DAMSCHRODER, David. 2008. Thinking About Harmony - Historical Perspectives on Analysis

This page intaentionally left blank

Thinking About Harmony

Focusing on music written in the period 1800–50, Thinking About Harmony traces the responses of observant musicians to the music that was being created in their midst by composers including Beethoven, Schubert, and Chopin. It tells the story of how a separate branch of musical activity – music analysis – evolved out of the desire to make sense of the music, essential to both its enlightened performance and to its appreciation. The book integrates two distinct areas of musical inquiry – the history of music theory and music analysis – and the various notions that shape harmonic theory are put to the test through practical application, creating a unique and intriguing synthesis. Aided by an extensive compilation of carefully selected and clearly annotated music examples, readers can explore a panoramic projection of the era’s analytical responses to harmony, thereby developing a more intimate rapport with the period. D D is Associate Professor of Music Theory at the University of Minnesota School of Music, where he teaches courses on tonal harmony and form, the history of music theory, and Schenkerian analysis. His current research is focused on harmony in the music of Franz Schubert, complemented by performance activities on fortepiano. His previous books include Music Theory from Zarlino to Schenker (with D. R. Williams), Listen and Sing, and Foundations of Music and Musicianship.

Thinking About Harmony Historical Perspectives on Analysis   The University of Minnesota

CAMBRIDGE UNIVERSITY PRESS

Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo Cambridge University Press The Edinburgh Building, Cambridge CB2 8RU, UK Published in the United States of America by Cambridge University Press, New York www.cambridge.org Information on this title: www.cambridge.org/9780521888141 © David Damschroder 2008 This publication is in copyright. Subject to statutory exception and to the provision of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published in print format 2008

ISBN-13 978-0-511-39686-1

eBook (NetLibrary)

ISBN-13 978-0-521-88814-1

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.

Contents

Preface

page vii

1 Chord identification

[1]

Arabic and Roman numerals [1] Daube’s three chords and the emergence of a function theory Chordal roots [17] Mendelssohn’s Wedding March and British harmonic theory

2 Chordal embellishment

[9] [24]

[31]

Rameau on suspensions [31] Kirnberger’s incidental dissonances [37] Embellishment in a phrase by Chopin [40] Koch’s Stammakkord and the dissonant 64 [43] A Beethoven/Schubert connection [46] Berlioz and Fétis on embellishment [49]

3 Parallel and sequential progressions [58] Parallel motion in thirds or sixths [58] Chains of descending fifths [65] Langle’s Tours de l’harmonie [75] Schubert’s transformation of the ascending 5–6 sequence

4 Harmonic progression

[85]

The artistic progression of harmonic triads [85] Rankings of chord successions [86] Portmann’s rules of succession [90] The privileged fifth [94] Succession by third [98] Succession by second [100] Koch’s model: Schubert’s composition [106]

5 Chordal hierarchy

[113]

Passing note, passing chord [113] Reductive analysis in the nineteenth century Hierarchy in fifth-related chords [126] Dehn on Beethoven [132]

[123]

[79]

vi

Contents

6 Modulation to closely related keys [139] An analytical pioneer: Lampe [139] Chromatic pitches as modulatory triggers [141] Non-modulatory analysis [149] Multiple meaning [156] Prout’s modulatory practice [161] 7 Chromatic chords: diminished/augmented Chords via “licence” [166] Enharmonicism [173]

[166]

Diminished seventh chords in Weber’s Euryanthe [177] Marx on diminished thirds (augmented sixths) [185] Weitzmann on diminished sevenths [190]

8 Chromatic chords: major and minor [198] bII: the strategy of denial [198] bII: strategies of inclusion [204] Non-diatonic goals of modulation [210] Rossini and the major mediant [213] Seyfried’s and Schubert’s modulations [220] A Wagnerian antipodal conundrum [224] A parallel progression in Verdi’s Luisa Miller [230] Epilogue

