Practice of Tonal Counterpoint.pdf

The Principles and Practice of Tonal Counterpoint The Principles and Practice of Tonal Counterpoint is a comprehensive textbook that combines practical, “how-to” guidance in eighteenth-century techniques with extensive historical examination of contrapuntal works and genres. Beginning with an introductory grounding in species counterpoint, tonal harmony, and figured bass, students progress through the study of chorale preludes, invertible counterpoint, and canonic and fugal writing. This textbook thoroughly joins principle with practice, providing a truly immersive experience in the study of tonal counterpoint and familiarizing students with contrapuntal styles from the Baroque period to the twenty-first century. Also available is a companion volume, The Principles and Practice of Modal Counterpoint, which focuses on sixteenth-century techniques and covers modal music from Gregorian chant through the seventeenth century. Features: • A balanced method to learning counterpoint combining technique, style, and composition • Guidelines for vocal and instrumental writing • Complete musical scores • A nine-part course of “creative study” on J. S. Bach’s Goldberg Variations • Exercises and self-tests provided in each chapter Douglass M. Green (1926–1999) was a founding member of the Society for Music Theory. He last taught at the University of Texas at Austin, where he was Professor of Music Theory until his death. Widely known as an expert in the music of Debussy and Berg, Green was the author of many articles and books on musical form and harmony, including the seminal analysis text Form in Tonal Music. He won several honors throughout his lifetime, including appointment as a Fulbright Scholar to Italy, the ASCAP-Deems Taylor Award, and the E. W. Doty Professorship of Fine Arts at UT-Austin. Green’s counterpoint classes remain legendary among his students. Evan Jones is Associate Professor and Coordinator of Music Theory and Composition at the Florida State University College of Music. He has received a Sproull Fellowship from the University of Rochester, a Doctoral Fellowship from the Social Sciences and Humanities Research Council of Canada, and the Alfred Mann Dissertation Prize from the Eastman School. He has published research on music by Lassus, Quantz, Schubert and Xenakis in peer-reviewed journals and essay collections, and edited a two-volume collection of essays on twentieth-century string quartets that received the Society for Music Theory’s Citation of Special Merit.

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The Principles and Practice of Tonal Counterpoint

Douglass Green and Evan Jones

First published 2016 by Routledge 711 Third Avenue, New York, NY 10017 and by Routledge 2 Park Square, Milton Park, Abingdon, Oxon, OX14 4RN Routledge is an imprint of the Taylor & Francis Group, an informa business © 2016 Taylor & Francis The right of Douglass Green and Evan Jones to be identified as author of this work has been asserted by them in accordance with sections 77 and 78 of the Copyright, Designs and Patents Act 1988. All rights reserved. No part of this book may be reprinted or reproduced or utilised in any form or by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying and recording, or in any information storage or retrieval system, without permission in writing from the publishers. Trademark notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Library of Congress Cataloging in Publication Data A catalog record for this title has been requested ISBN: 978-0-415-87829-6 (hbk) ISBN: 978-0-415-98866-7 (pbk) ISBN: 978-1-315-72037-1 (ebk) Typeset in ACaslon by Florence Production Ltd, Stoodleigh, Devon, UK Senior Editor: Constance Ditzel Assistant Editor: Denny Tek Production Manager: Mhairi Bennett Marketing Manager: Amy Langlais Copy Editor: Thérèse Wassily Saba Proofreader: Kilmeny MacBride Cover Design: Jayne Varney

Contents

Foreword by Jonathan C. Santore Preface Preliminary Information Chapter 1

Species Counterpoint in Major and Minor Modes 1.1 1.2 1.3 1.4 1.5

Chapter 2

Eighteenth-Century Thoroughbass and Chorale Harmonization 2.1 2.2 2.3 2.4

Chapter 3

Consonances: Note Against Note Unstressed Dissonance: Two Against One Unstressed Dissonances: Three Against One Unstressed Dissonance: Four Against One Stressed Dissonance: Syncopated Counterpoint

Realization of a Figured Bass Harmonic Rhythm The Appoggiatura Adding a Bass to a Chorale Melody

The Chorale Prelude 3.1 Aspects of the Simple Chorale Prelude 3.2 Composing for Organ 3.3 Composing a Simple Chorale Prelude

Chapter 4

Continuo-Homophony in Baroque Music 4.1 Melody with Basso Continuo Accompaniment 4.2 Closely Related Keys 4.3 Harmonic Progression

ix xi xiii 1 1 4 6 9 10 17 17 22 25 27 33 33 41 42 45 45 48 49

vi

Contents

4.4 Chord Substitution and Elision in the Harmonic Progression 4.5 Chord Groupings: Chord and Harmony Chapter 5

Sequences and Invertible Counterpoint 5.1 5.2 5.3 5.4 5.5 5.6

Chapter 6

Chapter 7

62 65 70 75 76 77 81

6.1 Inventions Based on a Motive 6.2 Inventions Based on a Theme

81 87

Three-Voice Counterpoint Texture Complementary Rhythm Triads and Seventh Chords Sequences in Three-Voice Counterpoint

Rounds and Canons 8.1 Rounds 8.2 Canons 8.3 Method for Composing a Two-Voice Perpetual Canon

Chapter 9

61

The Two-Part Inventions of J. S. Bach

7.1 7.2 7.3 7.4 Chapter 8

The Single-Voice Sequence Inclusive Sequences Invertible Counterpoint Invertible Counterpoint and Tonicization The Imitative Sequence The Double Sequence

49 52

Fugue 9.1 9.2 9.3 9.4 9.5 9.6 9.7 9.8 9.9 9.10 9.11

102 102 102 107 109 124 124 129 139 143

Characteristics of Fugue Analysis of the C-minor Fugue from WTC I Tonal Imitation: Subject and Answer Versions of the Theme Writing a Countersubject “Ricercare” and “Canzona” Types of Fugue Stretto Other Artifices Common to the “Ricercare” Type of Fugue Intervallic Inversion and Augmentation Episodes in the “Canzona” Type of Fugue The Double Fugue Other Types of Fugue

143 144 148 154 159 159 162 163 164 165 173

Contents

Chapter 10

Counterpoint in the Nineteenth Century 10.1 10.2 10.3 10.4

Chapter 11

Normal Counterpoint Descant Counterpoint The Quodlibet Fugue and Fugato as an Effect in the Nineteenth Century

Counterpoint in the Twentieth Century and Beyond 11.1 11.2 11.3 11.4

Consonance and Dissonance Contrapuntal Texture as Curtain of Sound Canon and Fugue Coda: Twenty-First-Century Counterpoint

