11 May 1747; see C. Wolff, ‘Apropos the Musical Offering: The Thema Regium and the Term Ricercar’, Essays, 324.

Two large late collections

unexpected headings and a dedication2 to create an eclectic collection ready for sale at the Leipzig Autumn Fair. The Musical Offering (BWV 1079) has earned a mixed reputation and attracted scholarly debate because of its many puzzling details.3 The discrepancy in timescale between its composition, publication and sale is problematic.4 The headings and mottos in Latin and Italian are highly unusual, and the dedication page, in German rather than courtly French, uses curiously ritualistic and religious words such as ‘weyhen’, ‘Opfer’, ‘rühmen’ and ‘verherrlichen’.5 The layout and disposition of the collection is also unconventional. In the 1880s Philipp Spitta viewed it as ‘a halfabstract accomplishment . . . dominated by technical considerations’.6 A century later, although demonstrating that the work was planned as a well-balanced unit, Christoph Wolff rejected the notion that it was intended for performance as a whole in spite of its sophisticated cyclical structure.7 In 2002, Gregory Butler’s deductions from the engraving, printing, paper and watermarks led to the following qualification of Wolff’s position: for purely practical purposes of marketing the product and performing it, not only is there no apparent ordering scheme for the collection, but also that its piecemeal distribution and dispersal seem to have been almost entirely haphazard and a function of choice in a free-market economy. That Bach had in mind a cogent abstract disposition scheme for the collection as a whole cannot, of course, be ruled out.8

In this chapter proportional parallelism will be used to investigate the possibility that Bach created an inner connection or even a unified whole within this collection.

Background information To appreciate Bach’s construction of the Musical Offering it is necessary to understand the format of the paper and the sections in which it was 2

3

4 5

6

7 8

BD II, Doc. 558a, NBR, Doc. 248, and Wolff, Essays, 252; Extract der eingelauffenen Nouvellen (Leipzig, 1747), 156 describes ‘two Ricercars in score, a trio sonata in parts and circular canons’. Many different methods have been used to solve and explain the riddles, e.g. H.-E. Dentler, Johann Sebastian Bachs ‘Musicalisches Opfer’ (Mainz: Schott, 2008). NBA KB VIII/1, 46; BD II, Doc. 558a; NBR, Doc. 248; Wolff, Essays, 252. M. A. Marissen, ‘Musical Offering’, in J. S. Bach, ed. Malcolm Boyd, Oxford Composer Companions (Oxford University Press, 1999). H. T. David, J. S. Bach’s Musical Offering: History, Interpretation and Analysis (New York: Schirmer, 1945), 96 (critique of Spitta’s view). Wolff, Essays, 255. G. Butler, ‘The Printing History of J. S. Bach’s Musical Offering: New Interpretations’, The Journal of Musicology 19/2 (2002), 331; history of scholarly reception, 306–8.

225

226

demonstrations

originally printed and sold. The two complete surviving copies of the collection have five sections.9 Following Butler’s usage,10 based on Wolff’s categorisation,11 I will refer to these five sections as A, B, C, D and E: A. The title page and dedication, including the date, ‘Leipzig den 7. Julii 1747’ were set with moveable type and printed on oversized luxurious paper (Royalpapier), one sheet folded in two, on Breitkopf’s Leipzig press.12 B. The Ricercar à 3 (185 bars) notated on two staves is followed by ‘Canon perpetuus super Thema Regium’ (5 bars) in abbreviated notation. Both are printed on oversized luxurious paper. An acrostic sticker, ‘Regis Iussu Cantio [three-part ricercar] Et Reliqua Canonica Arte [perpetual canon] Resoluta,13 was originally stuck to the blank front page. This section was engraved by Johann Georg Schübler in Zella.14 C. The four-movement Sonata is printed in parts for Flute (440 bars), Violin (440 bars) and Continuo (440 bars), each followed by a part for the Canon perpetuus (32 bars). This section was engraved by Johann Jacob Friedrich Schübler in Zella and printed in upright format on cheaper paper.15 D. The five canons, numbered 1–5, are headed ‘Canones diversi super Thema Regium’ and followed by a canonical fugue (78 bars) on two staves, together covering two printed sides in upright format. The acrostic sticker originally on section B was later stuck to the blank front page of this section.16 Section D was engraved by Johann Heinrich Schübler in Zella17 and printed in upright format on cheaper paper. E. The Ricercar à 6 (103 bars) is notated on six staves and followed by two canons in abbreviated notation,’Canon à 2 Quaerendo invenietis’ (16 bars), and the second canon à 4 (28 bars). It is printed on oversized luxurious paper and was engraved byJohann Georg Schübler in Zella. Butler has demonstrated that there were three stages in the composition and printing of the collection. The original, earliest version consisted of 9 11

12 13

14 16 17

10 Ibid., 316, responding to NBA KB VIII/1, 51. Ibid., 306–31, and Wolff, Essays, 252. NBA KB VIII/1; Wolff, ‘New Research on the Musical Offering’, Essays, 239–58, originally published in The Musical Quarterly, 57 (1971), 379–408; postscript revisions, Essays, 421–3; Wolff, ‘Apropos the Musical Offering’, 324–31. Butler, ‘Printing History’, 310. Ibid., 320: ‘The “Iussu” of the acrostic refers directly back to the parallel “Befehl” of the dedication.’ See also Chapter 2 for a discussion about the acrostic form. 15 Butler, ‘Printing History’, 310. Ibid. Wolff, Commentary to the facsimile reprint edition (Leipzig: Peters, 1977), 12. Butler, ‘Printing History’, 310.

Two large late collections

only three sections A, B and E, i.e. the title page and the two sections with the Ricercars.18 As a result of engraving errors on the plate for side 4 (leaf 2, bars 51–67),19 the whole of section E could not be printed, delaying Bach’s original plan to send sections A, B, and E to King Frederick. This delay forced Bach to rethink his plan for the collection, and to compose and engrave section D, possibly sending it rather than section E to the king, even though Section D, in Butler’s opinion, was merely a canonic appendix to the collection.20 It is unclear when the trio sonata, section C, was composed, but evidence shows it was printed last of all. If, as Butler suspects, the unplanned addition of sections D and C caused Bach to revise the order of the collection, this would account for the changed position of the Ricercar acrostic sticker from the first side of section B to that of section D.21 And the trio sonata, even though last to be printed, was probably designed to be inserted before the canonic appendix section D and after sections B and E, making the order of the collection A–B–E–C–D. The discrepancy in the print run of the five sections (section A, c. 100 copies, sections D and C, fewer than 50 copies), suggests further that Bach planned to include section A (i.e. the title page and dedication) with every sale, regardless of how many individual sections were purchased. Judging from the surviving copies, the combination A–B–E seems to have been the most popular.22

Numerical overview Table 9.1 gives an overview of the numerical structure of the collection in its final order. There are several notational features that affect the bar count: the bar lines in the six-part Ricercar are written full length at the breve (103 bars) and broken at the semibreve (206 bars) – unless otherwise stated, they are counted at the semibreve in the tables below;23 a repeat in the first movement of the Sonata creates a movement with 48 written bars, or 96 performed bars; and the puzzle canons are notated in abbreviated form. As Bach would have calculated the layout of the page according to the number of written bars rather than the number of bars in their undisclosed fully worked out length,24 the number of written bars has been used in the tables. One grey area is in the parts of the Sonata and Canon 18 23 24

19 20 21 22 Ibid., 328. Ibid., 315. Ibid., 329. Ibid., 330. Ibid., 327. 2a As they are also in NBA, BWV and BWV . Butler, ‘Printing History’, 328: Bach prepared the Abklatschvorlage for the engravers, who were not musicians, to use as a template of each plate.

227

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demonstrations

Table 9.1 Numerical structure of the Musical Offering. Original print BWV 1079/1 1079/4g 1079/3 1079/4h 1079/4h 1079/4h 1079/4 1079/2 1079/4i 1079/4k

Title B B C C C C D E E E

B&E C

Ricercar à 3 185 Canon cancrizans 5 Sonata Canon perpetuus [Fl] Canon perpetuus [Vn] Canon perpetuus [Cont] Canones Diversi Ricercar à 6 206 Canon à 2 16 Canon à 4 28

Totals

440

Canons

2:2:1

2:3

185 5 440

440 220

440 32 32 32 124

206 16 28

Block

185 185 5 5 440

32* 32 32 124

Block

32 32 32 124 206 16 28

440 : 440 : 220 440 : 660 190

206 16 28 250

perpetuus, written for flute, violin and continuo. I have chosen to count the 440 bars of the Sonata just once, although logically it could be counted three times, increasing the bar total of the collection by 880 bars, Table 9.1. When it came to the Canon perpetuus printed directly after the Sonata, Bach notated the parts differently because of the construction of the Canon perpetuus: the violin and continuo parts each have 32 bars, and the flute part, because of the overlap of the first and final two bars, is notated as 30 bars while played as 32 bars – shown in Table 9.1, column 6, as 32*. The flute and violin parts are canonic, whereas the continuo acts as accompaniment to the upper voices.25 Table 9.1 shows that there are canons in each of the four musical sections, with diverse canons in section D, at the end of each Ricercar in sections B and E, and at the end of the Sonata in section C. It has been assumed that Bach did this to save paper and to make printing production more economical. The numerical results tell a different story: Bach’s disposition of the canons in the sections was intimately connected to the proportioning of the work. There are 440 bars printed in B and E. Each of the three individual instrumental parts in section C also has 440 bars. The canon at the end of section C has 32 bars in each instrumental part, i.e. 96 bars, which together with the 124 bars of diverse canons in section D make 220 bars of canon. These totals create a logical large-scale structure with 25

This canon could not be written in abbreviated notation because the pivot of inversion changes twice in the course of the composition; see Hans T. David, J. S. Bach’s Musical Offering (New York: Schirmer, 1945), 26.

Two large late collections

several layers of proportion across the collection: 220 : 440 : 660 : 1320. At the macro level the collection has 1980 bars forming a 2 : 1 proportion: 1320 bars of trio sonata and 660 bars of canon and ricercar. As it is Bach who would have designed the manuscript layout for the non-musician engravers, deciding the number of bars per page, per plate and per movement, this numerical design with its proportioning within the sections is without doubt Bach’s – it is not a coincidence of random numbers.

(i) Original early version: sections A-B-E The numerical structure of sections B and E shows that the original version was ordered with logical building blocks in each section: 190 bars in B, 250 bars in E. Table 9.1 shows that there are 440 bars engraved in the first two sections to be sent to the engravers. Section B has 185 bars of Ricercar à 3 and 5 bars of the Canon perpetuus super Thema Regium. Section E has 206 bars of Ricercar à 6, counting at the semibreve, 16 bars Canon à 2 Quaerendo invenietis, and 28 bars of Canon à 4. There are no further 1 : 1 or 1 : 2 proportions in these two sections, but the logical ordering in blocks of 250 and 190 bars attests to conscious planning. Furthermore, the absence of a layer of proportion within these 440 bars strongly intimates both that Bach knew that A–B–E was not the ideally perfected publication, and therefore that when he sent A–B–E to the engravers he had ideas or even drafts of further sections he wished to include. There are, however, some striking proportions between the numerical value of some key words and the number of bars in the A–B–E collection (see (iii) below), and perhaps these parallels persuaded Bach that the 440 bars rendered this small collection sufficiently perfect to send to Frederick the Great as a complete unit, in fulfilment of his public promise. However at some point he changed his mind. Bach’s fair copy of each part of the collection was given to the engravers as the Abklatschvorlage and destroyed in the engraving process;26 no additional autograph manuscript of the entire collection has survived.27 There is however an autograph of the Ricercar à 6, P 226.28 It is written on 26

27 28

Butler, ‘Printing History’, 328. Butler explains, on page 325, that the engravers were skilled in both metal cutting and gunstock carving, but were not musicians, and so needed a perfect template. NBA KB VIII/1, 70. D-B Mus. ms. Bach P 226 fascicle 1. NBA KB VIII/1, 71 source B 1; this collection contains manuscripts formerly owned by C. P. E. and J. C. F. Bach and J. N. Forkel.

229

230

demonstrations

two staves, in a treble and bass clef, whereas the printed version is on six staves, with a G clef in the treble, four C clefs for soprano, alto and two tenors, and an F clef in the bass. The number of bars is identical in both manuscript and printed versions, with a long bar line at the breve and a short bar line at the semibreve creating the dual count of 103 bars and 206 bars. The Ricercar acrostic was cut from a wood block, printed by hand and deliberately stuck onto section B, and later D.29 It was planned with the composition and not as an afterthought.30 Its purpose in the original plan was to highlight the word ‘Ricercar’ and this in turn points to the presence of another parallel technique. There are 288 bars of Ricercar when Ricercar à 6 is counted at the breve, Ricercar à 3 = 185 bars, Ricercar à 6 = 103 bars. Table 9.3 shows that the numerical value of the word ‘Ricercar’ is 72,31 and this creates a 1 : 4 proportion with the Ricercars: 72 : 288.

(ii) Second instalment: sections C–D Table 9.2 shows the numerical structure of sections C and D. The trio sonata (BWV 1079/3) has 440 bars, arranged in a consecutive 1 : 1 proportion. There are 220 bars (48þ172) in the first two movements, and 220 bars with the da capo of the second, third and fourth movements (77þ30þ113), forming a perfect 1 : 1 and 2 : 3 proportion with 220 : 220 bars in 2 : 3 sections. Each of the three instrumental parts has this same structure. There is one repeat in the Sonata, which when included gives an alternate total of 488 bars. There are no proportions within these 488 bars. The 32-bar Canon perpetuus printed in section C creates a proportion with the canons in section D. Table 9.2 shows how a 1 : 1 proportion with 110 : 110 bars is formed by the 124 bars of canons and the 32 bars of the Canon perpetuus (4h) printed beneath the Sonata in each of the three parts in section C. With one part of Canon perpetuus each for flute, violin and continuo, there are literally 96 bars of canon 4h. This proportion creates a unity within sections C–D: a large-scale 440 : 220 bars, with the 440 bars of the sonata breaking into consecutive 220 : 220 bars, and the 220 bars of canons breaking into 110 : 110 bars. And this is part of the large-scale proportional scheme across the collection as a whole, Table 9.1. Whether buying sections A–B–C–D–E, A–B–C–E or simply A–B–E, the purchaser would own a perfectly proportioned collection. 29 30 31

Butler, ‘Printing History’, 324. Wolff, Essays, 420, note 31; Spitta and David assumed the acrostic to be a later idea of Bach. R(=17)+I(=9)+C(=3)+E(=5)+R(=17)+C(=3)+A(=1)+R(=17) = 72.

Two large late collections

231

Table 9.2 Numerical structure of Sonata and Canons in Sections C and D

C C C C C

C C C D D D D D D

BWV

Movement

Bars

1079/3.1 1079/3.2

Largo Allegro

1079/3.3 1079/3.4 Continuo Flute Violin 1079/4h 1079/4h 1079/4h 1079/4a 1079/4b 1079/4c 1079/4d 1079/4e 1079/4f

Andante Allegro

48 172 77 30 113 440 [440] [440] 32 32 32 18 8 4 8 8 78

D

Canon perpetuus Flute Canon perpetuus Violin Canon perpetuus Continuo 1.Canon 1 à 2 cancrizans 2. Canon à 2 violini 3. Canon per Motum contrarium 4. Canon per Augmentationem 5. Canon per Tonos Fuga canonica

Totals

220

1:1

1:1

48 172

96 172 77 30 113 488

77 30 113 220 : 220

32 32 32 18 8 4 8 8 78 110 : 110

32 18 8 4 8 8 78 78 : 78

* including repeats

(iii)

Word–music parallels

The acrostic sticker on the word ‘Ricercar’, the abbreviated puzzle canons and teasing title Quaerendo invenietis are all characteristic of common parallel techniques used in Bach’s time. What should the king, the performer or purchaser of the Musical Offering seek and expect to find? The compositional ingenuity of the canons has been praised, and solutions sought since the collection was published. The focus recently has tended towards the interpretation of meanings in the collection, including biblical allusions in the words Quaerendo invenietis and ‘Offering’, and parallel associations between the words ‘canon’ and ‘law’.32 The biblical and political parallels have been discovered in the phrases ‘Lex Regia’ and ‘Thema Regium’,33 by

32

33

Bars*

M. Marissen, ‘The Theological Character of J. S. Bach’s Musical Offering’, in Bach Studies 2, ed. D. Melamed (Cambridge University Press, 1995), 85–106, here 99, and Zedler, Lexicon, s.v. ‘Canon’. The Greek word ‘Canon’ still meant ‘rule’ or ‘yardstick’ and, according to Zedler, ‘was used figuratively of different things’. The word Thema (meaning theme) is a third declension neuter noun, whereas the word ‘Lex’ (meaning ‘law’) is a third-declension feminine noun, accounting for the different endings of the adjective ‘Regius’ (meaning ‘Royal’ or ‘Kingly’).

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demonstrations

Table 9.3 Number values of title words in the original print Words

Values

Totals

B RICERCAR B Canon perpetuus super Thema Regium

72 44+134+75+45+70

72 368

E E E C C

72+7 44+3+95+120 44+5 66 84+103+39

79 262 49 66 226

390

D Canones diversi super Thema Regium

67+82+75+45+70

339

339

D D D D D D

Canon 1 a 2 a 2 Violin in Unisono a 2 per Motum contrarium a 2 per Augmentationem contrario Motu Fuga canonica in Epidiapente Regis Iussu Cantio Et Reliqua Canonica Arte Resoluta

44+4 3+76+22+101 3+37+123+125 3+37+150+107+65 34+57+22+100 56+85+59+24+79+57+42+105

48 202 248 362 213 507 1580

D D D D

Dedication Copy Additions Notulis crescentibus crescat Fortuna Regis 104+132+66+90+56 Ascendenteq.[ue] Modulatione ascendat Gloria (Regis) 102(127)+122+64+59 THEMATIS REGII 91+47 Elaborationes Canonicae 129+62

Ricercar à 6 Canon à 2 Quaerendo invenietis Canon à 4 SONATA sopr’il Soggetto Reale

448 372 138 191

440

292

820 329

which rule the Christian is encouraged (James 2:8) to follow the Royal Law, the Lex Regia, ‘to love your neighbour as yourself’ rather than show favouritism.34 It is however the numerical parallels that must remain the focus here. Table 9.3 shows the main heading words of the collection and their value in the natural order number alphabet. It is striking that the title words in section B have a value of 440, proportionally parallel to the 440 : 440 : 220 bars in the collection. The words in sections E and C have a value of 390 and 292 respectively. The many different titles in section D form many totals, including a possible self-referential cumulative 1580. Although not all these were planned, several striking correlations combine with diplomatic evidence to suggest that Bach intentionally used the word value to create parallels with his musical structure. For example, the documented musical inspiration point of this collection, the royal theme, with its title Thema Regium35 34

35

Calov, Sacra Biblia, Novi Testamenti, vol. II (1682), James 2:8; Deutsche Bible, 1545, ‘königliche Gesetz’. This is stated clearly in both the dedicatory preface A and in subsequent advertisements.

Two large late collections

233

Table 9.4 Parallel values in words and bar structure Words

2:3

Canon Sonata

44 66

Totals

110

Headers in B–E

Value

Titles in Section B

Value

Thema Regium Quaerendo invenietis

45 + 70 95+120

Ricercar Canon perpetuus super Thema Regium

72 368

330

together with Bach’s early creative decision to use the musical forms and titles ‘Canon’, ‘Sonata’, and ‘Ricercar’ rather than ‘Fugue’. And alerting the reader to the presence of puzzle devices is the phrase Quaerendo invenietis, its form differing from the well-known biblical phrase ‘Quaerite et invenietis’, Matthew 7:7. As the prime purpose of the numerical value of a word in Bach’s time was to inspire creativity, it would not be surprising if Bach had used the numerical value of important words in conjunction with planning the numerical structure of his collection.

(a) ‘Canon’ and ‘Sonata’ parallel to the canons and sonata (110 : 220 : 440) Table 9.4 shows that the numerical value of the word ‘Canon’ is 44, and that of ‘Sonata’ is 66.36 Their total is 110, a foundational number in the musical structure, proportionally related to the 220 bars (110 : 110) of the canons in sections C and D and to the 440 (220 : 220) of the Sonata in section C, as well as to the overall structure of the collection. (b) Thema Regium and Quaerendo invenietis parallel to the structure The striking phrases Thema Regium and Quaerendo invenietis appear as headers in the early printing units, B and E. Table 9.4 shows that their joint numerical value is 330, again numerically related to the structure of the collection. There are 660 bars in the sections B–D–E, and 1320 in the three parts of the Sonata, in addition to smaller sections of 440 and 220 bars. Such a close numerical relationship suggests that these two key phrases, possibly even given by Frederick the Great, may have been an original Erfindungsquelle for the collection.37

36

37

C(=3)+A(=1)+N(=13)+O(=14)+N(=13) = 44; S(=17)+O(=14)+N(=13)+A(=1)+T(=19)+A(=1) = 66. Term used by G. P. Harsdörffer, Poetischer Trichter. 3 vols. (Nürnberg, 1651–3), vol. III, 72; see Tatlow, Bach and the Riddle, 78.

440

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(c) Section B titles, the ‘Ricercar’ sticker and the structural parallels The two headers in section B have a numerical value of 440, which is not only related to the structure of the entire work and to the first submission of sections A–B–E, but also related to the 44 of ‘Canon’, and the 44 bars of canon in section E, Table 9.1. According to the pre-publication announcement, Bach had promised to write a fugue, or ‘Prussian Fugue’.38 ‘Fugue’ would have been a more accurate description of the two Ricercars, yet Bach avoided the term. Bach’s ‘deliberate application of the ambiguous term ricercar’,39 with its specific numerical value, was bound to stand out, and Bach highlighted it further with an acrostic, which he stuck onto section B, thus providing a large and obvious clue to the inventive puzzles embedded in the collection. The deliberate choice of the word Ricercar, the sticker that highlighted the word, and the 440 : 440 parallel proportion between the value of the title words and the number of bars in this section, which Bach was to send to the king, provide solid evidence of Bach’s knowledge and use of the natural order number alphabet and of proportional structures in the organisation of his collections. The evidence is further strengthened by similar parallels found in the Canonic Variations and the Schübler Chorales, on which he was working in 1747/8.40 (d) Parallels with capitalised words There are only four title words in the entire collection that are in capital letters: ‘Ricercar’, ‘Sonata’ and ‘Thematis Regii’. The capitalised sticker ‘RICERCAR’, with its value 72, creates a 1 : 4 proportion between title and bars, 72 : 288 when the bars in the Ricercar in section B are counted at the breve. The capitalised word ‘SONATA’, with its value 66, together with ‘RICERCAR’ gives a value of 138 (66+72), which happens to be the total of the words in bold capitals added by Bach to the dedication copy ‘THEMATIS REGII’.41 The four capitalised words create a double parallel, 1 : 1 and 1 : 2 in 138: 138 and 1 : 2 phrases. The correlation may have been intentional, but the timeline suggests that the parallelism would have been unrelated to Bach’s musical planning, since ‘Thematis Regii’ was written in by hand later. 38 40 41

39 BD I, Doc. 49; NBR, Doc 257; Butler, ‘Printing History’, 324. Wolff, Essays, 254. See Chapter 8. T(=19)+H(=8)+E(=5)+M(=12)+A(=10)+T(=19)+I(=9)+S(=18)=91; R(=17)+E(=5)+G(=7)+I (=9)+ I(=9)=47; 91+47=138; NBA KB VIII/1, 59, 152, 156, reproduces images of THEMATIS REGII, SONATA and RICERCAR.

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Table 9.5 Random numerical structure of the printed title Line

Text

Value

1 2 3 4 5 6

Musicalisches Opfer Sr Königlichen Majestät in Preußen allerunterthänigst gewidmet von Johann Sebastian Bach

135 60 35+102+84+22+111 213+82 47 58+86+14

Totals 135 60 354 295 47 158 1049

Section D contains a potential allusion to Bach himself in the value of the canon headers, 1580 (Table 9.3, rows 10–15). Firm evidence of orthographic manipulation would be necessary before this numerical coincidence could be taken as Bach’s design. It is likely that if some of these larger totals had been approved by Bach, a student apprentice or someone at the publishing house would have helped to create them.

(e) Structure of the title pages The dedicatory title page seems the most obvious place to include a numerical parallel to the music. Table 9.5 shows that the printed title page has no numerical patterning, the sole symmetry being the centralisation of the words on the page. We must assume that Bach approved its final wording and layout when he oversaw the typesetting and printing of the title page in Breitkopf’s Leipzig workshop, and therefore that he was content with its lack of parallelisms.42 There is, however, an alternative title page for the collection in the hand of Johann Friedrich Reichardt (1752–1814),43 which is extremely interesting in view of its numerical structure and provenance. Table 9.6 shows that its total is 660, with several layers of proportion formed by various words. The words in Reichardt’s copy are distributed over four rows: Schuldiges Opfer der Dankbarkeit ⎮ Sr Maj. dem König Friedrich II 42

43

Zedler, Lexicon, s.v. ‘Müller, Johann Caspar’. In 1719 Bernhard Christoph Breitkopf (1695–1777) married the widow of the famous printer and publisher Johann Caspar Müller, taking over Müller’s publishing business and founding the Breitkopf family firm. Originally thought to be by Bach; see Kinsky, Die Originalausgaben der Werke J. S. Bachs (Vienna; Leipzig, 1937), 114, 62–6, 113–15 and 124. Schulze has recently identified it as Reichardt’s hand, BD V, Doc. C912b.

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Table 9.6 Perfect numerical structure of Reichardt’s title page, A.Wn. S. H. J. S. Bach 102

1 2 3 4 5 6

Text

Value

Schuldiges Opfer der Dankbarkeit Sr Maj. dem König Friedrich II dargebracht von J. S. Bach

103+57 26+91 35+22+21 53 78+2 84+47+41

160

660

160 : 80

Totals

2:1

1:1

1:1

117

160 117

78

78 53 80

80 172

250 : 250

53 80 172 330 : 330

dargebracht⎮ von ⎮ J. S. Bach.44 Table 9.6 arranges the words over six rows, and shows that the key words ‘Schuldiges Opfer’45 and ‘Friedrich II’ form a 2 : 1 proportion, 160 : 80. Excluding the main title ‘Schuldiges Opfer’, the words form a 1 : 1 proportion, 250 : 250 in a building block of 500. The numerical value of the entire title page is 660, which itself forms two groups of 330. As 660 is parallel to the number of bars in A–B– D–E, and integral to the numerical structure of the entire collection, this alternative title ought not be dismissed out of hand. The numerical correlation indicates that its creator understood the construction of Bach’s score. If Bach devised it, this new title page must have been a post-publication refinement.46 Whatever its provenance and chronology, Reichardt’s title is certainly more numerically perfect, and more intimately related to the structure of the Musical Offering, than the original title page A.

(f) The date and its possible significance It is generally accepted that the collection could not have been completed and ready for sale until the Michaelmas Fair in September, ten weeks after 7 July 1747, which is the date engraved in the dedication of the publication. It is not known why Bach chose this date, but numerical parallels suggests some reasons. The seventh day of the seventh month in 1747 (7+7+1+7 +4+7) has four sevens (28) with 1 and 4 remaining, which if written together is 14, giving a simple reference to Bach’s name. At the same time, 44 45 46

Call mark: A-Wn S. H. J. S. Bach 102. Original print with handwritten title page. Fritsch, Lexicon, s.v. ‘schuldige’ and s.v. ‘opfer’ shows that these words are riddled with inuendo. NBA KB VIII/1, 66 where Wolff suggests the title may have been written by Thomaskantor Christian August Pohlenz (1790–1843); in BD I, Doc. 173, Schulze and Neumann still believed the title page to be in Bach’s handwriting.

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if all the numerals in the date are added together (7+7+1+7+4+7 = 33), the total 33 is related to the value of some essential title words and to the bar total of the work. Arithmetical correspondences notwithstanding, the simplest suggestion, that 7 July 1747 was the date on which Bach was ready to send sections B and E to the engraver, seems more convincing.

Conclusion The Musical Offering is a perfectly proportioned work, fulfilling clearly two of the three characteristics found in every collection that Bach published: the bar totals of the whole and the parts are multiples of 10, and there are several levels of proportion across the structure. Missing is a clear allusion to Bach’s name in the overall bar totals, although perhaps he considered the prominent 1-2-3 number in the 1320 bars of the Sonata to be sufficient. The words in section B present an important demonstration that Bach used the natural order number alphabet. The correlation between the number of bars, the proportioned structure and the values of some key words also presents important evidence that Bach created a parallel proportion between two different forms. The terms Thema Regium and Quaerendo invenietis, ‘Ricercar’, ‘Canon’ and ‘Sonata’ may all have been sources of invention or Erfindungsquelle as he created and perfected the numerical structure of the collection. Bach prepared well-proportioned sections before sending them to the engraver: B and E with clues to the construction in highlighted key words and phrases; D and the canons in E well planned, neither motivated simply as a space-saving device nor as an appendage to the collection, but integral to the structure of 220 bars. If the Sonata was composed last of all, Bach ensured that its structure was parallel to that of the work as a whole. The 1980 bars of the Musical Offering are organised with a large-scale 2 : 1 proportion in 1320 : 660 bars and with many smaller layers of parallel proportion. Bach’s signature appears on the title page A, and may also be alluded to in the 1320 bars of the Sonata, and in the 1580 value of the canon headings in section D. Although hanging on the thread of numerical evidence, the parallelism of Reichardt’s alternative title page with the structure of the Musical Offering may suggest that Bach planned to exchange the original title page if it was ever reprinted. Christoph Wolff claimed that the work was ‘planned in a well-balanced way . . . in keeping with Bach’s characteristic behaviour in compiling and grouping compositions with some inner connection in order to form an

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opus perfectum’.47 The inner connection and perfected Harmony that Bach created in the Musical Offering can now be seen in its numerical construction.48 Furthermore his use of emblematic parallel devices can now be understood more fully. They were intended to attract attention and stimulate reflection on their meaning, thereby edifying the reader: the process of searching for that meaning was as important as finding it. Bach’s perfectly proportioned bar structure alone is sufficient to demonstrate the extent to which he made this collection eternally harmonious, acceptable both to God’s earthly representative and to God himself. Whether or not the original dedicatee rose to the challenge of seeking and finding it, the treasure in this musical offering was fit for a king.

II The Art of Fugue – a task for heaven? In Bach’s obituary, published in 1754,49 Carl Philipp Emanuel Bach and Johann Friedrich Agricola wrote: The Art of the Fugue. This is the last work of the author, which contains all sorts of counterpoints and canons, on a single principal subject. His last illness prevented him from completing his project of bringing the next-to-the-last fugue to completion and working out the last one, which was to contain four themes and to have been afterward inverted note for note in all four voices. This work saw the light of day only after the death of the late author.50

The autograph, P 200, of the ‘next-to-the-last fugue’ – Fuga a 3 Soggetti (BWV 1080/19) – shows that Bach stopped writing at bar 239, after which C. P. E Bach added the famous words: ‘N.B., While working on this fugue, in which the name B-A-C-H appears in the counter-subject, the author died.’51 When the work was published, however, this unfinished fugue ended at bar 233, at the foot of page 65, and was followed by a four-part church chorale ‘Wenn wir in höchsten Nöten sein’ (BWV 668), ‘which the deceased man in his blindness dictated on the spur of the moment to the pen of one of his friends’, and which the publishers were ‘proud to think . . . will make up for his lack [of completing the unfinished fugue] and compensate the friends of his Muse’.52

47 49 50 52

48 Wolff, Essays, 255. See Chapter 1. NBR, Doc. 306, 297 note 28; BD III, Doc. 666; it was written by the end of 1750. 51 NBR, Doc. 306, 304. NBR, Doc. 285; Wolff, Essays, 423. Reproduced in Wolff, ‘The Deathbed Chorale’, Essays, 282. NBR, Doc. 284, BD III, Doc. 645.

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The images of Bach dictating the chorale on his deathbed and his breaking off the completion of an impossible fugue, together with the role of various close relatives in its publication, have resulted in myths, interpretations and reinterpretations that continue to plague the work’s reputation. David Schulenberg gives an accurate analysis: The romantic search for cosmic truths and autobiographical references in the work, even when not based on equivocal evidence or anachronistic views of artistic self-expression, tends to devalue Bach’s achievement. This is because it focuses on superficial aspects of the work while disregarding its practical demonstration of compositional technique – probably its chief aim in the composer’s view – as well as its profoundly imaginative and expressive character.53

What Bach originally intended for the printed version has been impossible to ascertain. Solving the missing final fugue has been a regular pastime since publication, for which many scholars and composers have suggested plausible arguments, some using numerical clues,54 and some technical solutions to the incomplete fugue.55 Proportional parallelism suggests yet another, with a solution based on the parallel word–number–bar conceit, to show that 41 bars, i.e. J. S. Bach, is missing.

The sources Bach left two versions of The Art of Fugue, BWV 1080.56 Represented by the autograph manuscript P 200 and completed c. 1742, the first version has twelve fugues and two canons. It is the only major collection of his keyboard music to survive in an early version in an integral autograph manuscript.57 The second is represented by the original print, published posthumously. Although some of the plates may have been engraved under Bach’s direction, the final production and printing, presumably overseen 53

54

55

56

D. Schulenberg, The Keyboard Music of J. S. Bach, 2nd edn (New York; Oxford: Routledge, 2006), 397. See H.-J. Rechtsteiner, Alles geordnet mit Maß, Zahl und Gewicht. Der Idealplan von Johann Sebastian Bachs Kunst der Fuge (Frankfurt: Peter Lang, 1995); Chyron, Contrapunctus in versus. 12: Bachs vollendete Kunst der Fuge (Berlin: Chyron Verlag, 1997); V. Dequevauviller, L’art de la Fugue, un ‘Problème Algébrique’, (Paris, 1998); H.-E. Dentler, Johann Sebastian Bachs ‘Kunst der Fuge’: Ein pythagorisches Werk und seine Verwirklichung (Mainz; London: Schott, 2004). Donald Francis Tovey attempted a reconstruction in A Companion to ‘The Art of Fugue’ (London: Oxford University Press, 1931); Schulenberg, Keyboard Music, 404, considers Tovey’s solution unsurpassed. Tovey added 73 bars to the autograph, working out a full quadruple mirror fugue of 312 bars. 57 NBA KB, VIII/2. Schulenberg, Keyboard Music, 399.

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by Altnickol and C. P. E. Bach,58 was a compromise. The quadruple fugue was clearly incomplete, and as a magnanimous gesture by the publishers a chorale, ‘Wenn wir in höchsten Noten sein’ was printed on the final two pages, 66-7. Some have claimed further that the publication was printed in the wrong order and includes movements that do not belong, which casts a shadow over the status of the print: ‘It is far from certain that Bach had arrived at a firm conclusion regarding the organization of the print at the time of his death. In any case the form in which it appeared was not correct.’59 There are several significant handwritten comments on the consecutive manuscript P 200 and on the loose sheets stored with it. In c. 1745 Altnickol added a title which reads ‘Die Kunst der Fuga di Sign. Joh Seb. Bach’.60 In 1750 Johann Christoph Friedrich Bach wrote on p. 26 ‘Canon p(er) Augmentationem contrario motu’ with the comment ‘N.B. The late Papa had the following heading engraved on the plate: “Canon per Augment: in Contrapuncto all ottave,” but he had crossed it out on the proof plate and put it in the above-noted form.’61 The formation of the numerals used to correct the manuscripts demonstrates that Bach was working on the format even in early 1750.62 On the reverse of the final page of the unfinished fugue an unidentified scribe wrote the phrase ‘und ein anderen grundplan’.63 And, as mentioned above, after bar 239 of the unfinished fugue C. P. E. Bach claimed that his father had died while working on it.64 It was this entry, added possibly as late as the 1780s, that burnished the myth that ‘death stayed the composer’s pen at this passage’.65 The cold reality of diplomatic evidence, however, tells another story. Wolff writes about the unfinished page: The appearance of page 5 shows very clearly that Bach obviously had never planned to fill the sheet from top to bottom, in other words that he stopped writing deliberately at m. 239. The irregular and faulty ruling of the lower staff lines on page 5 did not permit the use of this part of the page for a dense fugal setting. Bach would never have started on such an untidy piece of paper had he planned to fill a larger portion of it than he did.66

Evidence in the published version of The Art of Fugue has also encouraged elaborate histories. A notice on the back of the title page of the

58 61 62 63 64

59 60 Ibid. Ibid. NBR Doc. 283. BD III, Doc. 645. NBR Doc. 280. BD III, Doc. 631. A. P. Milka, ‘Zur Datierung der H-Moll Messe und der Kunst der Fuge’, BJ 96 (2010), 53–68. It is not in the hand of Johann Christoph Friedrich Bach. 65 66 NBR, Doc. 285; BD III, Doc. 631. Wolff, Essays, 278. Wolff, Essays, 260.

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1751 first edition romanticises the effect of Bach’s illness upon the final fugue. It reads: The late Author of this work was prevented by his disease of the eyes and by his death, which followed shortly upon it, from bringing the last Fugue, in which at the entrance of the third subject he mentions himself by name, to conclusion.67

The print is punctuated by decorative features, the simplest of which are nothing more than elaborate double-bar lines, while the most complex involve scrolls, swirls, flowers and a monogram.68 The largest of these are at the end of movements 4, 5, 8, 14, 17 and 20. It is unclear whether they serve merely to fill in space, or whether they hold greater significance, such as marking a structural break in the work. Attracting the most speculation and interpretation is the monogram after Contrapunctus 8 on page 25. Philipp Spitta in the 1880s saw it as Bach’s, whereas Wolfgang Wiemer in the 1970s claimed it to be the monogram of the publisher, J. G. Schübler.69 Bach’s intention for the order and content of the collection has generally been seen through the eyes of the engraver and printers.70 New evidence has recently come to light, however, to show that his son Johann Christoph Friedrich Bach had a larger hand in the production and printing of the work than hitherto suspected,71 and that Bach himself changed some page numbers in the first three months of 1750.72 Intentionality and careful planning of this collection is strongly implied by the fact that the majority of the engraving was undertaken during Bach’s lifetime and probably under his direction. Regardless of when C. P. E. Bach wrote the description at bar 239, the documented B-A-C-H theme of the unfinished fugue has the ring of purposeful planning to it. The Art of Fugue is listed in Bach’s obituary, and thus must have been considered worthy of the late-departed master of fugue. It was also an extremely expensive project to pursue after Bach’s death: had the relatives not

67

68 69

70

71 72

NBR, Doc. 284; BD III, Doc. 645. The citation continues with the explanation of the inclusion of the chorale. See Chapter 2. W. Wiemer, Die wiederhergestellt Ordnung in Johann Sebastian Bachs Kunst der Fuge. (Wiesbaden: Breitkopf & Härtel, 1977), 37 and 39. G. Butler, ‘Leipziger Stecher in Bachs Originaldrucken’, BJ 66 (1980), 9–26; Butler, ‘Ordering Problems in J. S. Bach’s Art of Fugue Resolved’, MQ 60 (1983), 44–61; Butler, ‘Scribes, Engravers and Notational Styles. The Final Disposition of Bach’s Art of Fugue’, in About Bach (2008), 111–23. P. Wollny, ‘Beobachtungen am Autograph der h-Moll-Messe’, BJ (2009), 140–3. Milka, ‘Zur Datierung’, 68.

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thought it worthwhile, they would surely not have continued to sponsor it. David Schulenberg suggests that mistakes may have crept into the publication process as a result of misunderstanding between the editors and the engravers.73According to the 1751 advertisement, the collection consisted of twenty-four examples: ‘Die Kunst der Fuge, in 24 Exempeln entworfen durch Johann Sebastian Bach’.74 If twenty-four examples were intended, how were they counted, and what, if anything, is missing? Did Bach himself plan twenty-four? And if so, where are they? Butler argues that three movements were included erroneously – the 98 bars of BWV 1080/ 10a (no. 14 of the original print), and the 71 bars plus 71 bars of BWV1080/13Iii (nos. 18i and 18ii of the original print) – and that the unfinished fugue, Fuga a 3 Soggetti, with its 233 bars in the print and 239 bars in Bach’s manuscript, was never intended for inclusion in this collection.75 The obituary also mentions an Entwurff for the fugue ‘which was to contain four themes and to have been afterward inverted note for note in all four voices’.76 The question of whether or not Bach completed the ‘unfinished’ fugue has been discussed at length.77 Siegele has argued that the word Entwurff in the obituary meant plan, rather than sketch, and that Bach never fully worked out the end of the unfinished fugue, and therefore any search for a ‘lost’ fragment is in vain.78 Whereas Wolff, having demonstrated that Bach intended to copy the incomplete fugue onto a substandard piece of paper, states that: ‘Bach interrupted the manuscript at that point because its continuation was unequivocal; the remainder had at least been sketched, complete in outline’.79 Others still are of the opinion that Bach intended to include an entirely new complete missing final fugue as the twenty-fourth movement.80 The order and content of The Art of Fugue have been studied and discussed from many different angles,81 without a consensus of opinion. Owing to the inconclusive source evidence, it might seem futile to contribute further to the discussions. However, as proportional parallelism has been found in all of Bach’s collections and fair copies, it gives a new 73

74 76 77

78

79 81

Schulenberg, Keyboard Music, 399 and 489, note 28. discussing whether the engraver was J. G. Schübler or his younger brother Johann Heinrich Schübler. 75 BD V, Doc. C 638a; NBR, Doc. 282. Butler, ‘Scribes, Engravers’, 118. Wolff, Essays, 278. Most recently in Anatoly Milka, ‘Warum endet die Fuga a 3 Soggetti BWV 1080/19 in Takt 239?’ BJ 100 (2014), 11–26. U. Siegele,‘Wie unvollständig ist Bachs “Kunst der Fuge”?’, Bericht Bach-Konferenz 1985 (Leipzig: VEB, 1988), 223. 80 Wolff, Essays, 278. Siegele,‘Wie unvollständig?’, 219–25. e.g. Butler ‘Scribes, Engravers’, 116–20.

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objective measure against which to test the status of both Bach’s manuscript, P 200, and the posthumously published print. Numerical results show that the design of the publication was more polished than has hitherto been appreciated, and suggest that Bach had completed the quadruple fugue as far as he intended.

The print, the manuscript and their ground plans As the original publishers admitted to adding the final chorale movement, ‘Wenn wir in hochsten Noethen’, pp. 66–7, ‘to compensate the friends of his Muse’,82 this movement will be disregarded, and the numerical data from the print based on the first twenty-three movements, from Contrapunctus 1 to the Fuga a 3 Soggetti. Scholars are agreed that Bach oversaw the preparation of the engraving of the first plates. The first part of the print is therefore likely to hold clues to Bach’s numerical design, and possibly to his revised ground plan. What exactly the anonymous scribe meant by the word Grundplan in the annotation on the reverse of the final page of the unfinished fugue has not been established. The word is not listed in the lexicographical publications from Bach’s time, Grund-Riß being more common, with ‘plan’ cited as the French.83 The brothers Grimm, however, included it in their 1838 work, with ‘Grundrisz’ as a synonym for ‘Grundplan’.84 This leads logically to the question of whether the comment was written at the same time as the original publication in 1750 or some decades later when the word was more commonly used. At whatever point it was written, the annotation shows that someone in the eighteenth century believed there to be at least two groundplans. This can now be empirically verified by the numerical evidence and the characteristics of proportional parallelism. Table 9.7 shows that the first eight movements, Contrapunctus 1–8, have 790 bars and the first ten 1040 bars. Both totals are self-referential numbers forming rational blocks typical of Bach’s construction technique. Each implies a separate ground plan.85 There is also a block of 920 bars in 82 83 84

85

BD III, Doc. 645, NBR, Doc. 284. Wolff, ‘The Deathbed Chorale’, Essays, 283. Zedler, Lexicon, s.v. ‘Grund-Riß’; Fritsch, Lexicon, s.v. ‘Grund-Riß’. Grimm Wörterbuch, s.v. ‘Grundplan’, synonym ‘Grundrisz, horizontalprojection eines gebäudes’. In early architecture the plan was drawn with compasses and a ruler to establish the correct proportions between parts; and the specific measurements were required to put the plan into practice. It is unlikely that Bach drew up a musical plan with compasses and a ruler. 790 is related to 158 (Johann Sebastian Bach) and used in a 790 : 1580 structure: 1040 is both a 14 number (Bach) and a 3120 number (permutation of 2-1-3), which occurs frequently.

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Table 9.7 Numerical structures of The Art of Fugue, original print Pages

Title

Order

Bars

1–2 3–5 6–8 8–12 13–15 16–18 19–21 21–5 26–8 29–31 32–6 37–8 39–40 41–2 43–4 45–7 48–50 51–2 53–4 55–6 57–8 59–60

Contrapunctus 1 Contrapunctus 2 Contrapunctus 3 Contrapunctus 4 Contrapunctus 5 Contrapunctus 6 Contrapunctus 7 Contrapunctus 8 Contrapunctus 9 Contrapunctus 10 Contrapunctus 11 Contrapunctus 12 Inversus a 4 Contrapunctus a 3 Inversus a 3 Contrap. a 4 Canon Augmentationem Canon alla Ottava Canon alla Decima Canon alla Duodecima Fuga a 2 Clav Alio modo Fuga a 2 Clav

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

78 84 72 138 90 79 61 188 130 120 184 56 56 71 71 98 109 103 } 82 78 } 71 71

61–5

Fuga a 3 Soggetti

23

239 [41] ?

24? Totals Totals

23/24

1:2 78 84 72 138 90 79 61 188 130 120 184 56 56 71 71 98 109 103 } 82 78 } 71 71 [1300] 239 [41?] –

1:2

}

1:2

78 84 72 138 90 79 61 188 130 120

78 84 72 138 90 79 61 188

184 56 56 71 71 98 109 103 } 82 78 } 71 71 [1050] 239 [41?] 750?

1580

2080

790 : 1580

1040 : 2080

73 67

140

130 130 120 184 56 56 71 71 98 109 103 } 82 78 } 71 [1310] 239 [41?] 250? 1840 920 : 1840

Contrapunctus 1–9, which forms a plausible 920 : 1840 structure when the two repeats are included. The 1040 bars in the first ten movements suggests a large-scale 1 : 2 structure with 1040 : 2080 bars, that would create a total of 3120 bars and make The Art of Fugue parallel to Bach’s major keyboard collections.86 Table 9.8 shows that there are several layers of proportion within the ten movements that form the block of 1040 bars, suggesting an intentional 86

See Table 7.11.

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Table 9.8 Layers of proportion in Contrapunctus 1–10, 1040 bars Page

Title

1–2 3–5 6–8 8–12 13–15 16–18 19–21 21–5 26–8 29–31

Contrapunctus Contrapunctus Contrapunctus Contrapunctus Contrapunctus Contrapunctus Contrapunctus Contrapunctus Contrapunctus Contrapunctus

Totals

1 2 3 4 5 6 7 8 9 10

Bars

1:1

1 2 3 4 5 6 7 8 9 10

78 84 72 138 90 79 61 188 } 130 } 120 }

78 84

10

1040

1:1

72

1:3

3:4 78 84

78 84

138 90

138

72

72

138 90 79 61 188

79 61

120

120

79 61 188

188

130

130

520 : 520

260 : 260

130 : 390

numerical plan: a double 1 : 1 proportion with 520 : 520 bars in 5 : 5 Contrapuncti, a 1 : 1 proportion formed within one set of 520 bars, and a 1 : 3 proportion within the other. The building blocks of 300 and 400 bars within the two sets of 520 bars would have aided the numerical construction. A second numerical plan is suggested by the block of 790 bars in the first eight movements (Table 9.7 shaded column 1). These would form a double 1 : 2 structure with 8 : 16 movements in 790 : 1580 bars, self-referential numbers Bach had used in earlier structures. Although there are no layers of proportion within these 790 bars, it is the monogram central to the elaborate ornamentation at the end of Contrapunctus 8 that makes this structure stand out as plausible and intentional. It appears on page 25, and is positioned directly at the end of the 790-bar block, as if forming the end of a section. If this is Bach’s monogram and not Schübler’s, and if Bach oversaw the production of these first plates, the concurrence of the monogram and the self-referential 790-bar block strongly suggests that Bach had designed this parallel allusion, and that he did it to alert the reader to the structure. Indications of conscious numerical ordering continue in the subsequent movements. Table 9.9 shows that from Contrapunctus 9 to the end of the Alio modo Fuga a 2 Clavier on p. 60 there is a block of exactly 1300 bars, and from Contrapuntus 11 to the end, a block of 1050 bars. These blocks are typical of the composer’s procedure when he was aiming for a specific numerical construction. The layers of proportion within the 1040 bars, shown in Table 9.8, and the lack of proportions within the block of 790 bars, may indicate two concurrent numerical structures. The double 1 : 1

300 : 400

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Table 9.9 A double 1 : 1 proportion in pages 26–60: 14 movements in 1300 bars Page

Title

Order

26–8 29–31 32–6 37–8 39–40 41–2 43–4 45–7 48–50 51–2 53–4 55–6 57–8 59–60

Contrapunctus 9 Contrapunctus 10 Contrapunctus 11 Contrapunctus 12 Inversus a 4 Contrapunctus à 3 Inversus a 3 Contrap. a 4 Canon Augmentationem Canon alla Ottava Canon alla Decima Canon alla Duodecima Fuga a 2 Clav Alio modo Fuga a 2 Cl

9 10 11 12 13 14 15 16 17 18 19 20 21 22

Totals

Bars 130 120 184 56 56 71 71 98 109 103 82 78 71 71 1300

1:1 130 120 184 56 56 71 71 98 109 103 82 78 71 71 650 : 650

proportion formed by 7 : 7 movements and 650 : 650 bars in the 1300-bar section, shown in Table 9.9, supports the idea of the 790 : 1580 structure. If Bach was aiming for a total of 1580 bars in this section, he would know that he had just 280 bars left to add. Whatever his numerical plan, the block of 1050 bars, or 1300 bars, would have facilitated its execution. After the Alio modo Fuga, the numerical construction of the print goes awry. The published version reproduces 233 bars of Fuga a 3 Soggetti, making a structure of 790 : 1533 bars. Had the publishers followed Bach’s instructions to continue the fugue exactly to bar 239, however, it would have been 790 : 1539 bars, exactly 41 bars short of the 1580 bars required to form the perfect 1 : 2 self-referential proportion, 790 : 1580. It is not without significance that exactly 41 bars, the numerical value of J. S. Bach, seem to be missing at the very point where his son wrote ‘the author died’, in the very fugue based on a B-A-C-H theme. If Bach copied the final page of the unfinished fugue onto substandard manuscript paper, as evidence suggests, then he intentionally stopped writing at exactly this point. Why waste high quality paper to indicate forty-one blank bars? This simple 790 : 1580 structure raises many questions that are hard to reconcile with the sources. There seem to be only twenty-three movements. The publishers introduced a twenty-fourth in the full knowledge that it had

Two large late collections

247

Table 9.10 Two possible ground plans, self-referential and proportioned Pages Title

Bars

1:2

1–25

Pages Title

Contrapunctus 1–8 790 790 1–31 Monogram 26–60 Movements 9–22 1300 1300 32–60 61–5 Fuga a 3 Soggetti 23 239 239 61–5 Never composed 24? [41] [41] Totals

2370

790 : 1580

Bars

Contrapunctus 1–10 1040 1040 Ornate end bracket Movements 11–22 1050 1050 Fuga a 3 Soggetti 23 239 239 Never composed 24? [41] [41] Never composed 24? [750] [750] 3120 1040 : 2080

not been part of Bach’s scheme. The twenty-fourth movement, or the missing forty-one bars were neither composed, nor, it seems, ever intended to be composed. The layout of the print supports the idea that Bach intended the full 239 bars to be printed, and that there were fortyone bars missing in the overall structure of this work. If he had calculated that bars 233–9 should be written at the top of printed p. 66, the ‘missing’ forty-one bars would also have fitted onto pp. 66–7, even though they were to be kept blank. The staves and the page numbers for pp. 66 and 67 may have been engraved so they were ready to print before Bach died. As the staves were empty, the publishers, having no template for these sides and not knowing Bach’s wishes, decided to engrave the chorale on the plates.87 A second ground plan based on 1040 : 2080 is significant because of its relationship to the number 3120, the bar total of several keyboard collections, and its self-referential parallels, as both a permutation of 2-1-3 (B-AC) and because 1040 and 2080 contain the number 14 of ‘Bach’. However, movements 11–23 fall far short of 2080 bars. Table 9.10 shows that, without repeats and including the ‘missing’ 41 bars of the unfinished Fuga a 3 Soggetti, a massive 750-bar final movement would be required to reach the total 2080.88 In view of the length of Bach’s previous fugues, and the existing structure, this possibility can be ruled out. It is important when exploring alternative numerical plans to consider whether Bach might have included the repeats in his numerical plan. Following Hofman’s guidelines, only 140 bars are repeated in the

87

88

1:2

Milka,’Zur Datierung’, cites several plausible reconstructions to solve the problems of the ordering and content of the final movements. I have not tested these numerical structures. Contrapunctus 1–10: 1040 bars, 11–22: 1050 bars, Fuga a 3 Soggetti: 280 bars, Mvt 24: 750 bars.