[238]

Biographies of music theorists [244] Notes and references [287] Select bibliography of secondary literature Index [328]

[322]

Preface

“In the following Sheets I presume to lay before the Public, an Essay, calculated for the use of those who wish to study musical composition, to teach music with propriety, or to judge of the music they hear, practise, and encourage.” So begins the Preface to Augustus Frederic Christopher Kollmann’s An Essay on Musical Harmony, According to the Nature of That Science and the Principles of the Greatest Musical Authors (1796). And so begins mine. Kollmann’s premise – that one’s engagement with music is enhanced through attention to the mechanics of its construction – has withstood the test of time, even if what goes by the name “music” in Western culture by now has become so variegated that few essayists could presume to address it globally. I certainly am not so qualified or so disposed. Instead, I propose to focus my investigation of how harmonic analysis emerged as a field of musical endeavor principally on how musicians during the first half of the nineteenth century practiced it. My scope widens beyond that frame to accommodate eighteenth-century ideas that formed the foundation for developments after the turn of the century and to engage authors who refined existing approaches even as compositional and analytical practices headed in new directions later. Practitioners of a wide range of modern methodologies will find antecedents in abundance, though the authors I address did not regard their contributions as antecedent to anything: they were in the thick of things, coparticipants in the musical culture defined by the composers whose works they scrutinized, and thus they felt themselves to be ideally qualified to make judgments and to propose productive modes of thought. Though I mention Riemann, Schenker, and Schoenberg on occasion, my principal interest is in assaying what the analytical landscape was like before those well-studied giants emerged. There was never a unified analytical practice that composers, critics, performers, and music lovers of the early nineteenth century all embraced; nevertheless the ideas I present are representative of what at least some citizens of that period regarded as worth the effort and expense of publication. Even if from our modern perspective their conceptions occasionally seem peculiar or off the mark, a careful exploration of their contributions offers a means for developing a more vibrant and intimate relationship with the music and the era. We now take it for granted that professional musicians will possess the array of skills necessary for analyzing musical scores. How this aspect of musicianship

viii

Preface

evolved in conjunction with the shaping of the tonal music repertoire is a fascinating story. Aided by an extensive compilation of carefully selected and clearly annotated music examples, readers are invited to explore a panoramic projection of the era’s analytical responses to harmony, thereby developing a keener rapport with the period and at the same time expanding their own capacities to think carefully about the art. On the pages that follow I endeavor to integrate two distinct areas of musical inquiry: the history of music theory and music analysis. The intersections and juxtapositions that permeate the work should offer much to researchers and analysts who generally confine themselves to a narrower purview. Various notions that shape harmonic theory are put to the test through practical application. The synthesis of these two areas of study should prove to be one of the book’s most intriguing and revelatory features. In his Observations sur la musique (1779), Chabanon ponders the relationship between musical creations and the principles of the art: “One has never seen basic principles spring up before exempla, nor reason dictate to genius what it must do. Genius operates under the influence of a guiding sensibility, creating laws inadvertently. Later, contemplating the works borne of genius, the faculty of reason reveals to their creator the secret of their inner workings. From such exempla, reason formulates the principles of the art.” I introduce and assess a broad range of analytical techniques with the intent of vividly recreating modes of thinking current in the nineteenth century. These ideas are not all congruous: the process of exploration and invention that unfolded over centuries is a story of competing priorities, conflicting strategies, and clashing notational systems. Readers whose prior exposure to analysis stems from a single source – say, the ubiquitous undergraduate harmony textbook written by a seemingly infallible author – may be in for a shock: hardly anything you have learned is accepted universally. Be forewarned that my account does not dismiss or temper the conflicts, contradictions, and occasional dead ends that were and remain inevitable in a communal creative process that has as its focus such a wondrous and complicated subject as the corpus of music written by the likes of Beethoven, Schubert, and Chopin. As author I have learned to play the role of chameleon, adopting whatever analytical and notational practices I am presenting at a given moment. It is my hope that a clear presentation, extensive and abundantly annotated music examples (many of them reprinted directly from the original sources), and informative endnotes will provide a framework congenial to my readers. Also note that a thumbnail sketch of each author appears in the Biographies of music theorists at the end of the book (beginning on p. 244). (These sketches include a listing of the treatises cited, along with an English translation of each title.)