Credits Answers for Self-Tests Notes Index of Musical Examples

vii

193 193 193 201 203 219 220 225 232 241 242 243 251 255

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Foreword

When Douglass Green passed away in 1999, his magnum opus, The Principles and Practice of Counterpoint, was almost completely finished, with only the final chapter of the second volume left unwritten. Throughout his long and distinguished career as a theorist, composer, organist, and church musician, counterpoint was always his primary interest (without much prompting, he would point out that his official title at the Eastman School of Music had been Professor of Counterpoint). He began work on Principles after moving to the University of Texas at Austin in 1977; early iterations of the text were used by hundreds of Doug’s students at UT-Austin and Indiana University (where he taught during a sabbatical), many of whom have gone on to teaching in their own counterpoint classrooms, and making do with faded photocopies of Doug’s text. I first made Doug’s acquaintance as one of those students; later (after getting through those courses successfully!), I summoned up the courage to ask his daughter out on a date, and eventually became his son-in-law. As a family member with expertise in the field, Doug’s heirs turned to me after his death to shepherd the book through the publication process. Extensive discussions about Principles with his friends, colleagues, and former students made it clear that, while Doug’s innovative approach to contrapuntal pedagogy was as fresh and valid as ever, the prose of the text would require some editing for a more contemporary audience. This was a difficult prospect for all of us who loved Doug and were reluctant to change his final work. On the other hand, I strongly felt that the best testament to Doug’s memory would be the publication and continuation of Principles as a living text, meeting the evolving needs of contemporary counterpoint teachers and students. For these reasons, when Constance Ditzel at Routledge expressed an interest in an updated version of Principles, I suggested that we find a co-author who respected Doug’s pedagogical aims, but would not feel constrained by his memory, someone who was an active counterpoint teacher with a sympathetic but independent pedagogical approach. I believe we’ve found this person in Evan Jones. On behalf of Doug’s family, I’d like to thank Evan Jones, Constance Ditzel, and Routledge for introducing his work to new generations of counterpoint students, and for keeping alive the memory of an esteemed and beloved teacher, mentor, and friend. Jonathan C. Santore, Ph.D. Professor of Music Theory and Composition and Chair, Department of Music, Theatre, and Dance Plymouth State University (New Hampshire)

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Preface

It was a great honor to be asked to prepare Douglass Green’s two-volume manuscript for publication. Spanning repertoire from the Baroque period through the nineteenth, twentieth, and twenty-first centuries, the present volume provides an accessible and effective introduction to developments in contrapuntal styles and genres over a lengthy historical span. Beginning with an introductory grounding in species counterpoint, tonal harmony, and figured bass, students progress through the study of chorale preludes, invertible counterpoint, and canonic and fugal writing. A graded program of compositional and stylistic study is complemented by frequent exercises, self-tests, and opportunities for guided analysis, including a nine-part course of “creative study” on J. S. Bach’s Goldberg Variations. This textbook thoroughly joins principle with practice, providing a truly immersive experience in the study of tonal counterpoint and familiarizing students with contrapuntal styles over the last three hundred years. The rationale for this volume (and its companion, The Principles and Practice of Modal Counterpoint) is that it is impossible to study counterpoint and only counterpoint. Just as the examples in this book illustrate the interaction between distinct but interdependent musical voices, the study of tonal counterpoint necessarily interacts and overlaps with the study of harmony, form, and style, and engages an extensive breadth of musical literature. Without duplicating a course in tonal harmony in every detail, this book reviews diatonic chordal successions, thoroughbass symbols, harmonic rhythm, nonchordal dissonance, and tonicization and modulation, so that student compositions can convincingly convey a viable harmonic framework. Guidance is also provided in related areas such as vocal and instrumental ranges and textures and the compositional design of complete works; although such matters are relevant to a much wider range of music than is included in this book, they must be considered in order to put contrapuntal principles into practice. Further, it is crucial to look beyond compositions with an explicitly contrapuntal basis, and to encounter a variety of other works that allude to or borrow from contrapuntal models. Students will encounter not only a diverse sampling of inventions, canons, and fugues, but also selections from sonatas, concertos, operas, oratorios, symphonies, and a variety of other solo, chamber, and orchestral repertoire. This inclusive approach also motivates the exploration of ways in which Baroque precedents inform composers and compositions from later periods, and the exploration (through listening and performance) of connections between contrapuntal principles, compositional practices, and musical results. Studying contrapuntal aspects of music by J. S. Bach and other Baroque composers such as Corelli, Pachelbel and Handel alerts the student to the continuing role of counterpoint in later periods. Musical selections

by Mozart, Beethoven, Berlioz, Mendelssohn, Wagner, Verdi, Franck, Brahms, Tchaikovsky and Tárrega provide ample opportunities to compare late eighteenth- and nineteenth-century contrapuntal textures to their Baroque models. The final chapter surveys contrapuntal practices in twentieth- and twenty-first-century music, and demonstrates a continuing interest in counterpoint even by composers who have adopted wholly new systems of tonal organization. Given this broad stylistic span, it is critically important to access and to participate in the music under consideration—not only by listening but, when possible, by performing vocally and/or instrumentally—so that the completion of compositional exercises and analytical activities will be securely grounded in a vivid and very personal musical experience. This book can and should be used in a variety of ways. The organization of topics and the extensive discussion of the examples that are included should certainly enable the reader to glean a thorough understanding of contrapuntal styles and techniques simply by perusing the volume in whole or in part. Musical selections are considered in detail, and frequent self-tests (with answers at the back of the book) allow the reader to test comprehension. Greater rewards will accrue, however, if users are encouraged to take advantage of opportunities for cooperative learning and to pursue further creative and analytical avenues beyond the limits of this volume. Completed exercises can be shared with fellow students—either before or after correction, or at both stages—to allow everyone to learn from others’ work. Longer exercises could even be completed cooperatively, especially when multiple compositional decisions must be made in succession. Analytical assignments, especially the “creative study” assignments at the end of each chapter, can be tackled individually or in teams, and could possibly lead to in-class presentations; in that context it would certainly be appropriate to coordinate an analytical presentation with a live performance, which could be rendered using the original instrumentation or a completely new instrumentation (perhaps involving voices or single-line instruments covering individual parts). Ideally, the discovery process should continue even beyond the musical selections included herein. Projects or presentations could focus on other inventions, sinfonias, or fugues by J. S. Bach that are not included here, or on individual movements from sonatas or suites by Bach or others.1 Students could also be assigned to track down a post-Baroque fugue and to investigate its construction, or simply to examine the contrapuntal character of almost any instrumental duo, trio, or quartet. Projects of this sort would complement the exploratory orientation of this book and would surely serve to highlight the role of counterpoint in the wider musical sphere. I would like to thank Constance Ditzel (at Routledge) and Jonathan Santore for selecting me to co-author this volume and its companion, and for providing immeasurable assistance along the way. This volume has also benefitted greatly at various stages from the help of Aurora Montgomery, Denny Tek and Mhairi Bennett at Routledge, Kelly Derrick and others at Florence Production, and Thérèse Wassily Saba. Musical examples were expertly realized by Chris Burton and Szu-Yu Chen. I would like to thank all my colleagues at the Florida State University College of Music for their support, and all the students who have taken my counterpoint classes over the years. Special thanks to my wife, Kim, for her patience, her selflessness, and for the pleasure of her companionship. Finally, I owe a debt that can never be repaid to my esteemed co-author, with whom it has been my very great privilege to collaborate in the manner that we have. Evan Jones July 2015

Preliminary Information

Pitch and pitch class Throughout this study we will use the system of identifying specific pitches whereby middle C is designated C4, C5 is one octave higher than that, C3 is one octave lower, and so on. Other pitches in the octave above C4 are designated similarly, such as G4 or B4, and the same for other octaves. Thus: EXAMPLE 0–1

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C1, C2, C3, C4, etc. are different pitches but are all of the same pitch class. We will differentiate when necessary between pitch and pitch class throughout the book. Where such differentiation is irrelevant to the point being made, we will speak simply of a note.