248

demonstrations

Table 9.11 Another possible numerical ground plan Pages

Title

Movement

Bars*

1–28 32–60

Contrapunctus 1–9 Movements 10–22 Fuga a 3 Soggetti Never composed Never composed

1–9 10–22 23

920 1310 239 [41] [250]

920

2760

920 : 1840

Totals

24?

1:2 1310 239 [41] [250]

* including repeats

collection,89 and it is in this constellation that one can see a third numerical scheme, typical of a mid-course change of numerical plan. Table 9.11 shows a total of 2760 bars formed by the 920 bars in Contrapunctus 1–9, and a speculative 1840 bars to form a 1 : 2 proportion of 920 : 1840 bars, and a 3 : 5 proportion with 9 : 15 movements, were 250 bars allocated to the putative fugue 24, and 280 bars retained for the unfinished quadruple fugue (i.e. 239+41 bars). Two hundred and fifty bars would be a lengthy fugue, although not impossibly long. Excluding the unfinished fugue, with its 239 bars, Bach’s next longest written90 keyboard fugue appears to be the ‘Wedge’ (BWV 548), which has 231 bars, while his fugue for solo violin (BWV 1005/2) is 354 bars. The earlier version of this collection, manuscript P 200, has only fourteen or fifteen movements. Bach wrote it c. 1742 and it is a record of his fair and composing copies of the collection in progress as he solved and invented fugal material. Although the material is arranged coherently,91 Table 9.12 shows that the movements together lack any evidence of largescale numerical ordering. It is an example of a manuscript waiting to be revised and woven into a perfectly proportioned collection. Table 9.13 shows the changes to the bar length and order of movements as P 200 was transformed into the printed collection. The length of six of the fifteen movements remained the same: IV, VII, VIII, IX, X, and XI, while the metre of several was changed to create twice as many bars with as little alteration as possible. 89

90 91

NBA, KB VIII/1, 15 where Klaus Hofmann discusses what looks like repeat marks in the printed score and concludes that any musical significance can clearly be excluded. More than likely he improvised many longer. Schulenberg, Keyboard Music, 400, citing Wolff, ‘The Compositional History of the Art of Fugue’, Essays, 265–81.

Two large late collections

Table 9.12 Order in P 200, reordered in the print P 200 Order I II III IV V VI VII VIII IX Resolutio Canonis X XI XII XIII XIV XV Totals

Print Bars 37 35 39 90 65 49 79 61 103 103 188 184 66 56 71 55 1281

Bars

Order

78 72 84 90 130 120/98 79 61 103 – 188 184 – 112 142 109

1 3 2 5 9 10 & 16 6 7 18 – 8 11 – 12+13 21+22 17

1519

Table 9.13 Transformation genre-wise manuscript to print; 1 : 1 : 1 in 2 : 1 : 2 Title

P 200 Print Order Bars

Contrapunctus 1 Contrapunctus 2 Contrapunctus 3 Contrapunctus 4 Contrapunctus 8 Contrapunctus 11 Canon Augmentationem Canon alla Ottava Canon alla Decima Canon alla Duodecima

I III II – X XI XV IX – –

Totals

1 2 3 4 8 11 17 18 19 20

78 84 72 138 188 184 109 103 82 78

1:1:1

2:1:2

78 84 72 138

4 fugues

188 184

2 triple fugues 109 4 canons 103 82 78

372 : 372 : 372

4:2:4

The lack of working scores prevents a reconstruction of the order in which Bach made the revisions, although clues to the process of transformation can be detected in the proportioned sections and building blocks. Table 9.13 shows how three rational sections of

249

250

demonstrations

Table 9.14 Transformation process bar-wise manuscript to print Print 5 6 7 8

P 200 IV VII VIII X

90 79 61 188

Changes

Print

Length Length Length Length

90 79 61 188

unchanged unchanged unchanged unchanged

Totals

418

372 bars still required to reach desired total of 790 bars 1 2 3 4 9 10

I III II — V VI

37 39 35 — 65 49

Half time-value +4 Half time-value +6 Half time-value +2 Newly composed Newly composed Half time-value +22

78 84 72 138 130 120

790 920 1040

372 bars were created genre-wise from pre-existent and newly-composed movements:92 the first four simple fugues, the two triple fugues and the four canons. The idea may have been suggested by the 372 bars of the consecutive triple fugues X and XI in P 200. To create the parallel layers of 372 bars he had to add 138 bars to the simple fugues I, III and II, and 160 bars of canon to the pre-existent canons XV and IX. Table 9.14 shows how the 790-bar block in the first eight movements, Contrapunctus 1–8, was formed with minimal revisions to seven preexistent movements: the length of Contrapunctus IV, VII, VIII and X remained identical in the print as Contrapuntus 5–8; minor adjustments were made to I, III and II to become Contrapunctus 1–3, and Contrapunctus 4 was newly composed to reach the required total, 790 bars. Whether Bach had formed the layers of 372 bars shown in Table 9.13 before he formed the 790-bar building block is impossible to say. With 90 bars in Contrapunctus 5, a consecutive section of 700 bars would achieve the desired 790 bars. To reach 920 bars (for the 920 : 1840 structure), all Bach needed was a further 130 bars, which he achieved by halving the time-value of Contrapunctus V from 65 bars to 130 bars in the print. The block of 1040 bars in Contrapunctus 1–10 required a further 120 bars, achieved by adding 22 bars to VI after the time-value had been halved. Consecutive blocks of bars are 92

Noted by J. Cleaveland in private correspondence, November 2009; T. Daniel, Bachs Unvollendete Quadrupelfuge aus ’Die Kunst der Fuge’ (Cologne: Dohr, 2010) also notes groupings of 372 bars. See Table 9.12 and the 372 bars in 1 : 1 proportions in the Six Sonatas (BWV 525–30).

Two large late collections

251

Table 9.15 Altnickol’s title page parallel to Bach’s name Altnickol, 1745, P 200

Marpurg? 1752, Original print

Words

Value

Johann Sebastian Bach Die Kunst der Fuga

58þ86þ14 18 80þ26þ34

Totals

Total

1:1

Value

158 18 140

158

316

158 : 158

18 140

Die Kunst der Fuge

18 80þ26þ39

more commonly seen in a proportioned construction before the movements are reordered in a final version.93 Bach may have left the consecutive proportions in the print of The Art of Fugue because he wanted the parallel conceit to be detected.

Title page Bach seems not to have overlooked the form of the title page. Wolff writes: It was . . . in 1747 or later, that Bach formulated the title Die Kunst der Fuga (added in the hand of his son-in-law Altnickol to the autograph fair copy of the earlier version) or, entirely Germanised, Die Kunst der Fuge (the title of the 1751 edition). Although the title does not appear in Bach’s own hand, there is no reason to doubt its authenticity.94

Table 9.15 shows that the ‘Die Kunst der Fuga’, the title form used by Altnickol in 1745, has a total of 158, parallel to the total for ‘Johann Sebastian Bach’, and also possibly an intentional allusion to the ground plan structure 790 : 1580. Schulenberg suggests that the word ‘Fuge’ would have had an archaic ring to musicians of the time,95 and because the spelling ‘Fuga’ is inconsistent with the remaining German, the whole title page draws attention to itself – a characteristic typical of orthographic adjustments in hybrid parallel techniques.96 Just as the unfinished fugue and the monogram at bar 790 may be alerting a reader to the ‘missing’ 41 bars in the 1580 structure, so Altnickol’s title might be a further deliberate clue to one of the ground plans for the collection. If so, it would indicate that, as late as 1747, when Altnickol wrote the title, Bach’s plan for the collection was 790 : 1580 with the final 41 bars missing. 93 94

For example the early stages of construction of the Inventions and Sinfonias in Chapter 8. 95 96 Wolff, Learned Musician, 436. Schulenberg, Keyboard Music, 398. See Chapter 2.

18 145 163

252

demonstrations

It seems likely that Bach may have undertaken this fugal project in response to a public statement in 1739 by Mattheson, in which he expressed a wish to see engraved prints of double fugues with three subjects by ‘the famous Mr Bach of Leipzig, who is a great master of fugue’.97 This would agree with the timeline for the earliest drafts and concept in the late 1730s, as he was working on CÜ III and WTC II.98 Another possibility, suggested by Butler, is that the unfinished fugue was printed to be circulated to members of Mizler’s corresponding society, but never intended to be part of The Art of Fugue collection.99 This is an attractive suggestion for several reasons: it may confirm the deduction of 239 + 41 bars for the unfinished fugue, it provides a rationale for the publication of the 280 bars of the Schübler Chorales, BWV 645–50, also engraved by the Schübler brothers, and it sheds light on the fugue’s relationship to the Schübler Chorales. If Bach was intending to send a farewell contribution to the society, whose members shared his view of Harmony and unity, he would have needed a 280-bar work to accompany the Fuga a 3 Soggetti in order to solve the riddle of its missing B-A-C-H fugue. Table 9.16 shows the double 1 : 1 and 1 : 2 parallel formed by the Schübler Chorales and Fuga a 3 Soggetti, and the 280 : (280 41) bars. The parallel supports Butler’s idea that the fugue had another purpose outside The Art of Fugue. A two-work parcel circulated to the members would have been a fitting personalised farewell to the erudite members of the society. The clue was in the B-A-C-H theme that had yet to be worked out. The operation involved the relationship of the 280 bars of Schübler to B-AC-H as 14, and the missing forty-one bars, as J. S. Bach, to create the perfect unity, 280 : 280. Even if Bach had intended this small-scale 1 : 1 gift, I strongly suspect that the ‘unfinished’ fugue was also intended for the large-scale publication, where the solution to the riddle of the missing forty-one (J. S. Bach) bars was aided by the personalised monogram and its 790: 1580 structure.

Summary and conclusion At least three numerical ground plans have been suggested by the bar structure in conjunction with the principles of proportional parallelism. All 97 98 99

Schulenberg, Keyboard Music, 396, note 20, citing Mattheson, Capellmeister, 441. Schulenberg, Keyboard Music, 389. Butler, ‘Scribes, Engravers’, 117–18; Milka ‘Warum endet’, 23–4.

Two large late collections

Table 9.16 Plan for a personalised printed gift for the Mizler society? Work

Reason

Bars

Implied parallel

Schübler Chorales printed 1748 Fuga a 3 Soggetti – prepared 1749?

Unknown Mizler?

280 280 [41]

280 280 1:1

three are large-scale 1 : 2 structures, all are multiples of ten, two have a reference to Bach’s name, and all involve the same solution for the missing fugue on the B-A-C-H theme. Bach’s health began to fail while he was preparing The Art of Fugue for publication, and perhaps this caused him to cut down his ambitions, and to plump for the simplest plan: the personalised 790 : 1580 with its missing 41 bars. It created parallels with his other published collections, and he could reuse the ‘unfinished’ fugue for a simple 280 : 280 personalised present to his colleagues of Mizler’s society. Although the final print did not quite reproduce Bach’s intentions, the numerical clues in the publication and P 200 show it to be less imperfect than hitherto imagined. Many musicians and scholars have risen to the challenge of working out the unfinished fugue on B-A-C-H. Reflecting on the procedure, Tovey wrote: I confess that I enjoyed writing my quadruple mirror-fugue. But nothing less than the hope of thinking Bach’s thoughts after him would have induced me to enter on such a task; and I do not recommend it as an exercise. We need not hope to capture Bach’s spirit by wrestling with his technique . . . now there is no doubt that Bach thought mirror-counterpoint a useful exercise, at all events for himself, if not for less advanced students. Did he, then, set no limits to the abstruseness of his problems? Did he never ask whether there was a point beyond which technique degenerates into idle mechanism?100

Bach’s view of Harmony gives abundant justification for his creation of a large-scale 1 : 2 collection. The planned missing bars of the unfinished fugue were integrally woven into the harmoniously proportioned structure. The Thuringian Buttstett and many other Lutherans believed that the nonsounding Harmony of the human frame was a visible demonstration that the body will be resurrected. Likewise they believed that musical sounds used on earth, because of their Harmony, will survive in eternity, and be

100

Tovey, A Companion, 63.

253

254

demonstrations

used as Heavenly Music and Harmony, although God will compose the melody.101 Might the ‘unfinished’ fugue be a task for Heaven? In spite of the multiple theories, sources and complex questions surrounding Bach’s intentions for this work, the solution suggested by proportional parallelism is extremely simple: a double 1 : 2 proportion in 8 : 16 movements with 790 : 1580 bars, including the deliberate omission of forty-one uncomposed bars. The monogram that Bach positioned prominently after the end of bar 790 acts as a beacon highlighting this structure. It is possible that he originally intended to include a similar monogram after the forty-one blank bars on the page at the end of the collection. The reader of such an emblematic lusus ingenii might then have recognised that the solution of Bach’s puzzle lay not in asking ‘what is missing’ but ‘who is missing’. Planning this collection must have been a joyful process. Bach knew that by the time it was published, and his former colleagues and students were vying to be the first to solve the insoluble fugue, his earthly remains would be cold in the grave, and he would be beyond time, in a place where puzzling fugues and all manner of Harmony would resound eternally.102

101

Appendix, 1716-IV.

102

Appendix, 1723-II.

10 Collections of concertos

Twelve Keyboard Transcriptions (BWV 972–82, 592) Six ‘Brandenburg’ Concertos (BWV 1046–51) Er fing bald an zu fühlen, daß es mit dem ewigen Laufen und Springen nicht ausgerichtet sey, daß Ordnung, Zusammenhang und Verhältniß in die Gedanken gebracht werden müsse . . . Er studierte die Führung der Gedanken, das Verhältniß derselben unter einander, die Abwechselungen der Modulation und mancherley andere Dinge mehr. J. N. Forkel, 1802

This chapter discusses two contrasting sets of works to which the title ‘concerto’ was assigned in the early eighteenth century: Bach’s arrangement of instrumental concertos by mostly Italian composers, made c. 1713–15 and usually known as the Early Keyboard Transcriptions (BWV 972–82 with 592), and Bach’s only collection of orchestral concertos, dated 1721, known as the Brandenburg Concertos (BWV 1046–51). Bach’s concerto collections for solo and multiple harpsichords and orchestra from c. 1738 (BWV 1052–64) are discussed in Chapter 14 ‘Lost compositional blueprints’.

I Learning the tricks of the trade through the Early Keyboard Transcriptions According to Forkel, whose information came from Bach’s sons,1 transcribing Vivaldi’s concertos was an important formative experience for Bach, from which he learnt about compositional order and proportion. Describing Bach’s early attempts at composition of keyboard music, and his growing recognition and dislike of works by ‘finger composers’, or

1

Forkel’s claim is supported by extant letters, e.g. BD III, Docs. 793–5.

255

256

demonstrations

‘Clavier hussars’, who ‘let their fingers first play for them what they are to write, instead of writing for the fingers what they shall play’, Forkel continues: But Bach did not long follow this course. He soon began to feel that such eternal rushing and leaping would not do; that order, connection and proportion (Ordnung, Zusammenhang und Verhältniß) must be brought to the thoughts, and that, to attain such goals some kind of guide (Anleitung)2 was necessary. Such an opportunity presented itself in the newly published Concertos for violin by Vivaldi. He so often heard them praised as admirable compositions that he conceived the happy idea of arranging them all for his clavier. He studied the chain of ideas, the proportion between them (das Verhältniß derselben unter einander), the variations of the modulations, and many other particulars.3

Forkel’s tantalising claim about the significance of these concertos has provoked many a discussion about the proportions, order and connection in Bach’s transcriptions and their relation to Vivaldi’s originals,4 in terms of periodicity, tonal and modulatory planning, changing degrees of harmonic rhythm and voice leading.5 The focus in this chapter will be on how Bach used this concerto material to hone his skills in proportional ordering. Many of Bach’s concerto transcriptions have survived in individual copies as well as in three collections. Among the individual copies is one made by W. F. Bach, BWV 594, D-LEu N.I.5138, in which he failed to mention either Vivaldi as the original author or J. S. Bach as the arranger.6 As none of the three surviving collections is in Bach’s hand, it is not clear whether it was Bach himself who revised them into a unified collection, or whether his transcriptions were left as individual concertos. In this chapter, I will be using evidence of the numerical structure, provenance and 2

3

4

5

Fritsch, Lexicon, s.v. ‘Anleitung’ includes two meanings: (1) Die Unterweisung, lead, guidance, and (2) Der Anlaß, the occasion, motive, inducement, opportunity. The word ‘guide’ is used here for ‘Anleitung’. Forkel, Ueber Johann Sebastian Bachs Leben, Kunst und Kunstwerke (Leipzig, 1802), §V, 42. NBR, 441–2. Author’s adapted translation. P. Graf Waldersee, ‘Antonio Vivaldi’s Violinconcerte unter besonderer Berücksichtigung der von Johann Sebastian Bach bearbeiteten’, Vierteljahrsschrift für Musikwissenschaft 1 (1885), 356–80; H.-J. Schulze, ‘Entstehung und Überlieferung der Konzerttranskriptionen für Orgel und Cembalo’, Studien zur Bach-Überlieferung im 18. Jahrhundert (Leipzig; Dresden: Peters, 1984), 146–73; C. Wolff, ‘Vivaldi’s Compositional Art and the Process of “Musical Thinking”’, in Nuovi Studi Vivaldiani 4, ed. A. Fanna and G. Morelli (Florence: L. S. Olschki, 1988), 1–17, reprinted in Essays (1999), 72–83; K. Hofmann, ‘Zum Bearbeitungsverfahren in Bachs Weimarer Concerti nach Vivaldis “Estro Armonico” op. 3’, in Das Frühwerk Johann Sebastian Bachs. Kolloquium Universität Rostock 1990, ed. K. Heller and H.-J. Schulze (Cologne: Studio, 1995), 176–202, among others. 6 Wolff, Essays, 83. Schulze, Bach-Überlieferung, 171.

Collections of concertos

alterations typical of Bach’s revision and ordering practice to see whether any stands out as being characteristic of a faithful copy of a collection originally compiled by Bach.7 The concertos on which the transcriptions are based have been identified,8 and variations between the known originals and Bach’s transcriptions recorded. In all, Bach made seventeen concerto transcriptions. There is nothing to suggest that all seventeen were intended as an artistic or conceptual whole,9 but the analysis below strongly suggests that the twelve transcriptions in a sequential copy by Bach’s second cousin, Johann Bernhard Bach (1676–1749),10 P 280,11 were indeed selected, constructed and adapted to make a perfect numerical collection. Unless J. B. Bach devised the perfect structure himself, it was Bach, as the title page of P 280 indicates, who created its numerical unity and layers of parallel proportion.

1

Two early collections: D LEm Poel. mus. Ms. 29 and P 804

The least likely of the three surviving collections to have been originally compiled by Bach is D LEm Poel. mus. Ms. 29 made c. 1780–90 by the copyist Carl August Hartung (1723–1800).12 The four concerto transcriptions (BWV 592a, 984, 983, 973) are written consecutively on pages 2–36 in this miscellaneous collection of manuscripts, followed by three chaconnes ascribed to, but not composed by, Bach (BWV Anh. 82, 83 and 84), pp. 37ff. The four concertos have a total of 857 bars (respectively 272, 192, 172 and 221) and none of the characteristics of a Bachian collection. Originally belonging to Forkel, the manuscript was later owned by Griepenkerl, until it found its way into the Poelitz collection in the music library of the Leipzig Städtische Biblioteken.13 The second collection of concerto transcriptions has survived among the manuscripts of Johann Peter Kellner, copied in a variety of hands and

7

8 10

11 12 13

We do not yet know who besides Bach used the technique of proportional parallelism. It is possible that Bach’s students were taught it, and therefore that the student who made the compilation also made the alterations to create the proportional ordering. 9 NBA KB V/11, 24–5, and Schulze, Bach-Überlieferung, 164–7. NBA KB V/11, 17. Not to be confused with Johann Bernhard Bach (1700–43), son of Sebastian’s eldest brother, Johann Christoph. D-B Mus. ms. Bach P 280. Copyist identified in www-bach-digital.de. NBA KB V/11, 34–5, source ee: D LEm Poel. mus. Ms. 29. P. Krause, ‘Von der privaten Musiksammlung zur Fachbibliothek. Zur Vorgeschichte der Musikbibliothek der Stadt Leipzig’, Studien zum Bach-und Bibliothekswesen 2 (1982), 45–7, cited in NBA KB V/11, 34.

257

258

demonstrations

Table 10.1 Concerto transcriptions bound consecutively in score P 804,14 proportioned in P 280 BWV 974 976 985 987 983 986 984 973/1 973/2 973/3 972/1 972/2 972/3 977/1 977/2 977/3

Copyist in P 804 Anon, JPK JPK W. N. Mey W. N. Mey W. N. Mey W. N. Mey J. Ringk Unknown

P 804/4 P 804/15 P 804/28 P 804/34 P 804/35 P 804/46 P 804/52 P 804/54

P 804 No mvt 2

No mvt 3 Unknown

P 804/55 Incomplete

W. N. Mey W. N. Mey

Totals

P 804/56

P 280

Bars 350 248 238 201 172 90 192 132 132 25 25 64 64 51 51 35 35 105 105 59 59 9 9 35 } 35 }

2006/2041

550

1:2:2

Block

132 25 64 51 35 105 59 9 70 70 : 140 : 140

200

bound in the large manuscript P 804, a random miscellany with fifty-seven fascicles and almost 400 pages of varying paper types.15 The concertos are written on ten different fascicles, three of which are bound consecutively, and none reflecting any original ordering. Stinson writes of P 804: Many of the fascicles have been trimmed to give the volume a uniform size, and this process has resulted in the loss of headings and musical text in several places . . . One assumes this took place after Kellner’s death, for it is hard to imagine that he would have badly damaged his own copies . . . It is possible that whoever assembled P 804 did so by combining Kellner-circle copies and manuscripts that were never in Kellner’s possession.16

It is highly unlikely therefore that the ten concertos in P 804 represent an early Bachian collection of ten. Table 10.1 lists the concertos and shows that they have a total of 2041 bars with no large-scale proportions, typical of a random collection of works.

14 16

15 D-B Mus. ms. Bach P 804. Source for copyists NBA KB V/11, 31. R. Stinson, The Bach Manuscripts of Johann Peter Kellner (Durham, NC; London: Duke University Press, 1989), 19–20.

Collections of concertos

Three of the transcriptions, BWV 973, 972 and 977, are bound together consecutively in fascicles 54–6, and form a block of 550 bars, within which are three perfect proportions – a unit and structure typical of Bach’s handiwork (Table 10.1, shaded column). As these three have the same number of bars in the third and most important manuscript source of these collections, P 280, the proportions and the 550-bar unit may be an indication of Bach’s numerical adaptations as he organised these three transcriptions into a larger collection.

2

A copy of Bach’s original collection of twelve concertos, P 280

Bach’s Eisenach cousin Johann Bernhard Bach made a fair copy of twelve of Bach’s concerto transcriptions c. 1715,17 and Bernhard’s son, Johann Ernst, who studied with Johann Sebastian in 1737, made the title page in 1739. The resulting discrete and consecutive collection of twelve concerto transcriptions, P 280, remains unchanged today. Its numerical construction displays all the characteristics of proportional parallelism and strongly suggests that J. B. Bach was faithfully copying a collection that Bach had revised and polished. Table 10.2 shows the numerical content of the collection of twelve (BWV 972–80, 592, 981–2), with its total of 3150 bars. The first six concertos have 1400 bars, and a 1 : 3 proportion with 350 bars of the third concerto (BWV 974), and 1050 bars in the remaining five concertos, Table 10.3. The second group of six concertos has 1750 bars and several layers of proportion. Because of the positioning of the twelve concertos there is a consecutive block of 1400 bars formed by six concertos (BWV 975–80) at the centre of the collections, Table 10.4. Smaller-scale layers of proportion are evident throughout the construction. The personalised reference in the parallel 1400-bar blocks, the many layers of proportion, and the changes to the number of bars made to achieve the perfect numerical result, are all characteristic of Bach’s method of ordering. The original title page belonged to a single concerto transcription, but an unknown later hand wrote over the original to make it read ‘XII Concerto di Vivaldi’.18 A later scribe, possibly Zelter,19 also allocated a Roman numeral to each of the twelve concertos in the collection. Table 10.2, column 4, shows the original compositions on which Bach based the twelve 17

18

Rainer Kaiser, ‘Bachs Konzerttranskriptionen und das “Stück in Goldpapier”. Zur Datierung der Bach-Abschriften P 280 und Ms. R9’, BJ 86 (2000), 307–12. 19 NBA KB V/11, 27. Ibid., 29.

259

Table 10.2 Consecutive collection of twelve transcriptions copied by J. B. Bach, P 280 BWV 1

2

3

4

5

6

972/1 972/2 972/3 973/1 973/2 973/3 974/1 974/2 974/3 975/1 975/2 975/3 976/1 976/2 976/3 977/1 977/2 977/3

Movement Larghetto Allegro Largo Allegro Adagio Presto Largo Giga Largo Allegro

Model

JSB keys

Vivaldi Op.3 Nr.9 (RV 230)

D major

Vivaldi Op.7 Nr. 8 (RV 299)

G major

A. Marcello Oboe concerto (D 935)

D minor

Vivaldi Op.4 Nr. 6 (RV 316)

G minor

Vivaldi Op.3 Nr. 12 (RV 265)

C major

Unknown

C major

+/

Bars

1

Adagio Giga

Sub totals 7

978/1 978/2 978/3

Allegro Largo Allegro

Vivaldi Op.3 Nr. 3 (RV 310) Bars 1–14 repeat

F major 1–14 }

51 35 105 132 25 64 55 41 127 } 149 43 60 91 32 125 59 9 35 }

Bars* 51 35 105 132 25 64 55 41 254 149 43 60 91 32 125 59 9 70

1:1 51 35 105 132 25 64 55 41 254

1238

1400

508 : 254

64 32 152

64 32 166

64 32 166

Blocks

1:1

BWV 8

9

10

11

12

979/1 979/2 979/3 979/4 979/5 979/6 980/1 980/2 980/3 592/1 592/2 592/3 981/1 981/2 981/3 981/4 982/1 982/2 982/3

Movement

Model

JSB keys

Torelli violin

B minor

Adagio Allegro Andante Adagio Allegro Largo Allegro

+/

68–9 TS 27–8 TS

Vivaldi Op.4 Nr. 1 (RV 381)

G major +4-6

J. E. Saxe-Weimar Grave Presto Vivace Presto Prestissimo Adagio Allegro

B. Marcello Op. 1 Nr. 2 (C 788)

C minor

J. E.Saxe-Weimar Op. 1 Nr. 1

B♭ major

+3 1 +1

Bars 47 6 71 27 11 87 87 56 54 } 148 40 86 40 45 50 156 } 79 108 80

Bars*

1:1

47 47 6 6 71 TS 71* 27 TS 27* 11 11 87 87 87 87 56 56 108 108 148 40 86 40 45 50 312 79 108 80

Sub totals

1526

1750

500+262

Totals

2764

3150

762 : 762

* including repeats

Blocks

148 40 86 40 45 50 312 79

800

1:1

148 40 86 40 45 50 312 79 108 80

108 80

800 188 : 188

262

demonstrations

Table 10.3 Two consecutive, proportioned sets of six transcriptions in P 280 P 280 BWV Bars 1 2 3 4 5 6

972 973 974 975 976 977

Totals

+/

191 221 350 252 248 1 138 ? 1400

1:3

350

Block Block P 280 BWV Bars

191 191 221 221 350 252 248 138 138

350 : 1050 900

252 248

7 8 9 10 11 12

500

978 979 980 592 981 982

Totals

+/

Block Block

262 249 251 +4-6 274 447 267 +3

262 249 251 274 447 267

1750

1250

500

Table 10.4 Parallel proportions within the collection of twelve transcriptions, P 280 P 280

BWV

1 2 3 4 5 6 7 8 9 10 11 12

972 973 974 975 976 977 978 979 980 592 981 982

Bars 191 221 350 252 248 138 262 249 251 274 447 267

Totals

3150

1:1:1 191 221 350 252 248 138

1:1

Block

1:1

191 221 252 248 138 262 249 251 274 447 267

1400 : 1400 : 1400

262 249 251 274 447 267

350 252 248 138 262 249 251

1750 : 1750

1:1 191 221 350

500

252 248

400 500

249 251

262 249 251

1400

500 : 500

762 : 762

transcriptions, and shaded column headed +/ indicates the few but strategic changes he made to the number of bars in a movement.20

(a) A perfectly proportioned set of six transcriptions, BWV 972–7 The first six works in P 280 have 1400 bars. 1400 is a multiple of the value of the surname ‘Bach’ – 14  100. To achieve this total and the internal proportions within the construction, Bach would have had to select and order six works of suitable length. We can see that he contracted the length 20

Ibid., 76, 97 and 111 for a description of the changes.

Collections of concertos

by one bar in the third movement of the fifth concerto, BWV 976/3, to create a movement with 125 bars Table 10.3, column +/ .21 The source of the sixth concerto, BWV 977, is unknown, but it was probably changes to this work that enabled Bach to achieve his desired total and the layers of proportion within the set. Schulenberg describes this concerto as ‘one of the more attractive and idiomatic of the transcriptions’,22 with effective keyboard writing in the outer movements, but less effective part writing in the Adagio. Its second movement, BWV 977/2, is remarkably short, and a correction in bars 30–2 of the third movement is particularly weak contrapuntally, although the two bars are essential to the perfect numerical scheme. Perhaps Bach isolated the need for the two-bar extension, but left a student to provide the solution, as he sometimes did.23 Notice in Table 10.3 how the one-bar change to BWV 976 perfects the 500-bar block and how the unknown but suspected changes in BWV 977 facilitate a block of 900 bars. The 1 : 3 proportion of 350 bars in the third concerto and 1050 bars in the remaining five would become integral to the numerical plan of the twelve-work collection.

(b)

A well-ordered set of six transcriptions, BWV 978–82 with 592

Changes to the number of bars had a positive effect on the overall proportions in the second six transcriptions, BWV 978–982, with 592, the extra bars in BWV 980 facilitating the creation of a second 500-bar block, and the changes to the final concerto in the collection, BWV 982, creating a block of 1250 bars, Table 10.3. The cumulative bar totals in the twelve transcriptions reveal just how symmetrical and perfectly executed the layers of proportion are, Tables 10.3 and 10.4.

(c)

A perfectly proportioned set of twelve transcriptions – P 280

Table 10.4 shows that in addition to the 1400 bars of the first six concertos, there is a block of 1400 bars formed by the outer five concertos, and by the central six concertos of the collection, N.B. there is a self-referential 1400 at the centre. These central six concertos consist of three consecutive and 21 22

23

Ibid., 76. D. Schulenberg, The Keyboard Music of J. S. Bach, 2nd edn (New York; Oxford: Routledge, 2006), 129. For example in BWV 182/8, P 103, where he drew bars 67–90 and someone else filled in the blanks.

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symmetrically arranged blocks; 500 : 400 : 500 bars. The documented adaptations Bach made to the structure of BWV 976, BWV 980, and possibly to BWV 977 show that this numerical design was deliberate. The ordering (Ordnung) of the three blocks of 1400 bars creates a connectivity (Zusammenstimmung) within the collection through a large-scale 1 : 1 : 1 proportion (Verhältniβ) with the personalised B-A-C-H number. The positioning of the third transcription BWV 974, with its 350 bars, reveals yet another layer of 1 : 1 proportion formed by a block of 1750 bars in concertos 3–9 and the 1750 bars of concertos 7–12. The two blocks of 500 bars integral to the central 1400-bar construction are symmetrically positioned within the collection.

(d) Smaller-scale layers of proportion and order There are several further proportions between the four groups of three concertos. The final shaded column of Table 10.4 shows that the first three concertos, BWV 972–4, have 762 bars, as do the first three of the second collection of six, BWV 978–80, forming a further perfect double 1 : 1 proportion between six concertos in the twelve-concerto set. Table 10.2 shows that there is also a smaller-scale proportion within the first three concertos: a perfect 1 : 2 proportion formed between the 254 bars in the final movement of the third concerto and the 508 bars in the remaining eight movements. A parallel can be seen in Bach’s construction of BWV 978–80 when he chose a 262-bar concerto as the seventh concerto in the set (BWV 978) and then created a block of 500 bars by carefully selecting his model and expanding it by 4–6 bars (BWV 980/2).24 He facilitated the proportions with the least possible intervention by including two TS at the change of time signature in the Torelli movements, BWV 979/3 and 4, allowing a two-bar flexibility as he made the adjustments to the next concerto in the collection, BWV 980. There are similar signs of numerical manipulation in the remaining six concertos. To facilitate the 988 bars essential to reach the 1750 bar total in the final three transcriptions, BWV 592, 981 and 982, Bach crafted a block of 800 bars between the first and the last eight movements in these concertos. The final columns of Table 10.2 show how the symmetrical arrangement of 188 bars at the beginning and end of the block facilitates this structure. The loss of several of his models prevents an exact reconstruction of Bach’s method of achieving this perfect numerical plan. However, the 24

NBA KB V/11, 97.

Collections of concertos

proportions and blocks formed by the bar totals strongly suggest that he constructed the collection by breaking the twelve transcriptions into smaller groups and making the refinements to the bar lengths accordingly: two groups of six, four groups of three, and then sections of two concertos, or vice versa. The manipulation and alteration of the structure of the final work in a collection – or in this collection of twelve, to the final works in a working group – is a well-known characteristic, typical of Bach’s revision procedure.25 The fact that the collection of twelve is so immaculately structured, including many layers of proportion and with a reference to the surname ‘Bach’ at the heart of the numerical structure, leads me to conclude that Johann Bernhard Bach’s manuscript P 280 is a faithful copy of J. S. Bach’s original lost autograph of the collection, and that P 280, at least in its combination of transcriptions and its numerical structure, should be afforded the same status as one of Bach’s revised autograph scores. Johann Sebastian Bach may have prepared these twelve as a perfected collection with a view to publication. Roger of Amsterdam, the publisher of Vivaldi’s L’Estro armonico (Op. 3), had a thriving music business, with a healthy sales catalogue that included collections of concertos by various European composers and authorised agents from Halle, Hamburg and Leipzig, among other places. This suggests the possibility that in 1713 Bach was already developing ideas to supplement his regular income, perhaps as an editor or publisher of collections, just as he did in the 1730s and 40s when he was a sales agent for music books and musical instruments.26 As far as we know, however, Bach did not approach a publisher with these transcriptions. The collection seems to have remained a private exercise in proportional ordering compiled for his own use and possibly as an illustration for friends and students. The perfect numerical structure of these transcriptions also raises several questions about the practice and transmission of the technique of proportional parallelism. The manuscript P 280 is in the hand of Johann Bernhard Bach, who succeeded Bach’s elder brother as organist of Georgenkirche, Eisenach in 1703. The close relationship between these two branches of the Bach family was strengthened through the baptism of their children. In 1715 Bernhard Bach travelled to Weimar to be godfather when Bach’s son Johann Gottfried Bernhard (1715–39) was baptised. Although the manuscript P 280 is not dated, Bernhard’s handwriting suggests that it was copied 25

26

H. Eppstein, ‘Fragen der Ordnungsprinzipien’, in Bach in Leizpig: Bach und Leipzig, ed. U. Leisinger (Hildesheim; Zürich: Georg Olms Verlag, 2002), 131–5. Wolff, Learned Musician, 412.

265

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out in a matter of weeks rather than over a number of years, and therefore it is possible that Bernhard made the copy in 1715 in conjunction with the Weimar baptism. Naturally the reference to the B-A-C-H name through 14 in the parallel alphabet was also relevant to Bernhard Bach. Did he know about the perfect proportions embedded in the structure, and did he learn the art of proportional parallelism through the copying procedure, while also noticing the periodicity, tonal planning, degrees of harmonic rhythm and other essential ingredients in the music? Or was it Bernhard himself who pieced together this particular constellation of twelve transcriptions in such perfect proportional order?27 Forkel’s testimony, based on a comment that probably originated with Sebastian Bach himself,28 suggests not. Bach studied the concertos because he was looking for an opportunity to learn that ‘order, connection and proportion must be brought to the thoughts, and that, to attain such goals some kind of guide was necessary. Such an opportunity presented itself in the newly published Concertos for violin by Vivaldi’.29 A wide variety of musical techniques have been used over the years to account for the beauty of the proportion and connectivity in these transcriptions.30 The parallel proportions of the twelve-concerto collection, P 280, illustrate the literal ‘order, connection and proportion’ that Bach introduced as he made the transcriptions. Although he did not learn proportional ordering from Vivaldi, transcribing these twelve Italianate concertos gave him the opportunity to sharpen his large-scale ordering skills. The manuscript P 280 is not a random gathering of twelve transcriptions. It is a tightly designed, intentionally revised collection interconnected through layers of perfect proportion. Indeed, Forkel’s description seems to be the documentary ‘smoking gun’ for Bach’s conscious development of what I have since named ‘proportional parallelism’.

II Dedication and imperfect perfection in the Brandenburg Concertos The proportioning skills Bach learned through the keyboard transcriptions came to fruition when he turned his attention to adapting and revising the 27

28 30

The provenance and transmission of proportional parallelism is the subject of my current research. 29 Wolff, Essays, 74. Forkel, Ueber Johann Sebastian Bachs Leben, §V, 42; NBR, 441–2. Wolff, Essays, 83.

Collections of concertos

numerical order, connectivity and proportion in his own compositions. Among the earliest to be compiled was the collection known today as the six Brandenburg Concertos. His autograph score, Am. B. 78, is signed and dated 24 March 1721, dedicated to Margrave Christian Ludwig of Brandenburg, and with the title Six Concerts avec plusieurs Instruments.31 The presentation score was in the margrave’s possession until his death in 1734, when it was sold to Johann Philipp Kirnberger, who was in the service of Princess Anna Amalia of Prussia, to whom he bequeathed his music. On the death of Anna Amalia the score was ‘lost’ or, more accurately, forgotten, for over a century.32 It was not until after the rediscovery in 1849 of the whole collection that it became known as the ‘Brandenburg Concertos’. The style of Bach’s dedication is unusually obsequious, with many repetitious formulae and much false modesty: ‘begging you most humbly not to judge their imperfections . . . but rather to accept . . . the most humble devotion I attempt to show by this means’.33 In light of the fame and popularity of the collection today it is hard to believe that Bach was genuinely concerned about its imperfection. Numerical evidence however strongly suggests grounds for his contrition. Bach had a series of perfectly designed plans for this six-concerto collection, but because of a copying oversight and a subsequent new idea, the execution of the plan was never perfect, and the flaws immortalised in the presentation copy. Although several individual concertos from the collection circulated in copies in Bach’s time, he may never have performed the collection as a whole, nor even owned a score of the entire set of six. The collection was not listed among the compositions in his estate or in his obituary. Several variants of the fifth concerto have survived.34 One can be found in a set of parts, St 132, BWV 1050a, copied in the middle of the eighteenth century by J. C. Farlau, probably from the earliest version of this concerto. It has a short cadenza in the first movement,35 and its third movement is four bars shorter than the version in Bach’s presentation copy, Am. B. 78. The other main variant of the fifth concerto is also a set of parts, St 130, made by Johann Sebastian and Johann Christoph Friedrich Bach, probably just before the dedication copy of the collection of six was

31 32 33 34

35

NBA KB VII/2, Am. B. 78. M. Boyd, Bach: The Brandenburg Concertos (Cambridge University Press, 1993), 19–21. Ibid., 11. Alfred Dürr, ‘Zur Enstehungsgeschichte des 5. Brandenburgischen Konzerts, BJ 61 (1975), 63–9. St 132: the first movement has 153 bars and 18 bars cadenza, written as 171 9 bars.

D

267

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demonstrations

compiled, revised and completed. It is the same length as the fifth concerto in the dedication copy, with its 65-bar cadenza in the first movement.36 Besides three movements of the first concerto, BWV 1046, which were adapted from the hunting cantata Bach composed for Duke Christian of Saxony-Weissenfels in 1713, ‘Was mir behagt, ist nur die muntre Jagd’, BWV 208,37 we do not know how many other movements or complete concertos Bach had to hand before he began to form the six into the Brandenburg collection. Nor do we know how long he took to construct the collection after its commission by the margrave, possibly in 1719. The handwriting, rastration and visible alterations in Am. B. 78 led Heinrich Besseler and Christoph Wolff to conclude that Bach was unobservant and in a hurry when he made the autograph score.38 The process of making the presentation score began very well. The pages were prepared in advance, with bar lines ruled precisely, and the disposition of the staves on each page planned carefully in a manner typical of Bach’s fair copies. The manuscript was paginated in a highly individual manner, using beautifullyformed letters instead of numbers, as if to emphasise the uniqueness of the collection.39 But then a faulty rastrum caused the staves to become less parallel, and the combination of Bach’s creativity and his copying errors compelled him to go beyond his original carefully planned scheme.40 Table 10.5 shows the disposition of bars and movements in the final presentation score Am. B. 78. There is an implied parallel construction, with a double 1 : 1 and 1 : 2 proportion in 1110 : 1110 bars and 2 : 4 concertos in its 2220 bar total, and a double 1 : 1 proportion with 1250 : 1250 bars in its alternative total of 2500 bars. This was not Bach’s first plan. The rastration, anomalies in the layout, changes in the score, and the proportions suggest that there were several phases in the evolution of its numerical structure. A copying error in the first movement of the fourth concerto, BWV 1049/1, appears to have forced Bach to change his numerical plan. When he reached bar 345, where he could have indicated a full da capo to bar 1 at the return of the opening A section, Bach continued to bar 352, noticed his

36

37 38

39

40

For source evidence see NBA KB VII/2, reviewed in English in Boyd, Brandenburg Concertos, 86–90. Boyd, Brandenburg Concertos, 11–15. C. Wolff, ‘Die Rastrierungen in den Originalhandschriften Joh. Seb. Bachs und ihre Bedeutung für die diplomatische Quellenkritik’, in Festschrift für Friedrich Smend zum 70. Geburtstag (Berlin: Merseburger, 1963), 84. For easier reference, I will use the standard editorial pagination 1r, 1v, 2r, 2v, etc., instead of Bach’s. Boyd, Brandenburg Concertos, 38–44, and Wolff, ‘Die Rastrierungen’, 80–92.

Collections of concertos

269

Table 10.5 The dual numerical structure and proportioning within Am. B. 78 BWV 1046

1047

1048

1049

1050

1051

Movements 1 2 3 4 5 6 7 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3

Adagio Allegro Menuet Trio Polonaise Trio Andante Allegro assai Andante Allegro assai Allegro Andante Presto Allegro Later cadenza Affetuoso Allegro Adagio Allegro

Bars 84 39 107 24 28 32 32 118 65 139 136 1 48 352 71 244 162* [65] 49 232 130 62 65

D17

D75

84 39 107 24 28 32 32 118 65 139 136 1 48

84 39 107 24 28 32 32 118 65 139 136 1 48 75

75

65 49 232 130 62 65 1110 : 1110

Totals

1:1

17

352 71 244 162

D78 D45

D

1:1

2220

1:1

17

118

352 71 244 162*

65 49 310

78

45 140 : 140

84 39 124 24 28 32 32

130 62 65

45

65 139 136 1 48 427 71 244 162* 65 49 310 130 62 110

1250 : 1250

1250 : 1250

2500

2500

* with/without the 9-bar opening ritornello

oversight and remedied it by indicating a return with a dal segno in bar 353 to bar 9. This is highly unusual notation for Bach. When he arranged this concerto for solo harpsichord and instruments, BWV 1057, P 234, he used the conventional da capo after bar 344 to indicate a return to bar 1 for the entire 83-bar A section. The layout consequences of the copying oversight in BWV 1049/1 could not be accommodated within the Andante movement, and so Bach was forced to carry the final bars of the Andante onto page 49v, thus beginning the Presto movement in the middle of a page, rather than at the beginning, as originally planned. By the end of the Presto, with careful compression of the bar lines, the problem had been ironed out, and the fifth concerto could begin at the top of page 50r. The

270

demonstrations

additional eight bars in BWV 1049/1 confirm Wolff and Besseler’s opinion that Bach was distracted or hurried when he was making the copy, and this affected his numerical plan, although in the end he was able to make a virtue out of a necessity. The second significant anomaly in the score concerns Bach’s use of prepared orchestral staves for the harpsichord solo in the first movement of the fifth concerto, BWV 1050/1. From evidence in the rastrology Wolff has demonstrated that Bach changed his plan for this movement while he was writing out the presentation copy.41 Following his usual practice of planning the layout of fair copy scores in advance, Bach ruled the staves of the first movement of the fifth concerto with a wider-gauge rastrum for the harpsichord and a narrower-gauge rastrum for the instruments. In spite of his careful prepararation, he ended up writing a 64-bar harpsichord cadenza using every stave, regardless of width, on the three pages 67r, 67v and 68r. Wolff concluded from the surviving early version of this concerto, St 132, and the ruling of the six pages with harpsichord and instrumental staves, 67r–69v, that Bach had originally intended to use a 19-bar harpsichord cadenza on the harpsichord staves on pages 67r–69r, and to write out the tutti da capo on page 69v. The numerical and practical implications of these two notational anomalies, and Bach’s corrections, will now be used to detect and attempt to reconstruct the various numerical plans that Bach may have had as he prepared and copied the presentation score, Am. B. 78.

(a) Evidence of a first plan Wolff suggested that Bach intended to write the short cadenza and the reprise of the opening tutti of the fifth concerto on pages 67r–69v.42 The cadenza can be described as 19 bars long or, if the layout of Bach’s score is followed, as an 18-bar cadenza with a full 9-bar tutti da capo. There are 180 bars in the movement when the da capo tutti is written out, whether in the format 153 bars-Cadenza 18-Da Capo 9 bars, or 153 bars-Cadenza 19Da Capo 8 bars. Bach’s notation of the A section da capo return in the first movement of the fourth concerto (BWV 1049/1) also helps reconstruct his first plan for the layout of the score. Table 10.6 tests the numerical structure of Wolff’s hypothesis, showing the number of bars with the full 41 42

Wolff, ‘Die Rastrierungen’, 84: ’unaufmerksam und eilig’. Ibid., 83. ‘die 19-taktige Kadenz mit Da-capo-Teil auf den beiden unteren Cembalo-Systemen ab Bl 67r’.

Collections of concertos

271

Table 10.6 Reconstruction of Bach’s numerical plans from autograph evidence, Am. B. 78 Wolff BWV

Bars

First plan [

D]

1046 346 [17] 1047 322 – 1048 185 – 1049/1 344/352 [83/75] 1049/2 71 – 1049/3 244 – 1050/1 153 – Cadenza 18 – Tutti 9 – 1050/2 49 – 1050/3 232 [78] 1051 257 [45] Totals

2230/38 2453

Bars

Second plan [

D]

1:1

346 [17] 322 185 344 [83] 344 71 71 244 244 152 (sic! ) 152 18 18 [9] – 49 49 232 232 257 2220

Bars 346 322 185

257

346 322 185 352 71 244 153 (sic! ) [XX] 9 49 232 257

[109] 1110 : 1110 2220

Final solution

D

1:1 346 322 185 352 71 244 153

17

75

65 9 49 232 257

78 45

Bars 17

75

65

78 45

363 322 185 427 71 244 153 65 9 49 310 302

1110 : 1110 215 65 140 : 140 2500

da capo return of the first movement in BWV 1049/1 – the logical solution Bach used later for BWV 1057 – and with the 18-bar cadenza and 9-bar da capo return in the first movement of the fifth concerto, BWV 1050/1. These features create a collection with 2230 bars without any obvious large-scale proportion, or 2238 bars if Bach originally intended to write out the tutti return from bar 9, as he had in Am. B. 78. If all the da capo indications in the collection are counted, the total in Wolff’s reconstruction is 2453 bars. None of these totals is typical of a perfected Bachian structure. The anomalies in the rastration and the adjustment of the layout of the 19-bar (18-bar) cadenza, together with the characteristics of proportional parallelism, however, suggest a perfect numerical plan that Bach could have intended when he began to copy the collection of six. This is shown in the second column of Table 10.6, First plan. Taking the 18-bar cadenza and the number of written bars, i.e. excluding the da capo repeats, and using the logical full da capo return of BWV 1049/1 at bar 344,43 there would have been 1110 bars written on the score in the fourth and fifth concertos (BWV 1049 and 1050), creating a double proportion with 1110 bars of the first three and the final concerto: 4 : 2 concertos with 1110 : 1110 written bars. This is most likely to have been Bach’s original layout before he made his copying error in the fourth concerto, BWV 1049. It was 43

1:1

Notations he chose for the later concerto transcription of this movement (BWV 1057/1).

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Table 10.7 Rastration of BWV 1050/1 and Bach’s changing numerical plans Page Bach’s rastration

Am. B. 78

Wolff

Plan 1

Plan 2

Plan 3

67r 67v 68rK 68v 69r 69v 70r

Solo cadenza Solo cadenza Solo cadenza Affettuoso Affettuoso Affettuoso Allegro

Solo cadenza Solo cadenza Solo cadenza Solo cadenza Solo cadenza Da Capo Affettuoso

Solo cadenza Solo cadenza Solo cadenza Solo cadenza Solo cadenza Solo cadenza Affettuoso

Da Capo tutti Affettuoso Affettuoso Affettuoso Allegro Allegro Allegro

Solo cadenza Solo cadenza Solo cadenza Da Capo tutti Affettuoso Affettuoso Affettuoso

Instruments & Soloist Instruments & Soloist Instruments & Soloist Instruments & Soloist Instruments & Soloist Instruments & Soloist Instruments. New

intended to have a ground plan of 344 bars, with a full da capo of the 83bar A section. In this first plan Bach seems to have intended the short 18bar cadenza, and to indicate the 9-bar tutti as a da capo return to the opening,44 rather than copying it on page 69v. Not writing out the 9-bar tutti return would have allowed a luxurious layout of the 18-bar cadenza on the wider staves prepared on pages 67r–69v, the multiple demisemiquavers and the figuration comfortably filling six pages, with an average of three bars on each, as shown in Table 10.7, Plan 1. Table 10.6 shows the numerical reconstruction with 152 bars and the 18-bar cadenza. This is one bar shorter than Bach’s probable model, BWV 1050a, St 132, but reducing a cadenza or the lead-in to it by one bar would have been no problem for Bach, even while writing out a fair copy.