Preface

Idealistically I might hope that all musicians for whom the performance and study of tonal music is a daily occupation would find the contents of this book pertinent and fascinating, yet I suspect that its most avid readers will be scholars in the disciplines of music theory and musicology at the graduate level and beyond. My coverage emphasizes breadth, under the assumption that readers stimulated by what I present will want to proceed directly to the treatises cited. (Though my research was done the old-fashioned way – microfilms, interlibrary loans, visits to rare book rooms – certainly many readers will live at a time when the sources cited are available on a virtual internet library.) I have purposefully steered clear of influences from modern agendas as much as possible. I gratefully acknowledge my debt to several generations of scholars who have come before me. For any translation that I borrow, the source is named within the citation. All other translations are my own. I wish to thank the University of Minnesota Graduate School for a Grant-inAid of Research, Artistry and Scholarship, which enabled me to acquire an immense collection of microfilms and antiquarian editions of theoretical treatises to supplement the holdings of the University library, and for the support of a Bush Supplement Sabbatical Program Award. The digital photography units of the Sibley Music Library (Eastman School of Music), the Yale University Library, and the University of Minnesota Library have created a collection of vivid images that allow the authors under discussion to communicate directly with modern readers. My work has evolved from formative study under several inspiring teachers, whom I wish to acknowledge here: Allen Forte, John Rothgeb, David Russell Williams, and the late Douglass Green and Claude Palisca. I also thank four of my students who assisted in the project’s final stages: Christopher Brody, Carl Heuckendorf, Peter Purin, and Peter Smucker.

Conventions regarding note relations, chords, keys, and Roman numerals Throughout the book, harmonic (vertical) pitch combinations (such as C-E-G on p. 9) are indicated with a hyphen (-), while melodic (horizontal) pitch successions (such as C–E–G–C on p. 26) are indicated with a dash (–). Keys and chords are distinguished as follows: C Major (with a capital M) is the key of C Major; C major (with a small m) is a C major chord. During the discussion of a historical analyst’s methodology, his analytical notation will be adopted. In all other contexts Roman numerals are presented in capital letters regardless of a chord’s quality, though modified by an accidental if the chord is altered. Thus C Major: I–II–V–I and not I–ii–V–I; and C Minor: I–II–Vs–Is (closing on a major tonic), not i–ii˚–V–I.

ix

1

Chord identification

Arabic and Roman numerals The pitches C, E, and G are used in three of the most basic chords of Baroque G C thoroughbass practice: EC (a chord in 53 position), GE (a chord in 63 position), and E C (a chord in 6 position). The esteemed Berlin theorist Johann Philipp G 4 Kirnberger, writing in 1771, asserts that “these three consonant chords are really just three different representations of one and the same chord, the perfect triad.”1 Though the chords could be compared in ways that emphasize their differences, pitch content is here proposed as their defining G B C feature. GE is more closely allied with EC than with GE or other chords with bass D E, or with AF or other chords in 63 position. The principle of chordal inversion, first disseminated by German authors in the early seventeenth century, has by now become a potent tool for simplifying the classification of chords.2 As had Jean-Philippe Rameau,3 France’s preeminent authority on music theory, Kirnberger espouses a root-oriented approach, as the traditional thoroughbass perspective organized around characteristic intervallic numbers gradually waned. Though neither Rameau nor Kirnberger develops a practice of analytical chord labeling akin to modern Roman-numeral usage, their persuasive assertion of the chordal root’s importance became a bedrock within the analytical practice that was emerging around them. John Frederick Lampe, a German musician who migrated to London in the 1720s, charts two divergent paths for analysis in his 1737 thoroughbass manual for keyboardists [1.1]. First he analyzes the score’s bass line (labeled Thorough Bass). For performing musicians, these notes were the traditional focus of attention, since the figures of thoroughbass practice were dependent upon them. For example, the symbol 63 (or its abbreviation 6) placed above or below a bass note instructs the performer to play the bass along with a simple or compound sixth and third above it. Without mentioning Rameau, Lampe mirrors the Frenchman’s occasional practice of labeling these bass pitches according to their positions within the scale. Rather than translating Rameau’s space-demanding terms “not[t]e tonique” (or “son principal”), “seconde note du ton,” and “mediante,” he employs conveniently thin symbols: K. for the key note (tonic), 2d. and 3d. for the second