Clefs Over the centuries there have been many different clefs used for the notation of music. primarily be using treble and bass clefs in this book, but an acquaintance with the two most “C-clefs” (alto clef and tenor clef) is important. Musicians who can easily read only treble are at a distinct disadvantage when encountering the great choral, orchestral, and chamber

We will common and bass music of

xiv

Preliminary Information

the past are closed books to them. Those who have not mastered alto and tenor clefs are urged to obtain copies of several string quartets and to play each part separately at the piano or on another instrument. Most useful for this purpose, insofar as they have extended passages in tenor clef for cello, are the last three quartets of Mozart (K. 575, 589, 590), the late quartets of Beethoven (Opp. 127, 130, 131, 132, 133, 135), or any quartet from the nineteenth century or later.

Notation In all but the most introductory-level classes, instructors often gloss over matters relating to the writing down of music. Correctly written scores are important—mainly to avoid ambiguity. Remember, what is written on paper is not the music but instructions to a performer: the symbols tell the player precisely what to do and what not to do. Without clear instructions there can be no music, or at best only a distorted version. It is also important to use traditional notational practice unless there is a good reason not to do so. Because of its familiarity, traditional practice makes the score easy to read. Sloppy writing or unnecessarily innovative notation tends to confuse. Finally, good notational practice increases credibility. A performer will lose confidence in a composer who places clefs in the wrong position, who writes time signatures at the beginning of every staff, who omits key signatures at the beginning of every staff, who does not know which direction the stems and ties should go, or who does not line up vertically all the notes that are to be attacked simultaneously. (An instructor may lose some confidence in a student for the same reasons.) Needless to say, the use of music notation software is no substitute for a secure knowledge of notational rules. Many books on the subject of musical notation are readily available, but for our purposes the following points should suffice: 1. Brackets. When two or more staves are combined into a system they are bracketed together at the left. Straight brackets are used to indicate that the system represents ensemble music—that is, more than one performer is to take part. Curved brackets indicate that two (sometimes three) staves are united as a grand staff for a single performer, as in keyboard or harp music. In the following example (a) is for ensemble music, (b) for keyboard. EXAMPLE 0–2(a)

Qui

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me,

qui-tur

se

se

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qui

me,

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me,

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se

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qui

Preliminary Information

xv

EXAMPLE 0–2(b)

2. Stem directions. When a staff is devoted to a single voice or part, stems for notes written on the middle line or above go down. Notes written below the middle line or above go up. On the other hand, if a staff has two voices written on it, the stems of the higher voice go up regardless of the placement of the notes and the stems of the lower voice down. Even if the lower voice crosses above the higher voice, the stem directions of the lower voice still go down and those of the higher voice still go up. The crossing of parts is thus clear. See the second beat of (b) in the example above. 3. Ties. When a staff is devoted to a single voice, ties go in the opposite direction from the stems. When two voices are written on the same staff, ties go the same directions as the stems. Compare the ties in (a) above to those in (b).

Calligraphy If you are composing or completing assignments by hand, you should practice careful calligraphy for the same reasons as good notation: chiefly for clarity, but also for credibility. Those who doubt that great composers were careful with their calligraphy should take a look at facsimiles of some of the autograph manuscripts of Bach, Haydn, Mozart, Chopin, Mussorgsky, Wagner, Schoenberg, Webern, Berg, and Stravinsky. Beethoven was an exception, and as a result he suffered much from seeing his works printed with numerous mistakes, as his letters attest. 1. Size. Musical symbols should be of a proportionate size to the staff on which they are being written. This is true not only of note heads, but of stem lengths, accidentals, and clefs. 2. Placement. Be sure that accidentals are placed directly in front of the note head to which they refer. When two notes a second apart are written on the same staff and are to sound simultaneously, accidentals referring to these notes go in front of both notes. Do not try to squeeze in an accidental between them. 3. Flags. These are the curvy parts of single eighth-notes or shorter rhythmic values. When two or more flags are on the same stem, start the second further down the stem. 4. Rests. Rests are as shown below. By tradition the symbol for a rest the value of a whole-note is also used for a whole measure in any meter, regardless of whether or not the measure contains the equivalent of four quarter-notes.

xvi

Preliminary Information

Exercises Each chapter calls for a number of exercises that help you to assimilate the material of the chapter. These are designed gradually to increase your skill as a contrapuntist. Do the exercises in pencil so that you can freely erase and correct mistakes. At various points throughout the chapter you will come across Self-Tests. These are included to let you know whether you have grasped the material presented. Answers are provided at the end of the book. If you score lower than about 75 percent on any self-test, you should go back and study the material more carefully.

Harmonic Intervals: Consonance and Dissonance1 There are several ways of defining consonance as opposed to dissonance. Over the years opinions as to which intervals are consonant and which dissonant have varied, and the precise meaning of the terms themselves has not had a uniform explanation from writers on music. For instance, in 1597 Thomas Morley defined a consonant sound as one which “delights” the ear, a dissonant sound as one which “offends.”2 Many others, especially those writing before the nineteenth century, also spoke of “pleasantness” and “unpleasantness” as aspects of consonance and dissonance respectively.3 In our own time writers often describe the difference in terms of relative stability or instability. A consonance sounds relaxed, not particularly demanding further motion: it is more or less stable. A dissonance sounds tense, demanding resolution to a more stable sound. A slightly different way of putting this is that a dissonance needs explanation—in order to understand it the listener must depend on its resolution to a consonance. To complicate matters still further, intervals that are generally acknowledged as consonances are not necessarily perceived to be equally consonant. Thirds and sixths are both considered consonant intervals, yet the third is stable enough to end a piece of music while its inversion, the sixth, is not. And the perfect fourth has, over the years, been in the ambiguous position of being consonant in some contexts and dissonant in others. Until the eighteenth century, theorists regarded as most consonant those intervals whose ratio was made up of the smallest numbers. For example, if one vibrating string produces the note C2, a string half its length will produce C3, an octave higher. The ratio of the two pitches is 2:1, and the resulting octave is a perfect consonance. If the ratio between the two strings is 3:2, a perfect fifth results. It is called a perfect consonance, but is slightly less stable than the octave. The ratio 4:3 gives the perfect fourth, which is the inversion of the perfect fifth and less stable than the fifth. The imperfect consonances are given by the other ratios: 5:4 and 6:5 result in the major and minor third respectively, and their inversions are the minor and major sixths, ratios 8:5 and 5:3.4 Sixths are less stable than thirds. It would appear, then, that the “stability” of an interval is in direct proportion to the ratio that produces it—that is to say, the ratio made up of two adjacent lower numbers gives a more consonant interval than does a ratio deriving from higher numbers or from numbers not adjacent. Thus, the perfect fifth (3:2) is more stable than the major third (5:4), but the major third is more stable than the major sixth (5:3). It was during the seventeenth century that the laws of vibrations of strings were discovered. When a string vibrates it does so not only in its full length, but also in halves, thirds, fourths, and so on. Not