(b) A second numerical plan As Bach began to copy his presentation score, the only deviation he made from his original 1110 : 1110 numerical plan was to change the layout of the first movements of the fourth and fifth concertos. Table 10.6 shows that the first plan was dependent upon the full da capo return after bar 344 at the end of the B section in the first movement of the fourth concerto. Unaccountably Bach added eight bars to his ground plan as he was copying, making the movement 352 bars with 75 bars repeated by a dal segno indication to bar 9: this destroyed his first plan. Table 10.6, Second plan, shows how he got around the problem of the additional 8 bars. By scrapping the 18-bar cadenza, or excluding it, and writing out the 9-bar tutti 44

I use the description ‘opening tutti’ to avoid the historically misleading term ‘ritornello’. J.-C. Zehnder, ‘Ritornell-Ritornellform-Ritornellkonstruktion-Aphorismen zu einer adäquaten Beschreibung Bachscher Werke’, BJ 96 (2012).

Collections of concertos

return in the fifth concerto, he was able to salvage his 2220-bar plan with its large-scale double 1 : 1 and 2 : 1 proportion. Table 10.7, Plan 2, shows that although the solution used only one of the six pages he had ruled out for harpsichord and instruments, it nonetheless disguised the copying ‘errors’. The modified plan also required the approach to the cadenza to be extended by one bar, from 152 to 153 bars, as it appears in Am. B. 78.

(c)

The ingenious solution

The double proportion of Bach’s first two plans could have worked, but he decided against it even as he was writing out the first movement of the fifth concerto. When it came to the point, it seems that he could not compromise by excluding a cadenza. The movement was crying out for elaboration, and he needed to ensure that the cadenza would be included in the numerical perfection. The simplest way would be to introduce a cadenza of a specific length. He knew the exact length of his ground plan, 2220 bars, and the length of the repeated da capo sections, 215 bars. The least disruptive way to create a new plan from his existing structure was to include the da capos and a cadenza of a specific length. This would at least limit the damage caused by his errors. Table 10.6, Final solution, and Table 10.7, Plan 3, show the resulting 2500-bar disposition and layout. Enacting this plan was a compromise, causing Bach to disfigure the score, overwrite ‘64’ bars rest at bar 154, at the end of page 66v, ignore the carefully sized staves on 67r–69v, and above all to lose the beauty of the original numerical structure. By adding a cadenza of exactly 65 bars, from bar 154 to bar 218 of BWV 1050/1, Bach could redeem it slightly by creating a 1 : 1 proportion within the now-included da capo bars, with the 75 da capo bars from 1049/1, and the da capo bars from 1046/3, 1050/3 and 1051/3, making the final solution satisfyingly personalised with a 1 : 1 proportion in 140 : 140 bars using the ‘Bach’ number 14  10, as shown in Table 10.6, Final solution. The parallel 1110 : 1110 proportion, with its large-scale double 1 : 1 and 1 : 2 proprtion, could have been perfectly executed in Am. B. 78 by excluding the 65-bar cadenza, had Bach remembered to write out the 9-bar tutti da capo return onto page 68v, where it would have fitted perfectly, as it had on the Solo Harpsichord/Cembalo Concertato part of St 130. But again an error crept in,45 and an imperfection was immortalised, an imperfection for which Bach felt compelled to apologise in his dedication to the 45

Wolff, ‘Die Rastrierungen’, 84.

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margrave. On the bright side, his oversight gave him the flexibility of one more page on which to copy out the Allegro. The documented break he took from copying at the end of page 69v46 coincides with his need both to replace what seems to have been a faulty rastrum, and to take stock of the layout consequences of yet another copying oversight. Perhaps it was his consciousness of the less than perfect working out of his revised plan, highlighted by the heavily overwritten indication of the 64-bar rest, that caused him to make the quasi-apology in the dedicatory plea: ‘begging you most humbly not to judge their imperfections’. Compared with the simplicity and perfection of the original double perfect proportion and its layout, 4 : 2 concertos in 1110 : 1110 bars, the 2500-bar version was a compromise. The curiously obsequious wording of the title may hold a parallel allusion, but if it does, I have not found any with the 2500 or 2220 bars of the structure. Above all, though, the revisions demonstrate the lengths to which Bach was prepared to go to achieve unity within this collection. It would be wonderful to end this chapter by demonstrating how Bach created a united collection within his harpsichord concertos, or even a mega collection of concertos; but this cannot be. If it ever existed, the blueprint is now lost.47 Bach’s early keyboard transcriptions, on the other hand, generously compensate for the loss, displaying the order, connectivity and proportion described by Forkel: the numerical evidence strongly intimates that while selecting, adapting and transcribing these concertos Bach was using the exercise to hone the skill of creating layers of parallel proportion across a collection. This would become an essential part of Bach’s compositional technique, a method of demonstrating a morally correct way to treat music, so that it reflected the order of God’s universe, and at the same time pleased God and man.48 When it came to organising the numerical content of his own compositions, Bach demanded equal perfection. In the Brandenburg Concertos he aimed to produce an immaculate score with perfectly set out staves complementing its perfectly designed numerical structure. The apology ‘begging you most humbly not to judge their imperfections’ shows the spiritual disappointment he felt over imperfectly executing the Harmony of a beautiful and eternally pleasing plan.

46 48

Ibid., 83., the end of Bach’s gathering K. Appendix, 1687-III, 1691-IV 8, 1708-IV.

47

See Chapter 14.

11 Collections of organ works

The Great ‘Fifteen’ [sic] Leipzig Chorales (BWV 651–65) Six Trio Sonatas (BWV 525–30) Large-scale parallel collections? In Summa, wir können die Tugend der Music unmöglich beschreiben, welches auch der Sel. Lutherus gestehet. So können wir auch nicht alle Ursachen erforschen, warum Gott die liebe Music zu seinem Dienste verordnet hat, wir müssen uns behelffen, daß wir wissen, wie wir sie dem allmächtigen Schöpfer zu Ehren gebrauchen und anwenden, auch uns für allen Mißbrauch derselben hüten sollen. A. Werckmeister, 1691

The many hours Bach spent playing and improvising in church and at home resulted in a vast number of compositions for the organ. Towards the end of his life he lavished time and energy revising and compiling some of these into collections, only three of which were published before he died.1 In this chapter I will consider two organ collections that he compiled but did not succeed in publishing: the ‘Leipzig chorales’ or the ‘Great Eighteen’ (BWV 651–68), and the Six Trio Sonatas (BWV 525–30). I will also investigate a group of collections and ask if they were part of a larger, unfulfilled publication plan.

I

Fifteen of the best – the Leipzig organ chorales

The ‘Great Eighteen’ organ chorale preludes can be found on pages 56–99 and 106 of P 271.2 In his best handwriting, on carefully prepared manuscript paper, Bach wrote out the first thirteen (BWV 651–63) between 1739 and 1742, just after Clavier Übung III had been published. A few years 1 2

CÜ III, the Canonic Variations (BWV 769) and the Schübler Chorales (BWV 645–50). D-B Mus. ms. Bach P 271, fascicle 2.

275

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later, probably in 1746–7, he added the fourteenth and fifteenth (BWV 664–5) to the manuscript, and it was his son-in-law and former pupil, Johann Christoph Altnickol,3 who wrote in the sixteenth and seventeenth (BWV 666–7) in 1750 or later. Later still an unknown scribe added the fragmentary 26 bars of the eighteenth (BWV 668) on page 106 of P 271. Bach left neither a contents page nor a title for this group of chorale preludes, leaving both to the wisdom or folly of future publishers. The modern designation ‘Great Eighteen’ is explained by its nineteenth-century publication history. The word ‘Great’ was first used by Felix Mendelssohn in 1846 when he published a collection of fifteen chorale preludes, 15 Grosse Choral-Vorspiele für die Orgel,4 choosing the adjective ‘gross’ to contrast with the collection of small ‘klein’ chorale settings he had published a year earlier from Bach’s Orgelbüchlein.5 Mendelssohn’s ‘Great’ fifteen consist of Bach’s first thirteen of P 271 (BWV 651–63), a thirty-bar setting of ‘Wir glauben all’ (BWV 740), and the second setting that Altnickol had copied into P 271 (BWV 667). The myth of a collection of eighteen can be traced to Poelchau and the title page he made for manuscript P 271, which he owned until 1836.6 For some reason, possibly mistaking the title page for an original, later nineteenth-century editors adopted Poelchau’s appellation, and the name and number stuck. But what did Bach really intend? Had he compiled a collection of thirteen, fifteen, seventeen or eighteen organ chorales? Were the final three added under Bach’s direction, or without his knowledge? Was he hoping to rework these settings into a bigger and more perfect collection? Or was it complete and ready for publication when he added the double barline after the fifteenth chorale? Evidence from clues in the manuscript binding, revisions and handwriting, and from the numerical structure, strongly indicates that Bach designed a perfectly proportioned collection of 1200 bars in fifteen chorale preludes. There is also evidence to suggest

3 4

5 6

Bach’s pupil 1744–8 and married to Bach’s daughter Lieschen in January 1749. R. Stinson, J. S. Bach’s Great Eighteen Organ Chorales (Oxford University Press, 2001), 120. Mendelssohn’s collection, 15 Grand Preludes on Corales, was published as vols. 3 and 4 in the series ‘John Sebastian Bach’s Organ Compositions on Corales (Psalm Tunes)’ (London: Coventry & Hollier, 1846), and reprinted by Breitkopf & Härtel with German titles in the same year. 44 kleine Choralvorspiele, (Leipzig: Breitkopf & Härtel, 1845). Stinson, J. S. Bach’s Great Eighteen, 65. W. Breig, ‘The “Great Eighteen” Chorales: Bach’s Revisional Process and the Genesis of the Work’, in J. S. Bach as Organist: His Instruments, Music, and Performance Practices, ed. G. Stauffer and E. May (Bloomington; Indiana University Press, 1986), 102 claims the manuscript title was made by Bach Gesellschaft editor Wilhelm Rust.

Collections of organ works

that Altnickol’s additions were made under Bach’s direction, with a view to a posthumous publication project based on P 271.7

Manuscript When Bach compiled the collection of fifteen chorale preludes he began with works he had composed over twenty years earlier in Weimar. Stylistic characteristics suggest that none of the chorales were composed after 1717 or before 1708.8 The earliest versions have survived in P 801, P 802 and P 803, copies made by Johann Gottfried Walther and Johann Tobias Krebs. The exchange of musical material and ideas between Walther, Bach and Krebs would have been natural as they were all located in Weimar at the same time: Walther as organist at the Stadtkirche from 1707, Bach working at the court there from 1708 until 1717, while J. T. Krebs (1690–1762) studied in Weimar with Walther c. 1710–14 and then with Bach c. 1714–17. Unfortunately Bach’s autographs of these early versions have not survived.9 Table 11.1 compares the number of bars in the surviving early and final versions of these works. The shaded column +/ lists the additions Bach made when he revised them for P 271. Leaving the first page of his newly copied collection blank as if for a title, Bach prefaced the first chorale prelude with the letters J. J. (Jesu Juva)10 and wrote the first fifteen consecutively in almost perfect calligraphy and without wasting any space. His inconsistent use of the term ‘Fine’ at the end of these works appears to have no bearing on his intentions for the collection: in the first fifteen, the word ‘Fine’ is written at the end of all but the tenth (BWV 660), where there is no space, the thirteenth (BWV 663) and the fifteenth (BWV 665). Bach’s final additions to the collection were made in 1746 or 1747, when he wrote in the fourteenth (BWV 664) and the fifteenth (BMV 665), and it was Altnickol who added the sixteenth and seventeenth immediately after Bach’s fifteenth. Arguing from evidence of watermarks, handwriting style and circumstances,11 Wollny dates Altnickol’s additions to 7 9

10

11

8 See §III and Table 11.7 below. Stinson, J. S. Bach’s Great Eighteen, 4. Bach may have already formed the twelve copied by Krebs into an early collection. NBA KB IV/ 2, 25 explains that in P 802 J. T. Krebs also copied BWV 601, 621f, 637, 639, 642, 651a, 652a, 654a–656a, 657, 658a–660a, 660b, 661a–663a, 714, 717, 720, 722a, 727, 729a, 732a, 738a, 762, 767 and 768, while J. G. Walther copied BWV 638, 653a and b, 665a, 666a, 667b, 721 and 770. Although C. F. Geßner, Der in der Buchdruckerei wohl unterrichtete Lehr-Junge (Leipzig, 1743), 332–6, lists standard German abbreviations, he does not give J. J. P. Wollny, Die achtzehn grossen Orgel-choräle BWV 651–668 (Laaber: Laaber-Verlag, 1999), preface, summarised in Stinson, J. S. Bach’s Great Eighteen, 34.

277

Table 11.1 The Collection of ‘Great’ organ preludes: origins, additions and proportionally perfected structure of fifteen The Great ‘Eighteen’. Original early versions. Early

Title

651a 652a 653a 654a 655a 656a 657a 658a 659a 660a 661a 662a 663a 664a 665a

Kom heiliger Geist Komm heiliger Geist An Wasserflüssen Babylon Schmücke dich, o liebe Seele Herr Jesu Christ, dich zu uns wend O Lamm Gottes unschuldig Nun danket alle Gott Von Gott will ich nicht lassen Nun kom der Heyden Heyland Nun kom der Heyden Heyland Nun kom der Heyden Heyland Allein Gott in der Höh sey Ehr Allein Gott in der Höh sey Ehr Allein Gott in der Höh sey Ehr Jesus Christus, unser Heyland

Totals

Final version showing proportional perfection in collection of fifteen

Bars 48 193 77 95 73 112 52 27 34 42 46 37 93 96 52

+/

P 271 BWV

+58 +6 +6 – – +6 – – – – +46 – +1 – –

JSB JSB JSB JSB JSB JSB JSB JSB JSB JSB JSB JSB JSB JSB JSB

651 652 653 654 655 656 657 658 659 660 661 662 663 664 665

1077 123

Bars 106 199 83 95 73 118 52 27 34 42 92 37 94 96 52 1200

666 667

Jesus Christus unser Heyland Komm Gott, Schöpffer

38 – 26 –

JCA JCA

666 667

38 26

Total 668

Vor deinen Thron

45 ?

??

668

1264 26a

Total

[1290]

}

1:1

1:2

106 199 83 34 34 19 11

106

199 83 95

95 73

118

73 118

118 52 27 34

52 27 34

52 27

52 27 34 42 92

42 92 37 94 96

52

1:2 106

199 83 95 73

16 33

2:1

106

42

[147]

1:1

92 37 94 96 52

600 : 600 200 : 400

37

52 300 : 300

158 : 79

94 96 52 400 : 800

Collections of organ works

between August 1750 and April 1751, after Bach’s death and possibly without Bach’s authorisation.12 Elisabeth Juliana Frederica ‘Lieschen’ Altnickol, née Bach (1726–81) inherited some of her father’s manuscripts.13 P 271 was listed among C. P. E. Bach’s estate in 1788 alongside copies of Bach’s music made by Altnickol and originally owned by Lieschen. Altnickol died in 1759, and Lieschen in 1781,14 which suggests that Altnickol and his wife may have owned P 271 before it was passed on to C. P. E. Bach.15 This does not explain whether Bach had completed a fifteenprelude collection, or whether he had a new revised plan that involved permitting Altnickol to add a sixteenth and seventeenth (BWV 666 and 667). The incomplete eighteenth chorale ‘Vor deinen Thron’ (BWV 668) was added to P 271 by an anonymous scribe, not following the collection of seventeen, but several pages later, after Bach’s 1747 copy of the Canonic Variations.16 The fragment is from a revised version of the chorale added to the posthumous print of Bach’s Art of Fugue. Scholars have puzzled over why Bach extended some settings rather than simply copying all of his earlier versions when he compiled the collection. Werner Breig, for example, wondered about the connections between the early and expanded versions, and asked why Bach expanded the first (BWV 651a) to more than double its original length by presenting the cantus firmus in its full form.17 Stinson suggests some answers: Bach’s first three entries into this manuscript are the only ones with a significant amount of added material. One might also say, therefore, that these three entries are the most revised. This statement suggests that when he began to compile the Great Eighteen, Bach’s energy was particularly high. Could it be that later on in the process his enthusiasm waned? This would explain not only the four-year hiatus between the thirteenth and fourteenth settings, but also the likelihood that the collection was never properly completed.18 12

13

14

15 17 18

Altnickol’s handwriting style in P 271 is identical to that in manuscripts which also contain the hand of Bach’s last pupil, Johann Gottfried Müttel. The watermarks on the paper of these joint manuscripts are typical of Naumburg, where Altnickol lived. Müttel continued his twelvemonth study period in Naumburg with Altnickol, having arrived in Leipzig after 5 May 1750. Müttel became a godparent, together with Anna Magdalena, to the Altnickols’ first-born child in May 1751, which suggests some intimacy with the Bach family. See Wolff, Learned Musician, 504 note 50 Y. Kobayashi, “Zur Teilung des Bachschen Erbes”, in Acht kleinen Präludien und Studien über BACH (Wiesbaden: Breitkopf & Härtel, 1992), 69, and Stinson, J. S. Bach’s Great Eighteen, 33. P. Wollny, ‘Zur Überlieferung der Instrumentalwerke Johann Sebastian Bachs’, BJ 82 (1996), 12–13, and Stinson, J. S. Bach’s Great Eighteen, 33. 16 Wolff, Learned Musician, 407. See Chapter 9, §II. Stauffer, The Organ Preludes of Johann Sebastian Bach (Ann Arbor: UMI, 1980), 103, 109. Stinson, J. S. Bach’s Great Eighteen, 53.

279

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Although Stinson’s explanation is plausible, the numerical evidence presents an entirely different scenario. Table 11.1 shows the number of bars Bach added as he revised the settings from their early versions. The minimal revisions in the calligraphy of P 271 indicate that Bach had already worked out how and where to add the extra bars before he made his clean copy. For example in BWV 651, to which Bach had added 58 bars to the original 48, there are only eight autograph revisions – small details of rhythmic notation and two changes of pitch19 – and they all appear in the newly composed sections.20 By making small adjustments to five settings and doubling the note values of a sixth, Bach added 123 bars to his early versions and formed a collection that displays the three characteristics of a published Bachian collection: the bar total, 1200, is a whole round number, there are perfect proportions on at least two structural levels (1 : 1 in 600 : 600, a further 200 : 400, and 300 : 300 within the 600 bars, and a second large-scale 400 : 800 shown in Table 11.1), and there is an obvious signature carefully and deliberately grafted into the numerical structure. The signature is formed by 158 bars in BWV 651 and BWV 665, which before their expansion had formed a telling 100-bar building block. By adding 58 bars to BWV 651a he reached the signatorial 158 bars. This number was emphasised by positioning centrally the 79 bars of BWV 657a and 658a, which remained unchanged, to create a 2 : 1 proportion. Once this was accomplished he was short of only 65 bars to achieve a final total of 1200 bars. Doubling the time value of BWV 661a transformed its 46 bars to 92 and left him to find solutions for the remaining 19 bars. These he wove into the existing settings through tiny adjustments of between one and six bars, so as to create as many smaller-scale perfect proportions as possible.

Parallel proportions in the collection of fifteen There is nothing approximate about the bar totals or the intentionality with which Bach made the revisions. The fifteen consecutive settings in Bach’s fine handwriting display several layers of perfect proportion arranged symmetrically across the entire collection, both in the number of bars and the number of works.

19 20

Ibid., 40–1 for tabulation of Bach’s revisions. Ibid., 38, citing R. Marshall, The Compositional Process of J. S. Bach. 2 vols. (Princeton University Press, 1972), vol. I, 4–5.

Collections of organ works

Bach’s compilation of this collection of fifteen must be understood in the context of his compositional productivity in the 1740s. Having successfully published CÜ III by the end of September 1739, the next three years saw him planning and revising the Goldberg Variations, compiling WTC II and working on The Art of Fugue. His plans were extraordinarily ambitious and time did not always permit their fulfilment. Stinson has suggested that Bach’s diminishing enthusiasm for the organ chorale project caused the four-year gap between completion of the thirteenth and fifteenth chorales, the final two having less extensive revisions implying ‘the likelihood that the collection was never properly completed’.21 The numerical results contradict this. Bach must have designed the 1200-bar construction, with its parallel proportions, and its self-referential 2 : 1 proportion embracing the whole, before he began copying BWV 651. As the bar totals of BWV 664 and 665 were to be identical to their models, BWV 664a and 665a, he could wait until he found time to write them into the collection, which he did between 1742 and 1746. The indisputable numerical result and Bach’s carefully crafted proportions demonstrate that he had brought a collection of fifteen organ chorales to completion. It was ready to send to the engravers. But for some reason Bach waited.

Theological motivation for the fifteen? Did Bach choose the chorales forming the self-referential proportion 158 : 79 because of their texts and any personal significance as well as for their length: ‘Kom, [sic] heiliger Geist’, and ‘Jesus Christus, unser Heiland’ with ‘Von Gott will ich nicht lassen’ and ‘Nun danket alle Gott’? The incipits of the settings in the order Bach arranged them in P 271 suggest a theological progression. Starting with a plea for divine help, invoking both Jesus and the Holy Spirit (J. J. and BWV 651–2), the journey begins with the dark experience of separation from God (BWV 653–4), and the prayer for salvation through Jesus (BWV 655–6), progressing to qualities of redemption (thanksgiving, in BWV 657, and confidence, in BWV 658) followed by the threefold prayer for the return of Christ (BWV 659–61), the threefold acclamation ‘to God alone be glory’ (BWV 662–4), and ending with the Rapture, through the mystical union of the soul in the final chorale during the Eucharist. Tracing the soul’s journey from depravity through redemption to sanctification, these fifteen organ chorales 21

Stinson, J. S. Bach’s Great Eighteen, 53.

281

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appear to express a theological completion. If this theological unity is Bach’s design it is matched by the unity and proportional perfection that he may have believed made the collection eternal. In 1739 Bach submitted fifteen Mass and catechism settings in c. 1200 bars (alternative count at the semibreve) to the engravers22 before he changed his mind and expanded it into what became CÜ III. He would also have devised the numerical plan for the perfect collection of fifteen chorale preludes (BWV 651–65) early in 1739 or sooner. The two collections, each with fifteen chorale settings and 1200 bars, would form a double 1 : 1 proportion. Unfortunately it is impossible to reconstruct the exact content and length of Bach’s original submission of CÜ III to the engravers in 1739 because the original manuscript of this first version was destroyed in the engraving process, and the surviving print disguises the original layout. However, the compositional history, the dating, Bach’s documented revisions and the double parallel strongly suggest he had an unfulfilled plan to publish the fifteen chorale preludes alongside the fifteen settings: 15 : 15 settings in 1200 : 1200 bars. Table 11.2 shows the disposition of this hypothetical 1739 plan. But things changed as soon as Bach decided to expand CÜ III into the form we know today. This change, I suspect, explains why it was no longer a priority for Bach to finish copying BWV 664 and 665 into P 271, or to send it to the engravers.

Altnickol’s additions If Bach had completed a perfectly proportioned collection, why did Altnickol write out two more settings in the manuscript, on pages 96–9, after Bach’s death? What was he thinking when he copied then onto the blank pages of Bach’s carefully compiled manuscript? If his intention was solely to preserve two further chorale preludes he could have done this on separate sheets of his own paper, and stored them with Bach’s manuscript. Bach had deliberately left pages 96–9 blank at the end of the collection of fifteen chorales, and when he picked up the manuscript bundle again, in about 1747, it was to write a version of his recently published Canonic Variations from page 100. The 12 first of these five variations is in 8 time. Altnickol’s two additional chorale 12 preludes are both in 8 time. Could it be that Bach had intended to complement the exuberant set of canonic variations on the angels’ song ‘Vom himmel hoch’ with chorale preludes affirming ‘our Saviour Jesus Christ’, 22

See Table 7.1.

Collections of organ works

283

Table 11.2 Speculative plan, c. 1739, for a double 1 : 1 publication of organ collections BWV 1739 plan for the ‘Great’ 15 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665

Kom [sic] heiliger Geist Komm heiliger Geist An Wasserflüssen Babylon Schmücke dich Herr Jesu Christ O Lamm Gottes unschuldig Nun danket alle Gott Von Gott will ich nicht lassen Nun kom der Heyden Heyland Nun kom der Heyden Heyland Nun kom der Heyden Heyland Allein Gott in der Höh Allein Gott in der Höh Allein Gott in der Höh Jesus Christus, unser

Totals

Bars 106 199 83 95 73 118 52 27 34 42 92 37 94 96 52

BWV CÜ III early submission 1739 669 670 671 672 673 674 675 676 677 678 680 682 684 686 688

Kyrie, Gott Vater in Ewigkeit Christe, aller Welt Trost Kyrie, Gott heiliger Geist Kyrie, Gott Vater in Ewigkeit Christe, aller Welt Trost Kyrie, Gott heiliger Geist Allein Gott in der Höh sey Ehr Allein Gott in der Höh sey Ehr Fughetta on Allein Gott in der Höh Dies sind die heiligen Zehen Gebot Wir glauben all an einen Gott Vater unser im Himmelreich Christ, unser Herr, zum Jordan kam Aus tiefer Noth schrey ich zu dir Jesus Christus, unser Heyland

1200

P 271

Text

666 667 769a/1 769a/2 769a/3 769a/4 769a/5

96–7 98–9 100 101 101–3 103–4 104–6

Jesus Christus Komm Gott, Schöpfer Vom Himmel hoch Vom Himmel hoch Vom Himmel hoch Vom Himmel hoch Vom Himmel hoch

Totals

84 122 120 32 30 34 48 126 20 60 100 91 64 108 118 1157

Table 11.3 Proportioned additions to P 271, c. 1747–50 BWV

Alt Bars

Bars 38 26 18 23 56 27 42 230

2:3 38 26 18 23 56 27 42 92 : 138

‘Jesus Christus unser Heiland’, (BWV 666), and a plea for the Holy Spirit to descend, ‘Komm, Gott Schöpfer, heiliger Geist’ (BWV 667)? He could easily have conveyed this to Altnickol, although there was no urgency for Altnickol to act on the instruction. Table 11.3 shows that the numerical structure of the consecutive entries on pages 96–106, Altnickol’s additions before Bach’s copy of ‘Vom Himmel hoch’, form a notional grouping of 230 bars, proportioned 2 : 3 in 3 : 4 movements.

284

demonstrations

If Bach had authorised Altnickol’s additional chorale preludes for a greater numerical purpose, the proportions and this bar total may help answer some puzzles long associated with manuscript P 271.23

II Six family favourites – the Trio Sonatas Perhaps more than any other keyboard collection, the set of six Trio Sonatas for organ, (BWV 525–30), is a reflection of life at the heart of the Bach family in the Leipzig school apartment. Compiled and copied between 1727 and 1731, the stylish and fluent autograph manuscript, on pages 2–55 of P 271, breathes confidence and self-assurance. By this stage Johann Sebastian was a keyboard virtuoso, a church music leader and the head of a household which included a young wife, seven children and various relatives, servants and private students. The status of Thomaskantor brought with it the expectation and aspiration that his sons would be trained to pursue successful careers, and Bach did not shirk this responsibility. The first ideas of the progressively difficult collections of Inventions and Sinfonias and Preludes and Fugues are recorded in workbooks for his first-born son, Wilhelm Friedemann. The technical demands of the collection of six sonatas, demanding total independence of hands and feet, suggest that it was the next stage, if not the culmination, of this keyboard training. Between 1727 and 1730 Wilhelm Friedemann graduated from school, and read law at university while preparing for the music profession. Anna Magdalena and Wilhelm Friedemann made a copy of the collection, P 272, between 1730 and 1733, possibly in time for the start of Wilhelm Friedemann’s new post as organist of the Sophienkirche in Dresden, on 1 August 1733.24 Whether or not the reconstructed timeline is correct, the perfect numerical structure of the collection speaks of a composer whose eyes were raised beyond time-bound paternal responsibilities to the eternal calling of a Lutheran musician answerable to a heavenly father. Bach’s concise and economical handwriting covers fifty-four sides on twenty-eight sheets of manuscript paper folded together, P 271, 2–55, whereas in their copy, P 272, Wilhelm Friedemann and Anna Magdalena required eighty-four sides.25 He wrote BWV 525–30 and two great preludes and fugues, in B minor (BWV 544), private collection, and in E minor 23 24 25

See Table 8.6 and discussion in Chapter 8, §I. Williams, The Organ Music of J. S. Bach, 2nd edn (Cambridge University Press, 2003), 7. Six Sonatas for Organ (BWV 525–530). Facsimile of the Autograph, ed. W. Goldhahn, trans. R. Clément (Berlin; Leipzig, 1987), preface.

Collections of organ works

(BWV 548), P 274, on paper, with the watermark ‘M A’, which he used mostly in 1731 and which may suggest that the fair copies were made for the organ recitals he gave in Dresden at this time.26 Each of the six sonatas in P 271 has three movements, and they appear in the following order: Sonata 1 in E flat major (BWV 525), Sonata 2 in C minor (BWV 526), Sonata 3 in D minor (BWV 527), Sonata 4 in E minor (BWV 528), Sonata 5 in C major (BWV 529) and Sonata 6 in G major (BWV 530). However, it was not always so. Construction of the paper foldings and orthographic evidence show that Bach was unsure of the order when he began compiling the collection.27 Every thread of evidence in this manuscript has been explored with conventional source-study techniques and has led to a variety of reconstructions of Bach’s original order. Evidence from the numerical structure confirms much of what has already been detected, and largely support Kilian’s 1988 reconstruction.28 It also sheds new light on the position of the collection in Bach’s grander publication schemes.

Bars and proportions The numerical structure fulfils all three characteristics of proportional parallelism. Table 11.4 shows the three parallel bar totals, 1560, 1696 and 1860 (with repeats and da capo) caused because four movements in the trio sonata collection have repeat indications (BWV 525/2, 525/3, 527/2 and 530/2) and three movements have a da capo indication (527/1, 527/3 and 529/1). There is a TS feature between the fourth and fifth bars of BWV 528/1, which is observed in the 1560 bar total but not in the 1860. The second and third movements of all the sonatas combine to form a block of 1000 bars when the da capo is included. This may be evidence of Bach’s numerical working as he introduced the newly written sixth sonata into the collection.There is a double 1 : 1 proportion in the 1560 bars, with 780 : 780 bars in 9 : 9 movements. There are further layers of perfect proportion within the double 1 : 1 of the 1560 bars. The 1860-bar total is riddled with multiples of 372 bars: six movements have 744 bars and twelve movements have 1116, a 2 : 3 proportion with 1 : 2 movements. As if to emphasise this multiple, the bar total of both 26

27

28

P. Wollny, Die achtzehn Grossen Orgelchoräle BWV 651–668, preface. See also BD II, 294 and 294a. J. Butt, ‘Bach’s Organ Sonatas BWV 525–530; Compilation and Reconstruction’, The Organ Yearbook 29(1988), 80–90. Dietrich Kilian, NBA KB IV/7, Sechs Sonaten und verschiedene Einzelwerke (Leipzig: VEB, 1988).

285

Table 11.4 The dual numerical structure and proportioning within the Trio Sonatas, P 271 BWV 525/1 525/2 525/3 526/1 526/2 526/3 527/1 527/2 527/3 528/1 528/2 528/3 529/1 529/2 529/3 530/1 530/2 530/3

Bars Adagio Allegro Vivace Largo Allegro Andante Adagio e dolce Vivace Adagio–vivace Andante Un poc’allegro Allegro Largo Allegro Vivace Lente Allegro

Bars Movements * including repeats

58 28 64 78 48 172 112 32 144 64 45 97 104 54 163 180 40 77 1560 18

} }

D48

1:1 58 28 64 78 48 172 112

}

TS

D51

1:1

1:1

Block

58 28 64 78 48 172

28 64 48 172

112 32 144 64 45 97 104 54 163

D36

}

1:1

180 40

32

32

32 180

144 64

64 45 97 104

54 163

45 97 54 163

180 40 77

77

77

54 163 40 77

780 : 780

390 : 390

390 : 390

195 : 195

1000

9:9

4:5

5:4

2:2

2+3

Bars* 58 56 128 78 48 172 160 64 180 65 45 97 155 54 163 180 80 77 1860 18

2:3

1:1

58 56 128 78 48 172 160 32 180

1:1 58

56 64 78

64

48

48 172 160 32 180

32

32

65 45 97 155 54 163

1

65 45 97 155 54 163

180 80 77

180 80 77

744 : 1116

372 : 372

372 : 372

6 : 12

3:3

4:4

372 6

Collections of organ works

Sonata 3 and Sonata 5 is 372 bars, a highly unusual occurence in any collection by Bach. Units of 372 bars also feature prominently in the structure of the Art of Fugue, which he planned a few years later.29

Construction Bach compiled this collection largely from previously composed material. As many of the earliest versions have not survived we cannot be sure what changes he made to these pre-existent movements, but the general consensus of opinion is that only four of the eighteen movements were newly written: BWV 525/2, BWV 529/3 and BWV 530/1 and 2, and that the sixth sonata (BWV 530), is the only one in this collection composed specifically for organ.30 Sources show that several movements were adapted from instrumental and keyboard concertos, for example the 65-bar Adagio that became the first movement of the fourth Sonata (BWV 528) was originally a 65-bar Sinfonia that had opened the second part of the cantata ‘Die Himmel erzählen die Ehre Gottes’ (BWV 76), P 67, written for and performed on the second Sunday after Trinity in Leipzig on 6 June 1723, when Wilhelm Friedemann was just thirteen years old. Evidence from the paper foldings,31 rastration, fascicle structure and late numeration of the sonatas suggests the order in which Bach compiled the collection. The sixth sonata, BWV 530, was written on the paper with the earliest watermarks even though it was ultimately placed last in the collection. Bach wrote the staves for this sonata with a five-tipped rastrum different from the one he had used for sonatas BWV 525–9. And the first sonata, BWV 525, was copied last of all. Butt writes: Bach’s uncertainty regarding the order is substantiated by Kilian’s suspicions that the room left for the sonata numbers in the title of P 271 and in Anna Magdalena’s portion of P 272 (i.e. titles to BWV 529 and BWV 530) is greater than that between all other words and titles. Thus Bach did not number the sonatas until the first (and possibly second) manuscript of the cycle was complete. Certainly, though, by the time Bach began the last page of BWV 529 he had decided on the present ordering scheme.32

The evidence leads Butt to suggest that Bach placed BWV 525 fourth in the collection, to make a consecutive set of three minor and three major 29 30 31

See Table 9.8. Williams, The Organ Music of J. S. Bach, 4; Butt, ‘Bach’s Organ Sonatas’, 80. 32 NBA KB IV/7, 17–27; Butt, ‘Bach’s Organ Sonatas’, 86–8. Ibid., 89.

287

288

demonstrations

sonatas, while Kilian maintains that Bach intended BWV 525 as the fifth. The patterning of the proportions seems to favour Kilian’s reconstruction. The recurrence of groups of 372 bars and 220 bars, and the striking group of 1000 bars as the total of the second and third movements, suggests how Bach compiled and refined the collection. Before he began, Bach had already composed material for BWV 526–9/2, 525/1 and 3, and possibly for 530/3. To create a perfect structure he could either revise these movements, or simply ensure that the newly composed movements created the perfect structure. The newly composed movements are shaded in Table 11.4: BWV 529/1 and 3, BWV 525/2 and BWV 530/1 and 2 (possibly 3). To create a 1000-bar block with the pre-composed second and third movements Bach needed to add only 231 bars, or 308 bars if BWV 530/3 was not already composed. The position of these newly composed movements at the end of the 1000-bar block are typical of Bach’s constructional procedure. He may have decided upon the 163 bars of BWV 529/3 first, then 40 bars for 530/2 (and possibly 77 bars for 530/3), and last of all the shortest movement in the entire set, 28 bars for 525/2. Had he already copied BWV 530/2 (and 3), he would have had just two movements, 525/2 (28 bars) and 529/3 (163 bars) with which to make the adjustments to achieve the block of 1000 bars. The symmetrical ordering of the proportional blocks also supports Kilian’s reconstructed positioning of BWV 525.

Repeated pattern There is an uncanny parallel between the structure of BWV 526 and the Sonata from the Musical Offering, BWV 1079/3. Table 11.5 shows that the two have the same number of bars, the same tempo indication (Largo and Allegro) and similar metres, although they were composed fifteen or so years apart. Is this a constructional coincidence or Bach’s design? Was Bach using the same numerical template? Or does the coincidence of the C minor Largo with 48 and 172 to make 220 bars have some greater significance? Units of 220 bars would become central to the entire Musical Offering collection, which by the time it was complete, had become 440 : 220 : 1320.33

Parallels How and when Bach decided on the final bar total for the Trio Sonatas (BWV 525–30) – whether he aimed first for 1860 because it was 372  5, 33

See Table 9.1.

Collections of organ works

289

Table 11.5 Structural inspiration or coincidental parallelism? Six Trio Sonatas, c. 1730 BWV

Movement

526/2

Largo

526/3

Allegro

Totals

Bars 48 172

Musical Offering, pre-1747 Key

Time

BWV

Movement

E♭/C minor

3 4

1079/1

Largo

C minor

2

1079/2

Allegro

220

Bars

Key

Time

48

C minor

3 4

172

C minor

2 4

220

or whether his primary objective was a complete keyboard collection with 1560 bars, to create a proportion with his other keyboard collections – is open to speculation. The 1560 bars place these organ sonatas in a proportionally parallel relationship to his scheme for the published and revised keyboard works. Moreover the totals 1560 and 3120 are connected numerically with the Bach family name through the permutation of 2-1-3, investing the 1560-bar total with additional significance. Peter Williams wondered if Bach originally intended the Trio Sonatas to be the second part of his published Clavier Übung, asking: The advertisement for No. 5, in Dok. III, page 202, spoke of a seventh partita, which would have made a volume comparable to Kuhnau’s Clavierübung: Were the organ sonatas to have been the original Clavier Übung II, replaced, perhaps because they were too difficult, by the present Clavier Übung which included the French Overture or a seventh partita?34

Williams’ question can be tested in several ways using evidence from the proportional relationship, chronology and numerical construction. Given the 2 : 1 relationship, 3120 : 1560, seen in Table 11.6, between the bar totals of the two parts of the Clavier Übung and the Trio Sonatas, it seems highly likely that Bach had planned an association between the two collections. By 1723 he had completed his first two-section keyboard collection with its 3120-bar total. Given Bach’s method of numerical construction, it seems probable that from as early as 1723 he had thought of creating a second two-section keyboard collection with a parallel 3120 bars. The date and length of the Trio Sonatas suggests that at one time they may have been intended as companions to the keyboard partitas in CÜ I: they were constructed during the period 1727–31, while he was refining and composing the CÜ I partitas, and in 1726 Bach published Partita 1 (BWV 825) 34

Williams, The Organ Music of J. S. Bach, 2.

290

demonstrations

Table 11.6 Large-scale parallels between five collections Collection

Date

Bars

Aufrichtige Anleitung & WTC I Orgelbüchlein 46/48 of 164 completed Organ Sonatas BWV 525–30 Clavier Übung I and II [Neumeister Chorales]*

Rev. 1720s Rev. post 1726 c. 1727–30 Complete 1735 Late 1740s

3120 780 1560 3120 3120

1:1:1 3120

1:2

1:2

3120 780 3120 3120

1560 3120 3120

1560

with its 249 bars, which, with the addition of five more partitas of this length, could easily have reached a total of 1560 bars. Perhaps Bach had imagined composing a set of six partitas and a parallel set of six trio sonatas, 1560 : 1560 with their 3120 bar totals parallel to his first unpublished keyboard collection: AA and WTC I. By the time he had published the 379 bars of Partita 2 (BWV 826) and 342 bars of Partita 3 (BWV 827) in 1727, however, there was little or no hope of creating a six-partita collection with just 1560 bars without dramatically reducing the length of the remaining three partitas to an average of just over 196 bars each.35 This gives an important timeline. By 1727 it would not have been possible to incorporate the 1560 bars of the Trio Sonatas into a Clavier Übung collection of 1560 : 1560 bars, and this suggests that the Trio Sonatas were either revised before 1727 to make a 1560 : 1560 bar structure, or revised after 1727 for a different purpose. Pursuing the idea that Bach wrote them for his son, and the fact that the 3120 bars of the AA and WTC I also began life in Wilhelm Friedemann’s Clavier-Büchlein, Bach may have been content with the 3120 : 1560 relationship between these three instructive and edifying keyboard collections. Furthermore, while he was revising the Trio Sonatas into their double 1 : 1 division of 9 : 9 movements with 780 : 780 bars, Bach was also making the final revisions to the Orgelbüchlein, adding a few settings to make the incomplete book 780 bars long to provide yet another source that might be useful for his sons. As it happens the Neumeister Collection of chorales also has 3120 bars, although the demonstration is beyond the scope of this book.36 Table 11.6 shows the large-scale parallels based on the number 3120 with its allusion to the name B-A-C-H.

35

36

Partitas 1–3 have 970 bars. To create a six-partita collection of 1560 bars partitas 4–6 would have required a cumulative total of 590 bars. See Chapter 14§2, and Tatlow, ‘Narrative of Number in the Neumeister Chorales’, unpublished paper presented at 15th Biennial International Conference on Baroque Music, Southampton, 2012.

Collections of organ works

Wilhelm Friedemann was 23 when he finally moved from the Bach household; not 15, as his orphaned father had been forty years earlier when he had had to make his way alone in life. Compensating for all he had missed in his youth, Johann Sebastian lavished years of patient tuition on Wilhelm Friedemann with the best of intentions. Protective nurture of this kind all too frequently has an adverse effect as loving patience can turn to heavy-handed correction, and paternal demands for perfection break a child’s spirit. Wilhelm Friedemann evidently found it hard to escape the long shadow of his father’s approval. The respite he experienced after his father’s death in the 1750s, when he felt able to marry and compose freely, was sadly short-lived. His final years were marked by professional and social conflicts that left him jobless and destitute. In contrast, Carl Philipp Emanuel appears to have escaped the negative effect of parental expectation. No trace exists of a Büchlein for this second son, who by the age of thirty had not only completed a law degree, but held down a couple of responsible posts, composed two sets of six sonatas (the ‘Prussian’ (1740) and the ‘Würtemburg’ (1743)), married well, in 1744, and produced several children, including in 1749 a young artistic Johann Sebastian. But all this was unknown when Bach compiled the six Trio Sonatas. In 1733, with what appeared to be an enviable head start as an organist, and with an invaluable portfolio of personalised compositions in his luggage, Friedemann began his first highly prestigious job as an organist. His father had provided him with several perfectly crafted sets of keyboard compositions aimed to give this first-born son eternal joy as well as early professional success.

III

Parallels on a grand scale

The manuscript P 271 is made up of three separate works in Bach’s hand that at some point were bound together by Bach or his heirs:37 the Trio Sonatas on pages 2–55, on pages 56–95, and 96–99 the great chorale preludes, and on pages 100–6 the Canonic Variations. Immediately below the final variation, continuing on a subsequent page that later became detached, an unknown scribe copied out a revised version of Bach’s setting of ‘Vor deinen Thron’, which became known as the eighteenth chorale prelude. We do not know how Bach left P 271 or its constituent parts when 37

Stinson, J. S. Bach’s Great Eighteen, 30.

291

292

demonstrations

Table 11.7 Large-scale parallel proportions evolving between keyboard collections Date

Planned

Bars

1739 1739–42 1746–7 1739 1727–32 1749–50 1747

Early 1739 Early 1739 Early 1739 Mid-1739 1727–32 1749–50 1747

1:1

1:1

Clavier Übung Part III – original 15 c.1200 1200 P 271, 56–90, Preludes 1–13 1052 1052 P 271, 90–95, Preludes 14–15 148 148 Clavier Übung Part III 2090 2090 2090 P 271, 2–55, Six Sonatas JSB 1860 1860 P 271, 96–99, Preludes 16,17, JCA 64 64 P 271, 100–6, Canonic Variations 166 166

Totals 1751

1:1

1200 : 1200 2090 : 2090 1744–9

1748–9 1748–9

The Art of Fugue – 790 : 1580[ 41] bars Schübler Chorales

Totals

2370 280

2370 280 2370 : 2370

he died: the binding suggests that the Trio Sonatas (BWV 525–30) were added last of all and possibly after his death. The parallel proportions between Bach’s published works and works in P 271 suggest that it may have been part of an unfulfilled publication plan, and that its binding was therefore intentional, in line with Bach’s wishes. Table 11.7 shows that the three works in P 271 have a total of 2090 bars. The double parallel between Bach’s revision of the first fifteen chorale preludes into a collection of 1200 bars (Table 11.1) and his original submission to the engraver of fifteen CÜ III settings in approximately 1200 bars strongly suggests a plan to publish the fifteen chorale preludes alongside the fifteen settings: 15 : 15 in 1200 : 1200 bars. History shows, however, that Bach changed his mind, overturning this plan in favour of a version of CÜ III that was far more complex and unifying.38 Although he did not copy chorale preludes 14 and 15 (BWV 664–5) into P 271 until 1746–7, his numerical plan for the collection would have been formulated and perfected before he copied the first prelude into the manuscript in 1739. Table 11.7 shows the new parallel formed towards the end of the 1740s by the 2090 bars of P 271 and the 2090 bars of CÜ III, incorporating three further works for organ into a large-scale united scheme. The belief that perfect structures would ensure the work’s survival into eternity would

38

See Chapter 8.

Collections of organ works

have been the perfect motivation to authorise Altnickol to add sixty-four extra bars of chorale preludes to complete the 1 : 1 parallel with CÜ III – 2090 : 2090 bars. In the common number alphabet the value of J. S. B. is 29, as is the value of both W. F. B and C. P. I.[sic]B.,39 thus making 29 and the parallel 2090 useful personalised numbers appropriate for a collection to be bequeathed to his children. In fact the 2090 bars in P 271 suggest yet another very late proportion, with The Art of Fugue. Table 11.7 shows that the 280 bars of the Schübler Chorales with the 2090 bars within P 271 together create a set with 2370 bars, a total identical to that implied by The Art of Fugue.40 Bach composed numerous great organ works, some of which he formed into perfectly proportioned collections, some of which were published, and some deliberately left as revised manuscripts.41 The large-scale parallel proportions across these works may suggest that Bach was aspiring to create a collected organ series, possibly several Orgel Übung volumes, their massive proportions perhaps best understood as an intentionally formed unity that rendered the art work perfect, perhaps as a guarantee of its survival in eternity.42 This weighty belief would explain the motivation behind many curiosities and anomalies in Bach’s late publication schemes, including why he published the Schübler chorales and why he hand-copied into P 271 a version of the Canonic Variations, even though it was already published. Although Bach’s improvisation skills were silenced on 28 July 1750, the most perfect of his works would outlive him, to inspire and edify following generations on earth, and possibly to contribute to the joys of eternity.

39 41 42

40 See Chapter 2, note 141. See Chapter 9. The Six Great Organ Preludes and Fugues (BWV 543–8), are discussed in Chapter 14. See the Appendix and Chapter 3

293

12 Great passions and cantatas

St Matthew Passion (BWV 244) St John Passion (BWV 245) St Mark Passion (BWV 247) Gott ist mein König (BWV 71) Wenn auch ich stets den Endzweck, nemlich eine regulirte kirchen music zu Gottes Ehren, und Ihren Willen nach, gerne aufführen mögen, und sonst nach meinem geringen vermögen der fast auf allen Dorffschafften anwachsenden kirchen music, und offt beßer, als allhier fasionierten harmonie möglichst aufgeholffen hätten. J. S. Bach, 1708

Over the course of his twenty-seven-year cantorship at St Thomas, Bach composed around two hundred church cantatas and three passions for use in Leipzig church services. When he constructed these sacred vocal works he began, like Steffani,1 with the free-texted arias stipulated in the poetical text. As he set these smaller units to music he created layers of parallel proportion, gradually incorporating the choruses, chorales and recitatives while ensuring proportional order at every stage, until the multimovement work became a perfectly united whole. No original score has survived for the Passion according to St John (JP), the crowning jewel of Bach’s first Leipzig cantata cycle, performed on Good Friday, 7 April 1724. Bach may have hoped to compose a new passion setting for his second Good Friday in Leipzig,2 but did not manage to do so,3 and instead reused a revised version of JP for Good Friday 1725.4 It

1 2

294

3

Mattheson, Capellmeister; 240, see Chapter 4, note 19. Ulrich Leisinger, ‘Die zweite Fassung der Johannes-Passion 1725. Nur ein Notbeihelf?’, in Bach in Leipzig, Leipziger Beiträge zur Bach-Forschung, Bd. 5 (Hildesheim: Olms, 2002), 33. 4 Ibid., 31. 30 March 1725.

Great passions and cantatas

was not until at least two years later, on Good Friday, 11 April 1727, or even 15 April 1729, that the Passion according to St Matthew (MP) was performed, represented in the version copied later by Johann Christoph Farlau, Am. B. 6/7 (BWV 244b).5 In 1729 Bach changed the words and reused the music of ten of its arias for a funeral cantata, ‘Klagt, Kinder, klage es aller Welt’ (BWV 244a) in honour of Prince Leopold of Anhalt-Cöthen.6 He performed MP again in 1736 and 1742, and perhaps also in 1743 or 1746. It was for the 1736 performance on Good Friday, 30 March that he revised its structure and prepared what became its iconic autograph score, P 25.7

I

The greatly harmonious Passion according to St Matthew

Its many layers of proportion and simultaneous bar totals make P 25 the ideal score to show Bach’s method of creating numerical order and parallel layers of proportion in a texted multi-movement work. Table 12.1 shows the dual numerical structure of P 25, with the bar numbers of each movement, and the da capo repeats. The total of 2400 bars includes the length of each aria without its da capo repeat and omits Chorale 17, due to its lack of score. Together Chorale 17 and all the da capo sections have exactly 400 bars, thus making the parallel total of 2800 bars.8 The small roman numerals on the tables indicate their position and description in Picander’s print of the text. The differences between Am. B. 6/7 and the 1736 version, P 25, suggest that Bach’s early plan may have been for a passion structure of 2300 or 2700 bars: i.e. the exchange of Chorale 29 for 29a (99 bars instead of the early 13 bars of 29a), the 51 bars rather than 52 bars of Aria 60, and the omission of Chorale 17.

First beginnings: setting Picander’s text Picander, alias Henrici (1700–64), compiled the Passion text, using the gospel narrative from Matthew chapters 26 and 27, and composing free-texted 5 6

7

8

NBA KB II/5, 32–5. The funeral took place on 23 or 24 March 1729. A copy of the original 1729 text booklet has survived, and was reprinted in 1732, but the music has been lost, and so it is not possible to see the changes Bach made. D-B Mus. ms. Bach P 25. Some time between 1743 and 1746 Bach repaired P25 after some unknown damage, the new glued-on strips of paper and supplementary script on the title page and the past twelve sheets (24 pages) showing Bach’s later handwriting. Both the NBA edition and BWV2a have 2800 bars.