2

Thinking About Harmony

1.1 Lampe: A Plain and Compendious Method of Teaching Thorough Bass (1737), plate 6 (adjacent to p. 29), ex. XVI. “But let the 4th [G above bass D] be sounded or not sounded, it is still the Fifth Cord with the seventh Note to that, which accompanies the second Note to the Key” (p. 31). Lampe here displays the kinship between D-F-G-B and D-F-B, both derived from the dominant seventh, G-B-D-F. “K.” is Lampe’s abbreviation for “Key Note” (tonic). Lampe’s commentary spells out in words what we now often abbreviate with symbols: “the Fifth Cord with the seventh Note to that” is our V7; “the second Note to the Key” is our 2.

and third scale degrees.4 Another potential source for Lampe’s practice is a German tradition, surviving in several manuscript copies of compositions by J. S. Bach, in which the bass notes are marked by numbers and the letter f (for Finalis).5 In the second layer of analysis in 1.1, Lampe focuses on the progressive element, the progression of chordal roots, which he displays on a separate staff labeled Natural Bass. (Lampe’s natural bass corresponds to Rameau’s basse fondamentale, or fundamental bass, which likewise is often presented on its own staff below the bass, as in 1.17.6) The symbols “K . . . 5th. . . . K,” simple though they may seem, and appearing within this unassuming manual for keyboardists, mark the inauguration in print of harmonic analysis in the modern sense. What Lampe conveys corresponds to what the symbols “I–V–I” convey today. Falling within a theoretical outlook generally referred to by the German term Stufentheorie (scale-step theory), the procedure tracks the positions of a harmonic progression’s roots within the scale of the prevailing key. The parenthetical G below Lampe’s fifth chord hints that determining a chord’s root (natural bass or fundamental bass) is not necessarily a mechanical process. It is in fact a topic we shall explore in detail later in this chapter. Whereas Lampe’s analysis of the natural bass translates comfortably into Roman numerals as I–V–I, that of the thorough bass into I–II–III may now seem peculiar. Yet similar analyses, employing either Roman or Arabic numerals, persist among authors both renowned and obscure well into the nineteenth century, as examples by Christoph Gottlieb Schröter, Emanuel Aloys Förster, Siegfried Dehn, and Johann August Dürrnberger illustrate [1.2]. Even past the middle of the twentieth century Carl Dahlhaus questions

Chord identification

1.2a Schröter: Deutliche Anweisung zum General-Baß (1772), p. 191. “Scale of the most common harmonic settings in C Major.” Schröter’s Roman numerals indicate the scale degrees of the bass pitches – not the roots.

1.2b Förster: Anleitung zum General-bass [1805], examples appendix, p. 16, ex. 140. The use of Arabic numerals both for traditional figured bass and to indicate the scale degrees of the bass pitches could easily cause confusion. An Arabic 6 was inadvertently omitted above bass E at the downbeat of measure 2.