Preliminary Information

xvii

only is the fundamental pitch of the string produced, but also overtones in increasingly smaller intervals. The same is true of the column of air in an organ pipe or a wind instrument. Thus the early theorists with their consonances based on small numbered ratios were justified, for the first—and therefore most prominent—overtones correspond very precisely to these ratios. A pitch produced by a musical instrument is a complex sound, made up of various pitches. We speak of the fundamental as the first partial, the first overtone as the second partial, and so on. EXAMPLE 0–3 (-)

(-)

1

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3

4

5

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6

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12

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2nd partial fundamental = 1st partial

The first six partials correspond to the pitch classes of a major triad, but beyond that some of the partials do not correspond very closely with the pitches used in Western music. The seventh and eleventh partials, for instance, are perceptibly lower than the notated Bb4 and F#5 in the example above (hence the minus signs above them). Moreover, the overtones from the seventh partial upwards are too close together to be perceived as consonances, for they are notes of adjacency—a whole step or smaller. Therefore tradition has it that the first six partials along with their octave replicas give us our consonances, as shown below:5 EXAMPLE 0–4

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The fifth and eighth partials produce the minor sixth, the third and fifth partials the major sixth. Consonances, then, are the perfect intervals and major and minor thirds and sixths. But it is not quite so simple as this, for there is a problem regarding the perfect fourth. Beginning in the fourteenth century, composers have tended to treat the perfect fourth as a consonance only when it appears between

xviii

Preliminary Information

two upper voices. When one of the notes comprising the perfect fourth is the lowest sounding voice, this interval has been perceived as so unstable as to be for all intents and purposes a dissonant interval. Possible reasons for this rather odd phenomenon are demonstrated below: EXAMPLE 0–5 (a)

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CREATIVE STUDY 9: GOLDBERG VARIATIONS, VARIATION 10 Consult a score for Variation 10 from the Goldberg Variations (BWV 988) by J. S. Bach. This variation is not a fugue, but it is marked “Fughetta” and it evokes the sound of a fugal exposition (how?). What is the order in which the four voices enter over the first half? What is the order of entrances in the second half, and how does that relate to that of the first half? Notice that the first two entrances are subtly different from each other; comparing the first downbeat and the fourth downbeat of each one, the first entrance (the subject) moves down a step and the second one (the answer) moves down a third. Where precisely is the change? Which of the following six entries correspond to the subject, which of them correspond to the answer, and which one is different from both? Can you find any recurring material in the voices that have something other than the subject or answer? Explain the use of Fns in measure 19, in terms of the key that is coming up. Explain the use of Fns in measures 25–26, in terms of the key that is coming up.

Chapter 10

Counterpoint in the Nineteenth Century

10.1 Normal Counterpoint Throughout the nineteenth century, when composers chose to write music in a contrapuntal texture, they did so in much the same way as had J. S. Bach and other eighteenth-century composers. Fugal movements from Haydn’s late masses and the oratorios The Creation and The Seasons (1796–98 and 1799–1801, respectively) foreshadowed many of the large choral fugues in the oratorios and masses of Beethoven, Schubert, Mendelssohn, Verdi, Brahms, and others. Despite some differences in harmony and modulatory schemes, these works tended to be written basically with the same contrapuntal techniques as those of the previous century. The type of counterpoint we have studied so far (which we will call, for lack of a better term, “normal counterpoint”) is characterized by two or more melodic lines that are harmonically consistent with each other. In other words, the lines themselves determine the harmony.

10.2 Descant Counterpoint Although descant counterpoint is usually associated with the nineteenth century, it can be found in earlier music as well. An essentially homophonic section of music is composed—a single melody and its accompaniment—and an additional melodic line added to it at some point in the music. Unlike with normal counterpoint, the individual lines within a texture of descant counterpoint give little or no indication of the harmony of the passage.

194

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EXAMPLE 10–1 Symphony No. 7, Op. 92, Allegretto, mm. 3–42 L. v. Beethoven 3

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The melody played by the cellos and violas beginning in measure 27 of Example 10–1 is heard simultaneously with the melody played by the second violins and contrasts strongly with it. Yet these two lines do not actually determine the harmony of the passage, because that harmony with the principal theme had already been stated in measures 3–26. Instead the cello/viola line seems to have been composed to fit the harmony. This technique is similar to the frequent appearance in contemporary hymnals of added descants for the sopranos (usually on the last stanza). The important difference here—the difference between normal counterpoint and descant counterpoint—lies in the fact that the simultaneously-sounding melodic lines are not the ones that determine the harmony, since that was already decided when measures 3–26 of the movement first stated the principal theme in the lower strings. Instead, the line is composed to fit into the predetermined harmony. A further illustration of descant counterpoint is found in the second movement of Mendelssohn’s “Italian” Symphony, shown in Example 10–2. The original theme is not harmonized homophonically but instead by a steady walking bass written in “normal” two-voice counterpoint, after which the flutes add two simultaneous descants. EXAMPLE 10–2 Symphony No. 4 (“Italian”), Op. 90, Andante con moto, mm. 1–15 F. Mendelssohn

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Bustling effect. A number of passages, especially in opera and other theatrical works, require the effect of busyness. Such a case is the opening of Berlioz’s Roméo et Juliette as well as Puccini’s La Bohème. A fast fugato generally is useful for this effect. Comic effect. In Verdi’s Un Ballo in Maschera, there are two stage villains who slink about to the theme of the fugato shown in Example 10–9. EXAMPLE 10–9 Un Ballo in Maschera (1859), Prelude, mm. 13–23 G. Verdi

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In Berlioz’s La Damnation de Faust, the scene in Auerbach’s cellar is peopled with drunken men who, after hearing Brander’s rendering of a coarse song about the death of a rat, decide the rat deserves a requiem. They improvise an Amen chorus on the main motive of Brander’s song (Example 10–10). In spite of their state of inebriation they give a correct fugal answer to the subject, though the basses jump in a half measure too soon. Before long, some voices enter on the weak beat to give an unsettled feeling to the work, but these are straightened out within a few measures (starting in m. 7).

EXAMPLE 10–10 La Damnation de Faust, Op. 24, deuxième partie, Fugue sur le thème de la chanson de Brander, measures 1–14 H. Berlioz

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EXERCISE 10–1 Following is a piano arrangement of the famous guitar piece Recuerdos de la Alhambra by Francisco Tárrega (1852–1909). Compose a descant for flute or violin, or voice (to be sung on a neutral syllable such as “ah” or “oh”). The descant should sound only on the repetitions of a section. Begin the descant after the initial notes of the section, as in Example 10–3b, p. 200). Be sure to use complementary rhythm. Try to make the descant a beautiful melody in itself.