295

296

demonstrations

Table 12.1 The dual numerical structure of the autograph score, P 25 BWV

Part One

244/1 244/2 244/3 244/4 244/5 244/6 244/7 244/8 244/9 244/10 244/11 244/12 244/13 244/14 244/15 244/16 244/17 244/18 244/19 244/20

Aria: (i) Kommt, ihr Töchter, helfft mir Recitative: Da Jesus diese Rede vollendet Chorale: Herzliebster Jesu, was hast du Recitative-Chorus: Da versammleten sich Recitative: (ii) Du lieber Heyland du Aria: (iii) Buß und Reu Recitative: Da ging hin der Zwölfen Aria: (iv) Bluthe nur, du liebes Herz! Recitative-Chorus: Aber am ersten Tage Chorale: Ich bin’s, ich sollte büßen Recitative: Er antwortete und sprach Recitative: (v) Wiewohl mein Herz Aria: (vi) Ich will dir mein Herze schencken Recitative: Und da sie den Lobgesang Chorale: Erkenne mich, mein Hüter Recitative: Petrus aber antwortete Chorale: Ich will hier [no score] Recitative: Da kam Jesus mit ihnen Recitative: (vii) O Schmerz! Aria a Duetto: (viii) Ich will bey meinem Jesu wachen Recitative: Und ging hin ein wenig Recitative:( ix) Der Heyland fällt Aria: (x) Gerne will ich mich bequemen Recitative: Und er kam zu seinen Jüngern Chorale: Was mein Gott will, das g’scheh Recitative: Und er kam und fand sie Aria à 1, à 2: (xi) So ist mein Jesus/Sind Blitze, Sind Donner Recitative: Und siehe, einer aus denen Chorale: O Mensch, bewein dein’ Sünde

244/21 244/22 244/23 244/24 244/25 244/26 244/27 244/28 244/29 Subtotals BWV

Part Two

244/30 244/31 244/32 244/33 244/34 244/35 244/36

Aria: (xii) Ach, nun ist mein Jesus hin! Recitative: Die aber Jesum gegriffen hatten Chorale: Mir hat die Welt trüglich gericht’ Recitative: Und wiewohl viel falsche Recitative: (xiii) Mein Jesus schweigt Recitative: (xiv) Geduld! Recitative-Chorus: Und der Hohepriester

Bars 90 8 11 49 10 105 9 45 37 12 39 13 48 13 16 15 [16] 15 30 81 7 10 102 15 16 35 136 TS

D

68 29

30

[16]

10

72

[1]

30 99

Bars*

90 8 8 11 11 49 49 10 10 173 173 9 9 74 74 37 37 12 12 39 39 13 13 78 78 13 13 16 16 15 15 16 16 15 15 30 30 91 91

1:1 90 8 11 49 10 173 9 74 37 12 39 13 78 13 16 15 16 15 30 91

7 7 10 10 174 174 15 15 16 16 35 35 137 137 30 99

1096

226

1322

Bars

D

Bars*

123 16 11 18 10 47 38

1:1

7 10 174

30 99

123 123 16 16 11 11 18 18 10 47 38

1:1

1:1

10 47 38

Great passions and cantatas

297

Table 12.1 (cont.) BWV

Part Two

244/37 244/38 244/39 244/40 244/41 244/42 244/43 244/44 244/45 244/46 244/47 244/48 244/49

Chorale: Wer hat dich so geschlagen Recitative: Petrus aber saß draußen im Aria: (xv) Erbarme dich, mein Gott Chorale: Bin ich gleich von dir gewichen Recitative-Chorus: Des morgens aber Aria: (xvi) Gebt mir meinen Jesum wieder Recitative: Sie hielten aber einen Rat Chorale: Befiehl du deine Wege Recitative-Chorus: Auf das Fest aber Chorale: Wie wunderbarlich ist doch Recitative: Der Landpfleger sagte Recitative: (xvii) Er hat uns allen wohlgetan Aria: (xviii) Aus Liebe will mein Heyland sterben! Recitative: Sie schrieen aber noch mehr Recitative: (xix) Erbarm’ es Gott! Aria: (xx) Können Thränen meiner Wangen Recitative: Da nahmen die Kriegsknechte Chorale: O Haupt voll Blut und Wunden Recitative: Und da sie ihn verspottet Recitative: (xxi) Ja! Freylich Aria: (xxii) Komm, süsses Creuz Recitative-Chorus: Und da sie an die Recitative: (xxiii) Ach Golgotha! Aria: (xxiv) Sehet, Jesus hat die Hand Recitative: Und von der sechsten Stunde Chorale: Wenn ich einmal soll scheiden Recitative-Chorus: Und siehe da Recitative: (xxv) Am Abend, da es kühle Aria: (xxvi) Mache dich, mein Herze, rein Recitative: Und Joseph nahm den Leib Recitative: (xxvii) Nun ist der Herr zur Ruh Aria Tutti: (xxviii) Wir setzen uns

244/50 244/51 244/52 244/53 244/54 244/55 244/56 244/57 244/58 244/59 244/60 244/61 244/62 244/63 244/64 244/65 244/66 244/67 244/68

Bars 12 33 46 16 35 52 30 16 43 11 2 12 61 40 12 91 18 16 10 6 54 66 15 52 26 16 37 18 53 45 17 80

D

Bars*

1:1

1:1

13

12 33 54 16 35 65 30 16 43 11 2 12 74

12 33 54 16 35 65 30 16 43 11 2 12 74

2 12 74

64

40 12 155

40 12 155

40 12 155

18 16 10 6 54 66 15 52 26 16 37 18 81 45 17 128

18 16 10 6 54 66 15 52 26 16 37 18 81 45 17 128

18 16 10 6 54 66 15 52 26 16 37 18 81 45 17 128

8

13

28

48

Subtotals

1304

174

1478 1400 : 1400 900 : 900

Totals

2400

400

2800

* including

D repeats

2800

1800

298

demonstrations

reflections on the dramatic events for the arias and choruses, numbered with lower case Roman numerals in the tables. No copy of the congregational text booklet has survived, but this passion setting was published in a later volume of his collected writings.9 Of the twenty-nine texts for which Picander specified a heading (‘Aria’, ‘Choral’, ‘Recit’, ‘Chor’, ‘Zion und die Gläubigen’), Bach set twenty-eight as individual movements, numbered in the tables i–xxviii. Rather than making Picander’s chorale ‘O Lamm Gottes’ a separate movement, Bach wove it into the opening chorus, thus rendering the libretto twenty-eight rather than twenty-nine sections, a choice motivated perhaps both by the parallel significance of the number 2810 and its amenability to proportional ordering. We do not know how much of the music Bach reused, how many movements were newly composed specifically for MP, or which he adapted to ensure the perfect numerical structure. The numerical results suggest, however, that he began with the twenty-eight free-texted movements from Picander’s text and built out the structure from these, proportioning each section as he went. Having decided which ensemble or voice would best suit each of the texts described as ‘Aria’, Bach appears to have organised first the numerical structure of the movements for tenor solo, bass solo and chorus, being fully aware of their lengths both with and without their da capo sections. The 1 : 1 proportion formed by these ten free-texted tenor and bass arias and the opening and concluding choruses, without their da capos, can be seen in the first shaded column of Table 12.2: a double 1 : 1 and 2 : 3 structure with a self-referential 410 : 410 bars in Part I : Part II, in 4 : 6 movements. The decision of the original NBA editors to write out the shorter ritornello da capos, rather than follow Bach’s layout literally, masks this numerical result. The 170 bars of da capo in these ten arias create a parallel bar total in these movements of 990 bars. Without the chorus, the tenor and bass movements in Part II have 330 bars, Table 12.2, shaded column 3. Corrections in P 25 and in Farlau’s score of the early version show that Aria 30, ‘Ach nun ist mein Jesu hin’, well known as an aria for alto solo, was originally for bass soloist and chorus.11 When he revised the score and changed the soloist from bass to alto, Bach knew that the neat 410 : 410 proportions formed by genre would disappear; a sign that the proportions

9 10 11

C. F. Henrici, Ernst-Schertzhaffte und Satyrische Gedichte, vol. II (Leipzig, 1729), 101–12. 28 as a numerus perfectus, and as 2  14 (B-A-C-H). In P 25 Bach first wrote a bass clef and the word ‘Basso’ before correcting the clef to alto, and overwriting the key signature and changing the designation to ‘Alto’.

Table 12.2 Proportional construction of P 25 from Picander’s poetic text Structure and proportions excluding Da Capo BWV Text Voice 1 5 6 8 12 13 19 20 22 23 27

i ii iii iv v vi vii viii ix x xi

SATB Alto recit. Alto Soprano Soprano recit. Soprano Tenor recit. Tenor Bass recit. Bass S, A, SATB

Subtotals

1:1 90

S+A

xii xiii xiv xv xvi xvii xviii xix xx xxi xxii

Bass-A, SATB Tenor recit. Tenor Alto Bass Soprano recit. Soprano Alto recit. Alto Bass recit. Bass

1:1

102 137

90 90 10 10 105 105 45 45 13 48 30 81 10 102 136 TS

13 48 30 81 10 102 136 TS

13 48 30 81 10 102 136 TS

410

670*

420

420

81

BWV Text Voice 30 34 35 39 42 48 49 51 52 56 57

1:1

Black 1 : 1 90 10 105 45

250 S+A

123 123 10 47 47 46 53* 53 12 61 12 91 6 54 54

Including Da Capo

1:1 123

123

47 46 53

47 53 12

61

61 12

91

91 6 54

54

1:1

2:3

– 90 – 10 68 173 29 74 – 13 30 78 – 30 10 91 – 10 72 174 [1] 137

2:1

90

90 173 74 78

91

91

174 137

137

174

123

123

210 400 : 400

T+B Recit. 10

46

13 48 30 81 10 102 136 TS

D

1:1:2 123 10 47 46 53 12 61 12 91 6 54

123 10 47 46 53 12 61 12 91 6 54

46 53 12 61 12 91 6 54

– – 10 – 8 12* – 13 – 12 64 155 – 6 –

47 54 65 12 74

47

47 54

65

65 74 155

54

54

54

Table 12.2 (cont.) BWV Text Voice 59 60 64 65 67 68

xxiii xxiv xxv xxvi xxvii xxviii

Subtotals Totals

S+A

Alto recit. Alto Bass recit. Bass SATB recit. SATB

53 80

15 52 18 53 17 80

410 : 410 750 820

1420

1:1

T+B Recit.

1:1:2

15 52

15 52 18

52 18 53

53 17

80 250 : 250 330 : 330 330 500

660

420

90

53 17 80 330 420 750

15 52 18 53 17 80

15 52 18

– – – 18 28 – 17 48 128

15 52 81

52 81

81

128

128

1000 420 : 420 173 200 : 200 : 400 990 : 660 660 : 330 1840

383

1600

1650

990

Great passions and cantatas

were a constructional aid that could be destroyed in favour of a greater perfection. Aria 42 ‘Gebt mir meinen Jesum wieder’ has sixty-five bars, notated both as 53 D 12 bars and 52 D 13, depending upon whether the da capo returns to bar 2 or to bar 1. The figures suggest that Bach had planned to notate the movement as 53 D 12, even though the final alternative 2400-bar structure in P 25 requires the layout to be 52 D 13. Bach would have made this refinement when he copied the aria into P 25. As he expanded the structure, Bach ensured that it was well proportioned in all parts. Picander’s four arias that Bach set for soprano and alto in Part II form a block of 250 written bars, Table 12.2, shaded column 2. Such a precise total suggests that at least one of the arias was newly written or revised. Adding these to the tenor and bass arias, Part II now had a total of exactly 660 bars, ordered consecutively with a perfect double 1 : 1 proportion 330 : 330 in 5 : 5 movements, Table 12.2, column 4. This was still framed by the personalised key pattern and 410 bars formed by the tenor and bass arias (H in xii 30, A in xiv 35, B in xxvi 65. and C in xxviii 68). Bach continued to work with units of 330 bars in the next constructional stages as he wove the recitatives stipulated by Picander into the structure. Table 12.2, unshaded coloumn 2 shows that Part I has 670 bars and Part II has 750 bars. Bach added 90 bars of recitative to the 330 bars of Tenor and Bass material in Part II, with which he formed further proportions with consecutive blocks of 420 : 420 and 1000 bars across the whole. With so many numbers and possible proportions it is impossible to reconstruct Bach’s procedures. However, the whole round numbers of the final total, the proportions formed by consecutive blocks and by materials for voice category are all indicative of deliberate planning. Section 3 of Table 12.2 shows the structure including the da capo bars. The final column shows that the ten free-texted movements for chorus, tenor and bass have an alternative total of 990 bars, with a 2 : 1 proportion, 660 : 330 bars. By adding the alto and soprano arias to this Bach created a double 1 : 1 proportion from fourteen of Picander’s movements: 7 : 7 in 660 : 660 bars, with a total of 1650 bars for all the free-texted arias, proportioned 2 : 3 with 660 bars (soprano and alto) and 990 (chorus, tenor and bass). This remarkable result is based on numerical evidence documented in Bach’s fair copy and corroborated by bar numbers published by the most experienced editors of Bach’s manuscripts. Bach was clearly aware of how many bars there were in these free-texted movements, with and without their da capo repetition. His construction seems to have been based on Picander’s free-texted material rather than on

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his biblical divisions. The figures and layers of proportion reveal the numerical foundations of this work, similar to the unseen proportional foundations of a building of the period.12 The next stage in the compilation of the work was to weave the biblical narrative into the musical structure in the order stipulated by Picander. When Bach constructed his Christmas Oratorio in 1734 he created a proportion between the number of bars in the freely composed recitatives with chorus (213 bars) and the secco recitatives sung by the Evangelist (142 bars).13 There is no evidence of such a plan in the numerical structure of MP. There are 268 bars of chorales including the large 99-bar chorale setting of ‘O Mensch, bewein’, which had been used as the opening chorus for JP in 1725,14 and that Bach could therefore have inserted into his earliest version of MP. However, Farlau’s score, assuming that it represents Bach’s early version, shows that Bach originally chose instead the thirteen-bar Chorale 29a ‘Jesum laß ich nicht von mir’. As this lacks any proportional relationship within the chorale group of 182 bars, and as Bach replaced Chorale 29 when he copied P 25, it is not clear whether this was part of Bach’s original ordering. Bach’s use of multiples of 330 bars continued as he wove the recitatives into the expanding structure, see Table 12.2, section 3. There are exactly 990 bars in the first continuous section of the Passion (BWV 244/1–23). The length of this block is identical in both early and later versions of MP. Table 12.1 shows also the two consecutive blocks of 900 : 900 bars, and the 1 : 1 proportion with consecutive blocks of 1400 : 1400 across the whole. The recurrence of 990 bars in the structural layer formed by 330 : 660 of Part Two raises the question of whether Bach chose this particular number for any extramusical reason.

Biblical divisions? Convenience and access to a suitable text must have been considerations when Bach chose Picander’s setting. It was Picander and not Bach who chose the divisions of the biblical story. His Part One, the section of the Passion story before the sermon, focuses on Matthew 26:1–56, and Part Two, after the sermon, on Matthew 26:57–27:66. This corresponds to the divisions in the Haas edition of the Bible,15 suggesting that Picander may 12 15

13 14 See Chapter 4. See Table 13.9. NBA KB II/V and II/Vb. Biblia, ed. N. Haas (Leipzig, 1707). Chapter 26:I (vv. 1–16), II (vv. 17–29), III (vv. 30–5), IV (vv. 36–44), V (vv. 45–56), VI (vv. 57–68), VII (vv. 69–75); Chapter 27: I (vv. 1–10), II (vv. 11–26), III (vv. 27–30), IV (vv. 31–4), V (vv. 35–50), VI (vv. 51–61), VII (vv. 62–6).

Great passions and cantatas

have used this version to prepare his text. Bach’s numerical structure, however, does not correspond with these divisions; his consecutive 990bar section (BWV 244/1–23) covers the narrative up to Matthew 26:39, which is in the middle of Haas’s section IV. The Calov annotated Bible divides each chapter into only three sections,16 and again Bach’s 990-bar section falls in the middle rather than at the end of one of Calov’s sections. Although we can assume that Bach studied the text of Matthew 26 and 27 both before and while composing the music for MP, this lack of correspondence between the divisions in the Bibles he owned and his numerical groupings strongly suggests that he based his proportional ordering on Picander’s text. Nonetheless he did not slavishly adhere to its structure. Picander’s text stipulates eleven arias with a textual da capo,17 and Bach used a musical da capo form for eleven arias, but not for the same eleven as Picander. Picander recommended a da capo for the opening chorus, ‘Kommt, ihr Töchter’, the tenor aria ‘Geduld!’ and the bass aria ‘Komm, süßes Kreuz’, whereas Bach laid out his score for these three without this feature. Conversely Picander did not specify a da capo return for the soprano aria ‘Bluthe nur, du liebes Herz’, the alto aria ‘Erbarme dich, mein Gott’, nor for the bass aria ‘Gebt mir meinen Jesum wieder’, whereas Bach chose a musical and textual da capo for these three. Bach’s experience of improvisation and invention enabled him to adapt movements to any fixed bar total whilst working out the implications of a motive or figure. The da capo feature was a notational facility that allowed him sometimes to choose a ritornello da capo, sometimes a formal ABA da capo, and sometimes to write out a da capo section in full. What to modern eyes may seem an ‘inconsistency’ provided Bach with creative flexibility and at least three different ways of setting out a movement on the page while using the bar totals to create a perfectly proportioned structure.

The ‘early’ version, Am. B. 6/7 The early version, with its single rather than double choir settings, has an implied total of both 2300 and 2700 bars. Andreas Glöckner argues from evidence in Am. B. 6/7 that Farlau may not have copied what Bach intended for Chorale 17, as its omission causes illogical notation at the

16

17

Die Heilige Bibel: Deutscher Dolmetschung und Erklärung (Wittenberg, 1681): I (26:1–29), II (26:30–46), III (26:47–75); I (27:1–26), II (27:27–56), III (27:57–66). BWV 244/1, 6, 13, 20, 23, 35, 49, 52, 57, 65, 68.

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beginning of Recitative 18.18 Farlau’s copy may date to after 1755, or possibly later, to when he stayed in Leipzig some time between 1766 and 1770.19 How much of the passion was actually composed before Bach began to compile the early version is hard to ascertain. There is a fragmentary sketch of the Aria 65 ‘Mache dich, mein Herze rein’, in a viola part of the newly written D major Sanctus, BWV 232/III (performed 13 April 1727), and, in Am. B. 6/7 with less-than-ideal underlay, versions of Arias 35 ‘Geduld’ and 42 ‘Gebt mir meinen Jesum wieder’, suggesting that they may have belonged to an earlier work with a different text.20 A structure of 2700 bars with a consecutive 900 : 1800 proportion is suggested by the two blocks of 900 consecutive bars, shown in the final column of Table 12.1. These blocks remain identical in both early and later versions. However, as the thirteen-bar Chorale 29a was replaced by the extended ninety-nine bars of Chorale 29 ‘O Mensch bewein’ in 1736, I suspect that Bach never perfected the early version and included the shorter Chorale 29a as a practical expediency, due to lack of time, rather than because it was part of a perfected solution. Leaving the final chorale to the very end agrees with Marshall’s observation of Bach’s practice of composing or choosing the concluding chorale of a cantata after the completion of the other movements.21

Final version, P 25 Although we will probably never know which version of MP Bach performed and when, the surviving scores and Picander’s printed text contain sufficient evidence to suggest how Bach constructed the work proportionally from small to large scale, beginning with the free-texted arias and choruses and ending with a unified whole even more perfect than its individual parts. There are simultaneously both 2400 and 2800 bars in P 25. By 1736 Bach had used 2400 bars as the bar total of several earlier collections.22 Table 12.3 shows some of the major divisions in the consecutive construction of the 18 19

20 21

22

NBA KB II/Vb, 47. NBA KB II/Vb, 9 and 22. Farlau may have been a student of Bach’s son-in-law Johann Christoph Altnickol, and in this way gained access to an early version. Ibid., 32. R. Marshall, The Compositional Process of J. S. Bach. 2 vols. (Princeton University Press, 1972), vol. I, 68. Some chorales may not have been composed specifically, coming rather from a preexistent corpus of chorale settings, hence Bach’s practice of entrusting the copying of relatively unproblematic chorales to inexperienced scribes. In the Six Solos (BWV 1001–6) and the Six Sonatas (BWV 1014–19), see Chapter 5.

Great passions and cantatas

Table 12.3 Layout of autograph score P 25, showing working blocks within 2400-bar total BWV 244

Bars

2:1

1–16 18–24 25–39 40–51 52–62 63–8

520 260 670 330 370 250

520

Totals

2400

520 : 260

Page end

Block

780

Block

Block

780

260 670 330 620

670 330

2400

1000

620

330 370

1400

700

2400-bar structure of MP. These blocks of figures appear to reflect Bach’s handiwork as he copied out the score. There is a consecutive 2 : 1 proportion with 520 : 260 bars from BWV 244/1–24. Some of these large blocks of bars coincide with the end of a page in Bach’s autograph manuscript: Recitative 24 ‘Und er kam zu einen Jüngern’ ends at the bottom of a page, coinciding with the proportioned section of 780 bars; Aria 39 ‘Erbarme dich’ also ends at the bottom of a page, concluding a block of 670 bars; accompanied Recitative 51 ‘Erbarm es Gott‘, concluding a block of 330 bars, and forming a consecutive 1000-bar block (column 6) from Aria 25 to the end of Recitative 51; and finally the Passion ends with a block of 620 bars, consisting of blocks of 370 and 250 bars. These figures have already been seen in the constructional proportioning of the work (Table 12.2), and although random lists of figures will naturally form rational-looking patterns, these copying blocks appear to reflect Bach’s working and copying method.23 Creating the magnificent score, P 25, would have taken Bach many separate sessions. In order to ensure that he reproduced his predetermined proportional planning, he would have needed a method of recording and remembering the numerical construction. The numerical blocks in Table 12.3 suggest one method that may have helped him weave the recitatives into the construction of the whole as he undertook the mammoth copying task. At the same time, Bach organised parallel proportions within the documented total of 2800 bars,24 with its consecutive 1 : 1 proportion in 23 24

See discussion in Chapters 1 and 5. Bach uses clear double bar lines to indicate the end of a movement, including those with several sections of mixed style, when duets, accompanied recitatives and crowd scenes run together as one movement. Taking the double bar line as an indication of the end of a movement in P 25, there are far more than the 40 ‘movements’ used in the NBA edition.

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demonstrations

1400 : 1400 bars. The 2800-bar total may have been chosen specifically for its dual significance: 28 as the second numerus perfectus and 2800 as 200  14. The figure 2800 could also be translated as 200 minutes of music, according to the equation used to measure in bars the duration of a church cantata of any metre.25 Interesting as these possibilities are, the figures I find most intriguing are the 330s associated with the construction around Picander’s text, as Bach would use multiples of 330 bars again, both in 1733 for his B minor Missa and in 1747 in the structure of his Musical Offering for the king. This recurrence suggests some extramusical significance, perhaps royal, perhaps divine. Perhaps Anna Magdalena knew something of the Passion’s unseen and unheard constructional Harmony when she described it as ‘the great passion‘.26

II The Passion according to St John Bach’s aspiration to make a definitive calligraphic copy of his JP score was ill fated, as were his hopes for the success of the Passion’s first performance on 7 April 1724. ‘Thomaskirche’ had been printed as the location on the congregational text books, when at the last minute Bach learned that the Passion would be performed in Nikolaikirche instead.27 The performance went ahead regardless of the printing error, and a slightly revised version was heard in Thomaskirche the following year.28 We do not know if Bach’s Leipzig employers were pleased with their cantor’s first extended multimovement church work, but the fact that Bach modified it at least four times in the following fifteen years suggests that someone somewhere was displeased with something. The Lutheran community took a long time to accept new musical settings of the Passion story.29 In 1739, three years after completing his beautiful score of MP, Bach decided to make a similar presentation copy for JP from what had doubtless become a messy original. This too was an ill-fated enterprise. Just ten days before Good Friday 1739, the town clerk 25

26 27

28 29

See Chapter 4. The difference between 2700 and 2800 bars is a little over 7 minutes. Extending the length to 200 minutes could hardly have been Bach’s primary motivation for revising the Passion. ‘groß Bassion’, see Wolff, Learned Musician, 288; NBA KB II/5, 61, for facsimile. NBR, Doc. 115; Wolff, Learned Musician, 291. The council printed a new flyer announcing the change of location. Wolff, Learned Musician, 295. See Table 8.8. Historie der Kirchen-Ceremonien in Sachsen (1732).

Great passions and cantatas

interrupted Bach’s work to deliver an unwelcome message recorded for posterity: Upon a Noble and Most Wise Council’s order I have gone to Mr Bach here and have pointed out to the same that the music he intends to perform on the coming Good Friday is to be omitted until regular permission for the same is received. Whereupon he answered: it had always been done so; he did not care, for he got nothing out of it anyway, and it was only a burden; he would notify the Superintendent that it had been forbidden him; if an objection were made on account of the text, he remarked that it had already been performed several times.30

Bach normally made a new copy of a score only for a forthcoming performance, but the JP score lay unfinished at Recitative 10 until 1749, when he employed a young copyist, Johann Nathanael Bammler (1722–84) to complete the job. Dürr suggests that Bach may have abandoned the copying task due to lack of time, or because he decided to perform another work, or to perform JP in an earlier setting with an older set of parts.31 The unhappy exchange suggests another reason.32 Evidence from the numerical structure suggests yet another.

A reconstruction of Bach’s revised St John Passion The source material for JP is complicated by the fact that no original text book has survived, and that Bach’s score, P 28, is only partially autograph, and in early March 1739 probably did not represent his final revised version.33 Modern editors have pieced together clues from layers of overwritten parts and variants in later copies, agreeing on one point; that after the additions and changes to the middle versions, Bach’s final version was more or less identical to his first. This is the basis of my numerical reconstruction. The few minor numerical discrepancies between my reconstruction and the version in P 28 can be explained by the unclear state of Bammler’s model, and Bach’s cursory checking of his copying work. Four versions of the work prepared for specific performances have been isolated, while Bach’s revisions in the fragmentary section of P 28 account for a fifth. Wollny writes:

30 31

32

NBR, Doc. 208; BD II, Doc. 439. A. Dürr, Johann Sebastian Bach. St John Passion. Genesis, Transmission and Meaning, trans. A. Clayton (Oxford University Press, 2000), 11. 33 NBA KB II/4, 75. Ibid., 10–11.

307

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demonstrations

Table 12.4 Overview of bar structure of the different versions. 2010 bars RT is my reconstruction. BWV Movement 245/1 Chorus: Herr, unser Herrscher 245/2 Recitative: Jesus ging mit seinen Jüngern 245/3 Chorale: O große Lieb 245/4 Recitative: Auf daß das Wort erfüllet 245/5 Chorale: Dein Will gescheh, Herr Gott 245/6 Recitative: Die Schar aber 245/7 Aria: Von den Stricken meiner 245/8 Recitative: Simon Petrus aber folgete 245/9 Aria: Ich folge dir gleichfalls 245/10 Recitative: Derselbige Jünger 245/11 Chorale: Wer hat dich so geschlagen Aria: Himmel reiße, Welt erbebe 245/12 Recitative: Und Hannas sandte ihn 245/13 Aria: Ach, mein Sinn 245/14 Chorale: Petrus, der nicht denkt zurück 245/15 Chorale: Christus, der uns selig macht 245/16 Recitative: Da führeten sie Jesum 245/17 Chorale: Ach, großer König 245/18 Recitative: Da sprach Pilatus zu ihm 245/19 Arioso: Betrachte, meine Seel 245/20 Aria: Erwäge, wie sein blutgefärbter 245/21 Recitative: Und die Kriegsknechte 245/22 Chorale: Durch dein Gefängnis 245/23 Recitative: Die Juden aber schrieen 245/24 Aria: Eilt, ihr angefochtnen Seelen 245/25 Recitative: Allda kreuzigten sie ihn 245/26 Chorale: In meines Herzens Grunde 245/27 Recitative: Die Kriegsknechte aber 245/28 Chorale: Er nahm alles wohl in acht 245/29 Recitative: Und von Stund an 245/30 Aria: Es ist vollbracht! 245/31 Recitative: Und neigte das Haupt 245/32 Aria: Mein teurer Heiland 245/33 Recitative: Und siehe da 245/34 Arioso: Mein Herz! indem die ganze 245/35 Aria: Zerfließe mein Herze 245/36 Recitative: Die Jüden aber, dieweil es 245/37 Chorale: O hilf, Christe, Gottes Sohn 245/38 Recitative: Darnach bat Pilatum 245/39 Chorus: Ruht wohl 245/40 Chorale: Ach Herr, laß dein Totals

Bars 95 39 11 15 12 11 106 3 172 46 12

D 58

8

RT NBA V.1 V.2 153 153 39 39 11 11 15 15 12 12 11 11 114 114 3 3 172 164 46 46 12 12

V.3 V.4 1739

(99) 153

171

171 171

172

164

7

[7]

(59) 38 91 16 17 80 11 29 18 42 106 12 88 174 32 16 83 16 14 44 2 45 3 9 127 30 17 23 124 28 1857

22

17

48

38 91 16 17 80 11 29 18 64 106 12 88 191 32 16 83 16 14 44 2 45 3 9 127 30 17 23 172 28

38 91 16 17 80 11 29 18 64 106 12 88 191 32 16 83 16 14 44 2 45 7 9 127 30 17 25 172 28

29 (70)

(118) NO

3

7 NO NO NO

23

23 25 (58) NO

153 2010 2008 2009 2063

25 [25] 28

? 2016 2008

Great passions and cantatas The aim of the NBA – like all other publications which have since appeared – was . . . to present the St John Passion in a ‘final form’, even though Bach never completed the production of his projected definitive version . . . In fact, however, the reconstruction of a hypothetical ideal version produced the work in a form which was never actually realized in sound during Bach’s lifetime. The editorial decision of the NBA resulted in the fact that the constantly expressed wish to be able to perform one of Bach’s versions could never be realized from the material published at that time.34

The numerical variants of the different versions are shown in Table 12.4.35 Version 1 (performed 7 April 1724), reconstructed from ripieno voice parts and surviving duplicate string and continuo parts; Version 2 (performed 30 March 1725); Version 3 (probably performed on 11 April 1732) and Version 4, performed under Bach’s direction on 5 April 1749, which apart from some changes of words to movements 9, 19 and 20, was basically that of the conjectural first version of 1724. Versions 1 and 4 differ in length because of changes to Aria 9 ‘Ich folge dir gleichfalls’ (172 and 164 bars), Recitative 33 ‘Und siehe da’ (3 or 7 bars), and Recitative 38 ‘Darnach bat Pilatum Joseph’ (23 or 25 bars). The complexity of transmission notwithstanding, a well worked out numerical plan can be detected: first the ordering of the freetexted arias, then the orchestrated sections and finally the secco recitatives. Table 12.4 lists the numeration given in NBA II/4 and in most modern performing editions, together with the genre and short title of each of the forty movements in JP. It shows the number of bars in each movement, both written and including the da capo bars. My reconstructed version, which includes the da capo bars, is in the first shaded column, headed RT, with its 2010 bars. Next is Mendel’s hypothetical reconstruction given in NBA II/4 which, Wollny wrote, was ‘in a form which was never actually realised in sound during Bach’s lifetime’.36 The variants in versions 1, 2, 3 and 4, and in the fragmentary 1739 score, are given next. The most dramatic changes are between Versions 2 and 3. The final row shows that the bar totals in all the versions are very similar: 2010, 2008, 2009, 2063,37 2016 and 2008 bars. My reconstruction, RT, is almost identical to Version 1. It has several layers of proportion in its 2010 bars, as well as the triple 1 : 2 structure so characteristic of a finally revised Bachian structure. 34

35 36 37

P. Wollny, Johann Sebastian Bach: Johannespassion, Fassung II und IV. (Stuttgart: Carus Verlag, 2002), foreword, ix. Ibid., iv–v, based on the concordance of differences between the five versions. Ibid., Critical Commentary. Chorus 1, arias 11+, 13, 19 and chorale 58 were exchanged in Version 2, shown in brackets in Table 12.4, column V.2.

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demonstrations

Early numerical construction The numerical evidence again suggests that Bach began his proportional ordering with the free-texted material, some of which has been identified as loosely based on Brockes’ poetry, and some taken from passages in devotional books in Bach’s library.38 No printed text book for JP has so far been discovered. The two bass arias, BWV 245/24 (174 bars) and /32 (45 bars), and the two free-texted choruses, BWV 245/1 (95 bars) and /39 (124 bars) without their da capo sections create a small-scale double 1:1 with 2:2 movements in 219:219 bars. This was perhaps Bach’s starting point. He may have proceeded by creating next an 800-bar block with the free-texted arias for soprano, alto, tenor and bass, BWV 245/7, /9, /13, /20, /24, /30 and /32, without their da capo sections. Sources show that the early version of the soprano Aria 9 ‘Ich folge dir gleichfalls’, had 171 bars integral to this typically Bachian construction block. The ten chorales have exactly 140 bars, 51 in Part One and 89 in Part Two. Table 12.5 shows how these are inserted into the structure of the Passion to form five symmetrical layers of 28 bars (Columns 4–8), 1 : 1 : 1 : 1 : 1, which naturally also form a double 1 : 1 proportion with 5 : 5 pairs of chorales. Had Bach followed this numerical plan, his first version of JP would have had both 1856 written bars and 2009 bars including the da capo sections. However, as soon as he revised the length of the soprano Aria 9 ‘Ich folge dir gleichfalls’ from 171 to 172 bars, the work had exactly 2010 bars, as shown in my reconstruction, Table 12.4, column RT. Naturally the 800-bar unit in the arias disappeared with the revision of Aria 9, but it had served its purpose and was superseded by a larger, more perfectly proportioned structure. Table 12.6 shows that the twelve movements of freetexted material, including da capo sections, have exactly 1200 bars, forming a 1 : 2 proportion, 4 : 8 movements in Part I : Part II, with 400 : 800 bars, the 400 bars forming a further 1 : 1 proportion with 200 bars in the three tenor arias (13, 20, 32) and 200 bars in the Tenor Arioso 32 and Bass Aria 24. This perfectly proportioned 1200-bar total in the free-texted material is similar to the proportioning we see in Bach’s ordering of Picander’s freetexted material in MP. The 1200 bars of music are distributed with 530 bars in Part One and 670 bars in Part Two. Bach used a 670-bar total again when constructing the Missa of his B-minor Mass in 1732/3, and when creating the Missa

38

E. Axmacher, ‘Aus Liebe will mein Heyland sterben’, Beiträge zur theologischen Bachforschung 2 (Neuhausen-Stuttgart: Hänssler-Verlag, 1984).

Great passions and cantatas

Table 12.5 Symmetry and multiple proportions within the ten chorales BWV

Chorale

Bars

245/3 245/5 245/11 245/14 245/15 245/17 245/22 245/26 245/28 245/37

O große Lieb Dein Will gescheh, Herr Gott Wer hat dich so geschlagen Petrus, der nicht denkt zurück Christus, der uns selig macht Ach, großer König Durch dein Gefängnis, Gottes Sohn In meines Herzens Grunde Er nahm alles wohl in acht O hilf, Christe, Gottes Sohn

Totals

1:1:1:1:1

11 12 12 16 17 11 12 16 16 17

11

140

28

12 12 16 17 11 12 16 16 17 28

28

28

28

Tota in 1749/1750.39 By expanding the structure with the 140 bars of proportioned chorales, Table 12.5, Bach formed a 1 : 1 proportion with 670 : 670 bars. Missing from this scheme is the final Chorale 40 ‘Ach Herr, laß dein lieb Engelein’, not surprisingly in view of Bach’s practice of leaving the final chorale until last.40 Editors have assumed that a 171-bar version of Aria 9 ‘Ich folge dir gleichfalls’, was used for the first and subsequent versions of JP until Bach made revisions for Version 4. My numerical results suggest rather that the 172-bar version, in which one bar was interpolated at bar 147,41 was integral to Bach’s ideal plan dating back to the earliest construction. The 172-bar version is necessary to create the parallel 670 : 670 structure (Table 12.7), and both the 670-bar section of free-texted material of Part Two and the parallel formed by the addition of exactly 140 bars of chorales to the free-texted arias (Table 12.8) would both have been very early constructional decisions. I suspect that, although the 171-bar version was an original, pre-revised version, it was copied inadvertently into some parts, forcing them to be hand-corrected. As for the all-important 164bar version of this aria that Bach copied into P 28 just before he left the score for thirteen years, I do not think it had a part in any of his constructional plans for JP. It was never used in any other version, and it destroys the numerical scheme. For these reasons I conclude that this

39 41

See Tables 13.3, 13.5. NBA KB II/4, 200.

40

Marshall, Compositional Process, vol. I, 90–117.

311

Table 12.6 Proportions within 12 movements of free-texted material BWV

Free-texted material

RT

245/1 245/7 245/9 245/13

Chorus: Herr, unser Herrscher Aria (Alto) Von den Stricken meiner Aria (Soprano) Ich folge dir gleichfalls Aria (Tenor) Ach, mein Sinn

153 153 114 114 172 172 91

Free-texted material Part One

[530]

245/19 245/20 245/24 245/30 245/32 245/34 245/35 245/39

18 64 191 44 45 9 127 172

Arioso (Bass) Betrachte, meine Seel Aria (Tenor) Erwäge, wie sein Aria (Bass) Eilt, ihr angefochtnen Seelen Aria (Alto) Es ist vollbracht Aria (Bass) Mein teurer Heiland, laß dich Arioso (Tenor) Mein Herz, in dem die Aria (Soprano) Zerfließe, mein Herze Chorus: Ruht wohl, ihr heiligen Gebeine

2:1

1:1

91 530

44 45 9 127 172

Total

1200 800 : 400

Free-texted material

Chorales

140

Free-texted material and chorales

1340

Recitatives

[670]

Totals

2010

245/2 245/4 245/6 245/8

Jesus ging mit seinen Jüngern Auf daß das Wort erfüllet würde Die Schar aber und der Simon Petrus aber folgete Jesu

245/12 245/16 245/18 245/21 245/23 245/25 245/27 245/29

64 191

[670]

Recitatives

245/10 Derselbige Jünger war dem

18

Free-texted material Part Two

BWV

670

1:1:1 39 15 11 3 46

Und Hannas sandte ihn 38 Da führeten sie Jesum vom Caiapha 80 Da sprach Pilatus zu ihm 29 Und die Kriegsknechte flochten 106 Die Juden aber schrieen und 88 Allda kreuzigten sie ihn 32 Die Kriegsknecht aber, da sie 83 Und von Stund an nahm sie 14

245/31 Und neigte das Haupt und verschied

2

245/33 Und siehe da, der Vorhang

3

140

245/36 Die Juden aber, dieweil es 245/38 Darnach bat Pilatum Joseph

30 23

670 : 670

245/40 Chorale: Ach Herr, laß dein lieb

28 670

670 : 670

670 670 : 670 670 : 670 : 670

Great passions and cantatas

164-bar version was the result of an inadvertent error: Bach contracted the ritornello at the end, jumping over the eight-bar extension of the melody (bars 161–8) and thereby bringing the movement to a close eight bars too soon – an easy error to make if one is distracted. When he noticed his mistake, probably as he checked to see why he had extra space for Recitative 10, Bach laid down his pen. The 1739 copying error notwithstanding, Bach had already brought this work into perfectly proportioned order in 1724. With the 670 : 670 structure he needed only to weave in a further 670 bars to make a 1 : 1 : 1. Section 2 of Table 12.6 shows that there are exactly 670 bars in all the remaining recitative material and the final chorale. Recitatives 33 and 38 are shown in reconstructed early versions. In P 28 Recitative 33 ‘Und siehe da, der Vorhang’ has five bars, and Recitative 38 ‘Darnach bat Pilatum Joseph’ twenty-five bars. It seems that in this section too, Bach used rational building blocks to help him organise the material proportionally and achieve the 670-bar totals. He set the biblical narrative in a mixture of crowd scenes for chorus, and secco recitatives for the Evangelist sometimes for other named characters. Rational numerical blocks in the secco recitatives and final chorale may indicate Bach’s organisational method. Unfortunately this cannot be tested in more detail as the remaining recitative movements run into one another without double bars separating the Evangelist from the choral crowd scenes, and because we do not know whether the double bar lines in P 28 represent Bach’s divisions. Bach’s working manuscript would show which movements he composed directly into the score and which were fair copies. In its absence the numerical evidence must stand alone. Table 12.7 shows that the free-texted material and chorales are woven into the structure so as to create constructional blocks of bars that coincide with the end of a copying page. Although any list of forty numbers can be grouped in pleasing totals, the repetition of three groups of 300 bars and two of 230 bars at the end of a copying page in this score intimates that these blocks were planned in advance to help the copyist and composer, just as the engraver also measured his manuscript.42 Three blocks of 670 bars can be formed within these consecutive groups, unrelated structurally to the three sets of 670 bars formed as the work was constructed. These blocks may be evidence of a technique Bach

42

Chapter 4 note 79; C. F. Gessner, Der in der Buchdruckerei wohl unterrichtete Lehr-Junge (Leipzig: an der Oster-Messe, 1743), 161–2.

313

314

demonstrations

Table 12.7 Constructional blocks, page layout and proportion in P 28 BWV245 Bars 300s 230s 1–5 6–9 10–15 16 17–18 19–22 23–7 28–9 30–5 36–8 39–40

230 300 300 220 220 80 80 40 200 410 30 230 230 70 70 200

Totals

2010 900

230

230

1:1:1

Pages Bars Actus

230

1–13 230 300 — 220 14–27 520 80 — 40 27–35 120 200 — 410 — 30 — 230 — 70 36–84 940 200 85–92 200 670 : 670 : 670

2010

NBA

Bars P 28

I Hortus

1–5

230 End p. 13

II Pontifices

6–15

520 End p. 27

III Pilatus

16–26

647 End p. 64

IV Crux

27–37

390 End p. 83

V Sepulchrum 38–40

223 End p. 92 2010

used to help him achieve perfect proportions as he compiled this massive project in the midst of a demanding school schedule. In P 28 Chorale 5 ‘Dein will gescheh’ coincides with the end of a page, and the end of the 230-bar block. Aria 9 ‘Ich folge dir gleichfalls’, however, ends in the middle of a page, although it forms a block of 300 bars. Bammler seems to have repeated the layout of Bach’s lost original for the next few movements, ending Chorale 15 ‘Christus der uns selig macht’ at the bottom of page 27, which coincides with the end of a 520-bar block. Thereafter, few of Bammler’s page endings coincide with the blocks that may have been reflected in Bach’s original copying or ordering method.

Why four versions? If Bach had already compiled a perfect plan for the 1724 version, why did he continue to develop it? Why did he add movements and make changes that did not fit the plan, and why did he wait until 1739 to revise it only to return to the 1724 version? The additions suggest that Bach had new ideas, or that he was responding to critical comments. In 1725 he added a new opening chorale, ‘O Mensch bewein’ that would later become the final chorale of Part I of MP. Although it is unlikely that his vision for the two Passions was complete in 1725, it is possible that some of the expansions to JP were because he was hoping to make it more magnificent and parallel to the larger MP. Changes in liturgical habits, and his preoccupation with the Clavier Übung project, however, caused Bach to turn his attention

Great passions and cantatas

elsewhere. The Passion project may have become outdated, and he also became more interested in Mass settings.43 For whatever reason, Bach reverted to his original plan for the St John Passion and in 1749 allowed a young copyist to complete its score.

Ordered by biblical text? There is no shortage of theories and suggestions about Bach’s motivation for constructing the JP as he did. A particular favourite is the scheme first suggested by Martin Petzoldt. It is based on a traditional biblical expository technique that divides the St John passion narrative into five acts, shown as I–V in Table 12.7, each Actus ending with a congregational chorale and demonstrating ‘Evangelienharmonie’.44 Dürr writes: Whether or not this was intentional, the result is a certain symmetry. The framing sections A and E are reduced to a minimum. In the case of E this is obvious, whereas in A it is the result of the fact that St John omits accounts of the Last Supper and Gethsemane. The three central actus are not only longer with regard to the biblical narrative, but also have more ‘madrigalian’ poetry. Actus B contains three arias, actus C two arias and an arioso, and actus D three arias and an arioso. There are no recitatives based on free poetry. It should be emphasised that the following attempt to describe the probable thoughts and intentions of the compiler of the text is largely a matter of speculation.45

If this ordering of the biblical text lay at the heart of Bach’s compositional structure, it should be possible to detect it in the final stages of construction when the numerically flexible material for Evangelist and crowd was added. Table 12.7 column 2 shows the groups of consecutive bars that coincide with Petzold’s actus framework. The consecutive blocks of 230, 520 and 390 bars that correspond with page endings may be evidence of Bach’s planning and ordering of the material. However, many multiples of ten appear in consecutive blocks across this work. Bach would have required an overall plan to keep control of his structure as he pieced together the already-composed free-texted arias with the recitatives that he would write directly into the score. Breaking the text into bite-size units that ended with a particular movement and might finish at the bottom of a copied page, would help him to chart this progress. Bach paginated P 28

43 44 45

See Chapter 13, §I. M. Geck, Bach Johannespassion (Munich: Wilhelm Fink Verlag, 1991), 42. Dürr, Genesis, Transmission and Meaning, 52.

315

316

demonstrations

throughout, from page 1 to 92, and he would have planned the disposition of arias, and possibly sections of the 46-folio score.46 There is every reason to believe that Bach studied the gospel text and passion libretto and thought profoundly about their theological impact and construction before he composed the music. The numerical demonstration of his constructional design does not contradict Petzoldt’s textual explanation. The hortus plan would have been part of Bach’s precompositional organisation. The outworking, the Ausarbeitung, of the composition was stimulated by his understanding of the biblical texts. By the time he came to construct the work, however, most of the arias had been written and his focus was then to keep a practical eye on the layout of the score, and on its proportions. The problems of symmetry in Bach’s works, the parallels between music and architecture, ‘chiastic’ forms and their interpretation as a direct allusion to the cross of Christ47 and many other interpretative trends in Bach studies are not reviewed here.48 The aspiration and implications of proportional parallelism are quite different. With the constructional proportions in the free-texted movements, the building blocks of 800 and 1200 bars, and its large-scale 2:1 proportion, Bach was striving for perfection and unity with all that this implied.49 In the relative peace and quiet of the 1739 lenten period, without its weekly cantatas, Bach compiled the fascicles, planning out and paginating the score50 that would become known as P 28. He knew its 670 : 670 : 670 plan well, and in spite of any earlier aspiration to expand the structure, he was content with its simplicity. There were distractions and some problems with the town clerk. Bach nonetheless hoped to have the calligraphic score ready for Good Friday, and was on track. He picked up his pen and copied the joyful aria ‘Ich folge dir gleichfalls mit freudige Schritten’, lost in its sounds and comforting message. Thinking he had more space than planned on this page, he had begun to copy Recitative 10 ‘Derselbige Jünger war dem Hohenpriester bekannt’ when he was struck with a sickening realisation: he had jumped to the final phrase of the ritornello

46 47

48 49 50

NBA KB II/4, 14; Dürr, Genesis, Transmission and Meaning, 15–18. W. Breig, ‘Zu den Turba-Chören von Bachs Johannes-Passion’, Geistliche Musik. Hamburger Jahrbuch für Musikwissenschaft 8 (1985), 65. Dürr, Genesis, Transmission and Meaning, 124–7. See the Appendix for the theological background. NBA KB II/4, 14. Although the page numbers are in Bach’s hand, it is not certain whether he did this in 1739; but in view of the current belief that he did not revise Bammler’s work, it is unlikely he paginated it later on, in 1749.

Great passions and cantatas

of ‘Ich folge dir gleichfalls’, missing an eight-bar refrain, thus wrecking the layout of his score and the perfection of his numerical plan. With a 164-bar version of ‘Ich folge dir gleichfalls’, his numerical plan would never be perfect. Bach shelved the problem for over a decade, and turned his energies to an independently funded project that could not be thwarted by any worldly authority. P 28 would forever reflect the disappointment of its author.

III

The Passion according to St Mark

The music for Bach’s Passion according to St Mark (BWV 247), is lost.51 Until recently it was known only through the text, published in the third part of Picander’s collected poems, its title showing that it was performed on Good Friday, 1731. An original congregational text booklet discovered in 2009 by Tatiana Schabalina demonstrates that Bach performed it in a revised version in 1744 at the Thomaskirche.52 The surviving text booklet may even have been Bach’s personal copy.53 Although the numerical structure of the score cannot be tested, the changes between the 1732 and 1744 texts point to the nature of Bach’s 1744 musical and numerical revisions. As Bach began his numerical construction of both JP and MP by setting the freely composed arias in perfectly proportioned groups, adding next the choruses and free-texted accompanied recitatives to create perfect proportions, and finally the flexible secco recitatives and the chorales to weave together the large-scale structure, it can be assumed that he worked in a similar way when he constructed the St Mark Passion in 1731, and when he revised the plan in 1744. The following changes would have affected the numerical structure: (a) the Evangelist Recitative, ‘Und murreten über sie’ (BWV 247/6) was repositioned to create a unit with the Chorale and Recitative (BWV 247/8–10).54 (b) the Evangelist section (BWV 247/18–19) (1731) became an Evangelist recitative with chorale inset for the words: ‘Und sie wurden traurig,

51 52

53

NBA KB II/5, 249–66. Tatjana Schabalina, ‘“Texte zur Music” in Sankt Petersburg – Weitere Funde’, BJ (2009), 11–48; ‘IV. Die Markus Passion von 1744’, 30–48. 54 Ibid., 31. Ibid., 32.

317

318

demonstrations

und sagten zu Ihm: einer nach dem andern’, and ‘Bin ichs? Und der anderer: Bin ichs?’ (c) a da capo aria ‘Ich lasse dich, mein Jesu nicht’ was added after Petrus’ recitative (BWV 247/36).55 (d) a second da capo aria, ‘Will ich doch gar gerne schweigen’, was added after the Evangelist Recitative (BWV 247/96) ‘Jesus aber antwortete nichts mehr’.56 If the 1744 score were to be discovered, and if Bach had revised its numerical construction as he did in his other works, I would expect to find that the two new arias and the additional Evangelist-Chorus brought the bar total to a multiple of 100, possibly to a figure parallel to that of the MP, with its dual 2400/2800 bars. The repositioning of the Evangelist recitative ‘Und murreten über sie’ may also have been to facilitate forming a speculative large-scale 1 : 1 proportion.

IV

Cantatas

In his comprehensive study of the sketches and copies of all Bach’s vocal works, Robert Marshall demonstrates that very few of the cantatas were written in fair copy or in calligraphic handwriting throughout because Bach generally composed his cantatas directly into the scores. Marshall writes: The appearance of an autograph score can be affected by such unknowable biographical factors as the degree of ‘inspiration’ and patience at the command of the composer at the moment he penned a particular manuscript or composition. When Bach’s invention was flowing most freely, he was capable of composing an almost flawless score; and, if he wished, he could set it down in a careful calligraphic hand, so that an observer can hardly determine whether the manuscript is a fair copy or a composing score. Conversely, Bach at times copied from a preexistent source in an inattentive, hasty manner that produced a score that was neither calligraphic nor free of corrections.57

The majority of his cantatas have survived in a mixture of composing scores written in non-calligraphic script, frequently with layers of textual revisions. The few vocal works that are in fair copy throughout include ‘Ein Herz, das seinen Jesum lebend weiß’, P 44/3 (BWV 134),58 and Parts II and IV of the B-minor Mass, P 180, (BWV 232 II and IV).59 There are only 55 58

Ibid., 33. Ibid., 17.

56 59

Ibid., 34. Ibid., 18.

57

Marshall, Compositional Process, vol. I, 3.

Great passions and cantatas

four cantatas in Marshalls’s category of Bach’s almost perfect scores: ‘Aus der Tiefen rufe ich, Herr, zu dir’, NY private collection (BWV 131), ‘Gott ist mein König’, P 45/I (BWV 71), ‘Herz und Mund und Tat und Leben’, P 102 (BWV 147), ‘Jesus nahm zu sich die Zwölfe’, P 119 (BWV 22). It also includes: Magnificat in D, P 39 (BWV 243), Christmas Oratorio, P 32 (BWV 248), ‘Gloria in Excelsis Deo’, P 1145 (BWV 191) and ‘Tilge, Höchster, meine Sünden’ (Pergolesi, Stabat Mater), Mus. Ms. 30 199, fascicle 14 (BWV 1083).60 A brief investigation of the numerical structures of Bach’s surviving autograph cantata scores has nonetheless shown that the majority form a 1 : 1 proportion, based on the written length of the score, i.e. excluding the da capo sections. Although Bach would have had a rough plan of the length of his cantatas as he wrote them out,61 there is no evidence that his freeflowing compositional technique was inhibited by deciding in advance the length of an aria. The short, flexible recitatives were the means through which he created numerical perfection. However, it seems that when he revised cantatas for a specific occasion, going to the trouble of making a fair copy, or for cantatas intended to impress, such as the Leipzig audition cantatas, ‘Jesus nahm zu sich die Zwölfe’, P 119 (BWV 22), and ‘Du wahrer Gott und Davids Sohn’, P 69 (BWV 23), he made them numerically perfect, with at least two layers of perfect proportion. A comprehensive investigation of the first versions of Bach’s church cantatas using the principles of proportional parallelism might well complement the established diplomatic evidence and show that he composed the arias and free-texted movements first. Although such an investigation is beyond the scope of this book, two examples have been included to illustrate the potential of such a study.