1.2c Dehn: Theoretisch-praktische Harmonielehre (1840), table 1 (adjacent to p. 106). “Chart of the perfect triads with their inversions.” The complete chart from which this sample is extracted fills an entire page. The root-position chord (Stammakkord) is transformed into both first and second inversions (Umkehrung I, Umkehrung II). The Roman numerals I., III., and V., corresponding to the scale degrees of the bass pitches, are employed. Dehn’s perspective perpetuates an eighteenth-century tradition: for example, the “Carte des accords de musique” in Pierre-Joseph Roussier’s Traité des accords, et de leur succession (1764) contains chords corresponding to Dehn’s, under which the terms “tonique,” “médiante,” and “cinquieme-note” are positioned; whereas Louis-Charles Bordier employs the terms “tonique,” “mediante,” and “dominante” for these chords in his Traité de composition ([ca. 1770], p. 10).

3

4

Thinking About Harmony

1.2d Dürrnberger: Elementar-Lehrbuch der Harmonie- und Generalbaß-Lehre (1841), plate XIII. As did Lampe over 100 years earlier, Dürrnberger indicates the positions of both the bass and the root pitches within the prevailing key. The label “ernied. VII.” abbreviates the German verb erniedrigen (to flatten a note), acknowledging bass Bb as the lowered seventh scale degree in C Major.

the importance of differentiating “between 53 and 63 sonorities that share the same bass pitch. Chordal connection is based on the actual bass, not on the abstract basse fondamentale.”7 Though on occasion Lampe applies analytical notation to a natural bass, most of his examples and keyboard exercises display only the thorough bass, which he often analyzes lavishly. In contrast, in Two Essays on the Theory and Practice of Music (1766) the Irish musical amateur John Trydell analyzes the natural bass progression even when a staff displaying the root progression is not shown [1.3]. The incorporation of Trydell’s work as the “Music” article in the Encyclopaedia Britannica (Edinburgh, 1771) helped acquaint a wide, mostly British audience with a root-oriented perspective. Clearly Arabic numerals are overworked in these analyses. Using the same symbols for traditional figured bass, for measuring intervals above the bass, and for indicating the scale-degree positions of either bass or root pitches likely stymied some readers. John Holden, a Scotsman who was influenced by both Lampe and Rameau, uses Lampe-inspired Arabic numerals for harmonic analysis in the early portion of his Essay towards a Rational System of Music (1770) but converts to Roman numerals later, in the context of yet another use of numbers, intervallic ratios (in a chapter he calls “Of Harmonical Arithmetic”). He explains: “The degrees of the scale are here denoted by numeral letters, instead of figures, to avoid the confusion of too many figures.”8 Both Lampe and Holden are sensitive to alteration via an accidental: Lampe employs symbols such as “6 th.” and “7th.” for raised pitches, while Holden employs the symbols “sIV.” (which occurs in the “Scale of the adjunct fifth”: V. VI. VII. K. II. III. sIV. V.) and “VIIb.” (which occurs in the

Chord identification

1.3 Trydell: Two Essays on the Theory and Practice of Music (1766), plate 19, ex. 49. Trydell employs Arabic numerals for two contrasting purposes. The lower three rows of numerals represent interval sizes, calculated from the bass. The top row of numerals indicates the scale degrees of the chordal roots. As with Lampe, “K” identifies the key note. This analysis conveys approximately the same information as the modern notation I

IV6

V

I6

I64

IV

V

I.

“Scale of the adjunct fourth”: IV. V. VI. VIIb. K. II. III. IV.). Trydell employs “b6” and “b7” in his analyses of minor-key progressions: for example, for F major and G major chords in the key of A Minor. Meanwhile in Germany the analytical deployment of Arabic numerals, mentioned as a possible source for Lampe’s practice, begins to appear in print. Georg Andreas Sorge offers the following chart of triads in his Vorgemach der musicalischen Composition [1745–47]: 5. g 3. e 1. c 1

a f d 2

h g e 3

c a f 4

d h g 5

e c a 6

In his Compendium harmonicum (1760) Sorge employs the terms Grundharmonie, Secundharmonie (major keys only), Terzharmonie, Quartharmonie, Quintharmonie, Sextenharmonie (or Sextharmonie), and Septimenharmonie (for the subtonic in minor keys).9 Georg Joseph Vogler, the most creative, productive, and influential practitioner of harmonic analysis in the late eighteenth century, employs similar language in his