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CREATIVE STUDY 10: GOLDBERG VARIATIONS, VARIATION 30 Consult a score for Variation 30, the final variation from the Goldberg Variations (BWV 988) by J. S. Bach. Being a quodlibet rather than a canon, this variation interrupts the regular recurrence of canons (at successively larger intervals) that are included every three variations. No prior knowledge of the folk melodies that Bach used is needed in order to examine and appreciate Bach’s accomplishment in this piece.1 The opening tenor melody in eighths and sixteenths corresponds to the text “Ich bin so lang nicht bei dir g’west” (“I have been so long away from you”); the melody that first enters in the alto in quarter-notes and eighth-notes corresponds to the text “Kraut und Rüben haben mich vertrieben” (“Cabbage and beets have driven me away”). Which song does the soprano “voice” present in measure 2? How does the soprano part link effectively between the end of one tune in measure 4 and the beginning of the other tune in measure 5? Find all subsequent statements of the “Kraut und Rüben” tune (hint: all but one begin on the downbeat of a measure). What is the fugal term for overlapping statements of a subject, and which two voices realize that situation in measures 10–12? There are also many instances in which a voice that is not singing one of the songs (such as the tenor in measure 3) will anticipate or reiterate a motive in another voice. Find at least three more instances of the same “stepwise fifth” motive that is not officially part of either song.

Chapter 11

Counterpoint in the Twentieth Century and Beyond

To this point, our study of contrapuntal techniques has taken account not only of principles of melodic contour and character but also of harmonic organization, consonance and dissonance, and meter. In a musical context such as Example 11–1, however, there is no longer any distinction between consonance and dissonance, no longer any implied harmonic function, and no meter. Nonetheless, this example (part of an electronic composition by Iannis Xenakis) can be described as contrapuntal, because its musical character derives from the juxtaposition of multiple melodic entities and the collective effect that results. Within the specified five-octave range, sustained tones are notated as horizontal lines and glissandi are notated as slanting lines.1 Over the one-minute duration, then, a cluster of low, sustained tones is joined by both sustained and sliding tones in every register, which periodically coalesce in certain ranges of pitch. EXAMPLE 11–1 Mycenae-Alpha (1978), excerpt I. Xenakis

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220

Counterpoint in the Twentieth Century and Beyond

Needless to say, twentieth- and twenty-first-century counterpoint encompasses a much broader range of musical practice than that of previous centuries. Since so many strictures inherited from earlier eras were no longer followed consistently, this final chapter serves as a kind of epilogue. There are, however, many ways in which composers responded to earlier contrapuntal traditions and made use of familiar configurations and techniques.

11.1 Consonance and Dissonance While some composers retained an interest in traditional definitions of consonance and dissonance, many others disregarded such distinctions, and others actively flouted them. Arnold Schoenberg declared the dissonance to be “emancipated” as of his twelve-tone compositions of the 1920s, and Charles Seeger espoused a strategy of “dissonant counterpoint” whereby the roles of consonance and dissonance could be reversed.2 Although consonance was no longer a primary concern for many composers, the intervallic relationship between voices was still an important aspect of the effect of contrapuntal writing and of the moment-to-moment direction of the music. Example 11–2 presents a two-voice reduction of Hindemith’s harmonization of the medieval melody “Es sungen drei Engel” that is heard near the beginning of the Prelude to his opera Mathis der Maler.3 A third, more rhythmically active voice has been omitted. These two voices achieve more or less a first-species texture, involving a high proportion of consonant intervals.4 The major second in measure 19 is easily heard as resulting from passing motion; the sevenths and fourths in measures 20–22, while not as easily explainable, all involve the notes of an arpeggiated F-major triad in the top line, which stabilizes the passage and seems to excuse the resulting dissonances. EXAMPLE 11–2 Mathis der Maler, Prelude, mm. 16–23 P. Hindemith

Counterpoint in the Twentieth Century and Beyond

221

The opening of the Andante movement from Ruth Crawford Seeger’s String Quartet 1931, given in Example 11–3, begins with a two-voice texture in the viola and cello, soon to be joined by the second violin and then the first. Long pulsating tones grate against each other throughout most of the movement; the players reach local dynamic peaks on different beats and take turns changing pitches. Even though the voices are unsynchronized, their relationship is unquestionably a contrapuntal one. Most of the changes of pitch accomplish a kind of “leapfrog” effect: the cello leaps below the viola in measure 5 and then back above the viola in measure 8, after which the viola leaps above the cello in measure 13, the cello leaps above both of the other parts in measure 15, and the viola then leaps above the other parts in measure 18. Once all four voices are sounding, the leapfrogging only intensifies, the range continues to expand, and the harmonies thicken (with the eventual use of double-stops in all four parts).5 Although this movement’s harmonic language does not appear to depend on any sort of tonality, the succession of harmonies is very compelling, as is the contrapuntal character of the ongoing “dialogue” between the four parts.

EXAMPLE 11–3 String Quartet 1931, Andante, mm. 1–18 R. C. Seeger

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Answers for Self-Tests

Answers for Chapter 5, Self-Test 5–2 1. 2. 3. 4. 5.

repetition (repeat) inclusive altered sequence descending fifths Neapolitan sixth, diminished

Answers for Chapter 5, Self-Test 5–3 1. Double counterpoint at the octave works satisfactorily at either of these or other transpositional levels.

Due to the parallels, double counterpoint at the tenth does not work satisfactorily at any transpositional level.

Despite the parallel sevenths on the second beat of measure 2, double counterpoint at the twelfth works satisfactorily due to the implied deceptive cadence V7–VI in the first transpositional level shown. In the second version the parallel sevenths are more of a problem, unless the penultimate note in the bass becomes an A#, implying a vii°7–i cadence.

Answers for Self-Tests

249

2. (a) 8, 10, 12 (b) fifths, fourths (c) parallel (d) sixths, sevenths, tenth 3. (a) double counterpoint at the tenth (b) double counterpoint at the octave (c) double counterpoint at the twelfth (d) double counterpoint at the octave (e) double counterpoint at the twelfth (f) double counterpoint at the tenth

Answers for Chapter 5, Self-Test 5–4 1. (a) m. 3, bass, D# and E#; m. 4, soprano, E# (b) m. 2, An in both voices throughout; m. 2, last sixteenth-note in soprano, F#; m. 3, bass, An; m. 4, En in both voices throughout; m. 4, last sixteenth-note in soprano, C# 2.

Answers for Chapter 9, Self-Test 9–1 (a)

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Since the subject has no prominent ^5 near the beginning, and does not modulate, the answer is copied out exactly in the dominant key of C major (in other words, a real answer). (b)

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Since the subject does not modulate, the answer is simply to transpose it to the dominant key, ^ ^ ^ ^ changing the second note, 5 , from 2 to 1. (Remember that it is only the 5 s that occur at the very beginning of the subject that need to be changed from ^2 to ^1 in the answer.)

Answers for Chapter 9, Self-Test 9–2 (a) The CS begins on beat 3 of measure 3, by which point the crucial difference between subject and answer is past. (b) There are two versions of the CS: the first, written against the answer, begins with an upward leap of an octave. When this is placed against the subject in measure 5, this leap is contracted to a seventh. (c) The CS does not begin until well after the crucial difference between subject and answer. It begins on the second half of the first beat of measure 3, whereas the answer began two beats earlier.