‘Wo soll ich fliehen hin’, BWV 5 In 1724 Bach set himself the task of writing a new cantata each Sunday for the main church service, in addition to his other school duties and responsibilities. The cantatas had to be composed in a very short time. Invisible labour-saving techniques were a practical necessity, and many of the scores were left unrevised or in composing handwriting. The cantata ‘Wo soll ich fliehen hin’ (BWV 5),62 was written for a service on the nineteenth Sunday after Trinity, 15 October 1724 and its score and parts were left in their 60

Ibid., 15–20.

61

See Chapter 4.

62

Marshall, Compositional Process, vol. I, 10.

319

320

demonstrations

Table 12.8 Evidence of compositional proportioning in ‘Wo soll ich fliehen hin’, BWV 5. BWV Genre

Incipit

Bars

5/1 5/2 5/3 5/4 5/5 5/6 5/7

Wo soll ich fliehen hin Der Sünden Wust Ergieße dich reichlich Mein treuer Heiland Verstumme, Höllenheer Ich bin ja nur Führ auch mein Herz

60 14 104 16 69 11 12

Chorus Recitative: Bass Aria: Tenor Recitative: Alto Aria: Bass Recitative: Soprano Chorale: SATB

Totals * including

1:1 60 14 104 16 69 11 12

D

Bars*

18 78 14 68 172 16 56 125 11 12

286 143 : 143 142 428

2:1 78

1:1 78 14 172 16

172 125 125 11

12 250 : 125 214 : 214

D original state.63 The free-texted arias and choruses were the most timeconsuming to compose. The numerical construction of BWV 5 strongly suggests that while he was composing the three free-texted arias in this cantata, Bach kept an eye on the proportional ordering of all parts, just as he did when he composed his Passions. The well-proportioned building blocks of the freely composed material can be seen in Table 12.8: a double 2 : 1 proportion in the three free-texted movements, with 2 : 1 movements formed from 250 : 125 bars. Table 12.8 shows that, in conjunction with the selection of the final 12-bar chorale, Bach used the flexible recitatives to create two parallel 1 : 1 proportions across the whole work 143 : 143 bars, and including the da capo bars, 214 : 214 bars (final column). The perfectly proportioned block of 375 bars in the free-texted movements bears no relationship to the bar total of the finished product. This is because the number of bars was the means and not the end: Bach’s primary aim was to create a perfect 1 : 1 proportion, rather than to use specific numbers. As the current focus is on the use of the theory of proportional parallelism in Bach’s publications and fair copies, and not his unrevised composing scores or drafts, the ideal example to demonstrate Bach’s revision procedure in a cantata is ‘Gott ist mein König’, BWV 71, with its published parts and text, and an autograph score in fair copy.

63

Autograph score: GB-BL Stefan Zweig Collection, Ms 1; original parts in Leipzig, D-LEb Thomana 5.

Great passions and cantatas

Bach’s first publication: ‘Gott ist mein König’, 1708 The only one of Bach’s hundreds of church cantatas to be published during his lifetime was ‘Gott ist mein König’, BWV 71, composed and printed for the annual service celebrating the change of government in Mühlhausen.64 In 1708 the service was held on 4 February as part of the wider elaborate community celebrations,65 as it had been every year since 1687.66 The Mühlhausen town council consisted of forty-eight councillors, half of whom were elected from the church councils and half from the guilds of artisans. They were elected for life, and the honour tended to run in families.67 To qualify to become a councillor or a Ratsherr in Mühlhausen, the candidate must have studied at university or the equivalent for three years. As late as 1711 it was decreed that university studies must be in law, and that studies in subjects such as theology and medicine did not qualify the candidate.68 For the craftsman candidate, the three-year rule included experience abroad, or service as an apprentice at least ten miles away.69 Dr Conrad Meckbach (1637–1712) was an educated councillor, from the legal profession, who served as head of the civic adminstrators.70 He supported Bach throughout his time in Mühlhausen, first in his application for the organist’s post in 1707, and then endorsing Bach’s plan for the new organ and granting him release to go to Weimar in 1708. He was also the outgoing mayor in 1708.71 The following gestures intimate that the Bachs and Meckbachs remained on good terms: Bach gave Paul Friedemann Meckbach (1674–1731) a copy of the text booklet of ‘Gott ist mein König’ and in November 1710 invited him to become a godfather to his first-born son, Wilhelm Friedemann.72 64 65 66 67

68

69

70 72

NBA KB I/32.1. Ibid., 59–60 for an eyewitness account of an earlier year’s celebrations, on 4 February 1705. Ibid., 61. Before 1687 it was held on 8 January. E. Brinkmann, ‘Mühlhausens Bürgermeister und Ratsherren von 1525–1802’, Mühlhäuser Geschichtsblätter 28 (1927/8), 252–79. The list of all the councillors shows twelve Steinbach relatives dating back to Paul Steinbach, who served 1551–78, all but one of whom were butchers; seven Strecker relatives dating back to Liborius Strecker, who served 1584–1605, and nine Meckbach relatives, dating back to Jacobus, who served 1650–5. To prevent extreme nepotism, a rule was added in 1679 that grandfathers, uncles and close relatives might not sit on the council at the same time, expanding the original law preventing fathers, sons and brothers serving concurrently. Ibid., 253. This rule was relaxed in 1735 when doctors of medicine, of philosophy and of ‘Stadt Physicis’ were validated. Ibid. ‘Drey Jahre auf das Handwerk wandern’ in 1679 was qualified by the clause that every candidate must have ‘über zehn Meilen außerhalb gereiset’. 71 Syndikus and Stadtschreiber. NBA KB I/32.1, 61. On the front cover of Mus 11495. NBA KB, 42, 61. The occasion for the gift is unknown.

321

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demonstrations

Table 12.9 Perfectly proportioned, and personalised in every part BWV I II III IV

71/1 71/2 71/3 71/4 71/5 V 71/6 71/7a 71/7b

Bars Gott ist mein König von Alters her Ich bin nu achzig Jahr Dein Alter sey wie deiner Jugend Tag und Nacht ist dein Durch mächtige Kraft Du wolltest dem Feinde Das neue Regiment Glück-Heil und grosser Sieg Totals

38 47 38 41 35 37 32 71 339

Herr (47) Georg Adam Steinbach (50+18+78)

47 146

1:2

3:1

1:1

38 38 47 47 38 38 41 35 37

1:1:1

1:1

38 38 47 38

38 41 35

41 41 35 37 32 71

32 71

113 : 226 123 : 41 76 : 76 146

47 47 : 47

146 : 146 : 146

The two mayors were elected annually from among the forty-eight councillors. In 1708 the honour fell to the lawyer Adolff Strecker (1624–1720),73 and the butcher Georg Adam Steinbach (d. 1720). It was the fifth time Strecker had been elected mayor since becoming a councillor in 1669, and the first time for the artisan Steinbach, who had been elected to the council in 1684.74 Bach’s congratulatory cantata, ‘Gott ist mein König’, described on the original printed title page as a ‘Glückwünschende Kirchen MOTETTO’, was by far the largest and most sophisticated ever to be produced in Mühlhausen to celebrate council elections.75 The calligraphic autograph score, P 45, the original handwritten instrumental and vocal parts, St 377,76 the printed text, and the printed vocal and orchestral parts Mus 11495 have all survived.77 It must have taken some advance planning, because if the text booklet was printed for the celebrations on 4 February 1708, the printers would have required time to typeset and print the title page and the text with the names of the new mayors, the author of the cantata text and the composer. Table 12.9 shows the numerical structure of the cantata and its text, with layers of proportion that would have been carefully planned. The original printed booklet shows the five clear divisions I–V of the poetic text. Bach 73 75 76 77

74 Brinkmann, ‘Mühlhausens Bürgermeister’, 276. Ibid., 275. See note 66. Wolff, Learned Musician, 111, compared to those written by J. C. Ahle. D-B Mus. ms. Bach P 45 and St 377. NBA KB I/32.1, 13–38, NBA sources A, B and C. Mus. ms. Bach P 45 and St 377.

Great passions and cantatas

followed this, but divided section IV into two musical movements, and section V into three movements, creating an eight-sectioned composition. Unusually for a revised, published work by Bach, the bar total is not a multiple of 10. The cantata nonetheless has the expected overall proportion: a symmetrical arrangement of eight parts forming a 1 : 2 proportion in 113 : 226 bars. If the two verses of movement 7 are contracted into one movement, and movements 4 and 5 into one section, as in the text book, a double 1 : 2 proportion can be seen across the work, with 2 : 4 sections in 113 : 226 movements. There are several numerical relationships and parallel layers of proportion in the structure: 1 : 1 between 38 and 38 bars of the first and third movements, forming a 1 : 1 proportion with movement 4 and 5, 76 : 76 (shaded column 2). There is also a self-referential construction in the first four movements: 123 bars in movements 1–3 and 41 bars in the fourth. The cantata text and music honour the rulers of Mühlhausen in different ways. Firstly they honour God, the Three-In-One, and this is picked up in the literal 3 : 1 proportion of the Bible text in the version chosen for this celebration. Table 12.10 shows how Psalm 74:12, in the spelling and the line breaks given in the original printed text, forms a three-in-one proportion, a symmetrical arrangement of the numerical value of the first and third lines around the second line. Next, the cantata text and music honour Kayser Joseph I, who governed 1705–11. His name is highlighted in the text of movement 7 with elaborate lettering in the second stanza. The almost 84-year-old Adolff Strecker, who would die in office on 13 September 1708, is also recognised prominently in the font size and lettering of his name on the title page, and in the text of movements 2 and 3, with its reference to old age and ‘eighty years’.78 Above all, though, it is Georg Adam Steinbach who is honoured in the structure of the music. Although he is honoured with ornate lettering on the title page, the font is smaller than Strecker’s name and there is no obvious reference to him in the poetic text. However, Bach may have raised Steinbach silently and secretly above the other protagonists in the festivities through a common hybrid parallel form, taking the number value of Steinbach’s name, as given in the printed title page, and weaving these numbers into the structure of the music. Table 12.9 shows how the name Georg Adam Steinbach (50+18+78=146) forms a 1 : 1 : 1 with the musical structure, while his title ‘Herr’ (=47) forms a 1 : 1 proportion with the 47 bars of the second movement, ’Ich bin nu achzig Jahr’. There are no correlations between the numerical structure 78

Ibid., 57.

323

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demonstrations

Table 12.10 Numerical value and 3 : 1 proportion in Psalm 74:12, text BWV 71/1 Psalm 74:12

Value A=1–Z=24

Bars

Gott ist mein König von Alters her der alle Hülffe thut so auf Erden geschicht

59+46+39+53+47+71+30 26+28+56+66 32+27+44+80

345 176 183

183

704

528 : 176

Totals

3:1 345 176

of the cantata and the values of the names Joseph (69) or Herr Adolff Strecker (47+42+94). The cantata forms a 1 : 1 proportion with the number 146: movements 1, 6 and 7b, and movements 3, 4, 5 and 7a. The only movement excluded from this 146 : 146 scheme is the 47-bar second movement, 47 being the value of ‘Herr’, the title given to the mayors. The parallels seen between the numerical structure of Bach’s music and the names of those honoured at the celebration is typical of hybrid parallel techniques seen time and again in printed sources of the period. We know that Bach knew and used several parallel techniques, including the acrostic, but because of the inglorious reputation gained by the number alphabet in the 1950s, Bach scholars have failed to afford the number alphabet its rightful place alongside commonly used techniques. The parallel allusions to Kayser Joseph and to Adolff Strecker have been noted by scholars without asking why Steinbach was omitted. The numerical evidence suggests that Steinbach may not have been omitted after all. On the contrary, if the parallelism between the numerical value of Steinbach’s name and the structure of the cantata represents Bach’s handiwork, Steinbach was indeed highly honoured. It is possible to reconstruct how Bach formed this perfect numerical structure, even though we do not know how much material was newly composed, adapted or extended to fit his proportional scheme. Bach would have studied the prescribed text, including the deeper meaning of the biblical verses, then found the numerical value of the biblical verse, possibly deciding at this early stage to recreate its 3 : 1 proportion in his musical structure. As Bach rarely used a 3 : 1 proportion in his music, I suspect that the personalised 3 : 1 on 123 : 41 in the musical structure is a deliberate parallel to the 3 : 1 of the Bible verse. Next would have been to ascertain the numerical value of the names, and the decision to distinguish Steinbach. So far this is exactly the procedure described by Riederer for forming an occasional paragram.79 79

See Chapter 2.

Great passions and cantatas

Then came the task of organising the musical structure; allocating the movement divisions and deciding the genres and forces, planning the number of bars for each section, deciding to mirror the 3 : 1 in the selfreferential 123 : 41, seeing the potential for 339 to include 146+146+47, and deciding on 47 bars ‘Herr’ for ‘Ich bin nu achzig Jahr’. The structure has a quadruple allusion: a self-referential 3 : 1 in the 123 : 41 in the first four movements, mirroring the all-important 3 : 1 of the cantata text; the overall 1 : 2 in 113 and 226 in its 339 bars; and the 146 : 146 referring to Steinbach. This was a wonderful silent testimony to Bach’s motivation to strive for unity and perfection in his work. But it seems that the council did not appreciate the motivation behind his efforts. Only a few months after the performance of this cantata Bach would request his release, with the implicit reason that the council had thwarted his calling as a Christian musician.80 BWV 71 and its numerical perfection raises the possibility that Bach might have used the numerical value of the opening incipit of church cantatas more regularly to help give him a predetermined structure. Although he rarely revised the Leipzig cantatas, such a numerical template might have helped speed up the planning stages of his compositions. To prove or disprove such a hypothesis would require strict methodological conditions including the use of Bach’s original spellings in conjunction with the original texts and precise knowledge of his score layout.81 Bach’s sacred cantatas and passions have been the subject of hundreds of monographs, thousands of recordings and probably millions of performances. They have become so much a part of modern civilisation that it is easy to forget that 300 years ago they did not exist. Few people are immune to the beauty of the free-texted arias in MP. Their unheard 330s, 660s and 990s draw the listener just like the beauty of perfectly proportioned pillars supporting a baroque palace. Bach ended the St Matthew Passion score with the word Fine and the elaborated abbreviations: S. D. Gl.82 This visible declaration, combined with his unseen statement of parallel proportions, shows his profound desire to strive to achieve Harmony in his earthly church compositions;83 in his own words ‘to work towards the goal of a well-regulated church music to the Glory of God’.84

80 81

82

See Chapter 3. §4 Tatlow, ‘Text, the Number Alphabet and Numerical Ordering in Bach’s Church Cantatas’, in Bachs 1. Leipziger Kantatenjahrgang, ed. M. Geck, Dortmunder Bach-Forschung, 3 (Dortmund: Klangfarben, 2002), 121–33. 83 84 Soli Deo Gloria. Appendix, 1687-III, 1691-IV 5. NBR, Doc. 32; BD I, Doc. 1.

325

13 Festive cut-and-paste projects: masses

and oratorios

Latin Masses (BWV 233–6) Mass in B minor (BWV 232) Christmas Oratorio (BWV 248) Ascension and Easter Oratorios (BWV 249 and BWV 11) Daß diese Ordnung [1 : 2] von Gott in allen seinen Wercken oder Geschöpfen auf eine wunderbare Art beobachtet sey, kan leicht angemercket werden. J. J. Fux, translated by L. C. Mizler, 1742

Bach compiled the majority of his masses and oratorios from previously composed material using the so-called ‘parody’ technique. He constructed entirely new compositions by extending, reducing or retaining the original length of movements and reworking their texts.1 As he made these changes he created new parallel proportions in their structures. This chapter will illustrate the process, briefly in the four Latin Masses and the B-minor Mass,2 and in more detail in the Christmas, Easter and Ascension Oratorios.

I

Latin masses

From the late 1720s onwards Bach focused a great deal of creative energy on sacred Latin works. Some time between 1732 and 1735 he revised his 1723 Magnificat in E flat, making a fair copy in D major (BWV 243). He composed the Lutheran Missa in B minor (BWV 232/I) in 1733, the 1 2

326

Wolff, Learned Musician, 386. A full demonstration and discussion can be read in R. Tatlow, ‘Parallel proportions, numerical structures and Harmonie in Bach’s autograph score’, Exploring Bach’s B-Minor Mass, ed. Y. Tomita, R. A. Leaver and J. Smazcny (Cambridge University Press, 2013), 142–62.

Festive cut-and-paste projects: masses and oratorios

Lutheran Masses in A major (BWV 234); G major (BWV 236); G minor (BWV 235) and F major (BWV 233), around 1738, and a decade later added three discrete sections to the B-minor Missa to create a full-scale Missa tota (BWV 232/I–IV). Around this time he also transcribed numerous sacred Latin works by other composers, including Lutheran masses in C major (BWV Anh. 25), c. 1740–2,3 C minor (BWV Anh. 29) (now lost), and G major (BWV Anh. 167), begun c. 1732–5 and completed c. 1738–9;4 a Kyrie and Gloria from the Missa sine nomine by Palestrina;5 a Sanctus in both D and E majors from the Missa superba by Johann Caspar Kerll;6 the ‘Suscepit Israel’ (BWV 1082), from the Magnificat in C major by Antonio Caldara;7 and a Magnificat by Torri (BWV Anh. 30).8 Little is known about how Bach used these works in Leipzig services. Until recently it was assumed that throughout his cantorship Bach used only church cantatas every Sunday, and that the Latin masses were introduced in the 1750s by his successor Gottlob Harrer. However, Jeffrey S. Sposato has shown that the changeover was gradual, with Bach instigating the use of the masses from as early as the 1730s.9

The four Lutheran masses, BWV 233–6 Traditionally four of Bach’s Latin Masses have been grouped together, NBA editors Platen and Helms writing that ‘the uniformity of the compositional style allows one to assume that all four Lutheran Masses were conceived as a coherent series of works and were created about the same time.’10 This premise is supported by the similarity of overall form within the four masses – two large choruses, Kyrie and Gloria, followed by three solo movements – and by the fact that Bach constructed them in pairs, using previously composed material from two cantatas in each pair: movements from BWV 79 and 179 were used in BWV 234 and 236, and movements from BWV 102 in both BWV 233 and 235.11 Copies of all four masses were owned by C. P. E. Bach and listed as ‘Vier Messen in 3 5 7 8

9

10

4 NBA KB II/9, 55. Ibid., 59. D-B Mus. ms. Bach P 659. 6 Ibid., 23. D-B Mus. ms. Bach 16714. Ibid., 31. D-Coburg V 1109.1. Ibid., 42. D-B Mus. ms. Bach 2755. A. Thielemann, ‘Zur Identifizierung des Magnificats BWV Anh. 30 aus Johann Sebastian Bachs Notenbibliothek’ BJ 98 (2012), 217–24. ‘Bach, the Mass, and the Leipzig Lutheran Service’, in Geistliche Musik und Chortradition im 18. und 19. Jahrhundert—Institutionen, Klangideale und Repertoires im Umbruch, ed. A. Hartinger, P. Wollny and C. Wolff, (Wiesbaden: Breitkopf & Härtel, forthcoming). 11 NBA KB II/2, 15. Ibid.

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Table 13.1 Unified structure in three Lutheran masses. Altnickol’s copy, P 15/1–3 BWV Key, Scribe and Source Text 236

235

233

G major. J. C. Altnickol, P 15/1 J. S. Bach, Mus ms 972 Autograph

G minor J. C. Altnickol, P 15/2

F major J. C. Altnickol, P 15/3

Totals

Kyrie Gloria Gratias Domine Deus Quoniam Cum sancto spiritu Kyrie Gloria Domine Deus Qui tollis Quoniam Cum sancto spiritu Kyrie Gloria Gratias Domine Fili Qui tollis Cum sancto spiritu

Original BWV 179/1 BWV 79/1 BWV 138/4 BWV 79/5 BWV 179/3 BWV 17/1 233a ? ? BWV 102/3 BWV 102/5 BWV 40/1 BWV 102/1 BWV 72/1 BWV 187/4 BWV 187/3 BWV 187/5 BWV 187/1

+/

+ 8 bars + 4 bars 16 bars

+ 34 bars 12 bars + 11 bars + 38 bars +16 bars 20 bars

Bars 117 147 165 129 43 109 TS 128 171 136 55 92 112 118 102 114 209 78 105 2130

1:1:1 117 147 165 129 43 109 128 171 136 55 92 112 118 102 114 209 78 105 710 : 710 : 710

Partitur’ in the inventory of his estate made after his death, reinforcing the notion that the four belong together.12 Autograph scores of only two of the four masses have survived, but we have calligraphic copies of all four dating from c. 1740–59 in the hand of Bach’s son-in-law Altnickol: three in a consecutive manuscript P 15 (BWV 236, 235, 233) and the fourth in P 16 (BWV 234).13 The numerical evidence strongly suggests that Bach had indeed created a perfect collection, but of three rather than four masses. There are 710 bars in the G major mass (BWV 236), and 1420 bars in the masses in F major (BWV 233) and G minor (BWV 235). The final column of Table 13.1 shows the triple 1 : 1 : 1 proportion, 6 : 6 : 6 movements in 710 : 710 : 710 bars, with their self-referential total of 2130 bars (B-A-C), and the interlocking double 1 : 1 proportion, 6 : 6 movements in 710 : 710 bars formed between the masses in G minor and F major. Bach lengthened six and 12 13

C. P. E. Bach’s Nachlaß Verzeichnis, Wq 279. NBA KB II/2, 126–39. BWV 236, 235, 233 are in D-B Mus. ms. Bach P 15; BWV 234 in D-B Mus. ms. Bach P 16.

Festive cut-and-paste projects: masses and oratorios

329

Table 13.2 Mass in A (BWV 234). Double 1 : 1 proportion 300 : 300 bars in 4 : 4 movements Section 1

Original Kyrie Christe Kyrie Gloria Et in terra pax Domine Deus Qui tollis Quoniam Cum sancto spiritu

2 3 4 5 6 Totals

— — — BWV 67/6 — — BWV 179/5 BWV 79/2 BWV 136/1

+/

+1 9

Bars

1:1

72 17 59 111

72

100 113 74 54

100

600

300 : 300

2:1 72

17 59 111

111 100

15

100

113 74 54

113 74 54 200 : 100

shortened three of the eighteen movements (shaded column +/ ) and in this way was able to create layers of proportion and structural unity between this collection of three. Traditionally grouped with the other three is the Lutheran mass in A minor (BWV 234). Bach’s original manuscript score, D-DS Mus. ms. 971, is written in a mixture of his composing and fair calligraphy.14 It is perfectly proportioned, with many layers of symmetrical ordering. The two documented changes Bach made to achieve its perfect structure can be seen in Table 13.2. It has a total of 600 bars, divided by two layers of proportion: a 1 : 1 proportion in 300 : 300 bars, one of which forms a 2 : 1 layer, 200 : 100 bars. The Gloria section is structured 3 : 1 with 339 : 113 bars, parallel to figures Bach used in the cantata ‘Gott ist mein König’ (BWV 71), with its bar total 339 proportioned 113 : 226.15 There is also a propor3 tion formed by the metre, with three movements and 250 bars in 4 time (Kyrie–Gloria16–Qui Tollis) forming a 2 : 1 proportion with two movements and 125 bars in compound time (Quoniam–Cum sancto spiritu). The choice of 600 as the overall total may be the customary reference to Bach’s name: the divisors of the perfect number six being 2, 1 and 3, or B-A-C. The immaculate structure of the Lutheran Mass in A minor, BWV 234, bears no resemblance to the united collection of three, with their 710 : 1420, 1 : 2 and 1 : 1 : 1 structure. Numerically and dimensionally it has 14

3:1

Faksimile der autographen Partitur und Continuo-Stimme. With an Introduction by Oswald Bill and Klaus Häfner (Wiesbaden: Breitkopf & Härtel, 1985), 9. 3 16 See Table 12.9. ‘Gloria – et in terra pax’ has 65 bars in 4 and 46 bars in time.

74 54 339 : 113

330

demonstrations

more in common with Bach’s 1400-bar construction of parts II–IV of the B Minor Mass (Table 13.4).

II The ‘Catholic’ Mass in B minor The autograph score of the B-Minor Mass, P 180 (BWV 232), is a compilation of four discrete sections that Bach numbered sequentially: No. 1 Missa, No. 2 Symbolum Nicenum, No. 3 Sanctus and No. 4 Osanna, Benedictus, Agnus Dei et Dona nobis pacem; although he paginated only No. 1 Missa.17 He completed the score of the Missa in 1733, ending it with the abbreviation ‘Fine SDGl’. It remained a Lutheran mass until he added the other three sections in the late 1740s, revising it once more into a united Missa tota in the last months of his life, when he added a 49-bar movement ‘Et incarnatus est’ and four bars to the opening of the following movement ‘Crucifixus’.

Parallel proportions in the 1733 Missa Bach single-handedly copied the score of the Missa, P 180. With only a little help from family members, he wrote out the majority of the parts,18 before delivering them with a dedicatory letter dated 27 July 1733 to the new Elector of Saxony, Friedrich Augustus II, requesting a court title.19 Table 13.3 shows that the 1733 Missa has 1040 bars and several consecutive double 1 : 1 proportions in its twelve movements when the stile antico movements are counted at the breve:20 movements ‘Kyrie I–Gloria’ have 185 : 185 bars in 2 : 2 movements, and ‘Et in terra pax–Cum sancto spiritu’ have 335 : 335 in 4 : 4 movements. It is customary to see the Missa in twelve movements although the double barring Bach used in P 180 suggests that he thought of it in nine: there is no double bar line drawn between ‘Gloria’ and ‘Et in terra pax’; between ‘Qui tollis’ and ‘Qui sedes’; or between ‘Quoniam’ and ‘Cum sancto spiritu’. Table 13.3 shows a parallel numerical structure when the Missa in seen as nine sections and the stile antico movements are counted at the semibreve, including the ambiguous TS feature interpreted as a single bar. Its 1143 bars and nine 17

18 20

The pagination of the Symbolum Nicenum (97–112), Sanctus (153–63) and Osanna (169–88) is a later addition. 19 NBA KB II/Ia, 16–19; SLB Dresden Mus 2405-D-21. NBR, Doc. 162. 2a As in the NBA edition and BWV .

Festive cut-and-paste projects: masses and oratorios

331

Table 13.3 Multiple parallel proportions in the Missa in B minor. Autograph score, P 180 Stile antico at the breve Section 1 2 3 4

Bars Kyrie I Christe Kyrie II Gloria

Stile antico at the semibreve 1:1

Sections

Bars

1:1:1

126 126 85 85 59 59 100 100

1 2 3 4

Subtotals

Kyrie I Christe Kyrie II Gloria TS bar 100 Et in terra pax 370 185 : 185 5 Laudamus te

5 6 7 8 9 10 11 12

76 76 62 62 46 46 95 95 50 50 86 86 127 127 128 128

6 Gratias 92 7 Domine Deus 95 Qui tollis TS bar 49 49 8 Qui sedes 86 9 Quoniam 127 255 Cum Sancto Spiritu 128

Et in terra pax Laudamus te Gratias Domine Deus Qui tollis Qui sedes Quoniam Cum Sancto Spiritu

Subtotals Totals

126 126 126 85 85 85 118 118 118 175 175 175 62

62 92

86

670 335 : 335 1040 520 : 520

See Chapter 6.

62 92

144

329 : 329 1143 381 : 381 : 381

movements form a 1 : 1 : 1, and a symmetrically arranged double 1 : 2 proportion, with the 381 bars of the outer two movements surrounding 762 bars of the central seven movements. There is also a consecutive double 1 : 1 proportion in the first six sections, ‘Kyrie I’–‘Gratias’, shown in the final column of Table 13.3, with 3 : 3 movements with 329 : 329 bars. The proportions suggest that Bach was aware of both parallel structures. The perfection of its structure in 1733 begs the question of what Bach intended for this B-minor Lutheran Mass, and if he had a plan for its place in a larger numerical scheme. There is a noteworthy parallel between its 1040 bars and the large-scale 1040 : 2080 structures of the keyboard pairs that Bach was finalising at this time, Table 6.9.21 Perhaps he had in mind a collection of Lutheran masses with a 3120-bar total and a large-scale 1040 : 2080 bars, in which the 600 bars of the A-major Mass (BWV 234) played a part. By the late 1730s he had a collection of three Lutheran masses as a polished set of 2130 bars, Table 13.1, but numerically neither the Masses in B minor nor in A major belongs to this scheme. Perhaps this is part of the 21

1:1

332

demonstrations

Table 13.4 Parallel proportions in 1400 bars ‘Credo’–’Dona nobis pacem’ before the addition of 53 bars to Symbolum Nicenum P 180 Stile antico at the breve II

Symbolum Nicenum

1 2 3 4 5 6 7 8

Credo Patrem omnipotentem Et in unum Deum Crucifixus Et resurrexit Et in Spiritum Sanctum Confiteor Et expecto

III

Sanctus

9

Sanctus Pleni sunt coeli

IV

Osanna etc

10 11 12 13 14

Osanna Benedictus Osanna [repetatur] Agnus Dei Dona nobis pacem

Totals

Bars

1:1

45 84 80 49* 131 144 146 105

105

168

168

148 57 148 49 46

148

1400

Blocks

45 84

1:1

3:4

3:4

45

45 84

80 49 131 144 146

550 : 550

84

80 49 131 144 146 105

80 49 131 144 146 105

168

57 148 49 46

148 57 148 49 46

300

700 : 700

168

148 57 148 49 46 300 : 400

300 : 400

* before Bach’s late addition of 53 bars to Symbolum Nicenum

reason why Bach decided to develop his B minor Missa from its smallish 1040/1143-bar structure into a great Catholic Mass.22 Bach’s corrections to P 180 indicate that he compiled the extended Missa tota in several stages.Table 13.4 shows that the three sections, No. II ‘Symbolum Nicenum’, No. III ‘Sanctus’ and No. IV ‘Osanna’, were originally compiled as a group of exactly 1400 bars, with many parallel proportions. This was before Bach added 53 bars, made up of the 49-bar ‘Et incarnatus est’ and the four-bar amendment to the ‘Crucifixus’. Table 13.4 shows the largescale construction within the original 1400-bar version: 14 movements, with a double 1 : 1 proportion, 5 : 5 movements in 550 : 550 bars in the first 1100 consecutive bars. Mirroring the structure in the first four movements in the companion B minor Missa, Bach created a double 1 : 1 structure in the

22

Y. Kobayashi, ‘Zur Chronologie der Spätwerke’, BJ 74 (1988), 66.

Festive cut-and-paste projects: masses and oratorios

first four movements of the ‘Symbolum Nicenum’ with 129 : 129 bars in 2 : 2 consecutive movements. Section IV ‘Osanna’ has a consecutive block of 300 bars, the second ‘Osanna’ being indicated in words not music; although 448 bars are performed. There is a double 1 : 1 proportion with 7 : 7 movements in 700 : 700 bars, each of which forms a further double 3 : 4 proportion with 3 : 4 movements in 300 : 400 bars. Bach had used constructions with 1400 bars several times in his large sacred works, in the Easter and Ascension Oratorios, revised in the mid-1730s, Table 13.15, and in the 2800 bars of the MP, P 25 revised and copied in 1736, Table 12.1. At this stage the B-minor Mass consisted of a perfectly proportioned Missa with 1040 bars, and a perfectly proportioned three-section ‘Symbolum Nicenum–Sanctus– Osanna’, in 1400 bars. To create a united Missa tota across all four sections, Bach had to make some changes. Evidence from the gathering of paper, the layout and the handwriting shows that he made these changes while he was copying P 180. After he had finished writing out the ‘Crucifixus’ and the ‘Et resurrexit’, he decided to add four introductory bars to the ‘Crucifixus’. Then, before completing the ‘Et expecto’, he carefully left enough paper to accommodate the substitute vocal parts to the ‘Et in unum’ and add the ‘Et incarnatus’.23 The layout implies that Bach wrote the four extra bars on the score P 180 before he inserted the sheet on which he had copied ‘Et incarnatus est’. Instead of writing the four bars after ‘Et incarnatus est’ (page 112 of P 180), where there was space and where it would have been in consecutive performance order, he wrote the bars after ‘Et in unum Dominum’ (page 110 of P 180).24 Bach had used this technique of adding introductory bars to adapt a pre-existing plan already in 1733 when he added the opening four bars of the first ‘Kyrie’ to perfect the structure of the Missa.25 Table 13.5 shows Bach’s finally revised numerical structure, incorporating the additional 53 bars, with which he succeeded in creating proportional unity across the four sections. Bach’s notation of stile antico movements and the TS feature create a useful ambiguity to the bar count.26 In P 180 the stile antico movements are written with full-length bar lines at the breve and short bar lines at the semibreve, whereas in the orchestral parts of the Missa, Bach drew bar lines 23

24

25

J. Butt, Mass in B Minor (Cambridge University Press, 1991), 15 and Butt, ‘Bach’s Mass in B Minor: Considerations of its Early Performance and Use’, Journal of Musicology 9 (1991), 113. E. van Hengel and K. van Houten, ‘Et Incarnatus: An Afterthought? Against the “Revisionist” view of Bach’s B Minor Mass’, Journal of Musicological Research 23/1 (2004), 104–6 use the four extra bars to claim that ‘Et incarnatus’ was part of Bach’s original plan. 26 See J. Rifkin, Notes 44 (1988), 787–8 and Butt, Mass in B Minor, 44. See Chapter 1.

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demonstrations

Table 13.5 Parallel proportions in 2345 bars and 2640 bar totals of the B Minor Mass. Autograph score, P 180 P 180 stile antico at the breve Sections I

Missa

1 2 3 4 5 6 7 8 9 10 11 12

Kyrie Christe Kyrie Gloria Et in terra pax Laudamus te Gratias Domine Deus Qui tollis Qui sedes Quoniam Cum Sancto Spiritu

Bars

P 180 stile antico at the semibreve

Proportions 1:1

2:1

Bars

2:2:2:1

126 85 59 100 76 76 62 62 46 46 95 95 50 50 86 86 127 127 128 128

126 85 59 100 [370]

335 : 335

670

Subtotals

Proportions 1:1

126 85 118

126 85 118

175 TS 62 92

175 62 92

1:1

2:1

126 85 118 175 62 92

144 TS 86

144 86

255

255

90 84 80 49 53 131 144 251

90 84

II Symbolum Nicenum 13 14 15 16 17 18 19 20 21

Credo Patrem omnipotentem Et in unum Deum Et incarnatus est Crucifixus Et resurrexit Et in spiritum sanctum Confiteor Et expecto

45 84 80 49 53 131 144 146 105

45 80 49 53 131 144

47 121

47 121

84

146 105

80 49 53 131 144 251

III Sanctus 22 Sanctus 23 Pleni sunt coeli Subtotals

670 : 335

47 120 TS

47 120 TS

47 120 TS

670 : 335

IV Osanna etc. 24 Osanna 25 Benedictus [Osanna] 26 Agnus Dei 27 Dona nobis pacem

148 57 [148] 49 46

Totals

2345

148 57 49 46 [300] 670

1005

2345

148 57 148 49 46 2640

148

148

57 148

57 148 49 46

49 46

1320 : 1320 329 : 329 410 : 205

Festive cut-and-paste projects: masses and oratorios

at the semibreve in the second ‘Kyrie’ and ‘Gratias’, notating their rests in semibreves, adding ‘alla breve’ at the head of each movement and strongly drawn bar lines at the breve. The TS feature occurs three times in P 180: at 3 the change from 8 to before ‘Et in terra pax’, in the ‘Domine Deus’ from 3 3 to 4 before ‘Qui tollis’, and in the ‘Sanctus’ at the change from to 8 before ‘Pleni sunt coeli’. These are observed in the 2640 total, and shown as TS in Table 13.5. Bach wrote out some cumulative bar numbers on his score, which show they were a useful compositional aid. In the ‘Quoniam’ he wrote ‘94’ at the end of the final stave of page 72 and ‘100’ at the end of the first stave of page 73, coinciding with bars 94 and 100. He did the same thing a decade or more later when he wrote bar numbers 61, 100 and 141 onto the score of the ‘Confiteor’.27 Although it is notoriously difficult to identify the scribe of handwritten amendments in P 180, not least because of overwritten amendments made in the 1780s,28 it is unanimously agreed that these five cumulative bar numbers were written by Bach. Table 13.5 shows the immaculate parallel structure of the Missa tota. The 2345-bar total counts the stile antico bars at the breve, and is organised in sections of 670 bars, with 2 : 1 in the 670 : 335 bars of the Symbolum Nicenum and Sanctus, 1 : 1 between the 670 bars formed by the opening 370 bars of the Missa and the 300 bars of the Osanna, and the 670 (335 : 335) bars of the second part of the Missa. There is a striking parallel between these numbers and the numerical structure of Bach’s 1749 version of JP, with its 2010 bars and groups of 670 bars. The alternative total of the Missa tota, 2640 bars counting the stile antico bars at the semibreve, also shows a large-scale, symmetrical 1 : 1 proportion. It has 1320 : 1320 bars, and smaller-scale symmetrical proportioning with 2 : 1 in 410 : 205 bars of III ‘Sanctus’ and IV ‘Osanna’, etc. Here there is a self-referential B-A-C allusion in both the 1-3-2 numbers, and 41.29 These extraordinarily detailed numerical structures show that Bach’s revisions were not motivated solely by musical considerations. In spite of his eyes, headaches and heavy hands, he was driven and motivated to comb through this score time and again to perfect its grand structure, organising its 2345 bars around groups of 670 bars to make it parallel to his JP, and its satisfying 2640 parallel to the many works in which he had used the personalised 2-1-3 permutation. Bach was in control of every numerical 27 28

29

See Chapter 4. J. Rifkin, ‘Blinding us with Science? Man, Machine and the Mass in B Minor’, EighteenthCentury Music 8/1 (2011), 75–90; repr. in Understanding Bach 5 (2010), 49–63. See also U. Wolf, O. Hahn and T. Wolff, ‘Wer schrieb was? Röntgenfluoreszenzanalyse am Autograph von J. S. Bachs Messe in h-Moll BWV 232’, BJ 95 (2009), 117–51. See Chapters 1 and 2.

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demonstrations

detail as he created first a perfect Missa, then a perfectly proportioned Symbolum Nicenum-Sanctus-Osanna-Dona nobis pacem and as finally he integrated the Missa into the Missa tota scheme to create a unity across the whole while keeping the four discrete sections. Although their perfect parallel proportions were hidden and silent, he believed this effort was worthwhile because its Harmony would delight God and inspire man to greater devotion.30

III

Personalised oratorio projects – Christmas

The autograph score of the Christmas Oratorio, P 32,31 is recognised as an object of beauty. Alfred Dürr wrote of ‘the poise and confidence of Bach’s handwriting and the care he so obviously lavished on the manuscript’, and of Bach’s careful compilation of the score, ‘in such a way that every part of the oratorio begins with a new gathering. The autograph pagination, where it exists, also starts afresh with each part.’32 At the end of four of the parts Bach wrote ‘Fine DSGl 1734’; at the end of the final part ‘Fine SDGl 1734’; and he wrote ‘Oratorium’ in particularly large letters at the foot of the first page of five of the six parts.33 This word was used intentionally.34 Bach had experienced five-part oratorio cycles when he attended the Lübeck Abendmusiken in 1705.35 When he came to construct his own oratorio cycle,36 however, he chose a six-part structure for performances

30 31

32 33

34 35

36

See Chapter 3 and the Appendix. Bach kept each of the six parts separately, score, instrumental and vocal parts. It was only later that the complete score, P 32, was bound together. A. Dürr, ‘Commentary’, in Johann Sebastian Bach Weihnachts-Oratorium, 2nd edn, Documenta Musicologica (Kassel: Bärenreiter, 1984), 11. Ibid., 9 and NBA KB II/6. Pars 1 Oratorii, Pars 2 Oratorii, Pars 3 Oratorii, Pars 4 Oratorii, Pars 6 seu Ultima Oratorii. It is missing at the foot of Part 5. See Table 13.13 below. K. Snyder, ‘Oratorio on Five Afternoons. From the Lübeck Abendmusiken to Bach’s Christmas Oratorio’, in Bach Perspectives 8, ed. D. R. Melamed (Urbana: University of Illinois Press, 2011), 69. Some features suggest that Bach originally planned a five-part oratorio: Part V was added later and not assigned to a festival day; Bach omitted the words ‘Pars 5 Oratorio’ from both the title page on P 32 and the first page of Part V, although he did include them on the wrapper title page to the instrumental parts, St 112; the parodied movements in Part V did not come from BWV 213 and BWV 214, P 125, ‘Laßt uns sorgen’ (BWV 213), P 41, fascicle 1, ‘Tönet, ihr Pauken!’ (BWV 214), unlike most of the others. Such a plan would have been dropped once he began to perfect the numerical structure of the six-part oratorio.

Festive cut-and-paste projects: masses and oratorios

Table 13.6 Double 2 : 1 proportion [2310 : 1155 bars in 4 : 2 Parts] in the Christmas Oratorio. Autograph score, P 32 Bars Part Part Part Part Part Part

I II III IV V VI

Totals

590 499 602 554 553 667 3465

2:1

Bars including

590 499 602 554 553 667 2310 : 1155

D

895 611 716 600 651 667 4140

on the five festival days and one Sunday between Christmas and Epiphany, and he created a clear symmetry and unity within the visible structure; in the overall tonal scheme, as the six cantatas revolve around D major (D-GD-F-A-D); in the use of the chorale melody ‘Herzlich tut mich verlangen’ framing the Oratorio; and because five of the six parts open with a tutti chorus,37 end with a chorale in the same key, and have two arias in each part.38 In this section I will present an entirely new demonstration of its unity and symmetry; through its numerical structure, its relationship to the Easter and Ascension Oratorios and the relationship of all three with the passions and masses.

Three triple 2 : 1 proportions: 2310 : 1155, 4 : 2, 10 : 5 The Christmas Oratorio has three large-scale triple 2 : 1 proportions within its 3465 bars. Table 13.6 shows the first double 2 : 1 proportion, formed by Parts I, II, IV and VI in 2310 bars and Parts III and V in 1155 bars.39 The six parts have 3465 bars and 4140 bars, with and without da capo repeats respectively.40

37 38

39

40

Part II opens with a Sinfonia. S. Heighes, ‘Christmas Oratorio’, in J. S. Bach, ed. Malcolm Boyd, Oxford Composer Companions (Oxford University Press, 1999), 105. For ease of reference I will follow the NBA convention, using Roman numerals for the six parts, and through-enumerating the movements. All the bar numbers are based on the manuscript score, P 32. The figures in Column 4 include repeats and sections, and can also be found in the Schmieder BWV catalogue. The repeat of the stollen, the opening phrase in the chorales, is counted in both the 3465 and 4140 totals.

D

337

338

demonstrations

Table 13.7 Double 2 : 1 in 2310 bars [10 : 5 arias : opening choruses] in Christmas Oratorio Autograph score, P 32 BWV

Genre

Original source

Bars

248/4 248/8 248/15 248/19 248/31 248/39 248/41 248/47 248/57 248/62

Aria Aria Aria Aria Aria Aria Aria Aria Aria Aria

BWV 213/9 BWV 214/7 BWV 214/5 BWV 213/3 NEW BWV 213/5 BWV 213/7 BWV 215/7 BWV 248VIa/3 BWV 248VIa/5

138 120 131 152 146 138 70 144 96 176

Subtotal 248/1 248/24 248/24 248/36 248/43 248/54

2:1

D 88 D 80 D 112

138 120 131 152

1:1 138

138 120 131

120 131

152

152

146 138 70 144 96 176

D 46

1:1:1

146 138 70 144 96 176

1311 Tutti-Chorus Tutti-Chorus Tutti-Chorus Tutti-Chorus Tutti-Chorus Tutti-Chorus

Subtotal

BWV 214/1 BWV 214/9 BWV 214/9 BWV 213/1 NEW BWV 248VIa/1

201 96 96 240 126 240

D 137 D 98

201 96 96 240 126 240

201 96 96

201 96 96

126

126

240 240

240 240

999 2310 [

Totals

D 561]

1540 : 770 770 : 770 770 : 770 : 770

The second large-scale proportion is organised genre-wise and shown in Table 13.7. The libretto text included different types of material suggesting a variety of musical settings. Bach set the rhyming verses, marked ‘Aria’ in the original text book, as accompanied arias with a solo voice;41 the rhyming verses, marked ‘Tutti’ in the text book and opening five of the six parts of the oratorio, as tutti choruses (although without this assignation in P 32); direct citations from the Bible, marked ‘Evangelist’ in the original text book, as secco recitatives; free-texted recitatives, marked ‘Recit.’ in the original text book and score, as accompanied recitatives; texts from Lutheran chorales, marked ‘Choral’ in the original 41

The exceptions are BWV 248/29 ‘Herr dein Mittleid’ marked ‘ARIA’ in the text book, but ‘Aria Duetto’ in the score, set for soprano and bass soloists; and BWV 248/51 ‘Ach wenn wird die Zeit erscheinen?’ marked ARIA in the textbook, but ‘Aria Terzetto’ in the score, and set for soprano, alto and tenor soloists.

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339

Table 13.8 A double 2 : 1 proportion in the original Leipzig performance schedule Date

Section

Morning

Afternoon

2:1

25 December 1734 26 December 1734 27 December 1734 1 January 1735 2 January 1735 6 January 1735

Part Part Part Part Part Part

Nikolaikirche Thomaskirche Nikolaikirche Thomaskirche Nikolaikirche Thomaskirche

Thomaskirche Nikolaikirche

Twice Twice Once Twice Once Twice

I II III IV V VI

Nikolaikirche Nikolaikirche

textbook, as plain four-part harmonisations for eleven of the thirteen;42 and the three free-texted movements with biblical words assigned to specific characters43 and marked ‘Chorus’ in the text, he set for chorus.44 Tables 13.7 and 13.10 show that he assigned 2310 bars to the ten solo arias and five tutti opening choruses and 1155 bars to the remaining movements in the oratorio. This large-scale 2 : 1 proportion is parallel to the 2310 : 1155 formed within the six parts, shown in Table 13.6. They must have been planned. The third large-scale 2 : 1 proportion, formed not by bars, but by the schedule of the original performances stipulated by the church authorities, is shown in Table 13.8. The locations were printed with the anonymous libretto45 in the text booklet available in advance of the first performance on Christmas Day 1734. This is not integral to the work’s numerical structure, but nonetheless it is a perfect proportion worth noting. Four Parts were performed twice on their designated festival days (in both Thomaskirche and Nikolaikirche), and Parts Three and Five were heard only once (in Nikolaikirche). This visible double 2 : 1 schedule is parallel to the two invisible triple 2 : 1 mega-structures shown in Tables 13.6 and 13.7 above. The preaching and music roster for the season was drawn up well in advance. I suspect this visible proportion of space

42

43

44

45

No. 42 ’Jesus richte mein Beginnen’ and no. 64 ‘Nun seyd ihr wohl gerochen’, are extensively elaborated, and may have been the means with which Bach achieved the specific total. No. 21 chorus specified ‘Chor der Engel’. No. 26 ‘Lasset uns nun gehen’ is the response of the Shepherds, and no. 45 ‘Wo ist der neugebohrne König der Juden’ is asked by the Magi. There is a performance indication at the page turn before no. 23: ‘volti tutti’, and to no. 26: ‘volti chorus’; but nothing before or above no. 45. Picander may be the author. In NBA KB, Blankenburg and Dürr are agnostic, while K. Snyder and M. Rathey are more confident: Bach Perspectives 8, ed. D. R. Melamed (Urbana: University of Illinois Press, 2011), 81 note 27, and 57.

4:2 Nik Nik Nik Nik Nik Nik

Tho Tho Tho Tho

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and location gave Bach some private amusement, and may even have clinched his decision to enact the triple 2 : 1 across time.46 The three 2 : 1 mega-structures formed within 3465 bars and across a two-week period are sensational and might at first seem compositionally impracticable. A closer look at the ordering and parody process, however, shows that they would have facilitated the process of construction.

Construction of the 2310 well-proportioned bars When Bach began to compile the Christmas Oratorio he had many recently composed large-scale arias and choruses to hand. Of the sixteen solo arias and tutti choruses, only two – the solo Aria 31 ‘Schließe, mein Herze, dies selige Wunder’ and the chorus 43 ‘Ehre sey dir, Gott’ – were newly composed for the oratorio. Evidence from the text and music led Dürr to believe that Bach originally planned to set aria text 31 ‘Schließe mein Herze’47 to the 144 bars from BWV 215/7 ‘Durch die vom Eifer 2 entflammeten Waffen’, P 139 (BWV 215/7), in B minor and 4 . Although this could have worked, Bach decided instead to compose new music in 2 B minor and 4 time, but with 146 bars instead of 144. Similarly it is possible that he planned to reuse the 104 bars of BWV 213/13 ‘Lust der Völker, Lust der Deinen’, P 125 (BWV 213/13), in F major and two time, for chorus 43, but instead decided to compose new material in a 3 totally different style: a vivace chorus in A major in 4 time with 224 bars (126 D 98). Table 13.7 shows that the thirteen pre-existing and two newly composed tutti choruses and solo arias have 2310 (D 675) bars, made up of 1311 (D 440) bars of solo arias, including the new aria 31, and 999 (D 235) bars in the five tutti choruses, including the new chorus 43, to which Bach added 15 bars written on an extra sheet of paper into P 32. The 2 : 1 proportion formed by 10 arias : 5 choruses forms a further parallel, actualised by the lack of opening chorus for Part II.48

46

47 48

A unity (1 : 1) between time and space is formed by these 2 : 1 mega structures. For Gottsched’s views on the Aristotelian principle of unity of time and space, see M. Rathey, ‘Drama and Discourse. The Form and Function of Chorale Tropes in Bach’s Oratorios’, in Bach Perspectives 8, 42–68, and K. Berger, Bach’s Cycle, Mozart’s Arrow: An Essay on the Origins of Musical Modernity (Berkeley: University of California Press, 2007). Dürr, ‘Commentary’, 10. Part II of the Oratorio opens with a newly composed orchestral movement, no. 10, sinfonia, 63 bars.

Festive cut-and-paste projects: masses and oratorios

Table 13.7 shows that there are several further layers of perfect proportion within these 2310 bars : arias and tutti-choruses 2 : 1 and 1 : 1 : 1 with 1540 : 770 and 770 : 770 : 770. The two newly composed movements are essential to the formation of this perfect structure: the first four solo arias and the tutti choruses (including the 126 bars of no. 43) have 1540 bars, and the remaining six solo arias (including the 146 bars of no. 31) have 770 bars. The most plausible starting point of this proportional division is the bar lengths of four pre-existing movements, Aria 4 (138 bars), Aria 19 (152 bars), Chorus 36 (240 bars) from BWV 213, and Chorus 54 (240 bars) from BWV 248/VIa. The length of any new movement would then be determined by the decision to create a perfect 770 : 770 : 770 structure. Even if aria 31 and chorus 43 still had to be composed, their length was predetermined by his structural plan. Next he must decide upon the distribution of the 1155 bars between the recitative text, the chorales, the small choruses and the sinfonia which would open Part II.