5

6

Thinking About Harmony

1.4 Vogler: Gründe der Kuhrpfälzischen Tonschule in Beispielen [1778], table XXI, fig. 5. In this example of “Ten Cadences,” Vogler employs both consonant chords (diatonic I, IV, and V) and some more colorful options: half and fully diminished seventh chords and augmented sixth chords. Inverted chords receive two figured-bass analyses: one for the original chord, another for its root-position formulation. Vogler pays careful attention to alterations of pitches above the bass (note the numerous accidentals beside the figured-bass numbers) but has not yet formulated notation to mark a corresponding distinction between diatonic and modified roots (e.g. the label IV is employed both for root F and root Fs in C Major). Justin Heinrich Knecht borrows from Vogler’s model, including the use of Roman numerals, for the “Cadence” article in his Kleines alphabetisches Wörterbuch der vornehmsten und interessantesten Artikel aus der musikalischen Theorie (1795). He adds two additional cadences: V–VI and II–I.

Tonwissenschaft und Tonse[t]zkunst (1776): “denn betrachtet man den siebenten ohne die Siebente, und den fünften mit der Siebenten z. B. fünfter siebenter

G h d f: H d f . . .,”

whose translation merits some bracketed amplification, as: “for if one looks at the [chord on the] seventh [scale degree] without the seventh and the [chord on the] fifth [scale degree] with the seventh . . .”10 He also employs a Roman numeral: “VII vom C

H

d

f

as”

indicates that the pitches of the VII chord in C Minor are (capitalized) root B, D, F, and Ab, which he juxtaposes with its enharmonic equivalent: “VII vom A

h

d

f

Gis,”

(B, D, F, and root Gs in A Minor).11 A Roman-numeral label appears below each chord in his table of cadences published two years later [1.4]. At this point he does not acknowledge chromatic alterations of roots. In his later and more definitive Handbuch zur Harmonielehre (1802) he incorporates the analytical labels IVs and VIIs, in which the sharp indicates a raised root. This increased precision may reflect the influence of Johann Gottlieb Portmann,

Chord identification

1.5 Crotch: Elements of Musical Composition (1812), plate 10, ex. 148. This example employs the three principal major chords in the key of C Major. In other examples the labels do, fa, and sol (with underlines) denote minor chords on A, D, and E, respectively.

who in his Musikalischer Unterricht (1785) employs the label 47⫹ for a seventh chord on the raised fourth scale degree (e.g. Fs-A-C-E in C Major).12 Roman-numeral, Arabic-numeral, and non-numeral strategies competed as notation for harmonic analysis. In England, William Crotch dispenses with numbers altogether, instead employing sol-fa in his Elements of Musical Composition (1812) [1.5]. In Germany, Heinrich Christoph Koch in his Versuch einer Anleitung zur Composition (1782) presents a chart in which the roots of various inverted chords are indicated by Arabic numerals. For example, the number 6 is placed beside C-E-G-A in C Major. “The added number in each compartment containing a six-five, four-three, or [four-]two chord indicates the scale degree on which its root-position chord is built.”13 The Roman numerals in Gottfried Weber’s Versuch einer geordneten Theorie der Tonse[t]zkunst (1817–21) appear in one of three guises – capital, small, or small preceded by a degree circle – to indicate each triad’s quality (major, minor, or diminished, respectively), while an Arabic 7, if present, is either unadorned or slashed to indicate the chordal seventh’s quality (minor or major, respectively) [1.6]. Translations of Weber’s treatise had appeared in Copenhagen, Boston, and London by mid-century. In France, Daniel Jelensperger’s harmonic analyses in L’harmonie au commencement du dix-neuvième siècle (1830) incorporate a variety of supplementary symbols applied to Arabic numerals [1.7]. Whereas Weber’s symbols announce every chord’s quality, Jelensperger is selective: he employs additional notation only when a chord’s construction departs from the diatonic norm, be it major, minor, augmented, or diminished. The publication of Jelensperger’s work in a German translation in 1833 provided an impetus for the Arabic-numeral analysis in the treatises of Johann Christian Lobe after the middle of the century, contrasting the Weber-inspired Roman numerals of Ernst Friedrich Richter’s popular Lehrbuch der Harmonie (1853).14