Notes

Preface 1. It would be particularly exciting if several individuals or teams were assigned a partita or suite in which all movements are apparently based on a similar compositional framework, and then delivered presentations on each movement in order. David Beach cites J. S. Bach’s BWV 810, BWV 817, BWV 818a, BWV 833, BWV 1002, and BWV 1004 as works whose “movements [are] related throughout by common harmonic and voice-leading constructs [and] motivic associations.” See his Aspects of Unity in J. S. Bach’s Partitas and Suites: An Analytical Study (Rochester, NY: University of Rochester Press, 2005), p. 86.

Preliminary Information 1. Strictly speaking, when referring to harmonic intervals we should use the musical terms concord and discord, or the adjectives concordant and discordant, rather than the acoustical terms consonance (consonant) and dissonance (dissonant). The latter are matters with which physicists and physiologists have concerned themselves, using scientific approaches to the matter. Nevertheless, since the substitution by musicians of these terms is so widespread, we will not attempt to inflict the more accurate usage here. 2. Thomas Morley, A Plain and Easy Introduction to Practical Music, Ed. A. Harman (New York: W. W. Norton, 1973), p. 141. 3. For more on the evolution of the concepts of consonance and dissonance, see James Tenney, A History of “Consonance” and “Dissonance” (New York: Excelsior, 1988). For a discussion regarding the treatment of dissonance in modal music, see Douglass M. Green and Evan Jones, The Principles and Practice of Modal Counterpoint (New York: Routledge, 2011). 4. To clarify, ratios as simple as these are only really accurate in “just intonation”. A great number of different tuning systems were eventually proposed that deviated from the intervallic purity indicated by these ratios; even the equal temperament of a modern piano slightly “mistunes” all of these consonances. 5. These six partials were collectively referred to as the senario by Gioseffo Zarlino in Part I of Le istitutioni harmoniche (1558). See Catherine Nolan, “Music Theory and Mathematics,” in Thomas Christensen (Ed.), The Cambridge History of Western Music Theory (Cambridge: Cambridge University Press, 2002), pp. 272–304 (esp. p. 277).

Chapter 1 1. For a comprehensive introduction to the pedagogy of tonal counterpoint, see Ian Bent, “Steps to Parnassus: Contrapuntal Theory in 1725; Precursors and Successors,” in Thomas Christensen (Ed.), The Cambridge History of Western Music Theory (Cambridge: Cambridge University Press, 2002), pp. 554–602. 2. See Preliminary Information, note 1, above, on the distinction between dissonance and discord.

252

Notes

Chapter 2 1. We are speaking of the perceived beat. Often, especially in music dominated by sixteenth-notes, the meter signature may indicate a quarter-note as the beat while, because of a slow tempo, the listener perceives the true beat as the eighth-note. 2. In the sacred style of the sixteenth century, the accented passing tone occurs only on weak beats and in a descending direction. See Douglass M. Green and Evan Jones, The Principles and Practice of Modal Counterpoint (New York: Routledge, 2011), p. 196.

Chapter 3 1. Although the text of the chorale is the same as that used by Pachelbel in Example 3–2, the melody is entirely different. 2. These terms come from the fact that the largest pipe sounding at concert pitch is approximately eight feet tall and the one sounding an octave lower is approximately sixteen feet tall.

Chapter 4 1. Notice that the realization of the figured bass is independent of the violin melody: the two hands of the keyboard player perform a three-voice texture accompanying the violin part. Since we are not dealing here with a four-voice texture, the upper staff is free to move in parallel unisons or octaves with the violin melody. 2. There is a three-measure transition leading into the second movement that is not shown here. 3. Closely related keys are determined by the natural minor scale. Hence, in minor mode the key of the dominant is minor. 4. For a discussion of triads serving as prototypes of harmonic particular functions, see Eytan Agmon, “Functional Harmony Revisited: A Prototype-Theoretic Approach,” Music Theory Spectrum 17/2 (1995): 196–214. For an empirical study of harmonic function in a corpus of Bach chorale harmonizations, see Ian Quinn and Panayotis Mavromatis, “Voice-Leading Prototypes and Harmonic Function in Two Chorale Corpora,” in Mathematics and Computation in Music: Third International Conference, MCM (Berlin: Springer, 2011), pp. 230–40.

Chapter 5 1. For an illuminating examination of the “ancestry” of sequences commonly used by Corelli and Vivaldi, see Daniel Harrison, “Rosalia, Aloysius, and Arcangelo: A Genealogy of the Sequence,” Journal of Music Theory 47/2 (2003): 225–72. 2. In the dominant key (B minor) the three sixteenth-notes would have been G–A#–C#. In this case the change may have come about as a way to avoid the augmented second between G and A#. Alternatively, an exact sequence could have been produced by using the notes G#–A#–C#. 3. The sum is 9 rather than 8 because by tradition we speak (incorrectly) of a unison as 1. Actually, of course, the intervallic distance between the two notes of a unison is zero. 4. The distinction between generic and specific interval sizes (i.e. the difference between “a third” and “a minor third”) was introduced by John Clough and Gerald Myerson in “Variety and Multiplicity in Diatonic Systems,” Journal of Music Theory 29/2 (1985): 249–70. 5. Justifiable parallel fifths in the sequence are the result of non-chord tones of differing types.

Chapter 6 1. The approach taken here owes much to the article by Ellwood Derr, “The Two-Part Inventions: Bach’s Composers’ Vademecum,” Music Theory Spectrum 3 (1981): 26–48. For an insightful study of Bach’s Inventions

Notes

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253

from a Schenkerian perspective, see Olli Väisälä, “Bach’s Inventions: Figuration, Register, Structure, and the ‘Clear Way to Develop Inventions Properly’,” Music Theory Spectrum 31/1 (2009): 101–52. It will be noticed that the keys are restricted to those having no more than one sharp or flat and appear in ascending order. The use of the hemiola—a grouping of two beats within triple meter—at cadences was not new with Bach. From the late sixteenth century on, music in triple meter often preceded cadences by means of this rhythmic alteration. In Bach’s day the sign that we now think of as an inverted mordent or Schneller, introduced at measures 19 and 29, was understood to mean a trill. On page 8 of the Clavierbüchlein Bach gives an explanation of the manner of playing ornaments, this symbol, heading the list, is termed by Bach “Trillo” and begins with the upper note. For more on one-part forms, see Douglass M. Green, Form in Tonal Music: An Introduction to Analysis, 2nd ed. (New York: Holt, Rinehart and Winston, 1979), pp. 90–3. Since the chief motives in the A-minor Invention are already jagged lines, it is not appropriate to single out any particular one as causing tension. A better example can be found at measure 14 of the Invention No. 1 in C major, not included in this book, but well known to every pianist.

Chapter 7 1. On the use of triply invertible counterpoint in Bach’s Sinfonias and other works, see Daniel Harrison, “Some Group Properties of Triple Counterpoint and Their Influence on Compositions by J. S. Bach,” Journal of Music Theory 32/1 (1988): 23–49.

Chapter 8 1. For much more on Bach’s canonic compositions, see David Yearsley, Bach and the Meanings of Counterpoint (Cambridge: Cambridge University Press, 2002), especially Chapter 2, “The Alchemy of Bach’s Canons.”