Construction of the 1155 well-proportioned bars for the remaining movements The only duet and trio arias in the Christmas Oratorio are Aria 29 ‘Herr, dein Mitleid’ (soprano and bass), and Aria 51 ‘Ach wenn wird die Zeit erscheinen’ (soprano, alto and tenor), Table 13.9. Taking the duet aria ‘Ich bin deine’, P 125 (BWV 213/11), Bach transposed its 166 bars in F major to A major and changed the text to ‘Herr, dein Mitleid’, while keeping the music identical in length and layout, 166 (D 114) bars. The original source for no. 51, the trio ‘Ach wenn wird die Zeit erscheinen’ has not survived, but Dürr believes there was one: ‘the trio provides a further instance of a movement written out so neatly that we assume it to be a parody of a lost original’.49 These pre-existing ensemble arias have 355 bars. This left a neat total of 800 bars to distribute between the remaining movements. Table 13.9 shows that he allocated a further 355 bars for the Evangelist recitatives, the free-texted accompanied recitatives and the hybrid ‘Choral und Recit’, manipulating their lengths to create a perfect 2 : 3 proportion across the 355 bars by allocating exactly 142 bars for the Evangelist with his biblical texts, and 213 bars for the free-texted recitatives. This proportion illustrates the compositional limitation Bach 49

Dürr, ‘Commentary’, 11.

341

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Table 13.9 Proportioning in Recitatives, Duet and Trio in Christmas Oratorio BWV

Biblical/Secco

248/2 248/6 248/11 248/13 248/16 248/20 248/25 248/30 248/34 248/37 248/44 248/48 248/50 248/55 248/58 248/60

Evangelist Evangelist Evangelist Evangelist Evangelist Evangelist Evangelist Evangelist Evangelist Evangelist Evangelist Evangelist Evangelist Evangelist Evangelist Evangelist

Totals

Bars

BWV

Free/Accompanied

19 5 10 8 4 4 3 15 6 7 7 3 19 11 16 5

248/3 248/7 248/14 248/18 248/22 248/27 248/32 248/38 248/40 248/49 248/52 248/56 248/61 248/63

Recitative Chorale and Recitative Recitative Recitative Recitative Recitative Recitative Recitative Chorale Recitative Chorale Recitative Recitative Recitative Recitative Recitative

142

Aria–duet Aria–trio

Total

166 189

D 114

355 bars

Proportions

10 66 9 9 6 8 5 28 18 8 5 11 21 9

213

Total 248/29 248/51

Bars

2:3

355 bars

142 : 213

Originally BWV 213/3 Not new: original lost

1:1

355 bars

355 : 355

imposed upon himself. Following his standard Leipzig custom, he composed the recitatives directly into the score, writing the text of the Evangelist’s secco recitatives before adding bar lines or setting them to music.50 Describing an adjustment Bach made as he worked on the Evangelist’s recitative from Part V, no. 44 ‘Da Jesus geboren war zu Bethlehem’, Dürr writes:51 It begins on the recto and was clearly copied in before being set to music. Bach only later noticed that he would not have enough space on the next pages for the following chorus ‘Wo ist der neugeborne König’, and copied out the text again below, after the opening chorus.

50

51

R. Marshall, The Compositional Process of J. S. Bach. 2 vols. (Princeton University Press, 1972), vol. I, 90–117, esp. 91. Dürr, ‘Commentary’, 11.

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343

Table 13.10 1155 bars and proportional layers in the Choruses, Chorales and Recitatives BWV

Genre

Text

248/21 248/26 248/45

Chorus Chorus Chorus Recitative

Ehre sey Gott Lasset uns nun gehen Wo ist der neugeborne König

3 Choruses 248/5 248/9 248/12 248/17 248/23 248/28 248/33 248/35 248/42 248/46 248/53 248/59 248/64

Bars 65 27 28

Chorale Chorale Chorale Chorale Chorale Chorale Chorale Chorale Chorale Chorale Chorale Chorale Chorale

Wie soll ich dich empfangen Ach mein herzliebes Jesulein Brich an, o schönes Morgenlicht Schaut hin, dort liegt im finstern Stall Wir singen dir in deinem Heer Dies hat er alles uns gethan Ich will dich mit Fleiß bewahren Seid froh dieweil Jesus richte mein Beginnen Dein Glanz all Finsternüß verzehrt Zwar ist solche Herzensstube Ich steh an deiner Krippen hier Nun seid ihr wohl gerochen

Total of 49 movements in 1155 bars

16 15 16 8 14 10 13 11 53 12 12 14 68

BWV VIa/7

262 63 355 355

NEW NEW BWV 213/3

1155

Table 13.9 shows that the 355 bars of recitative created a further 1 : 1 proportion with the pre-existing Trio and Duetto: 355 : 355 in 710 bars.52 In order to achieve the final total of 1155 Bach allocated the remaining 445 bars to the composition of chorales, choruses and a new movement to open Part II. Only one of the remaining choruses had already been composed: no. 45 ‘Wo ist der neugeborne König’, taken from the now-lost St Mark Passion (BWV 247/39b).53 The other two, Chorus 21 ‘Ehre sei Gott’ and Chorus 26 ‘Lasset uns nun gehen gen Bethlehem’, were newly composed. The 120 bars of these three choruses left 325 bars to be distributed between the opening

53

NEW NEW BWV 247/39b?

120

13 Chorales 1 Instrumental 248/10 Sinfonia 30 Recitatives Evangelist & Free 142 : 213 bars 2 Mixed 248/29, 248/ 51 Duet and Trio

52

Originals

Bach may have had in mind some ordering correlation between this and the 710 and 1420 bars in the three Latin masses (see Table 13.1). Dürr, ‘Commentary’, 11.

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demonstrations

movement for Part II and the chorales. Just three of these were large-scale compositions – Sinfonia, no. 10 (63 bars); Chorale 42 ‘Jesus richte mein Beginnen (53 bars); and the final movement of the oratorio, Chorus 64 ‘Nun seid ihr wohl gerochen’ (68 bars), which was taken from BWV 248 VIa/7.

Perfect distribution of 3465 bars into six parts While allocating specific numbers of bars to arias, tutti choruses, recitatives, choruses and the sinfonia, Bach also had to keep an eye on their exact distribution between the six parts of the score in order to create the parallel 2310 : 1155 bar division in 4 : 2 parts – the distribution can be seen in Table 13.11. To make things easier he decided to keep the compilation of Part VI as it was in the original cantata,54 simply adding three Evangelist recitatives (55, 58 and 60) and the Chorale 59 ‘Ich steh an deiner Krippen hier’.55 Things nearly went awry when he discovered a flaw in his calculation and had to add ten bars to the opening movement of Part V, changing it from 116 (D 88) to 126 (D 98). The error was soon corrected, visibly on the score, and the second double 2 : 1 proportion within the six parts completed: Parts I, II, IV and VI in 2310 bars and Parts III and V in 1155 bars.

The printed text book Although neither the score, P 32, nor vocal and instrumental parts, St 112, of the Christmas Oratorio were compiled as a unit or printed in Bach’s lifetime, 56 the text booklet was, and its printed title page shows intriguing signs of poetic parallelism. Table 13.12 shows that the nine typeset lines of the title page in the natural order alphabet (A=1 to Z=24) have a value of 1000, (the year 1734 being counted as 17+34), with a 1 : 1 proportion in 500 : 500 formed by 4 : 5 lines (shaded column 4). Lines 2 and 8 with their value of 250 form a 1 : 3 proportion across the title page. Furthermore, the only two words in capital letters, ORATORIUM=123 and ANNO=41, 54

55 56

An earlier version of Part VI (BWV 248/VIa), is implied by changes to three duplicate instrumental parts, St 112, copied by Rudolph Straube. The possible earlier cantata may date from October or November 1734. H.-J. Schulze, Studien zur Bach-Überlieferung im 18. Jahrhundert (Leipzig; Dresden: Peters Edition, 1984), 120, note 485; NBA KB II/6, 166, 215ff. Dürr, ‘Commentary’, 11. Bach kept each of the six parts (score, instrumental and vocal parts) in a separate cover. Dürr, ‘Commentary’, 11.

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345

Table 13.11 Distribution of recitatives to create perfectly proportioned structure BWV

Part I

248/1 248/2 248/3 248/4 248/5 248/6 248/7 248/8 248/9

Chorus 201 Evangelist 19 Recitative 10 Aria 138 Chorale 16 Evangelist 5 Chorale-Recit 66 Aria 120 Chorale 15

Subtotal 248/10 248/11 248/12 248/13 248/14 248/15 248/16 248/17 248/18 248/19 248/20 248/21 248/22 248/23

Subtotal

D 137 D 88 D 80

Original Music Bars BWV 214/1

BWV 213/9

BWV 214/7

Double 2 : 1

D

201 137 201 NEW 19 NEW 10 NB 136 88 138 – 16 NEW 5 NEW 66 120 80 120 – 15

Part II Sinfonia Evangelist Chorale Evangelist Recitative Aria Evangelist Chorale Recitative Aria Evangelist Chorus Recitative Chorale

63 10 16 8 9 131 4 8 9 152 4 65 6 14

96 3 27 8 10 166 15 146 5 13 6 11 96 602

19 10 138 16 5 66

D

120 15

590

BWV 214/5

D 112

BWV 213/3

NEW NEW – NEW NEW 131 NEW – NEW 152 NEW NEW NEW –

D 112

499 Part III Chorus Evangelist Chorus Recitative Chorale Aria-Duet Evangelist Aria Recitative Chorale Evangelist Chorale Chorus

2:1 201

D

590

Subtotals 248/24 248/25 248/26 248/27 248/28 248/29 248/30 248/31 248/32 248/33 248/34 248/35 248/24

Bars

63 10 16 8 9 131 4 8 9 152 4 65 6 14

63 10 16 8 9 131 4 8 9 152 4 65 6 14

499 BWV 214/9

D 114

BWV 213/11

BWV 214/9

96 NEW NEW NEW NEW 166 NEW NEW NEW NEW NEW NEW 96

D 114

96 96 3 27 8 10 166 15 146 146 5 13 6 11 96 96 602

3 27 8 10 166 15 5 13 6 11

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Table 13.11 (cont.) BWV

Part I

Bars

Original Music Bars

Double 2 : 1

248/36 248/37 248/38 248/39 248/40 248/41 248/42

Part IV Chorus Evangelist Recit/Chorus Aria Recit/Chorus Aria Chorale

240 7 28 138 18 70 53

BWV 213/1

240 7 28 138 18 70 53

Subtotal 248/43 248/44 248/45 248/46 248/47 248/48 248/49 248/50 248/51 248/52 248/53

D 46

BWV 213/7

D

554 Part V Chorus Evangelist Chorus Chorale Aria Evangelist Recitative Evangelist Aria-Trio Recitative Chorale

Subtotal 248/54 248/55 248/56 248/57 248/58 248/59 248/60 248/61 248/62 248/63 248/64

BWV 213/5

240 NEW NEW 138 NEW 70 46 NEW

126 7 28 12 144 3 8 19 189 5 12

240 7 28 138 18 70 53

554

D 98

+ 10 bars

NEW? NEW BWV 247/39b Score lost – BWV 215/7 NB 120 44 NEW NEW NEW Original lost NEW –

126 126 7 28 12 144 144 3 8 19 189 5 12

D

553 Part VI Chorus Evangelist Recitative Aria Evangelist Chorale Evangelist Recitative Aria Recitative Chorale

2:1

7 28 12 3 8 19 189 5 12

553

240 11 11 96 16 14 5 21 176 9 68

BWV 248/VIa1 Score lost NEW BWV 248/VIa2 Score lost BWV 248/VIa3 Score lost NEW – NEW BWV 248/VIa4 Score lost BWV 248/VIa5 Score lost BWV 248/VIa6 Score lost BWV 248/VIa7 Score lost

D 675]

240 11 11 96 16 14 5 21 176 9 68

Subtotal

667 [

667

Bars Works

3465 bars 6

2310 : 1155 4:2

240 11 11 96 16 14 5 21 176 9 68

2310 : 1155

Festive cut-and-paste projects: masses and oratorios

Table 13.12 The numerical value of the title page in the original printed text booklet Line Title Text

A=1–Z=24

1 2 3 4 5 6 7 8 9

123 123 71 71 18+54+93=165 165 44 44 22+52=74 74 63+65=128 128 44+80=124 124 112+67=179 179 41+17+34=92 92

ORATORIUM Welches Die heilige Weynacht Über In beyden Haupt-Kirchen zu Leipzig musiciret wurde ANNO 1734

Totals

1000

1:1

500 : 500

1:3

1:3

123

123

71 165 44 74 128 124 179 92 41 250 : 750 41 : 123

allude to Bach’s name, form a 3 : 1 proportion and are symmetrically arranged across the title page. The name ‘Johann Sebastian Bach’ does not feature in this printed title page.57 Picander, the possible author of the libretto, was fully conversant with the inventive use of numbers and could have introduced this conceit.58 However, as the practice of parallelism in number words was so widespread almost anyone could have devised it.59

The recurrence of 2310 and its potential significance Bach had many reasons to use a 231-based figure for this oratorio. In addition to the permutations on his name and birthday, and its relationship to the properties of the numerus perfectus,60 the word ‘Oratorium’ written so prominently on the score and parts had a convenient value of 123.61 We will never know if he chose the word ‘Oratorium’ because of its numerical value, and if this became the Inventionsquelle62 that helped him decide to base his six-part oratorio on a permutation of 1-2-3, with 2310 : 1155 bars. 57

58 59

60 61

62

Note that the number 280, frequently recurring in Bach’s title pages, is the total of ‘welches die heilige Weynacht über’, lines 2–4. See Chapter 2, and Tatlow, Bach and the Riddle, 6–12. A comprehensive study of all known printed title pages of Bach’s works would be required before such a result could be used to support authorship. See Chapter 3. The words on the title pages Bach used as wrappers for the score and parts of each part, St 112 I–VI, are not numerically ordered. G. P. Harsdörffer, Poetischer Trichter. 3 vols. (Nürnberg, 1651–3), vol. III, 72.

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demonstrations

The multi-proportioned construction of the Christmas Oratorio demonstrates the highest ideal of perfect Harmony. It is an ‘Oratorium’ (123) with six (the first numerus perfectus) parts, four of which have 2310 bars and two 1155 bars, forming a double 2 : 1 proportion. The same grouping of parts (Parts I, II, IV and VI: Parts III and V) were performed twice and once respectively on their designated days: a schedule of performances with a visible 2 : 1 proportion reflecting the invisible large-scale double constructional 2 : 1 proportion. The additional invisible large-scale 2 : 1 proportion between the 2310 bars of solo arias and tutti choruses and the 1155 bars of remaining material created further layers of perfection, the ensemble arias and the recitatives forming another perfect 1 : 1 proportion (355 : 355 bars), and the recitatives themselves a 2 : 3 proportion (142 : 213 bars). Even though he was very experienced at creating large-scale parallels across collections by 1734, the magnitude and complexity of his solution for the six parts of the Christmas Oratorio is awe inspiring. His construction enabled those Leipzig parishioners who walked six times to hear the Christmas Oratorio in 1734–5, unwittingly re-enacting the perfectly proportioned performance schedule, to experience the dramatic unity of time and space,63 and the spiritual unity of Harmony.

IV

Personalised oratorio projects – Easter and Ascension

Unusually for manuscripts from Bach’s Leipzig period, the scores of both Easter and Ascension Oratorios are in calligraphic layout,64 with carefully planned staves and bar disposition, and exactly the number of staves on a page that the music requires.65 The corrections and the wear and tear to the score, P 34, of the Easter Oratorio (BWV 249) show that Bach performed it in different versions on several occasions. The original parts, St 355,66 and surviving published texts show that the music was probably first composed to Picander’s cantata text ‘Entfliehet, verschwindet, entweichet, ihr Sorgen’ (BWV 249a) for the birthday celebrations of Duke Christian von Sachsen Weissenfels on 23 February 1725. Six weeks later, and with a more biblical text, Bach revised the score to make the church cantata ‘Kommt, fliehet und eilet’ (BWV 249), for the service on 1 April 1725. 63

64 66

The classical ideal of dramatic time and space is applied here in its broadest sense, unity meaning literally 1 : 1 through the 2 : 1 2 : 1 parallels location : time. 65 NBA KB II/7, 32. Marshall, Compositional Process, vol. I, 56. NBA KB II/7 source A: Mus. ms. Bach St 355. Source B: Mus. ms. Bach P 34.

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Table 13.13 Parallel 1 : 1 proportion across the Easter Oratorio, Autograph score, P 34 BWV

Genre

Bars*

Change

Block

249/1 249/2 249/3 249/4 249/5 249/6 249/7 249/8 249/9 249/10 249/11

Sinfonia Adagio Chorus Recitative Aria Recitative Aria Recitative Aria Recitative Chorus

231 56 160 12 114 9 84 13 72 8 83

+ 1 bar

231 56 160

Totals

D 120 D 79

D 48

NEW

12 114

72

9 84 13 72

83

83

84

NEW

D 260

800

Bars*

160

114

D 13

1:1

231 56

NEW NEW

842

1:1

12 9 13

8

8

421 : 421

21 : 21

231 56 280 12 193 9 97 13 120 8 83 1102

* including Da Capo

A year later he changed the text again for a birthday cantata on 25 August 1726, in honour of Count Joachim Friedrich von Flemming: ‘Verjaget, zerstreuet, zerrüttet, ihr Sterne’ (BWV 249b). Recycling music in this way was a practical expedient that saved time for Bach and his musicians. The 1725 Easter setting, revised to ‘Kommt, eilet und laufet’, was performed once more in the 1730s and again in the 1740s. Apart from changes to the lengths of the recitatives, caused by alterations in the text, the structure of the composition remained relatively constant after 1725. The original score, with its increasingly illegible changes, caused Bach to copy it out some time around 1738 in his best calligraphy. In the new copy he wrote the words ‘Oratorium Festo Paschali’ above the opening movement, and while copying the opening Sinfonia he inserted an extra bar at bar 162/3.67 The only other significant change, which did not affect the numerical structure, was his reworking in the 1740s of the opening duet for full chorus. The numerical structure of Bach’s 1738 copy of the Easter Oratorio, P 34, can be seen in Table 13.13. It has 800 written bars of free-texted material with 42 bars of recitative, of which the arias and chorus cover 430 bars; or including the 260 bars of da capo repeats 690 bars. The revised Sinfonia (with 231 bars), Adagio and final chorus are all throughcomposed, and together have 370 bars. The additional bar to the opening Sinfonia that Bach inserted into his calligraphic copy creates a rational 67

Ibid., 53, ‘Einschub des zusätzlichen Taktes 163 in Satz 1’.

1:1 231 56 280 12 193 9 97 13 120 8 83 551 : 551

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demonstrations

800-bar block of free-texted material, that may have helped him reach his final desired total of 842 bars, or 1102 bars with da capo repeats. The four recitatives have a total of 42 bars and fall into a double 1 : 1 proportion with 21 : 21 bars. The structure both with and without the da capo bars contains a simultaneous 1 : 1 proportion: 421 : 421 bars in 5 : 6 movements and 551 : 551 bars in 5 : 6 movements. The full extent of Bach’s construction can only be appreciated when viewed alongside the Ascension Oratorio (BWV 11). Bach’s autograph score, P 44, fascicle 5, dated 19 May 1735, and set of original parts, St 356,68 show a mixture of fair, revision copy and composing handwriting.69 The clarity of the handwriting in the free-texted movements 1, 4 and 8 strongly suggests that these movements were already composed.70 They may originally have been written for BWV Anh. I 18, ‘Froher Tag, verlangte Stunden’, in 1732.71 Knowing he had 800 bars and 42 bars of recitative for his Easter Oratorio ‘Kommt, eilet und laufet’ made it easier to construct a second work with related proportions. It is not possible to ascertain whether Bach extended or adapted the movements in any way, as the originals are lost. The three outer movements form a block of 400 bars, Table 13.14. To these Bach added 158 bars; 101 bars of chorales and 57 bars of recitatives. As with the Easter Oratorio, the bar totals of the da capo repeats are a multiple of ten, and this time proportioned 40 : 120 making a simultaneous total easily workable. As Bach wove the recitatives into the structure, he surrounded the personalised block of 158 bars with 400 bars, forming integral double 1 : 1 and 2 : 3 proportions in 279 : 279 bars and 4 : 6 movements. The division of the recitatives shown as numbers 7a+b and 7c follows Bach’s separation of movements with a double bar line.72 Table 13.15 shows that by the time Bach wrote out and renamed his Easter Oratorio in 1738, P 34, it was half of an oratorio pair with the Ascension Oratorio. Together they had a parallel numerical structure of both 1400 bars, and 1820 bars with their 420 bars of da capo repeat. The proportions and rational blocks suggest the order in which Bach created this construction. Bach had 799 bars of Easter Oratorio, well formulated and revised several times, to which he added one bar to create an 800-bar block of 68

69 71 72

NBA KB II/8, D-B Mus. ms. Bach P44 fascicle 5. Vocal and orchestral parts, PL-Kj Mus. Ms. Bach St 356. 70 Marshall, Compositional Process, vol. I, 13. NBA KB II/8, 31. On the occasion of the reopening of the rebuilt Thomas School on 5 June 1732. The NBA edition includes a no. 7b, but because Bach did not use a double bar line between the two sections, I have chosen to put 7a and 7b together, as a section of 25 bars.

Festive cut-and-paste projects: masses and oratorios

Table 13.14 Constructional blocks in the Ascension Oratorio, BWV 11, P 44 fascicle 5 BWV

Genre

Bars

11/1 11/2 11/3 11/4 11/5 11/6 11/7a+b 11/7c 11/8 11/9

Chorus Recitative – Evangelist Recitative Aria Recitative Chorale Recitative Recitative – Evangelist Aria Chorale

186 31 6 11 79 6 22 } 8 25 9 152 112 62 9

Totals

Block

D

D D 558 D 160

Block 186

6 11 79 6 22 25 9

186 6 11 79 6 22 25 9

152 62 158

1:1

400

152 62 279 : 279

freely composed material, Table 13.15, rows 1–7. It seems he had to hand at least three movements towards his new Ascension Oratorio.73 Reusing two of these movements, the 186 bars to become the opening chorus ‘Lobet Gott in seinen Reichen’ and the 152 bars to become the aria ‘Jesu, deine Gladenblicke’, he designed the final newly composed chorale to a specific length, 62 bars, to create a 400-bar block which made a 1 : 2 proportion with the free-texted material in the Easter Oratorio, Table 13.15, first shaded column Bach had used similar proportioning, with blocks of 800 bars and 1200 bars of free-texted material, when he compiled his JP over a decade earlier.74 When Bach added the remaining material to the Ascension Oratorio, he ensured that its structure was proportionally parallel to the remaining material in the Easter Oratorio. The final rows of Table 13.15 show that Bach set the Ascension Oratorio’s additional aria ‘Ach bleibe doch’ (BWV 11/4) as 79 bars, the same number of bars as its recitatives and chorale (BWV 11/2, 3, 5, 6, 7). Together the additional material creates a selfreferential block of 158 bars and forms a 1 : 1 proportion of maximum perfection with minimal disruption. The recitatives in the Easter Oratorio also have their own small-scale double 1 : 1 proportion, 2 : 2 recitatives in 21 : 21 bars (BWV 249/4, 6 : BWV 249/8, 10), and with the 1 : 1 proportion in 79 : 79 bars of the perfectly proportioned additional aria and recitatives/

73

NBA KB II/8, rev. 1983.

74

See Chapter 12.

351

352

demonstrations

Table 13.15 A proportionally related pair of Oratorios: the Easter and Ascension Oratorios BWV

Genre

249/1 249/2 249/3 249/5 249/7 249/9 249/11

Sinfonia Adagio Chorus Aria Aria Aria Chorus

Subtotal

Bars 231 56 160 114 84 72 83

2:1 231 56 160 114 84 72 83

D 120 79 13 48

800

260

186 152 62

186 31 152 112 62 9

Subtotal

400

152

Subtotals

1200

11/1 11/8 11/9

11/4 11/2, 3, 5, 6, 7 249/4, 6 249/8, 10

Chorus Aria Chorale

Ascension Oratorio, additional aria Ascension Oratorio, recitatives, chorale Easter Oratorio, recitatives Easter Oratorio, recitatives

79 79 } 8 21 21

Subtotal 1400

231 56 280 193 97 120 83

217 264 71

1:1 231 56 280 193 97 120 83

217 264 71

800 : 400 79 79

8

21 21 100 : 100

Totals

Bars*

79 87 21 21

79 87 21 21

8 420 1820

910 : 910

* including Da Capo

chorale from the Ascension Oratorio, form a larger 1 : 1 proportion in 100 : 100 bars of extra material, ensuring that the oratorio pair was perfectly ordered, within its 1400-bar total. It also had a dual total of 1820 bars when the 420 bars of da capo repeats are included (Table 13.15 right-hand columns). 1400 bars was Bach’s first plan for Parts II–IV of the B-minor Mass. 2800 bars is the total of the revised St Matthew Passion score, copied c. 1736. Although he did not begin to write Parts II–IV of the B-minor Mass until the later 1740s, 1400 bars as the plan for the 1735–8 oratorios, together with the 1736 Matthew Passion, suggests strongly that Bach planned 1400 bars as the starting point and unifying structural feature for these large-scale sacred works. The genre-organised building blocks of 800 and 400 bars and the addition of 100 and 100 bars at the final stages of

Festive cut-and-paste projects: masses and oratorios

construction indicate how he pieced his works together to make them well proportioned in every part. The numbers 158 and 1400, probably referring to Bach as composer, have a prominent position in the structure, but the numbers may simply be the nuts and bolts of his structural technique. Of all these potentially meaningful numbers, however, those of the greatest signficance for Bach were probably the digits from numerus perfectus in the 231 : 231 and 1 : 1 proportions and their repetition as 2130 in the three Lutheran Masses and as 2310 in the structure of the Christmas Oratorio. There is a further numerical occurence that suggests Bach’s early intentional organisation. The two arias he already had before constructing the Ascension Oratorio were BWV 11/4 and BWV 11/8. Together they have 231 written bars, identical to the length of the Easter Oratorio Sinfonia to which Bach added one bar. Creating this double 1 : 1 and 1 : 2 proportion with 231 : 231 bars in 1 : 2 movements may have been part of an early planning stage, and suggests a further reason for his one-bar addition. It is another example of a self-referential allusion, a permutation of 2-1-3, a number that had featured prominently in the large-scale 2 : 1 proportion in 2310 : 1155 bars of the Christmas Oratorio, completed in early 1735. But perhaps the most startlingly obvious personalised number in these oratorios is the 1400-bar total of the Easter and Ascension pair. As a multiple of 100, forming several layers of proportions and parallels and with a selfreferential element, their joint numerical structure strongly suggests that Bach had revised them as a pair in preparation for publication. The perfection of the structures in these cut-and-paste parody works demonstrate Bach’s method of creating parallel proportions as they grew from smaller sections to larger multi-movement works, to groups of large works. It was worth the hard labour because he knew that their nonsounding Harmony reflected the creativity of God, who had put nonsounding unity and perfection in all his works of creation.75

75

For the theological background, see Chapter 3 and the Appendix.

353

14 Lost compositional blueprints

English Suites (BWV 806–11) French Suites (BWV 812–17) Orgelbüchlein (BWV 599–644) Great Preludes and Fugues (BWV 543–48) Harpsichord Concertos (BWV 1052–56, 1058, 1060–64) Proportional Parallelism Es war eine Zeit, in welcher man sie beynahe für die Hauptwissenschaft der ganzen Musik hielt, in welcher die ganze musikalische Theorie blos in Rechnungen bestand, und in welcher man glaubte, der ganze Ausdruck und die ganze Schönheit der Kunst beruhe blos auf den mathematischen Verhältnissen der Töne . . . Doch diese Zeiten sind nunmehr vorüber, und was ehedem hierin zu viel geschah, geschieht nun vielleicht zu wenig. J. N. Forkel, 1788

In their obituary of Bach, C. P. E Bach and J. F. Agricola published a list of his compositions, including sixteen unpublished compositions of which eight have specifications that imply that they were publication-ready collections on a par with the publications. Giving the numeration in the obituary, the eight are: (3) Five passions, of which one is for double chorus (6) Six trios for the organ with obbligato pedal (9) Twice twenty-four preludes and fugues in all keys for the clavier (10) Six Toccatas for the clavier (11) Six (English) suites for the same (12) Six more of the same, somewhat shorter (French suites) 354

Lost compositional blueprints

(13) Six sonatas for the violin without bass (14) Six of the same for the violoncello1 Few of these eight collections have survived in autograph scores, which raises several questions. The authors of the obituary may have exaggerated the achievements of the recently deceased cantor in order to burnish the image of his compositional heritage. Or Bach himself may have polished more collections than have survived. For example, there is just one extant passion in a fully autograph score, the St Matthew Passion, P 25 (BWV 244).2 Were the authors referring to compositions that Bach had revised into numerically perfect collections, or were they just listing expedient groups of works related by genre? Of the eight collections listed, only three have survived as unified collections in revised autograph manuscripts: the Six Trio Sonatas for organ (BWV 525–30), the first set of twenty-four Preludes and Fugues (BWV 846–69) in P 415, and the Six Solos for violin (BWV 1001–6) in P 967.3 We have no complete autograph manuscript for the second collection of twenty-four Preludes and Fugues (WTC II BWV 870–93) the Six Toccatas (BWV 911–16), the English Suites, (BWV 806–11), the French Suites (BWV 812–17), or the Cello Suites (BWV 1007–12). Surviving autograph manuscripts not listed in the obituary also demonstrate just how incomplete it was. Not mentioned at all, although surviving in autograph scores, are the perfected collection of six Brandenburg concertos (BWV 1046–51) and the fifteen chorale preludes (BWV 651–65). Entirely missing from the list are works united by genre, for which there is scant evidence to suggest Bach had formed them into collections at all. These include the Suites for Orchestra (BWV 1066–9),4 Suites for Lute (BWV 995–8, 1006a), Sonatas for Traverso Flute and Harpsichord (BWV 1030, 1034–5), Sonatas for Viola da Gamba and Harpsichord (BWV 1027–9), and the Concertos for one and more Violins and Orchestra (BWV 1041–3). Some manuscripts have numerical characteristics which suggest that Bach had begun but not completed the process of forming a collection – typically, where two or three works have been copied into a single consecutive source for which there are earlier versions. Although incomplete, these embryonic collections with two or three well-proportioned works in the same manuscript suggest that the copyist had access to an original in which Bach had begun to form a collection.

1

NBR, Doc. 306, 304.

2

See Chapter 12.

3

See Chapter 6, §I.

4

NBA KB VII/1, 7.

355

356

demonstrations

During the course of my research I have tested the numerical structure of numerous collections that Bach may just have grouped together. Their transmission history, complex source materials, surviving versions, modern editorial reconstructions and unclear numerical results made it impossible to reconstruct Bach’s perfect plan, if he had ever made one. Such was the case for the Six Toccatas (BWV 911–16). However, sometimes it has been possible to join the dots and catch a glimpse of Bach’s blueprint. Based upon the latest source evidence and the principles of proportional parallelism, this chapter gives a brief taster of what might have been Bach’s perfected numerical plan for some well-known collections.

I

French and English keyboard suites

Bach used his keyboard suites for teaching.5 They were in a constant state of revision and so, as the multiple variants in copies made by his students show, the surviving scores in Bach’s hand do not necessarily represent his final version.6 The collection of six suites known as the English Suites (BWV 806–11),7 and its companion collection known as the French Suites,8 were both under development in the early 1720s, and complete before 1725. There is no autograph copy of the English Suites, although Bach did correct one movement in the fair copy by his student Kayser, P 1072, which gives Kayser’s version an edge over other surviving copies. Table 14.1 shows its pleasing numerical structure: a total of 2070 bars, a large-scale 2 : 1 proportion with 690 bars of Prelude and 1380 bars of remaining movements, formed by 380 bars in the Allemande and Courante movements and 1000 bars in the remaining movements. The formation of compositional blocks of 1000 and 1070 bars in suites 1–3 and 4–6 is also an indication of Bach’s numerical construction. The French Suites (BWV 812–17) are a shorter collection, ‘the later but smaller pendant to the six English Suites’ as Schulenberg describes them.9 Bach copied five of the six French Suites into Anna Magdalena’s 1722 music book,10 the first four of which are incomplete. Later copies show that there were at least five different versions for each suite,11 5

6 8 10

D. Schulenberg, The Keyboard Music of J. S. Bach, 2nd edn (New York: Routledge, 2006), 276. NBR, Doc. 315. 7 Ibid., 281 and 311. Ibid., 281. A title first used in print by Forkel, 1802; NBR, 445. 9 Ibid., 300. A title first used in print by Marpurg, 1762; BD III, Doc. 715. Ibid., 229. 11 P 224, 1–20 Schulenberg, Keyboard Music, 301.

Lost compositional blueprints

357

Table 14.1 English Suites, Kayser’s copy, P 1072: 1 : 2 proportion 690 : 1380 bars BWV Prelude 806 807 808 809 810 811

Allemande Courante Sarabande Other 1 Other 2 Gigue Bars 2 : 1

Totals Block Block

37

32

20+72

32

48

36

40

[280]

317

317

110 [ 187 [

24 24

24 32

28+28 24 + 24

56 34

24 16

74 44

[258] [198]

368 385

368 385

D 54] D 26] 90 [D 18] 118 [D 38] 148 [D 47]

24

20

24

32

32

52

[184]

274

274

24

28

24

48

24

96

[244]

362

362

24

32

24 + 24

32

24

56

[216]

364

364

690 Totals

690 152

Totals 690

228

232

250

380

156

362

1380

1000

2070 1000 1070

Table 14.2 French Suites, Altnickol’s copy, US ML 96.B186: 1380 bars, 1000+380 bars BWV Allemande Courante Sarabande Menuet Alt 24 18 24 20 24 28

24 54 28 36 32 32

24 24 24 24 40 24

48 32 60 – – 24

Totals 138

206

160

164

812 813 814 815 816 817

Other

48 – 36+36 – – –

– 16 32 22+22 24+30+16 20+24+42

120

248

Gigue Totals Block Block 28 84 68 60 56 48

196 228 308 184 222 242

222 242

344

1380

1000

making it almost impossible to know which was Bach’s latest and preferred version. However the principles of proportional parallelism give a standard against which to check the various suriving collections. Results strongly suggest that the version made by Altnickol, ML 96. B 186,12 had been numerically revised, as it displays all the characteristics of a polished Bach collection. Until 1886 this manuscript was thought to be Bach’s autograph, and it is one of the sources on which Dürr based the NBA edition.13 Table 14.2 shows that its 1380 written bars have blocks of 1000 and 380 bars, parallel to the structure of the English Suites.

12 13

Washington, Library of Congress, ML 96. B 186. NBA KB V/8, 54; Schulenburg, Keyboard Music, 302.

196 228 308 184

380

358

demonstrations

Table 14.3 The Neumeister Collection, LM 4708 and Bach’s Orgelbüchlein, P 283: parallel structures Neumeister Collection, LM 4708

J. S. Bach Orgelbüchlein P 283

Short organ chorales By J. S. Bach and family circle Arranged in liturgical order Begun c. 1700 Revisions late 1740s 82 organ chorales 3120 bars in 82 chorales

Short organ chorales By Johann Sebastian Bach Arranged in liturgical order Begun c. 1708–12 Revisions after 1726 164 organ chorales 780 bars in 46/48 chorales

Two French Suites, BWV 812 and 814, have ambiguous instructions that affect the bar totals in the Menuet/Trio/alternative movements. These movements can either be counted literally as written in the score, which gives a total of 1320 bars, or with the alternativement indication followed literally, counting it after each Minuet/Trio, thus gaining an additional 60 bars, and the 1380-bar total. The latter solution creates a proportional parallel to the English Suites, with 690 : 1380 : 1380 bars, and parallel constructional blocks of 1000 bars. To test the 1320- or 1380-bar total and the hypothesis that Bach had revised these two collections to create such a numerically united whole, the ideal source would be a contemporary copy of both collections in one manuscript. Unfortunately if Altnickol or Kayser ever made such a copy, or even two separate copies, they have not survived. The numerical results raise many questions about Altnickol’s role as copyist of Bach’s final versions, suggesting that Bach in the last few years of his life may have commissioned Altnickol to make definitive copies of scores he had no time to polish himself.14

II Chorale collections – the beginning and end The next potential collection that Bach may have revised involves the Orgelbüchlein, P 283 (BWV 599–644), with Bach’s late and unexplained additions, and its relationship to the numerical structure of the Neumeister 14

Research into this topic is discussed in Y. Tomita, ‘Revisiting Altnickol’s 1744 Copy of the WellTempered Clavier, Book II’, unpublished paper, Sixteenth ICBM, Salzburg, July 2014.

Lost compositional blueprints

Collection, LM 4708 (including BWV 1090–5, 1097–1120), a collection of chorale preludes by German organists such as Johann Pachelbel, Johann Michael Bach (1648–94), Johann Christoph Bach (1642–1703), J. S. Bach and Georg Andreas Sorge (1703–78), surviving in a copy made by J. G. Neumeister (1757–1840).15 Table 14.3 shows the formal and numerical similarities between the two collections. Both are arranged in liturgical order, were begun in the early 1700s and revised decades later. The 164 titles that Bach copied into his Orgelbüchlein indicate his original plans for a collection with exactly twice the number of chorales as in the Neumeister Collection: 82 : 164. The numbers of bars in these two collections are proportionally related, 3120 and 780; and the way the later preludes were grafted into the Neumeister Collection is identical to Bach’s building-block technique. This extraordinary result led to a working hypothesis that perhaps the Neumeister manuscript was a faithful copy of an original collection, revised and completed in the late 1740s by Johann Sebastian Bach, who could have had pre-publication access to G. A. Sorge’s chorale preludes, or alternatively, revised by someone after 1750 using proportional ordering in the same way as Bach. It has been assumed that Bach never completed the Orgelbüchlein as it has so many unfilled gaps – he filled in the music of only 46, or 48,16 of the 164 titles he originally wrote. Russell Stinson has proposed a historical reconstruction of the order in which Bach added to the collection.17 There were three main phases, the final being around 1726 when, after a lengthy pause, Bach revised two chorales and added 16 bars and 1.5 bars in two entirely new chorale settings. The book with its familiar binding had a home in his rooms throughout his years at Weimar, Cöthen and finally in Leipzig, when he wrote out the chorale (BWV 613), made minor revisions to two others (BWV 620 and BWV 631), and gave a final two-bar tweak, counting half a bar that had been in the score for a decade or so, and writing in one-and-a-half bars with a deliberate setting of the words ‘O Sadness!’ C. P. E. Bach’s amendment to the title page, correcting the ‘6’ to ‘8’ to make a title word’ ‘48’, makes the numerical perfection clear: it has a large-scale symmetrically arranged double 1 : 1 proportion within the 780 bars, with 24 : 24 settings in the order known as ‘proportion by situation’ in 390 : 390 bars.

15

16 17

R. Tatlow, ‘Narratives of Number in the Neumeister Chorales’, unpublished paper, Fifteenth ICBM, Southampton, July 2012. C. P. E Bach wrote this number on the title page. Russell Stinson, Bach: The Orgelbüchlein (Oxford University Press, 1999).

359

360

demonstrations

Table 14.4 Five Great Preludes and Fugues. Mixed copyists. 1 : 2 in 1200 bars BWV

Key

544

B minor

545

C major

546 547 548

Source

C minor C major E minor

Totals

Prelude Fugue Prelude Largo * Fugue Prelude Fugue Prelude Fugue Prelude Fugue

Autograph Private collection J. G. Walther LM 4718 J. P. Kellner P 286/10 J. P. Kellner P 274 No. 1 J. S. Bach & J. P. Kellner P 274

Bars 85 88 31 54 111 144 159 88 72 137 231 1200

III

1:2

Preludes 85 88

31

31 54 111

144

144 159

88

88 72

137

137 231

400 : 800

400

The great organ preludes and fugues

The numerical evidence and documentary trail of the ‘Great Six Preludes and Fugues’(BWV 543–8)18 suggest that Bach created a perfectly proportioned collection of five ‘great’ preludes and fugues before 1731 from material he had already written, later revising BWV 545 and adding the A minor pair, BWV 543, to create the collection of six we know today, BWV 543–8. There is no extant autograph manuscript of a collection with either five or six large preludes and fugues. The origins of this prelude-andfugue collection go back at least as far as Bach’s Weimar years, although the dating of many sources remains uncertain. Dietrich Kilian’s virtuosic reconstruction of the source trail from copies and very few autograph manuscripts19 suggests that although Bach had composed the preludes and fugues in Weimar, it was not until his Leipzig years that he began to compile them into a collection. It also suggests that he first compiled a collection of five preludes and fugues with 1200 bars and several layers of proportion, possibly as late as 1730. The complex manuscript evidence supports this new idea of a lost collection of five. The surviving partial autograph of the B-minor 18

19

This exploration was stimulated by Russell Stinson’s article ‘Franz Liszt and His Early Reception of Bach’s Organ Works‘, Bach Notes: The Newsletter of the American Bach Society, No. 4 (Fall 2005), 1–5. NBA KB IV 5–6/1+2, 180.

Lost compositional blueprints

Table 14.5 1738/9 plan for three grand organ collections: 1 : 1 : 1, 1200 bars Collections of organ works

Settings

Date

Autograph

Bars

CU III early submission Great Chorale Preludes Great Preludes and Fugues

15 15 5

1739 1739 Before 1731?

Lost P 271 Lost

c.1200 1200 1200

3:3:1

1:1:1

prelude-and-fugue pair (BWV 544), has been dated to Leipzig 1727–31, the clear hand showing that Bach was copying from an original that may have been composed in his first years in Leipzig.20 The C major pair (BWV 545), went through at least three stages of revisions; stage two including a third movement, and it was not until after 1730 that it reached the final two-movement form of Am. B. 60. In Weimar, Bach had written and revised two versions of what would after a third revision become BWV 545.21 The version in which the prelude and fugue were separated or followed by a Largo (* in Table 14.4) from the Trio Sonatas (BWV 529/ 2) has survived in copies by Walther (Yale LM 4718), Kellner (P 286), a Berlin scribe (Stockholm, Stiftelsen Musikkulturens främjande), one of C. P. E. Bach’s copyists (P 290), and one in the hand of an anonymous scribe (Brussels, II. 3913). By this stage the prelude and fugue had reached their definitive lengths of 31 bars and 111 bars. The work would stay in this ‘Weimar’ version until some time after 1730, when Bach revised it again and omitted the Largo movement.22 Dating of the C minor pair (BWV 546) is uncertain. Its fugue was composed in Weimar and may originally have been preceded by the Fantaisie (BWV 562/1; 81 bars), before the existing prelude was composed. The dating of the second C major pair (BWV 547) has caused much debate. Musical and stylistic considerations led early scholars to believe it was composed in Leipzig as late as 1744, whereas Stauffer suggested 1719. Current opinion places it as an early Leipzig composition some time after 1723. Similar to the B minor pair, the partial autograph of the E minor pair (BWV 548) can be dated to Leipzig, 1727–31, although the clear hand shows that Bach was copying from an original, suggesting he had composed it earlier, probably in his early years in Leipzig.23 The

20 23

NBA KB IV 5–6, 390–1, and BWV2a. Ibid., pp. 390–1, and BWV2a.

21

NBA KB IV/5–6, 299.

22

Ibid., 306.

361

362

demonstrations

Table 14.6 Six Great Preludes and Fugues displaying proportional parallelism. Unknown copyist, Am. B. 60, 1740–59 BWV

Key

Am.B.60

Changes

Bars

545

C major

+ 6 bars 54 bars

31

546

C minor

547

C major

Prelude Largo Fugue Prelude Fugue Prelude Fugue Prelude Fugue Prelude Fugue Prelude Fugue

548 543 544

E minor A minor B minor

Totals

+ 10 bars

111 144 159 88 72 137 231 53 151 85 88 1350

1:1

1:2

31

Block

31 111

111

137

72 137

231 53 151 85 88 675 : 675

B-A-C

31

C

144 159 88 72 137 231 53

C

A

85

B

111

144 159 88 72

Block

151 85 88 225 : 450

C

151 88 350

1000

A minor pair (BWV 543), in its final form, seems to have been one of the last of the six to be revised. Bach could easily have extended movements he had composed in Weimar to create this well-proportioned collection. As a collection of five in 1200 bars, it would have been perfectly parallel to the revised collection of fifteen ‘great’ chorale preludes in 1200 bars (BWV 651–65), 1 : 1 and 1 : 3, with 1200 : 1200 bars, 5 : 15 works, although Bach did not finish copying the fifteen (BWV 651–65) into P 271 until the 1740s. Typically, though, Bach’s plans changed and he never made a clean copy of these twenty works in a single manuscript. Instead, he focused his energies on publishing Clavier Übung III, whose first fifteen movements in c. 1200 bars were originally submitted as a group to the engraver.24 I suspect that even in 1738/9, the fifteen ‘great’ chorale preludes and the five ‘great’ preludes and fugues had belonged to a grand, perfect scheme of parallel collections for organ, see Table 14.5. The first evidence of a collection of six rather than five preludes and fugues for organ is in the copy Am. B. 60,25 dating from the late 1740s and in the hand of an unknown scribe. It has markings by Kirnberger, one of its

24 25

See Tables 11.3 and 11.6. Ibid., source B 102, 107–8. P 276 also contains a collection of the six based on Am. B. 60.

Lost compositional blueprints

early owners, and the collection of six was transmitted through manuscripts copied by scribes associated with Bach’s sons and students in Berlin through Kirnberger and Agricola.26 It was first published as Sechs Preludien und Sechs Fugen in Vienna,27 announced in the Wiener Zeitung no. 87 on 17 October 1812.28 The 1812 collection contains the same six preludes and fugues as Am. B. 60, but in a different order.29 The preludes and fugues in Am. B. 60 are copied in the order shown in Table 14.6, with the A-minor and B-minor prelude-and-fugue pairs (BWV 543–4), after the E minor pair (BWV 548). If BWV 548 was copied without any changes from Bach’s lost original, the positioning of BWV 543 and its changes suggest that Bach added it to this collection of six last of all. BWV 543 and 545 are the only two preludes and fugues with an early version. The changes Bach made to these two are integral to the proportion even in the earlier set of five preludes and fugues. The 1350 bars and two layers of proportion of the collection of six in Am. B. 60 suggest that the manuscript was copied from an autograph collection compiled by Bach, or from a copy made in Bach’s household. Table 14.6 shows that three fugues form 350 bars, and the remaining 1000 bars are symmetrically arranged. There is a double 1 : 1, 675 : 675 bars and a further 1 : 2, with 225 : 450 bars in 675 bars. Note the bar changes made to the length of preludes BWV 543 and 545, and that the final pair to be added, BWV 543, is in the key of A minor, creating a B-A-C allusion that had been missing in the earlier collection of five. In Am. B. 60 the six preludes and fugues are written as a discrete collection, as if the unknown Berlin scribe was copying from a collection that had been revised to make it numerically perfect, however the autograph manuscript on which it was based is lost. There are two rational building blocks that may have helped in the construction process: 350 bars of original material, and 1000 bars after the revisions to the C major and A minor preludes.

26 27

28

29

NBA KB IV/5–6.1, 217–20. NBA KB IV/5–6, 256: ‘Die “Sechs grossen Präludien und Fugen” finden sich geschlossen und in der Reihenfolge BWV 545–8, 543, 544 in drei Hss (P 276, Am. B. 54. Fascicle 3, Am. B. 60) von denen sich Am. B. 60 als Vorlage der beiden anderen erweist.’ NBA KB IV/5–6, 256, 477: ‘Frühdrucke in Sechs Preludien und Sechs Fugen (Wien, 1812 ff) (Kunst-und Industrie Comptoir, später bei Haslinger) und Peters II (Griepenkerl, 1844). Vorlage(n) im Wiener Erstdruck nicht genannt. Griepenkerl erwähnt als Vorlage für BWV 543, 544 und 546–548 summarisch Abschriften von Dröbs, aus Sammlung Hauser und aus Forkels Nachlass/vgl. Oben BWV 547), ferner die Ausgabe bei Haslinger.’ Ibid., 256.

363

364

demonstrations

Table 14.7 A perfectly ordered collection of four solo concertos BWV

Mvts

Bars

1052

Allegro Adagio Allegro – Siciliano Allegro – Adagio Allegro Allegro Larghetto Allegro

184 75 274 112 30 258 122 57 160 89 39 200

1053

1054

1055

Totals

D6 D 12 D 12 D 63 D7 D 137 D 52 D 16

1600 [

IV

Totals

D 305]

1:3

533

400

339

328

1600

1:2

Block

Block

184 75 274

112 57 160 89 39

184 75 274 112 30 258 112 57 160 89 39

1000

1400

184 75 274 112 30 258

112 30 258 112 57 160 89 39 200

400 : 1200

200 200 : 400

Towards a collection of harpsichord concertos

The final exploration concerns Bach’s concertos for harpsichord, thirteen of which have survived. Six are for multiple harpsichords: three concertos for two harpsichords (BWV 1060–2), two concertos for three harpsichords (BWV 1063–4), and one concerto for four harpsichords (BWV 1065). The first collected edition was edited by S. W. Dehn and F. A. Roitzsch and published in 1854 by the Leipzig-based firm of C. F. Peters.30 We know that Bach formed many collections of six works and it is tantalising to imagine that he intended these six mixed keyboard concertos of a similar genre to become one collection, as intimated by their consecutive numbers in the modern Schmieder catalogue (BWV 1060–5). There is however no extant consecutive autograph manuscript to justify this notion. The solo harpsichord concertos have fared better. There is a consecutive manuscript in Bach’s hand, P 234,31 which contains seven of the solo concertos. This autograph manuscript, dating from around 1738,32 is a compositional score with numerous corrections caused by the transcription procedure,33 yet the layout and fluency of the handwriting gives the appearance of a 30

31

C. Wolff, ‘Die Rastrierungen in den Originalhandschriften Joh. Seb. Bachs und ihre Bedeutung für die diplomatische Quellenkritik’, in Festschrift für Friedrich Smend zum 70. Geburtstag (Berlin: Merseburger, 1963), 89. 32 33 D-B Mus. ms. Bach P 234, NBA KB VII/4, source A. NBA KB VII/4, 19. Ibid., 15.

Lost compositional blueprints

365

Table 14.8 Construction of a hypothetical collection of harpsichord concertos BWV

Key

Bars

Bars

1058

G minor P 234 J. S. Bach C minor St 136 J. C. Altnickol C major St 139 A. M. Bach C minor P 612 J. S. Bach

171 46 118 110 37 178 166 63 140 88 50 133

335

1060

1061

1062

Totals 1063

1064

Totals

D minor Am B 67 J. F. Agricola C major AMB 68 J. F. Agricola

1:3 171 46 118

D 23 325

110 37 178

369

289 68 224 133 [ 44 192

1300

Blocks 171 46

325 : 975

Blocks

Blocks

171 46

171 46 118

118 110 37 178 166 63 140 88

110 37 166 63 140 88 50 133

271

D 21 1300 [D 44]

1:1

63 140

50 133

133 350 : 350

900

400

581

D 8] D3

369

289 68 224 133 44 192

D 11]

950 [

950

325

well-designed collection. Based on diplomatic evidence, it has been suggested that Bach intended the first six of these, BWV 1052–7, to be a discrete collection.34 The manuscript contains a collection of six (BWV 1052–7), a seventh (BWV 1058), which is an arrangement of Bach’s violin concerto in A minor (BWV 1041) and a fragment of an eighth in D minor (BWV 1059), which has not survived in a complete form and which may have been based on a lost oboe concerto. Table 14.7 shows the structure of the first four (BWV 1052–5), typical of one of Bach’s published collections, with several layers of perfect proportion and an allusion to his name. Excluding da capo repeats, the cumulative total of the four concertos is 1600 bars, containing a double 1 : 3 proportion formed by the 400 bars of BWV 1053 and 1200 bars in the remaining three: 1 : 3 and 400 : 1200. Although he rarely used the 1 : 3 proportion, representing the interval of a twelfth (an

34

Ibid.