Chapter 9 1. The nature of a fugal exposition and the seemingly argumentative relationship between fugal voices points toward a rhetorical perspective on fugue. See Daniel Harrison, “Rhetoric and Fugue: An Analytical Application,” Music Theory Spectrum 12/1 (1990): 1–42. 2. An exceptional case is Fugue No. 22 in Bb major from Volume 2 of The Well-Tempered Clavier, in which ^ the first note is an incomplete upper neighbor to 1. The answer begins with an incomplete upper neighbor ^ to 5 . 3. The aberrant syncopations in measures 21–22 (middle voice, as well as the top voice in m. 22) can be explained as follows. If beat 3 of measure 21 had been written as a quarter-note rather than the eighth rest followed by two tied eighths, the result would have been unplayable by two hands. Instead, the syncopation presents a solution, and is then corroborated by its repetition in the next measure and also in the top voice.

Chapter 10 1. For a discussion of the tunes themselves and Bach’s “wonderfully self-ironizing gesture” of using such “lowly melodies,” see David Yearsley, Bach and the Meanings of Counterpoint (Cambridge: Cambridge University Press, 2002), pp. 120–3.

254

Notes

Chapter 11 1. The score for this piece was created using a machine called the “UPIC,” which was also used to produce the sound. For more information see Gérard Marino, Marie-Hélène Serra, and Jean-Michel Raczinski, “The UPIC System: Origins and Innovations,” Perspectives of New Music 31/1 (1993): 258–69. More of the score for this piece is given on pp. 12–15 of Perspectives of New Music 25/1–2 (1987). 2. Regarding Schoenberg’s statements, see Carl Dahlhaus, “Emancipation of the Dissonance,” in Schoenberg and the New Music, trans. Derrick Puffett and Alfred Clayton (Cambridge: Cambridge University Press, 1987), pp. 120–7. Seeger’s ideas are explored in Lyn Burkett, “Tensile Involvement: Counterpoint and Compositional Pedagogy in the Work of Seeger, Hindemith, and Krenek,” Ph.D. diss., Indiana University, 2001, and in Stephen P. Slottow, “Carl Ruggles and Charles Seeger: Strict vs. Free Imitation in Ruggles’s Canons,” Music Theory Spectrum 30/2 (2008): 283–303. 3. See David Neumeyer’s discussion of this piece in Chapter 4 of The Music of Paul Hindemith (New Haven, CT: Yale University Press, 1986). 4. Henry Martin considers the applicability of species principles to twentieth-century counterpoint, and proposes three categories of intervals for this repertoire: consonances as typically understood, “model consonances” (including major seconds, perfect fourths, and minor sevenths), and dissonances (including minor seconds, tritones, and major sevenths). See “Seven Steps to Heaven: A Species Approach to Twentieth-Century Analysis and Composition,” Perspectives of New Music 38/1 (2000): 129–68. 5. Ellie Hisama identifies the degree to which each sonority violates the standard low-to-high ordering of the four instruments (i.e. the “degree of twist”) throughout this movement. See “The Question of Climax in Ruth Crawford’s String Quartet, Mvt. 3,” in Elizabeth West Marvin and Richard Hermann (Eds.), Concert Music, Rock, and Jazz Since 1945: Essays and Analytical Studies (Rochester, NY: University of Rochester Press, 1995), pp. 285–312. Also see Joseph N. Straus, The Music of Ruth Crawford Seeger (Cambridge: Cambridge University Press, 1995), pp. 158–72. 6. Stephen A. Taylor, “Chopin, Pygmies, and Tempo Fugue: Ligeti’s ‘Automne a Varsovie’,” Music Theory Online 3/3 (1997). 7. Jonathan W. Bernard, “Voice Leading as a Spatial Function in the Music of Ligeti,” Music Analysis 13/2–3 (1994): 227–53; Jane Piper Clendinning, “Structural Factors in the Microcanonic Compositions of György Ligeti,” in Elizabeth W. Marvin and Richard Hermann (Eds.), Concert Music, Rock, and Jazz Since 1945: Essays and Analytical Studies (Rochester, NY: University of Rochester Press, 1995), pp. 229–56. 8. Ligeti’s technique was inspired by Conlon Nancarrow’s Studies for Player Piano. Nancarrow composed roughly fifty “studies,” most of which involve canons between parts playing in different tempi (prolation canons) and textures that would be unplayable by human pianists. The tempi are most often related by simple ratios, but several studies are based on irrational tempo relationships. See Kyle Gann, The Music of Conlon Nancarrow (Cambridge: Cambridge University Press, 1995). 9. Vermont Counterpoint for amplified flute and tape (1982), New York Counterpoint for amplified clarinet and tape (1985), and Electric Counterpoint for electric guitar and tape (1987). Reich’s Piano Counterpoint (1973, arr. 2011) is an arrangement for piano and tape of his much earlier composition “Six Pianos”. 10. Max Noubel, “Three Illusions . . . and Maybe a Fourth: A Hermeneutic Approach to Carter’s Recent Music,” in Marguerite Boland and John Link (Eds.), Elliott Carter Studies (Cambridge: Cambridge University Press, 2012), pp. 253–70 (especially pp. 263–7). 11. Nicholas Cook, “Prompting Performance: Text, Script, and Analysis in Bryn Harrison’s être-temps,” Music Theory Online 11/1 (2005). 12. Eric Clarke, Nicholas Cook, Bryn Harrison, and Philip Thomas, “Interpretation and Performance in Bryn Harrison’s être-temps,” Musicae Scientiae 9/1 (2005): 31–74. 13. There have actually been numerous completions of this fugue. Furthermore, Christoph Wolff argues that Bach in fact finished the fugue, but that the completion was lost. See his essay “Bach’s Last Fugue: Unfinished?” in his book Bach: Essays on His Life and Music (Cambridge, MA: Harvard University Press, 1991), pp. 259–64.

Index of Musical Examples

“Ach Gott, erhör’ mein Seufzen” (chorale melody) 14 “Ach Gott, vom Himmel sieh’ darein” (chorale melody) 7 “Alle menschen müssen sterben” (chorale melody) 14–15, 33–6 “Allein Gott in der Höh” (chorale melody) 5, 10 Bach, Johann Sebastian “Alle menschen müssen sterben” (chorale prelude), BWV 643 35–6 Canon, BWV 1077 (“Canone doppio sopr’ il soggetto”) 135 Canon 1 (from The Musical Offering, BWV 1079) 136 Canon 2 (from The Musical Offering, BWV 1079) 136 Canon 3 (from The Musical Offering, BWV 1079) 137 Canon 4 (from The Musical Offering, BWV 1079) 137–8 Canon 5 (from The Musical Offering, BWV 1079) 138 Canon 7 (from The Musical Offering, BWV 1079) 139 Concerto for two violins, BWV 1043, mvt. 2 65 “Der Tag, der ist so freudenreich” (chorale prelude), BWV 605 38–9 Flute Sonata, BWV 1034 62–3 (mvt. 1); 66 (mvt. 2) Flute Sonata, BWV 1035, mvt. 2 66 French Suite no. 4, BWV 815, mvt. 7 76 Fugue no. 1, BWV 846 (from The Well-Tempered Clavier, book I) 153, 160 Fugue no. 2, BWV 847 (from The Well-Tempered Clavier, book I) 103, 110, 144–6, 155 Fugue no. 3, BWV 848 (from The Well-Tempered Clavier, book I) 153, 157 Fugue no. 4, BWV 849 (from The Well-Tempered Clavier, book I) 154 Fugue no. 6, BWV 851 (from The Well-Tempered Clavier, book I) 109 Fugue no. 8, BWV 853 (from The Well-Tempered Clavier, book I) 162–4 Fugue no. 10, BWV 855 (from The Well-Tempered Clavier, book I) 77 Fugue no. 13, BWV 858 (from The Well-Tempered Clavier, book I) 158 Fugue no. 17, BWV 862 (from The Well-Tempered Clavier, book I) 158