166 63 140 88 50 133

1600

366

demonstrations

octave and a fifth), it can be found in the Early Keyboard Transcriptions (BWV 972–82),35 and was perhaps a deliberate parallel to associate the two collections. The building blocks with 1000 bars and 1400 bars respectively recall the structure and bar total of the Early Keyboard Transcriptions.36 The fifth and sixth concertos (BWV 1056–7) in P 234 show no particular numerical correlation, but there seems to be some ordering in a group of the remaining harpsichord concertos. Table 14.8 shows this speculative collection, not supported by any autograph manuscript. The first four concertos for two harpsichords (BWV 1058, 1060–2) have a rational total of 1300 bars, with a double 1 : 3 proportion in 325 : 975 bars and 1 : 3 concertos. This mirrors the structure of both the four solo concertos in P 234 (BWV 1052–5) and the first six Early Keyboard Transcriptions in P 280 (BWV 977–82). Deliberate construction is suggested by the consecutive block of 900 bars and the symmetrical block of 400 bars, and by the symmetrical arrangement of two sets of 350 bars, a unit also integral to the structure of the early transcriptions. Furthermore, the two triple harpsichord concertos (BWV 1063–4) may have been part of the plan for a united collection of harpsichord concertos. Its 950 bars are formed with a block of 325 bars, suggestive of embryonic planning. It is not possible to tell whether Bach intended a numerical association between the 1600 bars of BWV 1052–5, the 1020 bars of BWV 1056–7, the 1300 bars in BWV 1058, 1060–2, and the 950 bars of BWV 1063–4. The complex stemmata of sources for each concerto, and the loss of a copy of the complete collection in Bach’s hand, if it ever existed, prevent anything further beyond this hypothetical reconstruction.

V

Proportional parallelism – the lost blueprint

Bach used numbers to create perfect proportions, unity and beauty within his collections. The cryptic element in Bach’s works, documented by the puzzle canons and suggested by other technical lusus ingenii commonly used by composers of the period, has invited close interpretation and although many traditions of interpretation were still recognised in Leipzig at the time, with the ubiquitous use of number alphabet techniques crowning them all, modern interpretations have frequently been 35

See Table 10.1.

36

See Tables 10.3. and 10.4.

Lost compositional blueprints

inappropriate. It is natural to assume that Bach chose the numbers with which he created parallel proportions because of their extramusical significance, but it seems he did not. However beguiling number interpretations may be, it seems that the specific numbers in Bach’s parallel proportions were not of prime importance. They can of course be admired, but, like the bricks and areas of masonry in a building, their primary purpose is not to draw attention to themselves; they are part of the building as a whole. It is the proportions themselves that hold the significance, not the specific numbers. That the numbers frequently appear to be self-referential lends colour to the overall effect. All the collections and multi-movement works that Bach published or left in fair copy demonstrate the characteristics of proportional parallelism. Parallel propostions can sometimes be seen in his unrevised works and can be used to reconstruct the developmental stages of some collections. They are usually absent in editorially constructed collections. What would Bach’s contemporaries have thought about his use of proportional parallelism and how many of his closest associates would have known of it? Were his sons, immediate family and students aware of it and drawn into the practice? Was his close, trusted student, copyist and son-in-law, Altnickol, enlisted in the 1740s to help with the procedure as Bach revised many collections? Would his sons have looked down on their father’s perfectionism as an irritating and unnecessary waste of time? From today’s perspective it might be considered symptomatic of a compulsive disorder, although the evidence presented in Part I shows that in the early eighteenth century recreating the most perfect beauty and practising eurythmia would have been a praiseworthy pursuit. Many a God-fearing Lutheran at the time believed the Creator would wish every artist to strive for the perfection of the unity even though they knew that proportional perfection would never be heard in real time. This view was upheld until the late eighteenth century, when Johann Nikolaus Forkel wrote that ‘musical perfection is dependent upon notational perfection’,37 while describing the quantifiable perfection of music in the past tense. Discussing the critical objections and difficulties in poetry, Aristotle wrote: ‘In general, the impossible must be justified by reference to artistic requirements, or to the higher reality, or to received opinion. With respect to the requirements

37

G. Tomlinson, ‘Musicology, Anthropology, History’, in The Cultural Study of Music: A Critical Introduction, ed. Martin Clayton, Trevor Herbert and Richard Middleton (New York: Routledge, 2003), 36.

367

368

demonstrations

of art, a probable impossibility is to be preferred to a thing improbable and yet possible.’38 The case is now made for proportional parallelism. The path of discovering the theory was fraught with the Aristotelian paradox, but now it is formulated, I wonder if it would have seemed so paradoxical to Bach and his contemporaries. Authors in Bach’s immediate sphere have testified to every element of the theory, including the concepts of perfection, Harmony and parallelism with their far-reaching implications for cultural and creative endeavours of the time. If such an influential composer as Bach deliberately manipulated the number of bars to create perfect proportions in his scores that cannot be heard, surely our appreciation of his scores will be improverished if we ignore proportional parallelism. With the modern emphasis on sounding music we have lost the riches of many earlier written traditions. And yet generations of musicians have sensed Bach’s unheard proportions and commented on the architectural grandeur of his works. Are these claims mere empty rhetoric fuelled by a hagiographic desire to raise Bach to the level of an evangelist? Or is there something in his scores beyond real time that enables mankind to detect the perfect parallelism? And was Bach the only composer to use parallel proportions? Given the evidence from treatises written and published in the Thuringian area, it would be strange if other composers with a similar world view had not developed these or similar solutions to express Harmony and eternity; composers such as Kuhnau, Walther and Buttstett; or a generation earlier, Heinichen, Werckmeister; or across a devotional border, Fux in Vienna. One might imagine that the further from Thuringia, geographically and confessionally, the less likely a composer would be to use parallel proportions. Would it be surprising to find such layers of proportion in music written by composers born, bred and practising in France and Italy in the 1720s? If Bach taught the technique to his sons and students, did they hand it on to their students and sons, and when did the practice cease? When it was still a fresh memory, Forkel wrote: ‘It was a period of time when one took all of music to be the main science, when the whole of music theory consisted solely of calculations, and when one believed that all expression and all beauty in art depended solely on the mathematical proportions of tones . . . But these times are now over, and what happened in excess then, maybe happens too little nowadays.’39 Perhaps later composers used proportions as a 38

39

Aristotle, Poetics, trans. S. H. Butcher, XXV: ‘Critical Objections Brought Against Poetry, and the Principles on Which They Are to Be Answered’. Forkel, Allgemeine Geschichte der Musik (1788), 30.

Lost compositional blueprints

compositional and pedagogic tool, even though the practice would have held an entirely different significance. Throughout this research project I have used what has become known as historically informed methodology, working with sources that Bach himself could have known and used, and attempting at all times to think in terms and concepts that Bach would have understood. Nonetheless, this book is a product of the twenty-first century. It could not have been achieved without the work of the librarians, editors and researchers who devoted their lives to diplomatic source research and to compiling Bach documents, or without the online availability of Bach’s manuscripts and many rare books, including Zedler’s Lexicon and Fritsch’s Lexicon. At every stage the results are supported with data and documentary evidence, presented as objectively as possible, to help the reader assess the results, and in the hope of inspiring a new generation of musicologists to discover many new methods. At the end of some of his most iconic music collections Bach wrote the dedicatory letters ‘D. S. Gl.’40 A century earlier the Lutheran astronomer Kepler chose to end his Harmonic Motions of the Planets with a prayer expressing the anxieties of the creative process as he worked for God’s glory: O God, who by the light of Nature moves in us the desire for the light of grace, so that by it You may bring us over into the light of glory . . . I have now brought to completion the work of my covenant, using all the power of the talents which You have given me. I have made manifest the glory of Your works to men who will read these demonstrations, as far as the deficiency of my mind has been able to grasp its infinity. My intellect has been ready for the most accurate details of philosophy. If anything unworthy of Your intentions has been put forward by me . . . which You would wish men to know, inspire me also to set it right; if I have been enticed into temerity by the wonderful splendour of Your works, or if I have loved my own glory among men, while advancing in work destined for Your glory, mildly and mercifully pardon it; and last, be gracious and allow these my demonstrations to bring You glory and in no way obstruct the salvation of souls.41

Bach would surely have identified with Kepler’s experience and sentiments as he moulded the significant proportions of this same universal Harmony into earthly music and everlasting sounds.

40 41

Deo Soli Gloria; or reordered as ‘S. D. Gl’, Soli Deo Gloria. J. Kepler, Harmonices Mundi (Linz, 1619); translation adapted from Kepler, The Harmony of the World, trans. Aiton, Duncan and Field, (Philadelphia, 1997), 491.

369

Appendix A theology of musical proportions and

Harmony in Bach’s time The German texts are transcribed literally from the originals, including non-standardised spellings capitalisations, and some grammatically incorrect endings. The English translations tend towards dynamic rather than formal word-for-word equivalents. Fritsch, Teutsch-Englisches Lexicon (Leipzig: Fritsch, 1716) has been the guidebook for synonyms. Missing letters in the German and missing words necessary for the flow of the English texts are indicated in square brackets.

Andreas Werckmeister, Musicae mathematicae hodegus curiosus (Frankfurt; Leipzig: Calvisius,1687) 1687-I

1687-II

1687-III

1687-IV

370

For we now see, hear and perceive everywhere that God Himself created nature through His omniscient counsel, so that everything might strive to achieve unity [1 : 1] and therein take pleasure. Chapter 24, 69 Trias harmonica gives a beautiful image or parallel of the Holy Trinity Register, s.v. ‘Trias harmonica’, 170 Through a parallel [Fritsch: parable] we can certainly say that our nature and all things strive for equality [1 : 1]; thus God has shown us a model, [so] that we should strive for and delight in Him, the one [true] God, who is composed of a perfect Triad, or Three-in-Oneness; and it is already sufficient for us when we see that Nature leads and guides us to [this] equality and to an orderly, clear existence. Chapter 24, 69 We also see how God wants to lead us to good through music, and it would be desirable that all musicians and Christians take heed and understand this about music. Chapter 24, 69

Da wir nun sehen, hören, und überal empfinden, daß Gott selber nach seinen Allweisen Rath die Natur also zugerichtet habe, daß alles nach der Gleichheit strebe, und sich daran belustige. Trias harmonica gibt eine schöne Abbildung oder Gleichnüß von der heiligen Drey Einigkeit. Durch ein Gleichnüß können wir wohl sagen, wie unsere Natur und alles nach der aequalität strebet, also hat uns Gott ein Fürbild gezeiget, daß wir ja alle nach ihm, dem einigen Gotte, streben und uns an selben belustigen sollen, der da bestehet aus einer Volkommenen Triade oder Drey-Einigkeit, und wir haben schon gnung, wenn wir sehen, daß uns die Natur zur Gleichheit und ordentlichen vernehmlichen Wesen führet und leitet. Wir sehen auch wie uns Gott durch die Music zum Guten leiten wil, und [es] wehre zu wünschen, daß alle Musici, und Christen, dieses bey der Music in acht nehmen und verstünden.

Appendix

1687-V

Could there be a clearer parallel to show us as though in a mirror the Divine Threein-One nature than this [the Triad]? It would be harder to find a clearer [image]. Would to God that all pious Christians understood music to this extent, [because if they did] they would experience heartfelt joy over this model. Anhang. Chapter 5, 147

371

Kan wohl etwa ein Gleichnüß deutlicher vorgestellet werden, welches uns das Drey-Einige Göttliche Wesen gleichsam in einem Spiegel zeige, als dies? Deutlicher werden wir es wohl schwerlich finden. Wolte Gott! daß nur alle fromme Christen die Musicam in so weit verstünden, sie würden eine HerzensFreude über dieser Vorbildung empfinden.

Andreas Werckmeister, Der Edlen Music-Kunst Würde, Gebrauch und Mißbrauch (Frankfurt; Leipzig: Calvisius, 1691) 1691-I

1691-II

1691-III

1691-IV 1

1691-IV 2

Music should be used in worship services. It is a foretaste of Heavenly Harmony . . . The wisdom of God is presented to us through music. Evil people do not respect music very much. Summary of Chapter 1, 42 Christ himself introduced music in the New Testament . . . We should sing well with others in church services. A person who does not understand music should not despise it. Summary of Chapter 2, 42 How music must be made orderly in church so that devotion is not hindered. Summary of Chapter 3, 42 We can prove that music is an orderly matter, through the fundamentals of music, because the whole of Harmony is contained in the numbers 1, 2, 3, 4, 5, 6 and 8. Chapter 4, 8 When the proportion exceeds the 32nd part [demisemiquavers], the speed is unnatural because the senses cannot perceive it, and it becomes a dissonance. Thus we notice again that Nature does not want to stray too far from the unity, and wants to keep order. And that too great speed in music also must be avoided. Chapter 4, 8–9

Die Musica ist bey dem Gottesdienste zu gebrauchen befohlen. Ist ein Vorchmack Himlischer Harmonie . . . Durch die Music wird uns die Weißheit Gottes vorgestellet. Böse Leute achten die Musicam nicht viel. Christus hat die Musicam selber im Neuen Testamente eingeführet . . . Bey dem Gottesdienste sollen wir fein mitsingen. Wer die Musica nicht verstehet, soll sie auch nicht verachten. Wie die Music eine Ordnung in der Kirche erhalte: Damit die Andacht nicht verhindert werde. Daß auch die Music ein ordentlich Wesen sey, können wir aus den Musicalischen Fundamentis selbst beweisen, denn die gantze Harmonia bestehet in den Zahlen 1. 2. 3. 4. 5. 6. und 8. Wann aber . . .die proportiones über [den] 32. Theil kommen, so ist schon die Geschwindigkeit, weil sie der Sensus nicht begreiffen kan, der Natur zuwider, und wird gleichsam zur Dissonans. Also können wir wieder mercken, daß die Natur nicht zu weit von der Aequalität schreiten, und die Ordnung erhalten will. Und daß die gar zu grosse Geschwindigkeit in der Music auch muß vermieden werden.

372

1691-IV 3

1691-IV 4

1691-IV 5

1691-IV 6

1691-IV 7

1691-V

1691-VI

appendix

Music also has a certain order and measure as far as the height or depth of the pitch, or low or high sounds are concerned. Chapter 4, 9 Thus we see how various orders must be observed in Harmony, all of which strive after equality [1 : 1] so as not to cause confusion when one goes too far, or with too much variety. Chapter 4, 9 When this good order is present to a goodnatured person through the sounds [i.e. music], then that same person rejoices because his own image and the wisdom of God is [are] shown to him. Chapter 4, 9 Thus music is a mirror of divine creatures and of the wisdom of God, yes of God’s creatures and His image itself (in a certain measure), because it [music] consists of the same form and proportion as man: Thus we see once again how God took pleasure in putting a harmony in his creatures. Chapter 4, 12 To sum up, it is impossible for us to describe the virtue of music, as the blessed Luther has already established. Thus we cannot explore all the reasons why God ordained beloved music to his service either; [instead] we must be content to know how we should use and employ it to the glory of the almighty Creator, and guard ourselves against every possible misuse of it. Chapter 4, 12 Music is itself abused by various musicians when they seek their own glory through it. God’s glory must be sought. Music is God’s gift; therefore, a musician must neither envy nor hate another [musician]. Summary of Chapter 5, 43 One must seek God’s glory through the art of music. Bungling workmanship cannot

So hat auch die Music ihre gewisse Ordnung und Maße, was den Sonum gravem und acutum, oder die Tieffe und Höhe der Sonorum belanget. Also sehen wir, wie in der Harmonie vielerley Ordnungen müssen in acht genommen werden, welche alle nach der aequalität streben, damit nicht eine Confusion verursachet werde, wenn man zu weit, oder in die Vielheit gelangen würde. Wenn denn diese gute Ordnung einem guten Gemüthe durch die Sonos vorgetragen wird, so erfreuet sich derselbe Mensch, weil ihm sein Ebenbild und die Weißheit Gottes vorgestellet wird. Also ist die Music ein Spiegel der Göttlichen Geschöpffe und Weißheit Gottes, ja Gottes Geschöpffe und Ebenbild (auff gewisse Maße) selbst, weil sie in solcher Form und Proportion, wie der Mensch bestehet: Da sehen wir wieder, wie Gott Beliebung getragen, eine harmoniam in seine Geschöpff zu legen. In Summa, wir können die Tugend der Music unmöglich beschreiben, welches auch der Sel. Lutherus gestehet. So können wir auch nicht alle Ursachen erforschen, warum Gott die liebe Music zu seinem Dienste verordnet hat, wir müssen uns behelffen, daß wir wissen, wie wir sie dem allmächtigen Schöpfer zu Ehren gebrauchen und anwenden, auch uns für allen Mißbrauch derselben hüten sollen. Die Music wird von unterschiedlichen Musicis selber gemißbrauchet, wenn sie ihre eigene Ehre dadurch suchen. Gottes Ehre muß gesuchet werden. Music ist Gottes Gabe, darüm muß auch ein Musicus dem andern nicht mißgönnen, und einer den andern hassen. Durch die Kunst der Music soll man Gottes Ehre suchen. Hümplerwerck kan die

Appendix

1691-VII

1691-VIII

1691-IX

1691-X

1691-XI

inspire [the mind to] devotion. Joyful and sad music must be used at the right time. Summary of Chapter 6, 43 Joyful music does not belong to the godless world, that it might serve the devil. God must be served with joyful music. The devil is God’s ape. He also wants to have joyful music. And [he] can also delight worldly minded persons with slow and solemn music. He wishes to stealthily bring music out of the church. Summary of Chapter 7, 43 Musical variations can stimulate good thoughts in the pious heart. One must also sing new songs to God. Trumpets are also to be tolerated in church services. Summary of Chapter 8, 43 Solemn music has its usefulness. Everything must be used at the right time. Too great speed causes confusion in music. The many dissonances make music contemptible. Playing the fiddle in an alehouse is a gross abuse of music, causing great scandal. It can almost not be done with a good conscience. Organists and churchmen should not frequent drinking clubs with their music. Carousing is an abuse of music. Summary of Chapter 9, 43–4 The equality [1 : 1] of the musical pulse is compared to the pulse of blood vessels. Musicians must not be lazy; [such people] are not useful in the church. Too many different ways of performing music and [on] organs also make music annoying. Summary of Chapter 10, 44 The sentence given to the abuser of Music [Isaiah 5: 11–13]. One should not set amorous songs to [church] music. Beer fiddlers, that is what they really are. Music can be used for celebrations so long as there is no excess. Summary of Chapter 11, 44

373

Gemüther zur Andacht nicht bewegen. Freudige und traurige Music muß zu rechter Zeit gebrauchet werden. Die freudige Music gehöret nicht der gottlosen Welt, daß sie dem Teufel damit diene. Gott muß mit freudiger Music gedienet werden. Der Teufel ist Gotte Affe: Er will auch freudige Music haben: Und kan auch die Weltkinder mit langsamer gravitätischer Music belustigen. Er will mit List die Musicam aus der Kirche bringen. Music-Variationes können die frommen Hertzen zu guten Gedancken reitzen. Man muß auch dem lieben Gotte neue Lieder singen. Trompeten sind auch bey dem Gottesdienste zu erdulden. Gravitätische Music hat ihren Nutz. Alles muß zur rechten Zeit angewendet werden. Allzugrosse Geschwindigkeit verursachet confusiones in der Music. Die vielen dissonantien machen die Music verächtlich. Bierfiedlerey ist ein grosser Mißbrauch der Music. Verursachet grosse Aergerniß. Kan fast mit guten Gewissen nicht verrichtet werden. Organisten und Kirchendiener solten den Sauff-Gelaken mit ihrer Music nicht beywohnen. Sauff-Runda ist ein Mißbrauch der Music. Aequalität der mensur wird mit den Schlagen der Pulß-Ader verglichen. Musici müssen nicht faul seyn, sie bringen keinen Nutzen in der Kirche. Die Vielheit des Musicirens und Orgelns machet die Music auch verdrießlich.

Der Mißbraucher der Music Sententz. Man soll keine Buhlen-Lieder unter die Noten setzen. Bierfiedler, welche sie eigentlich sind. Bey Conviviis kan die Music wol gebrauchet werden, wenn nicht ein Excess dabey vorbey vorgeht.

374

1691-XII

appendix

The use of music in the celebration of the departed elders. The power and effect of music cannot be expanded upon here because of space. The abuse does not cancel out good use. One must strive against abuse. Summary of Chapter 12, 44

Gebrauch der Music bey den conviviis der gottseligen Alten. Krafft und Würckung der Music, kan hier beliebter Kürtze wegen nicht weitläufftig ausgeführet werden. Der Mißbrauch hebet den guten Gebrauch nicht auff. Dem Mißbrauche muß man widerstreben.

Andreas Werckmeister, Harmonologia musica oder kurtze Anleitung zur musicalischen Composition (Franckfurt; Leipzig: Calvisius, 1702) 1701-I

Whenever I am asked by various friends how such Harmony is formed, I find myself constrained to serve my neighbour with the gift God has given me; thus I could not refrain from explaining the advantages of the construction of this Harmony alone, but also the fundamentals of composition through mathematical demonstrations, in order to honour God and to be useful to my neighbour. Unpaginated Preface, [7]

Wann ich dann von unterschiedlichen Freunden, wie solche harmonia einzurichten sey, bin ersuchet worden, und ich meinem Nechsten mit der Gabe so mir Gott gegeben hat, zu dienen mich schuldig befinde: so habe nicht allein die Vortheile zum Bau diese harmoniae, sondern auch die Grundsätze zur Composition insgemein durch Mathematische demonstrationes, Gott zu ehren, und meinem Nechsten zum Nutz heraus zu geben nicht unterlassen können.

Johann Gottfried Walther, Praecepta der Musicalischen Composition, 1708. Herzogin Anna Amalia Bibliothek/Hs Q 341 c Transcribed in Peter Benary, Johann Gottfried Walther, Praecepta der Musicalischen Composition (Leipzig: Breitkopf & Härtel, 1955) 1708-I

Music is a heavenly-philosophical science based specifically on mathematics, which consists of sound, so long as the sound itself produces a good and artistic Harmony or agreement. Book 1, p. 1; Benary, 13

1708-II

What is necessary to make and produce a good Harmony is this, that it is not only composed after the artistic rules, but above all and primarily when it is used in

Die Music ist eine himmlischphilosophische, und sonderlich auf Mathesin [Mathematik] sich gründente Wißenschaft, welche umgehet mit dem Sono, so fern aus selbigen eine gute und künstl.[lerische] Harmonie oder Zusammenstimmung hervor zubringen. Eine gute Harmonie hervorbringen und machen, importiret vornehml. dieses, daß solche nicht allein nach denen Kunst Regeln wohl eingerichtet, sondern auch zuförderst und einig zu tugendsamen,

Appendix

1708-III

1708-IV

1708-V

1708-VI

virtuous and God-pleasing practices. Book 1, 5; Benary, 14 Even the blind heathen had noticed these qualities about Harmony . . . How much more therefore should we Christians use this noble gift of God correctly, so that God might take pleasure in his handiwork; for music not only shows man his own image (i.e. that he is harmonically proportioned), it [music] also confronts God with His own divine wisdom, in which He [God] rejoices. Thus writes M. Bartolus in his Musica Mathematica. Book 1, 6; Benary, 14. As man is a true expression of music, he grows merry, of course, when his own image is shown to him through musical proportions. Book 2, 6; Benary, 75 Musica poetica or musical composition is a mathematical science according to which one constructs and puts down on paper a lovely and pure Harmony of sounds, so that they can be sung or played afterwards above all to move Man to more ardent devotion to God and also to delight and please the ear and the mind. Book 2, 6; Benary, 75

Proportio quo vicinior aequalitati eo perfectior. Proportio quo remotior ab aequalitate eo imperfectior. That is, the closer a proportion is to the unity or equality, the more perfect and intelligible it is; the further a proportion is from the unity or equality, the more imperfect and confusing it is. Book 2, 20; Benary, 79.

375

und Gott wohlgefälligen Übungen angewendet werde. Dieses haben auch schon die sonst blinden Heyden erkennet . . . Wie viel mehr sollen wir Christen diese edle Gottes Gabe recht gebrauchen, damit Gott einen Gefallen an seinen Wercken haben möge; denn durch die Music wird dem Menschen nicht allein sein Ebenbild (neml. daß er harmonisch zubereitet sey) vorgelegt, sondern es wird auch Gott seine göttl. Weißheit vorgehalten, darinnen Er sich belustiget; schreibet M. Bartolus in seiner Musica Mathematica. [Abraham Bartolus, Musica Mathematica (Altenburg, 1614)]. Weil nun der Mensch ein rechtes Formular der Music ist, so belustiget er sich freylich, wenn ihm sein Ebenbild durch musicalische Proportiones vorgestellet wird. Musica Poetica, oder die musicalische Composition ist eine mathematische Wißenschafft, vermöge welcher man eine liebl. und reine Zusammenstimmung der Sonorum aufsetzet und zu Papier bringet, daß solche nachmahls kann gesungen oder gespielet werden, den Menschen fürnemlich zu eifriger Andacht gegen Gott dadurch zubewegen, und dann auch das Gehör und Gemüth deßelben zu ergetzen und zu vergnügen. Proportio quo vicinior aequalitati eo perfectior. Proportio quo remotior ab aequalitate eo imperfectior. Das ist Je näher eine Proportion der Unitaet oder Gleichheit, je vollkommener und begreifflicher ist sie; je weiter aber eine Proportion der Unitaet oder Gleichheit abgelegen, je unvollkommener und verwirrter ist sie.

376

appendix

Johann Heinrich Buttstett, Ut, Mi, Sol, Re, Fa, La, Tota Musica et Harmonia Aeterna (Erfurt: Buttstett, 1716). 1716-I

We see once again that this governing principle is present [in the laws of] musical proportion and Harmony, and how the sounding Harmony falls in our ears . . . thus the Harmony of the universe falls into our souls, rules and drives them: Since our souls are and remain in pure Harmony now, they can always stand in union with the universe, indeed with the Creator himself; for God is a God of order, and delights in it. But I always exclude the abusers, for as God takes no pleasure in those who abuse his word and his will, so the abusers of music cannot please God either. 54

1716-II

In Part Two the true foundation of music is shown, not only defending Guidonian solmisation, but also its use through the demonstration of a comes [i.e. a fugal answer], then also maintaining that one will make music in heaven with the very [same] sounds which we use here on earth. Title page The foregoing reasons should be enough to demonstrate that the sounds used here on earth and which Guido Aretinus called ut, re, mi, fa, sol, la, are the same we will also use in heavenly Harmony and music: God will compose the melody. 175–6. And in Mattheson, 1717, 458

1716-III

Hieraus sehen wir abermahl, daß auch dieses Regiment in den Musicalischen Proportionen und harmonia bestehe; und wie die klingende Harmonia in unsere Ohren fället . . . also fället die Harmonia des Gestirnes in unser Gemüthe, regieret und treibet dasselbe: So nun unsere Gemüther in reiner Harmonia sind und bleiben, können sie stets in vereinigung stehen mit dem Gestirn, ja mit dem Schöpfer selbst; Denn Gott ist ein Gott der Ordnung, und hat ein Wohlgefallen daran. Ich nehme aber allemahl die Mißbräuche aus; Denn wie Gott an denen, die sein Wort und Willen mißbrauchen und anders deuten, keinen Gefallen hat, also können die Mißbräucher der Music Gott auch nicht angenehm seyn. Im andern Theile aber das rechte Fundamentum Musices gezeiget Somisatio Guidonica nicht allein defendiret, sondern auch solcher Nutzen bey Einführung eines Comitis gewiesen, dann auch behauptet wird, daß man dereinst im Himmel, mit eben den Sonis, welche hier in der Welt gebräuchlich, musicieren werde. Vorige angeführte Rationes mögen genung seyn zu behaupten daß wir die Soni, so hier in der Welt gebräuchlich sind und welche Guido Aretinus mit ut, re, mi, fa, sol, la, benahmset hat, dereinst bey der Himmlischen Harmonie und Music auch gebrauchen werden: Die Melodie aber wird Gott componiren.

Johann Mattheson, Das Beschütze Orchestre (Hamburg, Schiller, 1717) 1717-I

But Mr Organist, since you prattle on about distinctions and explanations, why don’t you distinguish primarily between what is

Aber, Herr Organiste, weil ihr doch so viel von Distinctionibus und Explicationibus schwatzet, warum distinguiret ihr denn

Appendix

properly called Harmony (Harmonia propriè sic dictam) and Harmony in music (Harmonia in Musicis)? All your images, your grand and mighty clavis B, the proportions of the mercy seat, of the incense altar etc. demonstrate a Harmony, but a silent Harmony is not true music. It may make a three- or sixfold species of musical Harmony; but so long as a thing does not [make a] sound, I cannot call it musical Harmony. We will with the help of God deal in more detail with Harmony in the third volume, and let it be seen how far the properties of this word relate to music. All the panes in the windows have a Harmony, but that does not mean that music is inside them, unless one mistakes the noise for music, when for example a cavalier is dubbed a knight and [then] smashes the windows. Part II, Chapter 5, §3, 456–7 1717-II

We want to look at God’s words [and] how one can force music theory from it . . . Moses was charged to make a mercy seat [atonement cover] two and a half ells long and one and a half wide, therefore it was a Harmonic construction, from which to take the triad and music. I have an ironing table in my laundry room with the same width and the same length, but one could beat or grab it from now until eternity before it would make a single note, let alone a musical concord. Part II, Chapter 5, §16, 472–3

1717-III

There is no doubt whatsoever that the Lord God is pleased with proportions, and the universe demonstrates this, both in the microcosm and macrocosm, about which Robert Fludd, alias de Fluctibus, has written sufficiently. God is pleased with musical sounds and their proportions: I doubt that as little as I doubt Christ’s birth, because music is also His creation, indeed one of His best creations and gifts.

377

nicht hauptsächlich inter Harmoniam propriè sic dictam, & Harmoniam in Musicis? Alle eure Bilder, euer großmächtiger Clavis B, die Proportion des Gnaden-Stuhls, des Rauch-Altars etc. zeigen eine Harmoniam, aber eine Harmoniam mutam, non vero Musicam an. Es mag einer Harmoniæ Musicæ dreyerley oder sechserley Arten machen; so lange mir ein Ding nicht klinget, kan ichs nicht Harmoniam Musicam nennen. Wir werden aber mit der Hülffe Gottes in der dritten Eröffnung etwas ausführlicher de Harmonia handeln, und nach Vermögen sehen lassen, wie weit sich des Wortes Eigenschafft in Musicis erstrecke. Alle Scheiben in den Fenstern haben eine Harmonie, aber deswegen steckt keine Music darinn, es sey denn, daß man den Lerm vor Music halten wolte, wenn etwan ein Cavallier daran zum Ritter wird und die Fenster einschlägt. Wir wollen Gottes Worte ansehen, daraus man Theoriam Musices erzwingen will . . . Moses solte einen Stuhl machen, drittehalb Ellen lang und anderthalb Ellen breit, ergo war es ein Harmonischer Bau, daraus Trias Harmonica & Musica abzunehmen. Ich habe einen Tisch, der ist just so breit und just so lang, man braucht ihn im Waschhause zum Zeug glätten; aber einer möchte von nun an biß in Ewigkeit darauf schlagen oder greiffen, ehe er einen Thon, geschweige einen Musicalischen Zusammenklang von sich gäbe’. Daß Gott der Herr gefallen habe an Proportionen ist ausser allen Zweifel, und bezeugt auch solches der Univers, so wohl Microcosmus als Macrocosmus, wovon Robertus Flud, alias de Fluctibus, Zeuges genug geschrieben hat. Daß Gott auch gefallen habe an den Musicalischen Thonen und deren Proportion, daran zweifle ich so wenig als an Christi Geburt; denn es ist ja auch die Music sein

378

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But I [Mattheson] would have to be inhumanly gullible to believe that God had nothing besides the six Aretinian syllables in stock, and that He would have wanted to show our musical triad through the measurement of the mercy seat. Were one to claim that the mercy seat and other things in the Old Testament had been ordered because of music, no single mystical theologian would have ever thought of it. Can this prove that our (that is, our clumsy) music will last into eternity? Part II, Chapter 5, §17, 473–4.

1717-IV

The mercy seat was one ell long and wide and two ells high: therefore it sounded an octave . . . The opponent [Buttstett] states further on p. 174, in case you don’t believe me, that one can demonstrate this with or without the monochord that half of whole string sounds an octave, but that the mercy seat should also sound and mean an octave is just ridiculous. Let’s look at it logically. Major: Everything in duple proportion [2 : 1] sounds an octave. Minor: Moses’ mercy seat was proportioned 2 : 1. Ergo: We will make music in heaven with the same sounds we use in the world. Quod erat probandum. Another of the same kind appears in §6 p. 174 . . . Major: God has created and made the whole world in Harmony. Minor: But as we are assured in the scriptures that heaven and earth will pass away, wherein no word is given that Harmony will also pass away; therefore he infers that by good consequence, Conclusio: That music will remain eternally. Part II, Chapter 5, §17, 474–5

Geschöpff, ja seiner besten Geschöpffe und Gaben eine. Aber, daß ich darum glauben solte, Gott hätte keine andere, als die Aretinischen Sex voces im Vorrath, und hätte mit der Abmessung des Gnaden-Stuhls unsere Triadem in Musicis eben anzeigen wollen, so treuhertzig macht mich kein Mensch. Gesetzt auch der Gnaden-Stuhl der Rauch Altar, und andere Sachen im alten Testament, wären um der Music willen geordnet worden, welches doch keinem eintzigen Theologo Mystico jemahls im Sinn gekommen. Kan denn das beweisen, daß unsere (eben unsere Stückwerckische) Music ewig bleiben werde? Der Rauch-Altar war einer Ellen lang und breit, dabey zwo Ellen hoch; deswegen hat er eine Octavam geklungen . . . Der Gegner setzt p. 174 noch gar dazu, wer es nicht gläuben will, dem könne man es auf dem Monochordo, auch sine Monochordo weisen, daß eine gantze Säyte mit einer halben Säyte eine Octavam klinge; aber, daß der RauchAltar deswegen auch eine Octavam geklungen und bedeutet haben solte, ist ja ridicul. Wir wollen abermahl sehen, wie der Syllogismus zusammen hängt: Major. Alles was Proportionem duplem hat, klinget die Octav. Minor. Moses sein Rauch-Altar hat Proportionem duplam. Ergo. Werden wir im Himmel mit eben den Sonis, so hier in der Welt gebräuchlich musiciret. Quod erat probandum. Noch eins, auf eben denselben Schlag, kömmt §6. p. 174. vor . . . Major. Gott hat die gantze Welt Harmonice erschaffen und gemacht. Minor. Weil wir aber ex sacris versichert sind, daß Himmel und Erde vergehen werden, wobey sich doch kein Wörtgen findet, daß die Harmonie auch vergehen

Appendix

1717-V

1717-VI

Other parts [in Buttstett’s Ut Mi Sol] are sinful and blasphemous, so that they wilfully restrict and at the same time bind the Almighty, such as when [he claims that] one’s compositions will and must be built solely on the six syllables of the tonsured monk [Guido]. I will only pray: Father, forgive them, for they know not what they do. Part II, Chapter 5, §21, 480 Where the opponent [Buttstett] cites the 9th verse (which he falsely calls our Saviour’s words): that no eye has seen etc., saying that in fact these same sounds, albeit in the most excellent mode, are in Heaven, and that no ear has heard this most excellent Gradum etc, with which he also wants to prove that Heavenly music will be sung just with his sweet ut, re, mi fa. How can his eyes have seen this thing? Where have his ears heard it? And how can such a notion have entered his profane, chiliastic and hypocritical heart that this will and must come to pass? Part II, Chapter 5, §25, 488

379

werde; so folget daraus per bonam consequentiam, Conclusio. Daß die Music ewig bleibe. So ist doch andern theils sündlich und lästerlich, die selbständige Allmacht aus Eigensinn dergestalt einzuschränken und gleichsahm zu binden, als wenn sie just nach den sechs Sylben des geschornen Mönchen ihre Composition einrichten werde und müsse. Ich will nur bitten: Vater vergib ihnen, denn sie wissen nicht was sie thun. Endlich da der Gegner sich auf den 9ten Vers (welchen er unsers Heylandes Spruch fälschlich nennet) beruffet: daß kein Auge gesehen etc sagend, es werden zwar dieselben Soni, aber in Modo excellentiori, im Himmel seyn, und diesen Gradum excellentissimum habe noch kein Ohr gehöret etc gleichwohl aber damit beweisen will, die Himmlische Music werde just mit seinem lieblichen ut, re, mi, fa gesungen werden, wie haben denn seine Augen dis gesehen? Wo haben es seine Ohren gehöret? Und wie ist es in sein profanes, chiliastisches und werckheiliges Hertz gekommen, daß es also seyn werde und seyn müsse[?]

Bokemeyer in Johann Mattheson, Critica Musica, ‘Canonischen Anatomie’ (Hamburg: Mattheson, 1722) 1723-I

1723-II

Therefore I believe it a foregone conclusion that canons are the foundation of all harmonic art, from which then the glorious and inexpressible benefits can easily be judged. §XXIII, 340 There he [the first contrapuntalist] finds the beginning and end linked and has [discovered] the perpetual canon in order to remind himself of the eternal and

Darum halte ich es für eine ausgemachte Sache, daß die Canones das Fundament aller harmonischen Kunst seyn, daraus denn der herrliche[n] und unaussprechliche[n] Nutzen derselben leicht beurtheilet werden kann. Da findet er nun den Anfang und Ende verknüpffet, und hat den Canonem infinitum, um sich des ewigen und unendlichen Ursprungs, wie auch der in

380

1723-III

appendix

unending origin, as well as the harmony of all eternity as a rule of nature of the most perfect example of all of his artistic work. §XXIV, 342–3. Many [musicians] in fact write at the end of their completed church cantatas: Soli Deo gloria, whereas in their hearts it often means: Soli Musico [Cereri, Baccho, Veneri †] gloria. and in deed [it] remains soli carni, mundo & diabolo victoria. Most musicians, especially singers and instrumentalists, are lewd brutes, and not even sensible people, let alone Christians. How can they then serve Christ? §XXVI, 344

alle Ewigkeit bestehenden Harmonie, zu erinnern, als eine Regul der Natur, zum vollkommensten Muster aller seiner Kunst-Arbeit. Viele [Musicos] schreiben zwar hinter ihre verfertigte Kirchen-Stücke: Soli Deo gloria, allein im Herzen heißt es oft: Soli Musico [Cereri, Baccho, Veneri †] gloria. und in der That bleibet soli carni, mundo & diabolo victoria’. Die meisten Musici sonderlich die Sänger und Instrumentisten sind Bestien, und nicht einmahl vernünfftige Menschen, geschweige denn Christen. Wie sollen sie denn Christo dienen?

Johann Joseph Fux, Gradus ad Parnassum, trans. Lorenz Christoph Mizler (Leipzig: Mizler, 1742) 1742-I

These devotional thoughts are founded on the old truth: the more complex a thing is, the more imperfect it is; the more simple a thing is, the more perfect it is. That is why philosophers have always had to consider God to be the simplest of beings above all others, and hence, logically, also the absolutely most perfect. 35–6, note 12

Diese erbauliche[n] Gedancken gründen sich auf die alte Wahrheit: ie mehr eine Sache zusammen gesetzet ist, ie unvollkommener ist sie, und ie mehr eine Sache einfach ist, ie vollkommener ist sie. Drum haben die Weltweisen Gott allezeit vor das aller einfacheste Wesen unter allen Dingen, und also vor das allervollkommenste allezeit gehalten und der Vernunfft zu Folge davor halten müssen.

Johann Mattheson, Behauptung der Himmlischen Musik aus der Gründen der Vernunft, Kirchen-Lehre und heiligen Schrift (Hamburg: Herold, 1747). trans. Joyce L. Irwin, ‘Affirmation of Heavenly Music’, in Foretastes of Heaver (Latham MD: Rowman & Littlefield, 2015). 1747-I

This [Heavenly] music can never age, but will always remain new; for this reason it is called the new song. §149, 143

Diese Musik kann nimmer veralten, sie wird stets neu bleiben, und heisset eben deswegen das neue Lied.

Appendix

1747-II

People who do not recognise, respect, seek or love such a precious foretaste of eternal life; why would they serve in the heavenly Jerusalem? The more zealously they work against musical worship in this world . . . the more difficult it will be for them to be drawn to the pursuit of harmonious joy in eternity, which consists of nothing else. §149, 142–3

1747-III

Given that all possible kinds of joy will, without question, be encountered in eternal life, should not then also fine music by all rights (indeed, with all its possible styles) be counted among them as the first of all? §63, 73

381

Menschen, die solchen theuren Vorschmack Lebens nicht erkennen, nicht achten, nicht suchen, nicht lieben; wozu werden die in dem himmlischen Jerusalem dienen? Je eifriger sie auf dieser Welt dem Klingenden Gottes-Dienste entgegen handeln. . . je schwerlicher werden sie zu der ewigen harmonischen FreudenVerrichtung, die in nichts anders bestehet, gezogen werden. Da nun alle nur immer mögliche Arten der Freuden im ewigen Leben, ausser allem Streit, angetroffen werden; sollte denn nicht auch die edle Musik mit allem Recht (ja, mit allen ihren möglichen Arten) am vördersamsten darunter gezählet werden?

C. P. E. Bach, Agricola, Mizler, Venzky, ‘Nekrolog auf Johann Sebastian Bach’, Musicalische Bibliothek, Vol. 4 (Leipzig: Mizler, 1754), 158–76 1750/4-I

If ever a composer showed unity [1 : 1] in its greatest strength it was certainly our late lamented Bach. If ever a musician brought the most hidden secrets of Harmony into artistic practice, it was certainly our Bach. BD III, Doc. 666

Hat jemals ein Componist die Vollstimmigkeit in ihrer größten Stärke gezeiget; so war es gewiß unser seeliger Bach. Hat jemals ein Tonkünstler die verstecktesten Geheimnisse der Harmonie in die künstliche Ausübung gebracht; so war es gewiß unser Bach.

Heinrich Georg Neuss, Kurtzer Entwurf von der Music (Leipzig: J. S. Heinsius, 1754). 1754-I

When the Holy Spirit himself participates in the music, the art takes on the correct heavenly Harmony and arouses a fervent devotion. However, where the spirit of the world is at work [in the music], art lets itself be seen and arouses admiration. However, the correct harmonic entry into the minds [of people] is lacking; what remains is devotion, which should be the main purpose of music. A mind well ordered by the Holy Spirit recognises in itself, whether singer or musician, the

Wann der heilige Geist selbst in der Music mitwircket, so kommt die Kunst in ihre rechte himmlische Harmonie, und erwecket eine innigliche Andacht. Wo aber der Welt-Geist das Werck treibet, so mag gar wohl die Kunst sich blicken lassen und Verwunderung erwecken, es fehlet aber der rechte harmonische Eingang in die Gemüther und [es] bleibet die Andacht, welche doch der eigentliche Zweck der Music seyn soll, zurucke. Ein im heiligen Geiste wohl geordnetes Gemüthe vernimmt bald in ihm selbsten,

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spirit of the world or the spirit of God. Cap III, §4, 117 For it [music] is first [of all] a bright mirror of the eternal invisible God, from whom it has its origins . . . Therefore music retains the prize above many other works in creation, not only because of its external Harmony, but also on account of its secret power, which lies hidden in its internal proportion, number, measure and form, which is the clearest and most beautiful mirror of the eternal Godhead. Cap. I, §2, 92

wer Sänger oder Spielmann sey, den WeltGeist oder den Geist Gottes. Denn sie ist erstlich, ein heller Spiegel des ewigen unsichtbahren Gottes, aus dem sie ihren Ursprung hat . . . Also behält für vielen andern Wercken der Schöpfung die Musica den Preiß, daß sie nicht allein ihrer äusserlichen Harmonie nach, sondern auch wegen ihrer geheimen Kraft, welche in der inwendigen Proportion, Zahl, Maaß und Forma verborgen lieget; sey der allerdeutlichste und herrlichste Spiegel der ewigen Gottheit.