Fugue no. 18, BWV 863 (from The Well-Tempered Clavier, book I) 151 Fugue no. 19, BWV 864 (from The Well-Tempered Clavier, book I) 152 Fugue no. 21, BWV 866 (from The Well-Tempered Clavier, book I) 104 Fugue no. 22, BWV 867 (from The Well-Tempered Clavier, book I) 161 Fugue no. 14, BWV 883 (from The Well-Tempered Clavier, book II) 104 Fugue no. 16, BWV 885 (from The Well-Tempered Clavier, book II) 156–7 Fugue no. 17, BWV 886 (from The Well-Tempered Clavier, book II) 155–6 Goldberg Variations, BWV 988, var. 1 64 Invention no. 3, BWV 774 77 Invention no. 4, BWV 775 77, 82–3 Invention no. 6, BWV 777 63, 98–101 Invention no. 7, BWV 778 63, 92–3 Invention no. 8, BWV 779 94–6 Invention no. 9, BWV 780 87–9 Invention no. 10, BWV 781 96–8 Invention no. 13, BWV 784 70, 85–6 “Komm, süsser Tod” 20–1, 25 “Lasset uns mit Jesu ziehen” (no. 18 from Schemelli Gesangbuch), BWV 481 53 Trio Sonata (from The Musical Offering, BWV 1079), mvt. 3 103 “O Jesulein süss, O Jesulein mild” 18–19, 25 Orchestral Suite no. 2, BWV 1067, mvt. 3 130–2 Organ Fugue, BWV 552 (“St. Anne”) 67, 161 Organ Sonata no. 1, BWV 525, mvt. 1 69 Organ Sonata no. 4, BWV 528, mvt. 2 67–8 Sinfonia no. 3, BWV 789 112–14 Sinfonia no. 4, BWV 790 110 Sinfonia no. 6, BWV 792 104 Sinfonia no. 7, BWV 793 115–17 Sinfonia no. 8, BWV 794 109, 118–20 Sinfonia no. 9, BWV 795 120–3 Sinfonia no. 14, BWV 800 105 Toccata and Fugue, BWV 540 153

256

Index of Musical Examples

“Vater unser in Himmelreich” (chorale prelude), BWV 636 37 “Vom Himmel hoch, da komm ich her” (chorale prelude), BWV 606 40–1 Bartók, Béla “Diminished Fifth” from Mikrokosmos, Sz. 107 223 Music for Strings, Percussion, and Celesta, Sz. 106, mvt. 1 232–5 Beethoven, Ludwig van “Mir ist so wunderbar” (quartet from Fidelio, op. 72) 126–7 Symphony no. 7, op. 92, mvt. 2 194–5, 203 Berlioz, Hector La Damnation de Faust, op. 24 209–12 “Roméo seul” (from Roméo et Juliette, op. 17) 201–2 Brahms, Johannes Organ Fugue, WoO 8 174 String Quintet, op. 88, mvt. 3 174–92 Symphony no. 2, op. 73, mvt. 1 204–7 Variations on a Theme by Robert Schumann, op. 9, var. 10 133–4 “Christus, der uns selig macht” (chorale melody) 44 Corelli, Arcangelo Trio Sonata in G minor, op. 3 no. 11, mvt. 1 57–8 “Der Tag, der ist so freudenreich” (chorale melody) 38–9 “Dona nobis pacem” (round) 125 “Erhalt’ uns, Herr, bei deinem Wort” (chorale melody) 31 Franck, César Violin Sonata, mvt. 4 201 “Freu’ dich sehr, O meine Seele” (chorale melody) 5 Green, Douglass Marshall Gavotte 106 Handel, George Frideric Concerto Grosso, op. 6 no. 12, mvt. 2 23–4 Flute Sonata, HWV 367b, mvt. 2 54 Messiah, HWV 56 61 (nos. 2 and 3), 148 (no. 44) Sonata for violin and continuo, op. 1 no. 3, mvt. 1 46–8, 55 Suite, HWV 432, mvt. 3 70 “Herzlich tut mich verlangen” (chorale melody) 3 Hindemith, Paul Fugue no. 4 from Ludus tonalis 240 Prelude from Mathis der Maler 220 Honegger, Arthur Symphony no. 3, mvt. 2 226–7 “Jesu, meine Freude” (chorale melody) 4–5, 11, 12

“Komm, süsser Tod” (chorale melody) 20–1, 25 “Kookaburra sits in the old gum tree” (round) 125 “Liebster Jesu, wir sind hier” (chorale melody) 30–1 Ligeti, György Etudes, book I, no. 6 235–6 Lux aeterna 237–8 Mendelssohn, Felix Symphony no. 4, op. 90, mvt. 2 196–8 Messiaen, Olivier Quartet for the End of Time, mvt. 1 225–6 Mozart, Wolfgang Amadeus Requiem, K. 626, mvt. 2 166–72 String Quartet, K. 387, mvt. 4 174–6 “Nun danket alle Gott” (chorale melody) 2, 4, 11 “O Jesulein süss, O Jesulein mild” (chorale melody) 18–19, 25 Pachelbel, Johann “Alle menschen müssen sterben” (chorale prelude) 34–5 Schoenberg, Arnold Five Pieces for Orchestra, mvt. 3 230–1 Pierrot Lunaire, mvt. 8 228–9 Seeger, Ruth Crawford String Quartet 1931, mvt. 3 221–2 Stravinsky, Igor “The Dove Descending Breaks the Air” 224 Tárrega, Francisco Recuerdos de la Alhambra (arr.) 213–17 Tchaikovsky, Pyotr Ilyich Symphony no. 5, op. 64, mvt. 2 199–200 “Valet will ich dir geben” (chorale melody) 3, 8 “Vater unser in Himmelreich” (chorale melody) 6, 10, 37 Verdi, Giuseppe Prelude from Un Ballo in Maschera 208–9 “Vom Himmel hoch, da komm ich her” (chorale melody) 40–1 “Wachet auf” (chorale melody) 27–30 Wagner, Richard Prelude from Die Meistersinger von Nürnberg 202 Webern, Anton Variations, op. 27 no. 2 238–9 “Wer nur den lieben Gott lässt walten” (chorale melody) 3, 8 Xenakis, Iannis Mycenae-Alpha 219