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References to tables are given in bold type. Austria VIENNA Österreichische Nationalbibliothek (A-Wn) S. H. J. S. Bach 102. Musical Offering (BWV 1079), original print. Handwritten title by J. F. Reichardt, 236 Belgium BRUSSELS Bibliothèque Royale, Bruxelles (B-Br), Ms. II. 4085 (Fétis Nr. 2910) Suite in G minor for lute (BWV 995), copyist J. S. Bach 156 France PARIS Bibliothèque Nationale, Paris (F-Pn), Paris Ms. 17669. Bach’s personal copy of the original print, Goldberg Variations (BWV 988), and fourteen canons (BWV 1087), copyist J. S. Bach 199–200

396

Germany BERLIN Musikabteilung, Staatsbibliothek zu Berlin (D-B) 30 199, Fascicle 14 ‘Tilge, Höchster, meine Sünden’ (Pergolesi, Stabat Mater) (BWV 1083), copyist J. S. Bach., 319 11495, ‘Gott ist mein König’ printed original vocal and instrumental parts., 321–22 Am. B. 6/7, St Matthew Passion (BWV 244b), copyist J. C. Farlau., 295, 304 Am. B. 54, Fascicle 3, Prelude and Fugue in E minor (BWV 548), copyist Anon 401, 363

Am. B. 60, Fascicle 4, Prelude and Fugue in E minor (BWV 548), copyist unknown, 362, 362, 363 Am. B. 67, Concerto in D minor (BWV 1063), copyist J. F. Agricola, 366 Am. B. 68, Concerto in C major (BWV 1064), copyist J. F. Agricola, 366 Am. B. 78 Brandenburg Concertos (BWV 1046–1051), copyist J. S. Bach, 120, 267–68, 269, 270 P 15, Masses in G major, G minor, F major (BWV 236, 235, 233), copyist J. C. Altnickol, 328, 328 P 16, Mass in A major (BWV 234), copyist J. C. Altnickol, 328 P 25, St Matthew Passion (BWV 244), copyist J. S. Bach, 295, 296–97, 298, 299–300, 301, 302, 305–6, 355 P 28, St John Passion (BWV 245), copyists J. S. Bach, J. N. Bammler, 157, 307, 314–16, 311 P 32, Christmas Oratorio (BWV 248), copyist J. S. Bach, 319, 336, 337–38, 340 P 34, Easter Oratorio (BWV 249), copyist J. S. Bach, 348, 349, 350 P 39, Magnificat in D (BWV 243), copyist J. S. Bach, 319 P 41, Fascicle 1, ‘Tönet, ihr Pauken!’ (BWV 214), copyist J. S. Bach, 336 P 44, Fascicle 2, ‘Bleib bei uns’ (BWV 6), copyist J. S. Bach, 218 P 44, Fascicle 3, ‘Ein Herz, das seinen Jesum lebend weiβ’ (BWV 134), copyist J. S. Bach, 318 P 44, Fascicle 5, Ascension Oratorio (BWV 11), copyists J. S. Bach, C. P. E. Bach, 350, 351

index of sources

P 45, Fascicle 1, ‘Gott ist mein König’, (BWV 71), copyist J. S. Bach, 319, 322 P 67, ‘Die Himmel erzählen die Ehre Gottes’ (BWV 76), copyist J. S. Bach, 287 P 69, ’Du wahrer Gott und Davids Sohn (BWV 23), copyist J. S. Bach, 319 P 102, ’Herz und Mund und Tat und Leben (BWV 147), copyists, J. S. Bach, C. P. E. Bach, J. C. F Bach., 319 P 103, ‘Himmelskönig, sei willkommen’ (BWV 182), copyist J. S. Bach, 263 P 119, ‘Jesus nahm zu sich die Zwölfe’ (BWV 22), copyist J. S. Bach, 319 P 125, ‘Laβt uns sorgen’ (BWV 213), copyist J. S. Bach, 336, 340–41 P 139, ‘Preise dein Glücke’ (BWV 215), copyist J. S. Bach, 340 P 180, B-minor mass (BWV 232), copyist J. S. Bach, later additions by C. P. E. Bach, J. H. Michel, 4, 27, 108, 123, 141, 142, 142, 143, 319, 331, 334, 330–53 P 200, The Art of Fugue (BWV 1080), copyist J. S. Bach, titlepage J. C. Altnickol, additional words C. P. E. Bach, 107, 238, 239–40, 243, 248–50 P 219, Inventions and Sinfonias (BWV 772–801), copyist B. C. Kayser, 166–68, 167, 171–72 P 225, Second Clavierbüchlein for Anna Magdalena Bach, copyists, J. S. Bach, A. M. Bach, C. P. E. Bach., 18, 175–77 P 225, 76–77, Aria from ‘Goldberg Variations’ (BWV 971), copyist A. M. Bach, 197 P 226, Fascicle 1, Ricercar à 6 (BWV 1079/2a), copyist J. S. Bach, 229 P 226, Fascicle 9, 41-65. French Overture in C minor (BWV 831a), copyist A. M. Bach, 63, 177, 179 P 229 Six Sonatas for violin and harpsichord (BWV 1014–1019), copyist J. C. Altnickol, 43, 140, 146, 148, 150, 158 P 234, Harpsichord concertos (BWV 1052–1059), copyist J. S. Bach, 269, 363, 366 P 268, Six Solos for violin (BWV 1001–1006), copyist A. M. Bach, 134, 150 P 269, Six Cello Suites (BWV 1007–1012), copyist A. M. Bach, 134, 151–55

P 271, Fascicle 1, 2-55, Six Trio Sonatas (BWV 525–530), copyist J. S. Bach, 284, 285, 286, 292–93 P 271, Fascicle 2, 1v-20r, 56-95 15 Organ chorales (BWV 651–665), copyist J. S., 28, 215, 217, 293 P 271, Fascicle 2, 1v-20r, 56-95 15 Organ chorales (BWV 651–665), copyist J. S. Bach, 215, 275, 276, 278, 279, 282, 293, 361 P 271, Fascicle 2, 20v-22r, 96–99, 2 Organ chorales (BWV 666–667), copyist J. C. Altnickol, 215, 217, 275, 276, 279, 283, 293 P 271, Fascicle 2, 22v-25v, 100–106, Canonic Variations on ‘Vom Himmel hoch’ (BWV 769a), copyist J. S. Bach, 205, 209, 210, 215, 283, 292–93 P 271, Fascicle 2, 25v, 106, Fragment of Organ chorale (BWV 668), copyist unknown, 215, 276, 279, 293 P 272, Six Trio Sonatas (BWV 525530), copyists A. M. Bach, W. F. Bach, 288 P 274, Fascicle 1, Prelude and Fugue (BWV 547), copyist J. P. Kellner, 360 P 274, Fascicle 2, Prelude and Fugue (BW 548), copyists J. S. Bach, J. P Kellner., 285, 360 P 276, Six Preludes and Fugues (BWV 543–548), unknown copyists, 362 P 280, Concerto transcriptions (BWV 972–980, 592, 981-2), copyist J. B. Bach. Titlepage J. E. Bach., 127, 257, 259, 260–61, 262, 263–66, 365 P 283, Orgelbüchlein (BWV 599-644), copyists J. S. Bach, and unknown., 358 P 286, Fascicle 1, Prelude and Fugue (BWV 545/1 and 2), copyist J. P Kellner, 361 P 286, Fascicle 4, Prelude and Fugue (BWV 547), copyist unknown, corrections by J. C. Westphal, 361 P 401 The Well-Tempered Clavier Book 1, (BWV 846–869), copyist B. C. Kayser, 162, 164, 171 P 415 The Well-Tempered Clavier Book 1, (BWV 846–869), copyist J. S. Bach, 159, 160, 161, 162–64, 169, 171, 355

397

398

index of sources

Germany (cont.) P 610 Aufrichtige Anleitung, (BWV 772–801), copyist J. S. Bach, 156, 165, 169, 171, 172 P 612 Concerto in C minor (BWV 1062), copyist J. S. Bach, 365 P 801, Organ chorale ‘Allein Gott in der Höh’ (BWV 664a) copyist J. T. Krebs, 277 P 802, Organ chorales (BWV 651a–667b), copyists J. T. Krebs and J. G. Walther, 277 P 803, Fascicle 19, Organ chorale ’Allein Gott in der Höh) (BWV 663a) copyist J. T. Krebs, 277 P 804, Fascicle 22, 121–145. Five Solos for violin (BWV 1001, 1003–1006), copyist J. P. Kellner, 134, 142, 144–45, 158 P 804, Fascicles 54-56. Three Concerto transcriptions (BWV 973, 972, 977), copyists unknown, 258–59 P 967, Six Solos for violin (BWV 1001–1006), copyist J. S. Bach, 21, 133, 135, 137–38, 140, 143, 145, 145, 149, 150 P 1072, English Suites (BWV 806–811), copyist B. C. Kayser, 356, 357 P 1145 ‘Gloria in Excelsis Deo’ (BWV 191), copyist J. S. Bach, 319 St 111, Fascicles 1–4, Vocal and instrumental parts, St John Passion BWV 245, versions 1-4), copyists, J. S. Bach, J. A. Kuhnau, J. C. Köpping, C. G. Meiβner, J. H. Bach, J. N. Bammler, J. C. F Bach and others, 310 St 112, Vocal and instrumental parts, Christmas Oratorio (BWV 232), copyists J. S. Bach and many others, 336, 344, 347 St 118, Vocal and instrumental parts, B-minor mass (BWV 232), copyists J.S.B and others, 4 St 130, Instrumental parts, Fifth Brandenburg Concerto (BWV 1050), copyists J. S. Bach, J. C. F. Bach, 267, 273 St 132, fascicle 1. Instrumental parts, Fifth Brandenburg Concerto (BWV 1050a), copyist J. C. Farlau, 267, 270, 272 St 136, Concerto in C minor (BWV 1060), copyist J. C. Altnickol., 365

St 139, Concerto in C major (BWV 1061), copyist A. M. Bach, 365 St 162, Instrumental parts, Six Sonatas for violin and harpsichord (BWV 1014–1019a), copyists J. S. Bach, J. H. Bach, 108, 136, 146, 147, 355 St 355, Vocal and instrumental parts, Easter Oratorio, copyist J. S. Bach, J. A. Kuhnau, C. G. Meiner, J. N. Bammler., 348 St 377, Fascicle 1, Vocal and instrumental parts, ‘Gott ist mein König’ (BWV 71), copyist J. S. Bach., 322 Mus. ms. 40644, Möller manuscript, (63v-65v), Capriccio (BWV 992), copyist J. C. Bach, 51 DARMSTADT, Universitäts- und Landesbibliothek, Handschriften und Musikabteilung (D-DS) Mus. ms. 972, Missa in G major (BWV 236), copyist J. S. Bach, 328 DRESDEN Sächsische Landesbibliothek (D-Dl) Mus. 2405-D-21, the Dresden Parts of the B-minor Mass, copyists J. S. Bach, C. P. E. Bach. A. M. Bach, W. F. Bach, 330 LEIPZIG Bach-Archiv Leipzig (D-LEb) Thomana 93, Fascicle 1, ‘Wer nur den lieben Gott läβt walten’ (BWV 93), copyists J. G. Haupt, J. S. Bach, 218 Thomana 137, ‘Lobe den Herrn’ (BWV 137) copyists J. S. Bach, J. A. Kuhnau, A. M. Bach J. C. Bach., 218 Thomana 140, ‘Wachet auf’ (BWV 140), copyists J. S. Bach, J. G. Haupt, J. L Krebs., 218 Stadtbibliothek, Music Library (D-LEm) Poel. mus. Ms. 29, Concerto transcriptions (BWV 592a, 984, 983, 973), copyist Anon 430, 257–59 Rar Ib, 59 (formerly D-Gb Ms. Scholz 5.2.4), Italian Concerto (BWV 971), copyist L. Schulz, 178 Universitätsbibliothek (D-LEu) N. I. 5138, Concerto in C major (BWV 594), copyist W. F. Bach, 256 Great Britain LONDON

index of sources

London, British Library (GB-BL) Hirsch III. 37, Bach’s personal copy of the print of Clavier Übung I (BWV 825–830) Stefan Zweig Collection MS 1, copyist J. S. Bach, 320 Japan TOKYO Musashino Music School, Tokyo (J-Tma) Littera rara vol, 2-14, Lute solo (BWV 1006a), copyist J. S. Bach, 139 Ueno Gakuen College, Tokyo (J- Tuu) No callmark, Lute solo (BWV 998), copyist J. S. Bach, 157 Poland, KRAKÒW Krakòw, Biblioteca Jagiellonska (PL-Kj) Mus. ms. Bach St 356, copyists J. S. Bach, R. Straube, 350 United States BOSTON Boston Public Library, Music Department (US-Bp) Ms. M. 200.12, Italian Concerto (BWV 971) copyist J. C. Oley, 177

NEW HAVEN, CT Yale University, School of Music Library (US-NH) Deposit 31, Clavier-Büchlein for Wilhelm Friedemann Bach, copyist mostly J. S. Bach, 162 M 4708, Neumeister Collection, (including BWV 1090-1095, 1097–1120), copyist J. G. Neumeister, 290, 358, 361 NEW YORK New York City. Kallir-Frank private collection (US-NYkallir) No callmark ‘Aus die Tiefen rufe ich, Herr, zu dir’ (BWV 131), copyist J. S. Bach, 319 WASHINGTON DC Washington Library of Congress (US-Wc) ML 30 8b B 2 M 4 (Whittall Collection), ‘Meine Seel erhebt den Herren’ (BWV 10), copyist J. S. Bach, 218 ML 96 B 186 French Suites (BWV 812–817), copyist J. C. Altnickol, 356, 357

399

Index

References to tables are given in bold type. acrostic, 6, 12, 39, 42–4, 211, 230 Agricola, Johann Friedrich (1770–74), 18, 73, 128, 204–17, 238, 354–6, 363, 366 Ahle, Johann Georg (1651–1706), 42 Alain, Olivier (1918–94), 200 alchemy, 57 aliquot numbers, 103 alphabets, number, 5–6, 44, 57, 67, 323–4, 347–8, 366–9 milesian, 12, 44, 47, 57, 67 natural order, 12, 68, 232, 234–5, 237–8, 293, 324, 344 parallel, 266 trigonal, 44, 67 Altnickol, Elisabeth Juliana Frederica (1726–81), 279 Altnickol, Johann Christoph (1720–59), 240, 279, 303–4, 367 copies The Art of Fugue, 240, 251–2 French Suites, 356–9, 357 Lutheran Masses, 328 Six Sonatas (BWV 1014–1019), 158, 215, 140, 146–9 Leipzig Organ Chorales additions, 276, 279, 282–4, 293 Ammon, Johann Christoph, 83 anagram, 6, 39, 42, 61 Anise anisum, 53 Anna Amalia of Prussia, Princess (1723–87), 267 architecture, 19–20, 37, 98–9, 106, 112–13 Aristotle (384–322 BCE), 367 Arnstadt, 51

400

B and H, 12, 27, 62 B-A-C-(H) form, 12, 27, 252–3 in bar numbers, 211, 290 in key signature across works, 27, 68, 145, 173, 178–9, 363 in melodies, 62, 211, 238, 241, 246 intervallic symmetry, 103–4

in number alphabets, 65–8, 198, 266–74 permutation, 12, 69–70, 211, 243, 247, 289, 347, 353 Bach, Anna Magdalena (1701–60), 69, 155–8, 306, 356 numerical value of name, 69 transcriptions Clavierbüchlein, 1722, 356 Clavierbüchlein, 1725, 175, 197 French Overture in C minor, 177 Six Cello Suites, 149 Six Solos for violin (BWV 1001–1006), 134, 136–41, 151–5 Trio Sonatas (BWV 525–30), 287–8 Bach, Carl Philipp Emanuel (1714–86), 73, 94–6, 204, 221–2, 291, 293, 327, 354–6, 359 on Bach as teacher, 47, 96 Bach’s obituary, 238, 381 on Bach’s unfinished fugue, 240 numerical value of name, 68 publications, 104, 240 Bach, Johann August (1745–89), 208 Bach, Johann Bernhard (1676–1749), 257, 259, 260–1, 265 Bach, Johann Christoph (1642–1703), uncle to JSB, 359 Bach, Johann Christoph, brother to JSB (1671–1721), 49 Bach, Johann Christoph Friedrich, son to JSB (1732–95), 240–1, 267 Bach, Johann Elias (1705–55), 182 Bach, Johann Ernst (1722–77), 259 Bach, Johann Heinrich (1707–83), 140, 147, 222 Bach, Johann Nicolaus (1669–1753), 61 Bach, Johann Sebastian (1685–1750) for works ordered by BWV number see Bach-Werke-Verzeichnis

index

Art of Fugue (BWV 1080), 28, 30, 33, 43, 107, 127, 144, 198, 238–54, 242, 243, 244, 246, 249–50, 281, 287 Ascension Oratorio (BWV 11), 28, 31, 350–3 Aufrichtige Anleitung (BWV 772–801), 26, 32–3, 68, 164–6, 165, 168–72, 171, 174, 290, 290 Invention No.6 in E major (BWV 777), 164 Sinfonia No.2 in C minor (BWV 788), 166 Brandenburg Concertos (BWV 1046–51), 30–1, 266–74, 269, 271, 355 Brandenburg Concerto No.4 (BWV 1049), 21, 123, 270–2 Brandenburg Concerto No.5 (BWV 1050), 270, 272, 273–4 Canonic Variations (BWV 769), 30, 204–17, 214, 216–17, 234 canons (miscellaneous) Canon a 4 (BWV 1074), 30 Canon triplex a 6 (BWV 1076), 116 Fourteen canons (BWV 1087), 199–203, 200, 212 cantatas ‘Aus der Tiefen rufe ich, Herr, zu dir’ (BWV 131), 321 ‘Bleib bei uns, denn es will Abend werden’ (BWV 6), 218–19 ‘Du sollt Gott, deinen Herren, lieben’ (BWV 77), 5 ‘Du wahrer Gott und Davids Sohn’ (BWV 23), 319 ‘Ein Herz, das seinen Jesum lebend weiß’ (BWV 134), 318 ‘Entfliehet, verschwindet, entweichet, ihr Sorgen’ (BWV 249a), 348 ‘Gott der Herr ist Sonn und Schild’ (BWV 79), 327 ‘Gott ist mein König’ (BWV 71), 30, 319, 319–25, 324, 329 ‘Herr, deine Augen sehen nach dem Glauben’ (BWV 102), 327 ‘Herz und Mund und Tat und Leben’ (BWV 147), 319 ‘Ich freue mich in dir’ (BWV 134), 318 ‘Jesus nahm zu sich die Zwölfe’ (BWV 22), 319 ‘Kommt, fliehet und eilet’ (BWV 249), 349 ‘Laβt uns sorgen, laβt uns wachen’ (BWV 213), 341 ‘Meine Seel erhebt den Herren’ (BWV 10), 218–19

‘Siehe zu, dass deine Gottesfurcht’ (BWV 179), 327 ‘Verjaget, zerstreuet, zerrütet, ihr Sterne’ (BWV 249b), 349 ‘Wer nur den lieben Gott lässt walten’ (BWV 93), 219 ‘Wo soll ich fliehen hin’ (BWV 5), 319–20 Christmas Oratorio (BWV 248), 22, 29, 302, 319, 336–48, 337–8, 341, 342–3, 345–6 Clavier Übung series, 97, 180, 202, 353 Clavier Übung I (BWV 825–830), 30, 64, 64, 126, 172–81, 173, 174, 179, 180, 290 Partita 1 (BWV 825), 172, 175–7, 176 Partita 2 (BWV 826), 23, 25, 172, 174, 177 Partita 3 (BWV 827), 172, 175 Partita 4 (BWV 828), 4–6, 23, 172, 179 Partita 5 (BWV 829), 25, 172, 180 Clavier Übung II (BWV 831, 971), 64, 143, 173, 173, 174, 290 Italian Concerto (BWV 971), 30, 64, 177, 179 French Overture in B minor (BWV 831), 25, 27, 30, 63, 173 French Overture in C minor (BWV 831a), 27, 177 Clavier Übung III (BWV 669–689, 802–5), 28, 43, 123, 182–90, 187, 213, 221–2, 292, 362, 31–2 chorale preludes (BWV 669–689), 184, 185, 189 Vater unser im Himmelreich (BWV 682–683), 189 Wir glauben all an einen Gott and Fughetta: Wir glauben all an einen Gott (BWV 680–681), 189 Prelude and Fugue in E♭ major ‘St Anne’ (BWV 552), 186, 192 Clavier Übung IV, see Goldberg Variations Early Keyboard Transcriptions (BWV 972–82, 592). 258 BWV 972–4, 264 BWV 972–977, 262–3, 262 BWV 972–982, 173, 262, 263 592, 255–66 BWV 972–987, 31 BWV 977–982, 366 BWV 978–980, 264 Easter Oratorio (BWV 249), 28, 31, 348–53, 349

401

402

index

Bach, Johann Sebastian (1685–1750) (cont.) English Suites (BWV 806–811), 31, 356, 357 French Suites (BWV 812–817), 31, 355, 356–9, 357 Goldberg Variations (BWV 988), 22, 28, 30, 190–7, 192, 195, 201, 281 Great Six Organ Preludes and Fugues (BWV 543–8), 360, 362 Prelude and Fugue in E minor, ‘The Wedge’ (BWV 548), 248, 363 Harpsichord Concertos (BWV 1052–64) BWV 1052–65, 28, 365 BWV 1052–57, 364, 365 Harpsichord Concerto 6 in F major (BWV 1057), 21–2, 123, 269 Leipzig Organ Chorales (BWV 651–668), 28, 31 BWV 651–663, 275–93 BWV 651–665, 189 ‘Allein Gott in der Höh sey Ehr’ (BWV 664a), 281 ‘Fantasia super “Kom, heiliger Geist”’ (BWV 651), 280–1 ‘Jesus Christus, unser Heyland’ (BWV 665a), 281 ‘Jesus Christus, unser Heyland’ (BWV 666), 279 ‘Komm, Gott Schöpfer, heiliger Geist’ (BWV 667), 279 ‘Nun danket alle Gott’ (657a), 280 ‘Nun komm der Heyden Heyland’ (BWV 661a), 280 ‘Von Gott will ich nicht lassen’ (BWV 658a), 280 ‘Vor deinen Thron tret ich hiermit’ (BWV 668), 279 Magnificat in D major (BWV 243), 319 Mass in A major (BWV 234), see Masses, Lutheran Mass in B minor (BWV 232), 4, 22, 24–5, 28, 30–2, 108, 121–9, 310, 319, 330–6, 334 Masses, Latin, 326–30 Masses, Lutheran (BWV 233–6), 326–30, 328 Missa in A major (BWV 234), 31, 329, 331, 331 Missa in B minor (BWV 232 I), 27, 121, 123, 306 Musical Offering (BWV 1079), 30, 213, 224–38, 228, 231–2, 288

Neumeister Chorales (BWV 1090–1120), 290, 359 Oratorios, Ascension BWV 11: Lobet Gott in seinen Reichen, 28, 31, 350–3, 351–2 Christmas (BWV 248), 22, 29, 302, 319, 336–48, 337–8, 341, 342–3, 345–6 Easter (BWV 249), 28, 31, 348–53, 352 Organ Concerto in G major (BWV 592), 264 Orgelbüchlein (BWV 599–644), 31, 96, 358 ‘Christus, der uns selig macht’ (BWV 620), 359 ‘Helfft mir Gottes Güte preisen’ (BWV 613), 359 ‘Kom, Gott Schöpfer, heiliger Geist’ (BWV 631), 359 Passions St. John Passion (BWV 245), 31, 294, 306–17, 308, 311–12, 314 St. Mark Passion (BWV 247), 317–18, 343 St. Matthew Passion (BWV 244), 22–3, 25, 30–1, 43, 295–302, 296–7, 325, 355 Prelude in B minor (BWV 923), 162 Schübler Chorales (BWV 645–50), 30, 212, 213, 217–23, 219–23, 219, 234, 293 Six Solos for violin (BWV 1001–6), 21, 24, 27, 29, 33, 64, 133–45, 134–6, 136–41, 140, 149, 355 numerical structure, 135 Sonata 1 for solo violin in G minor (BWV 1001), 136, 137 Partita 1 for solo violin in B minor (BWV 1002), 24, 137, 143 Sonata 2 for solo violin in A minor (BWV 1003), 143 Partita 2 for solo violin in D minor (BWV 1004), 23 Sonata 3 for solo violin in C major (BWV 1005), 248 Partita 3 for solo violin in E major (BWV 1006), 21, 138–9 Suite in E major for lute (BWV 1006a), 139 Six Cello Suites (BWV 1007–1012), 31, 149–58, 152 Suite 1 in G major for solo cello (BWV 1007), 155 Suite 5 in C minor for solo cello (BWV 1011), 150, 156 Suite 6 in D major for solo cello (BWV 1012), 151, 153, 154 Six Toccatas (BWV 911–16), 356

index

Six Trio Sonatas (BWV 525–530), 25, 31, 215, 284–92, 286, 290, 355, 292–3 Sonatas for Violin and Harpsichord (BWV 1014–19), 27, 29, 31, 64, 140, 148–9, 355, 146–9, bar structure, 147 Sonata 6 in G major (BWV 1019), 32–3, 148 Sonata 6 in G major (BWV 1019a), 43, 175 Suites for Lute (BWV 995–98, 1006a), 139, 355 Prelude, Fugue and Allegro in E♭ major (BWV 998), 157 Suite in G Minor (BWV 995), 156 Suites for Orchestra (BWV 1066–69), 355 Suscepit Israel puerum suum (BWV 1082), 327 Tilge, Höchster, meine Sünden (BWV 1083), 319 Violin Concertos (BWV 1041–43), 355 The Well-Tempered Clavier (BWV 846–893), 26, 31–2, 159, 161, 168–72 Book 1 (BWV 846–869), 174, 188, 191, 290, 290, 355 Prelude and Fugue in C minor (BWV 847), 162 Prelude and Fugue in B♭ minor (BWV 867), 162 Book 2 (BWV 870–893), 281, 355 Prelude and Fugue in F minor (BWV 881), 162 birthday, 12, 70, 347–8 as book sales agent, 17–18 moonlight transcription anecdote, 120 name in numbers, 27, 66–7 obituary, 238, 242, 354–6, 381 as Pachelbel’s student, 49 as teacher, 47, 94, 96 in Cöthen, 133, 146, 150 in Leipzig, 93, 100, 159, 182, 360 in Lübeck, 336 in Weimar, 127, 133, 150, 321 Bach, Johann Sebastian (b. 1749), 291 Bach, Johanna Carolina (1737–81), 46 Bach, Johanna Judith, sister to JSB (1680–86), 49 Bach, Maria Barbara (1684–1720), 68 Bach, Wilhelm Friedemann (1710–84), 160, 256, 287, 291, 293, 321 Clavier-Büchlein vor, 32, 160, 162–3, 163, 166, 167, 290

transcriptions, Trio Sonatas (BWV 525–30), 284 writing, 88 Bach-Werke-Verzeichnis (BWV), BWV 2a BWV 5: ‘Wo soll ich fliehen hin’, 319–20 BWV 6: ‘Bleib bei uns, denn es will Abend werden’, 218–19 BWV 10: ‘Meine Seel erhebt den Herren’, 218, 219 BWV 11: ‘Lobet Gott in seinen Reichen’ (Ascension Oratorio), 28, 31, 350–3, 351–2 BWV 17: ‘Wer Dank opfert, der preiset mich’, 328 BWV 22: ‘Jesus nahm zu sich die Zwölfe’, 319 BWV 23: ‘Du wahrer Gott und Davids Sohn’, 319 BWV 40: ‘Darzu ist erschienen der Sohn Gottes’, 328 BWV 71: ‘Gott ist mein König’, 30, 319–25, 324, 329 BWV 67: ‘Halt im Gedächtnis Jesum Christ’, 329 BWV 77: ‘Du sollt Gott, deinen Herren, lieben’, 5 BWV 79: ‘Gott der Herr ist Sonn und Schild’, 327 BWV 93: ‘Wer nur den lieben Gott lässt walten’, 219 BWV 102: ‘Herr, deine Augen sehen nach dem Glauben’, 327 BWV 131: ‘Aus der Tiefen rufe ich, Herr, zu dir’, 319 BWV 134: ‘Ich freue mich in dir’, 318 BWV 136: ‘Erforsche mich, Gott’ 329 BWV 138: ‘Warum betübst du dich, mein Herz’ 328 BWV 147: ‘Herz und Mund und Tat und Leben’, 319 BWV 179: ‘Siehe zu, dass deine Gottesfurcht’, 327 BWV 187: ‘Es wartet alles auf dich’, 328 BWV 213: ‘Laβt uns sorgen, laβt uns wachen’, 341 BWV 232: Mass in B minor, 4, 22, 24–5, 28, 30–2, 108, 121–9, 310, 319, 330–6, 334 BWV 233–6: Lutheran Masses, 326–30 BWV 234: Mass in A major, 31, 329, 329, 331, 331 BWV 243: Magnificat in D major, 319

403

404

index

Bach-Werke-Verzeichnis (BWV), BWV 2a (cont.) BWV 244: St. Matthew Passion, 22–3, 25, 30–1, 43, 295–302, 296–7, 325, 355 BWV 245: St. John Passion, 31, 294, 306–17, 308, 311–12, 314 BWV 247: St. Mark Passion, 343, 317–18 BWV 248: Christmas Oratorio, 22, 29, 302, 319, 336–48, 337–8, 341, 342–3, 345–6 BWV 249: Easter Oratorio, 28, 31, 348–53, 349, 352 BWV 525–30: Organ Sonatas, 25, 31, 215, 286, 290, 292–3, 355 BWV 543–8: Great Six Organ Preludes and Fugues, 360, 362 BWV 548: Great Six Organ Preludes and Fugues, 248, 363 BWV 592: Organ Concerto in G major, 264 BWV 599–644: Orgelbüchlein, 31, 96, 358 BWV 613: ‘Helft mir Gottes Güte preisen’ (Orgelbüchlein), 359 BWV 620: ‘Christus, der uns selig macht’ (Orgelbüchlein), 359 BWV 631: ‘Komm, Gott Schöpfer, heiliger Geist’ (Orgelbüchlein), 359 BWV 645–50: Schübler Chorales, 30, 212, 213, 217–23, 219–23, 219, 234, 293 BWV 651: Fantasia super “Kom, heiliger Geist” (Leipzig Organ Chorales), 280–1 BWV 651–63: Leipzig Organ Chorales, 275–93 BWV 651–65: Leipzig Organ Chorales, 189 BWV 651–68: Leipzig Organ Chorales, 28, 31 BWV 657a: ‘Nun danket alle Gott’ (Leipzig Organ Chorales), 280 BWV 658a: ‘Von Gott will ich nicht lassen’ (Leipzig Organ Chorales), 280 BWV 661a: ‘Nun kom der Heyden Heyland’ (Leipzig Organ Chorales), 280 BWV 664a: ‘Allein Gott in der Höh sey Ehr’ (Leipzig Organ Chorales), 281 BWV 665a: ‘Jesus Christus, unser Heyland’ (Leipzig Organ Chorales), 281 BWV 666: ‘Jesus Christus, unser Heyland’ (Leipzig Organ Chorales), 279 BWV 667: ‘Komm, Gott Schöpfer, heiliger Geist’ (Leipzig Organ Chorales), 279 BWV 668: ‘Vor deinen Thron tret ich hiermit’ (Leipzig Organ Chorales), 279

BWV 669–88: Chorale settings in Clavier Übung III, 184, 185 BWV 680–1: “Wir glauben all an einen Gott /Fughetta; Wir glauben all aneinen Gott” (Clavier Übung III), 189 BWV 682–3: “Vater unser im Himmelreich” (Clavier Übung III), 189 BWV 740: “Wir glauben all an einen Gott,” 276 BWV 769: Canonic Variations, 30, 204–17, 214, 216–17, 234 BWV 772–801: Aufrichtige Anleitung, 26, 32–3, 68, 164–6, 165, 168–72, 171, 174, 290, 290 BWV 777: Invention 6 in E major (Aufrichtige Anleitung), 164 BWV 788: Sinfonia 2 in C minor (Aufrichtige Anleitung), 166 BWV 802–5: Duetti from Clavier Übung III, 189 BWV 803: Duetto 2 in F major (Clavier Übung III), 186 BWV 804: Duetto 3 in G major (Clavier Übung III), 186 BWV 806–11: English Suites, 31, 356, 357 BWV 812–7: French Suites, 31, 355, 356–9, 357 BWV 825: Partita 1 (Clavier Übung I), 172 BWV 825–6: Clavier Übung I, 175–7, 176 BWV 825–30: Clavier Übung I, 26, 30, 126 BWV 826: Partita 2 (Clavier Übung I), 23, 25, 174 BWV 826–7: Partitas.2–3 (Clavier Übung I), 172 BWV 827: Partita 3 (Clavier Übung I), 175 BWV 828: Partita 4 (Clavier Übung I), 23, 172 BWV 828–30: Partitas 4–6 (Clavier Übung I), 43, 179 BWV 829: Partita 5 (Clavier Übung I), 25, 172 BWV 831: French Overture in B minor (Clavier Übung II), 25, 30, 63, 173 BWV 831a: French Overture in C minor (Clavier Übung II), 177 BWV 846–93: The Well-Tempered Clavier, Books 1–2, 26, 31–2, 159, 168–72 BWV 846–69: The Well-Tempered Clavier, Book 1, 161, 174, 188, 290, 290, 355 BWV 847: Prelude and Fugue in C minor (The Well-Tempered Clavier, Book 1), 162

index

BWV 867: Prelude and Fugue in B♭ minor (The Well-Tempered Clavier, Book 1), 162 BWV 870–93: The Well-Tempered Clavier, Book 2, 281, 355 BWV 881: Prelude and Fugue In F minor (The Well-Tempered Clavier, Book 2), 162 BWV 911–6: Six Toccatas, 356 BWV 923: Prelude in B minor, 162 BWV 971: Italian Concerto, 30, 64, 173, 177, 179–80 BWV 972–4: Early Keyboard Transcriptions, 264 BWV 972–7: Early Keyboard Transcriptions, 262–3, 262 BWV 972–82, 592: Early Keyboard Transcriptions, 255–66, 262 BWV 972–87: Early Keyboard Transcriptions, 31 BWV 977–82: Early Keyboard Transcriptions, 366 BWV 978–80: Early Keyboard Transcriptions, 264 BWV 978–82: Early Keyboard Transcriptions, 263 BWV 988: Goldberg Variations, 22, 30, 190–7, 192, 195, 201, 281 BWV 995: Suite in G Minor (Suites for Lute), 156 BWV 995–8, 1006a: Suites for Lute, 139, 355 BWV 998: Prelude, Fugue and Allegro in E♭ major (Suites for Lute), 157 BWV 1001: Sonata 1 in G minor (Six Solos for Violin ), 136, 137 BWV 1001–6: Six Solos for Violin, 21, 27, 29, 33, 64, 133–45, 140, 355 BWV 1002: Partita 1 in B minor (Six Solos for Violin ), 24, 137, 143 BWV 1003: Sonata 2 in A minor (Six Solos for Violin ), 143 BWV 1004: Partita 2 in D minor (Six Solos for Violin ), 23 BWV 1005: Sonata 3 in C major (Six Solos for Violin ), 248 BWV 1006: Partita 3 in E major (Six Solos for Violin ), 21, 138–9 BWV 1007: Suite 1 in G major (Six Cello Suites), 155 BWV 1007–12: Six Cello Suites, 31, 149–58 bar structure 154–5

BWV 1011: Suite 5 in C minor (Six Cello Suites), 150, 156 BWV 1012: Suite 6 in D major (Six Cello Suites), 151, 153, 154 BWV 1014–9: Sonatas for Violin and Harpsichord, 27, 29, 31, 64, 140, 148–9, 355 BWV 1019: Sonata 6 in G major (Sonatas for Violin and Harpsichord), 32–3, 148 BWV 1019a: Sonata 6 in G major (Sonatas for Violin and Harpsichord), 175 BWV 1041–3: Violin Concertos, 355 BWV 1046–51: Brandenburg Concertos, 30, 31, 266–74, 269, 271, 355 BWV 1049: Brandenburg Concerto 4 (Brandenburg Concertos), 21, 270–2 BWV 1050: Brandenburg Concerto 5 (Brandenburg Concertos), 270, 272, 273–4 BWV 1052–57: Harpsichord Concertos, 364, 365 BWV 1052–65: Harpsichord Concertos, 28, 365 BWV 1057: Harpsichord Concerto 6 in F major (Harpsichord Concertos), 21–2, 269 BWV 1057/1: Harpsichord Concerto 6 in F major (Harpsichord Concertos), 22, 123 BWV 1060–5: Concertos for 2 Harpsichords (Harpsichord Concertos), 364 BWV 1063–4: Concertos for 2 Harpsichords (Harpsichord Concertos), 364 BWV 1066–9: Suites for Orchestra, 355 BWV 1074: Canon a 4, 30 BWV 1076: Canon triplex a 6, 116 BWV 1079: Musical Offering, 30, 213, 224–38, 228, 231–2, 288 BWV 1080: The Art of Fugue, 28, 30, 33, 43, 107, 127, 144, 198, 238–54, 242, 244, 245, 246, 249–50, 281, 287 BWV 1082: Suscepit Israel puerum suum, 327 BWV 1083: Tilge, Höchster, meine Sünden, 319 BWV 1087: Fourteen Canons, 199–203, 200, 212 BWV 1090–1120: Neumeister Chorales, 290 Bammler, Johann Nathanael (1722–84), 307–9, 314, 316

405

406

index

bar, 113–16 building blocks see building blocks counting, 120–9 evidence, 20–6 da capo, 21–2 non-conformist, 23 repeats, 20 half-bar, 24 measurement, 116–20 non-conformist, 23 time signature as see TS feature beats (within bars), 110 Becker, August (1668–1750), 71 Beer, Johann (1655–1700), 47–50 Bernhard, Johann Gottfried (1715–39), 265 Besseler, Heinrich (1900–69), 268, 270 Bible Old Testament Genesis 6:15, 59 24:6, 59 45:22, 59 Exodus 25:17, 80 1 Samuel 18:7, 59 1 Kings, 11, 59 Psalms, 60 74:12, 323, 324 119:72, 59 Sirach 33:33–34, 44 Isaiah 5:11–13, 373 New Testament 1 Corinthians 13:12, 59, 86 Matthew 26:1–56, 302 black magic, 44 Boethius (c. 480–525 CE), 73–4 Bokemeyer, Heinrich (1679–1751), 17, 84, 86–7, 96, 111–12, 200 Bongus, Petrus (d. 1601), 58 Bourée, 111, 135, 152, 154, Breig, Werner, 194–5, 197, 279 Breitkopf, Bernhard Christoph (1695–1777), 56, 235 printing, 226, 235 Brockes, Barthold Heinrich (1680–1747), 310 building blocks (of bars), 33, 141, 155, 195–6, 215, 218, 229, 236–7, 288–91, 313, 315, 317, 351, 363, 367 Burke, Edmund (1729–97), 99 Butler, Gregory, 31–2, 126, 183, 189, 205, 208, 211, 216–17, 225–7, 229, 242, 252 Butt, John, 150, 155, 195, 285, 287, 333 Buttstett, Johann Heinrich (1666–1727), 10, 13, 16, 54, 92, 103, 164, 253, 368, 376

Mattheson dispute, 14, 38, 52–3, 78–83, 88–9 cabbala, 42–4 cadence, 39, 115 calendars, 56, 70, 220 Calov, Abraham (1612–86), 86 Bible commentary, 28, 215, 303 cantata form, 116, 118–20, 218, 318–25, 337 see also collections and works, cantatas chiastic forms, 316 chorales, 28, 90, 184, 189, 204, 292–3 Christensen, Thomas, 9, 85 Christian Ludwig, Margrave of Brandenburg (1677–1734), 267 Christian of Saxe-Weissenfels, (1682–1736), 268, 348 chronogram, 6, 43, 47–50 clocks, 118 collegium musicum, 84 compositional planning, 14, 50, 105–7, 109, 129 units of measurement, 112–20 consonance, 77–8, 85, 88, 102, 93–4 Cöthen, 16, 100, 133, 146, 160 Crüger, Johann (1598–1662), 88 da capo, 303, 21–2 dance, 111, 114 decoration, 19, 36–8, 55, 111 devotion, 51, 84, 91, 96–7, 336–48 Dehn, Siegfried Wilhelm (1799–1858), 364 dispositio, 106, 128 dissonance, 85, 102, 371, 93–4 double proportion, 40 Dunsby, Jonathan, 34 Dürer, Albrecht (1471–1528), 38 Dürr, Alfred (1918–2011), 315, 340 elaboration, 19 emblems, 11, 28, 51 engravings, 32, 121–9, 205–11 Butler’s reconstructions, 183 dedicatory, 55 errors, 193–7, 227 Bach’s supervision of process, 241, 243 Enlightenment, 7 Eppstein, Hans (1911–2008), 32 Erfurt, 17, 42, 49, 53, 71 Predigerkirche, 86, 89 St. Andrew’s Church, 43 eurythmia, 11, 36–8, 72, 112, 127, 139, 367

index

Walther’s definition, 98, 111, 126–7 see also Gleichförmigkeit; symmetry Faber, Johann Christian (1669–1744), 57 Farlau, Johann Christoph (c.1735–70), 267, 295, 304 Fibonacci sequence, 105 Fludd, Robert (1564–1637), 75, 80 Forkel, Johann Nikolaus (1749–1818), 61, 127, 191, 221, 255–66, 274, 354, 367–8 Bach biography, 94 Franklin, Don O., 5 Frederick the Great, Friedrich II of Prussia (1712–86), 224, 227, 229 Friedrich Augustus II, Elector of Saxony (1733–63), Augustus III, King of Poland (1734–63) (1696–1763), 330 Fritsch, Thomas, Lexicon, 15, 56, 369 definitions, 17, 36, 80, 97, 109–10, 216, 236, 256 Harmonie, 77–8, 95 Fulde, Johann Gottfried, 53, 199 Fux, Johann Joseph (1660–1741), 62, 78, 91, 100, 368, 380 gavotte, 111, 114 Gerber, Heinrich Nicolaus (1702–75), 18 Gessner, Christian Friedrich (1701–56), 122 Gleichförmigkeit, 37–8, 109–12, 127 Glied, 109 Glöckner, Andreas, 303 Goldberg, Johann Gottlieb (1727–56), 191 golden section, 105 Griepenkerl, Friedrich Konrad (1782–1849), 257 Grimm, Wilhelm (1786–1859) and Jacob (1785–1863), 243 Guido d’Arrezo (991/992–after 1033), 8, 88–9, 103, 164, 376 H and B, 12, 27, 62 Hagelgans, Johann Georg (d. 1765), 59–60 Halle, 17, 37, 71, 100, 162–4 Liebfraukirche, 51 Hamburg, 84, 265 St. Catharine’s Church, 18 Händel, Georg Friedrich (1685–1759), 78 Harmony Bach and, 93–8 behavioural application, 86–8 defining beliefs, 73–8 definitions, 77–8, 95, 99 eternal implication, 88–9

musical harmony and, 78–85 of the spheres, 98 Hartung, Carl August (1723–1800), 257 heathens, 60, 89–90 Heinichen, Johann David (1683–1729), 9, 18, 368, 78 Henrici, Christian Friedrich see Picander hexachord, 8, 81, 103, 103 historically informed theory (HIT), 14–26, 369 Holy Spirit, 84, 281–3, 381 hortus, 316 hour (unit), 118 hourglass, 118 Hudemann, Ludwig Friedrich (1703–70), 71 Hunold, Christian Friedrich (1680–1721), 41–4, 128, 206 Iamblichus (c. 250–325 CE), 73 invention, 128, 237, 303 invention methods, 4–6, 206 composing by numbers, 104 golden section, 105 paragrams and chronograms, 47–50 parallel, 47 Inventionsquelle, 62, 347 Irwin, Joyce L., 83, 380 Johann Ernst, Prince of Saxe-Weimar (1696–1715), 127 Joseph I, Kayser of the Holy Roman Empire (1678–11), 324 Judaism, 89 Kayser, Bernhard Christian (1705–58), 32 transcriptions Aufrichtige Anleitung (P 219), 166–8, 171–81 English Suites (P 1072), 356, 357 The Well-Tempered Clavier I (P 401), 162–4, 171 Kellner, Johann Peter (1705–72), 134–6, 257 transcriptions Preludes and Fugues (P 286), 361 Five Solos for violin (P 804), 134–6, 158 Kepler, Johannes (1571–1630), 74, 105, 369 Kerll, Johann Caspar (1627–93), 327 Keyserlingk, Count Hermann Carl von (1696–1764), 191 Kilian, Dietrich (1928–1984), 285, 287, 360 Kircher, Athanasius (1601–80), 16, 57, 62–3, 100

407

408

index

Kirnberger, Johann Philipp (1721–83), 47, 104, 267, 362 Kittel, Johann Christian (1732–1801), 18, 83, 191 Kittel, Johann Gottlob (Micrander) (1732–1809), 70 Krebs, Johann Ludwig (1713–80), 18, 218 Krebs, Johann Tobias (1690–1762), 18, 277–80 Krügner, Johann Gottfried, senior (1684–1769), 184 Krügner, Johann Gottfried, junior (1714–1782), 184 Krügner, née Boëtius, Rosine Dorothee, 184 Kuhnau, Johann (1660–1722), 12, 50–1, 69, 71, 78, 88, 91, 218, 368 Lämmerhirt, Maria Elisabetha (1644–94), 16 Lämmerhirt, Martha Dorothea (1655–1727), 16, 89 Lange, Herman François de (c.1717–81), 104 Leaver, Robin A., 85, 121, 214, 326, 136 Leibniz, Gottfried Wilhelm von (1646–1716), 46 Leipzig, 17, 37, 49, 93, 98–100, 111, 118, 159, 265, 287, 361, 366 Easter fair, 56 Michaelmas fair, 205, 225, 236 Nikolaikirche, 306, 339 publishing, 15, 43, 55–6, 84–5 engravers, 122 printing, 126 Thomaskantor, 12, 51, 294, 327–30 Bach’s interview for post, 171, 319 Thomaskirche, 306, 317, 339 Leonardo da Pisa (c.1170–c.1250), 105 Leopold of Anhalt-Cöthen (1694–1728), 295 libraries, 16 Lippius, Johannes (1585–1612), 102 liturgy, 118, 120 Locke, John (1632–1704), 9 Ludus Melothedicus, 104 Ludwig of Braunschweig-Lüneberg (1718–88), 57 lusus ingenii, 12, 50, 52, 65, 211, 254, 366 lute, 105 transcriptions, 139, 156–7, 355 Luther, Martin (1483–1546), 85, 210–11 Männling, Johann Christoph (1658–1723), 52 marginalia, 108 Marpurg, Friedrich Wilhelm (1718–95), 103, 104, 204, 251, 356

Marissen, Michael, 225, 231 Marshall, Robert, 318 masses, 326–30 Matthäi, Conrad (1619–67), 8, 103 Mattheson, Johann (1681–1764), 4, 9–10, 14, 17–18, 47, 114, 252 Buttstett dispute, 14, 17, 38, 52–3, 78–83, 88–9 on compositional planning, 105–9 fifth rule of loveliness, 14, 110, 139 on Gleichförmigkeit, 37–8, 109, 127 on Harmony, 96, 98, 137 publications Grundlage eine Ehrenpforte, 18 Orchestre 1, 13, 52, 78 Orchestre 2, 18, 52, 82, 376 Orchestre 3, 77 Meckbach, Conrad (1637–1712), 321 Meckbach, Paul Friedemann (1674–1731), 321 Meiβner, Heinrich (1644–1716), 51 Menantes (Christian Friedrich Hunold) (1680–1721), 128, 206, 41–4 Mendelssohn, Felix (1809–47), 276 mercy seat, 79, 378 Mersennse, Marin (1588–1648), 85, 105 metre, 39, 110, 118, 180, 248, 306, 329 minutes, 116–19, 306 mirror counterpoint, 253 mirror image, 59, 65, 71, 86, 210, 371–2, 382 mirror structure, 210, 366 see also symmetry Mizler, Lorenz (1711–78), 62, 88, 91 autobiography, 4 Corresponding society, 9, 18, 69, 100–1, 106, 119, 204, 208, 252, 253 Mattheson and, 10 Musicalische Bibliothek, 116–17 modes, 34, 158, 178, 379–80 Möller manuscript, 51 monograms, 71, 253 morality, 13, 18, 52, 85–92, 274, 89–92 Morhof, Daniel Georg (1639–91), 11, 40, 51–2, 112 motivic parallelism, 34–5 mottos, 26, 43, 52–3, 55, 71, 91 Mühlhausen, 42, 51, 93, 321–3 Müller, Johann Caspar (d. 1717), 55–7, 122, 124, 235 Müller, Maria Sophia, 56 music abuse of, 84 Lutheran doctrine of, 13, 85–92, 94, 96

index

Mirror of wisdom of God, 86, 371–2, 382 of the spheres, 74 musica, 75, 77 Mylius, Johann Anton (1657–1724), 42 Neumann, Werner (1905–1991), 65 Neumeister, Erdmann (1671–1756), 41 Neumeister, Johann Gottfried (1757–1840), 290, 359 Neuss, Heinrich Georg (1654–1716), 3, 9, 16, 83–4, 86, 381–2 Newton, Isaac (1643–1727), 46 Nichomachus (fl c.100 CE), 7, 74 Niedt, Friedrich Erhard (1674–1717), 18, 38, 93–4, 111, 114 number alphabets see alphabets, number numbers 6, 68, 97, 102–3, 329 7, 60 10, 60 14, 27–8, 197–8, 201, 208, 236, 247, 252 28, 306 29, 68–9, 293 41, 27–8, 65–9, 246–7, 251, 323–4, 344 84, 4 158, 27–8, 68–9, 143, 235, 280–1, 350 280, 216 666, 59 790, 243, 245 1000, 59 1032, 68–9, 164, 170, 173, 176, 177, 179–80, 202 1040, 243, 245 1155, 341–4 1320, 229, 233, 237, 288, 335, 337, 358 2130, 328, 331 2310, 340–1 3120, 24, 26, 30, 68–9, 172–81, 202, 244, 247, 289–90, 331, 353 aliquot, 103, 133 Bach numbers, 67, 211 composing by, 104 perfect, 8, 27–8, 60, 68, 97, 102–3, 172, 198, 202, 208, 306, 329, 347, 353 symbolism, 58–60 numeri radicales Harmonici, 102 numerology, 5 numerus musicus, 11, 14, 102, 110–11, 115–16 numerus perfectus see numbers, perfect numerus poëticus, 40 Nuremberg, 45, 49 Egidienkirche, 45 Sebalduskirche, 45, 49

Oley, Johann Christoph (1739–1789), 177 oratorios, 336–48 Pachelbel, Johann (1653–1706), 45, 47, 89, 359 Pachelbel, Wilhelm Hieronymus (1686–1764), 45 Paczkowski, Szymon, 83 Palestrina, Giovanni Pierluigi da (c.1525–1594), 327 palimpsest, 108 paper, 23, 32, 176 expense, 32, 120 foldings, 285, 287 quality, 226, 242, 246 rough, 107 staves ruled on, 120, 123 watermarks, 150, 162, 279, 285 paragrams, 5–6, 12, 36, 42, 324 parallelism, 34 Bach’s name in imagery, 72 permutation, 36, 42, 68, 198, 211, 247 B-A-C, 12, 69–70, 243, 247, 289, 347, 353 B-A-C-H, 211 see also numbers: 1032; 1320; 2130; 3120 Petzoldt, Martin (1946–2015), 315–16 Picander (1700–1764), 46, 206, 295–302, 304–6, 347 planets, 56, 60, 74, 77 plans ground, 107, 112, 119, 248, 251 numerical, 23, 25, 32, 107, 134, 146, 168–72, 243–6, 268–74, 292, 309, 317 Plato (428–348 BCE), 74 Poelchau, Georg (177–1836), 276 polyphony, 95 Praetorius, Michael (1571–1671), 88, 118–20 printing symbols, 12, 55–7 progressio arithmetica, 14, 38, 104, 115, 126, 139 proportion double, 40 in figure, 39 by situation, 33, 40, 170 proportional parallelism, 6–7, 35, 366–9 significance, 98–101 characteristics, 12, 30–1, 35, 146, 150, 183, 209, 237, 259, 271, 285, 356–9 Ptolemy (c. 85–c.165 CE), 74

409

410

index

pulse, 113, 136, 193, 199–203, 373 Puttenham, George (1529–90) The Arte of Poesie, 38–46, 75–6 proportion in figure, 39 proportion by situation, 33, 40, 140 Pythagoras (fl. 530 BCE), 8, 73–4 quadrivium, 75 Rameau, Jean-Philippe (1683–1764), 9 rastrum, 120, 123, 270 Regensburg, 48 Reichardt, Johann Friedrich (1752–1814), 235 rhetoric, 52 Richter, C. F. (unknown), 18, 97 Riederer, Johann Friedrich (1678–1734), 44–6, 58, 206, 324 Riepel, Joseph (1709–1782), 62 Roger, Estienne of Amsterdam (c. 1665–1722), 265 Roitzsch, Ferdinand August (1805–89), 257, 364 Rolle, Christian Friedrich (1681–1751), 71 Sanduhr, 118 Sarabande, 115, 157 Schabalina, Tatiana, 317 Scheibe, Johann Adolph (1708–76), 119, 126, 128, 217–23 Schemelli, Georg Christian (c.1678–1762), 30 Schenker, Heinrich (1868–1935), 34 Schering, Arnold (1877–1941), 4 Schmid, Balthasar (1705–49), 184, 190, 205 Schmieder, Wolfgang (1901–90), 20, 24, 199 Schmolk, Benjamin (1672–1737), 45 Schübler, Johann Georg (1720–53), 217, 226, 241 Schulenberg, David, 242 Schulz, Leonhard (1814–60), 178 Schulze, Hans-Joachim, 16, 65, 150, 156, 235–6 Schwanberg, Georg Heinrich Ludwig (1696–1774), 134, 136–41, 146, 150 Schwenter, Daniel (1585–1636), 58 score layout and measurement, 20–6, 28–9, 113, 120–9, 325 semitone symmetry, 103 senarius, 8, 38, 75, 86, 97, 102 septenarius, 8, 86, 102 Siegele, Ulrich, 5 signature across key signatures, 155 numerical, 27, 62–8, 141, 147, 155, 173, 280 see also B-A-C-H written, 65–7, 66, 71, 134, 237

slate, 108 Smend, Friedrich (1893–1980), 3, 5, 27, 58, 65–8, 108, 211 solmisation, 89, 164 see also ut re mi solstice (spring), 70 Sorge, Georg Andreas (1703–78), 359 soul, 86, 93, 281 of music, 114, 128 speed, 86, 118, 136 Speerstra, Joel, 55 Spiess, Meynrad (1683–1761), 10, 64, 105–7, 112 Spitta, Philipp (1841–94), 4, 141, 184, 225, 241 Stauffer, George B., 361 Steffani, Agostino (1654–1728), 50, 69, 107–12, 294 Steinbach, Georg Adam (d. 1720), 322–4 Stiefel, Michael (1487–1587), 3 Stinson, Russell, 258–9, 279, 359 Stölzel, Gottfried Heinrich (1690–1749), 46 Strecker, Adolff (1624–1720), 322–4 symbols, printing, 12 symmetry, 11, 33, 316 B-A-C-H form, 103–4, 103 of the hexachord, 103, 103 as ideal, 36–8, 127 numerical, 68, 216 in poetry, 11, 38–46 structural, 194, 311, 337 title pages, 216, 235–6 see also eurythmia; Gleichförmigkeit; mirror structure tactus, 114, 128 Takt, 116–18 see also bar Taktart see time signature Talle, Andrew, 122 Telemann, Georg Philipp (1681–1767), 69, 78, 216 Temple in Jerusalem, 80 tempo see speed tempora, 118 tetrachys, 7 Thieme, Carl August (1721–95), 18, 97 thorough-bass, 90, 93–4 Thüringia, 53, 90–1, 368 Thüringian doctrine of music, 85–92 time measurement, 118–19, 306 time signature 6/8 and 6/4, 24 as bar line see TS feature

index

change, 25, 116, 199–200 stile antico notation, 24, 333–5 title pages, 96, 207, 216, 235–6, 251–2 Clavier Übung, 13 Tomita, Yo, 24, 30, 34, 358 Torri, Pietro (c.1650–1737), 327 transposition, 27, 63, 179–80, 341 trias harmonica, 8, 87–9, 97, 370 trigonal alphabets, 44, 67 TS feature, 24–6, 45, 123, 174, 186, 285, 330–6 Ubereinstimmung, 37, 78, 109, 112, 216 unison generative, 11 intervallic, 8, 20, 75 proportional, 33, 37–8, 80, 109, 111–13 unity, 11, 13, 35, 38, 73, 90, 93, 95, 110 generative, 85 Unterberg, Joanne ab (unknown), 58 ut re mi, 8, 62, 81, 88, 103, 159, 164 Verhältnis, 108–9, 114, 127 Virgil (70 –19 BCE), 102 Vitruvius (c. 75–15 BCE), 38 Vivaldi, Antonio (1678–1741), 265–6 Vollkommenheit, 59, 94 Walther, Johann Gottfried (1684–1748), 11, 13, 16–17, 45, 49, 51, 84, 89, 92, 102–3, 133, 277, 361 on eurythmia, 38, 98, 111, 126–7 Musicalische Lexicon, 17, 61, 74–7, 102–3, 111 Praecepta der Musicalischen Composition, 114, 374–5

on Tactus, 127–8 Walther, Johann Gottfried (d. 1727), 100 watches, pocket, 119 watermarks, 150, 162, 177, 225, 277, 279, 287 Weigel, Christoph (1702–77), publisher, 49 Weimar, 16, 42 Bach in, 127, 133, 150, 321 Stadtkirche, 277 Walther in, 17, 51 Weissenfels, 16, 42, 48–9 Weltig, Adam Immanuel, 69 Werckmeister, Andreas (1645–1706), 9, 17, 50, 83, 90–2, 159–64, 275 Harmonologia musica, 96, 374 Musicae mathematicae hodegus curiosus, 16 Noble Art of Music, Der Edlen Music-Kunst 13, 85–8, 357 Wilcke, Anna Magdalena see Bach, Anna Magdalena Wilhelm Ernst of Saxe-Weimar (1683–1728), 42, 57 Williams, Peter, 97, 191, 211, 289 Wolff, Christian (1679–1754), 46 predestined harmony, 100–1 Wolff, Christoph, 6, 178, 191, 200–1, 212–15, 221, 225, 237, 240, 242, 251, 268, 270 Wollny, Peter, 121, 277, 285, 309, 327 Yearsley, David, 216 Zarlino, Gioseffo (1517–90), 75 Zedler, Johann Heinrich (1706–51), 15, 34, 37, 45–6, 52, 55, 59, 77, 98–9, 109, 127 Zelenka, Jan Dismas (1679–1745), 83 Zelter, Carl Friedrich (1758–1832), 259–66

411