7

8

Thinking About Harmony

1.6 Weber: Versuch einer geordneten Theorie der Tonse[t]zkunst (1817–21, 21824), vol. 2, table 1112, fig. 193 [Warner, p. 347]. This example shows the full range of Weber’s qualitative symbols. Ernst Friedrich Richter adds a prime after a capital Roman numeral (e.g., III’) to designate an augmented triad, which Weber avoids, and places the circle after rather than before a small Roman numeral to designate a diminished triad in his Lehrbuch der Harmonie (1853). Salomon Jadassohn follows Richter’s practice in his Lehrbuch der Harmonie (1883). Concerning the augmented sixth chord, here labeled °II7, see pp. 166–171, below.

1.7 Jelensperger: L’harmonie au commencement du dix-neuvième siècle (1830, 21833), p. 49 [Häser, p. 44]. In Jelensperger’s system an ascending virgule ( ) through a number indicates a raised root, while a descending virgule ( ) indicates a lowered root. Parentheses signify modifications of chordal quality from the diatonic norm: a left parenthesis for minor quality, a right parenthesis for major quality, both left and right parentheses for diminished quality. The leading tone serves as seventh scale degree in Jelensperger’s minor scales. In this example the second chord, because major in quality and built on the lowered seventh scale degree, is labeled 7 ). In that the 3 chord in Jelensperger’s minor keys is of augmented quality, a right parenthesis here accompanies the 3 below the third chord to indicate major quality. (Jelensperger regards C-E as a representative of C-E-Gn.) Likewise since 2 in a minor key is of diminished quality, a right parenthesis is applied to indicate the modification to major. For further discussion of this example, see pp. 310–311, n. 31, below.

Harmonic analysis organized with reference to scale steps (the Stufentheorie perspective) was pursued and developed chiefly by British and German musicians. Though Jelensperger worked in and published from Paris, he had arrived there from German-speaking Mulhouse (near Basel), and his treatise’s German translation appears to have had a greater impact than did the French original. (Jelensperger’s death the year after the work was published certainly was a blow to scale-step thinking in

Chord identification

France.) The gradual extension of the Stufentheorie perspective – how it was adapted to chart modulation from key to key, how it absorbed a wide range of dissonant and chromatically altered chords, and how a sense of chordal hierarchy gradually evolved among some of its practitioners – will be a central focus in the chapters ahead. Yet we should acknowledge from the outset that not all musicians who concerned themselves with issues of harmony followed this path. The music examples in most French treatises lack a chord-by-chord harmonic analysis. And in Germany an alternative premise for analytical investigation was formulated early on. In 1756 a young musician named Johann Friedrich Daube published a provocative work called General-Baß in drey Accorden – Thoroughbass in Three Chords. Only three chords? The idea was in the air – it had even been hinted at by Rameau, whose perspective was beginning to make inroads east of the Rhine – and a number of musicians gave it serious attention. A few even proposed some analytical terms and symbols for practical application. Before continuing our discussion of the Stufentheorie, we now take some time to explore the early formulation of this competing conception, now generally referred to by the German term Funktionstheorie (function theory). Its development during the period on which our study is focused was not extensive, compared to the flourishing of numerous strains of Stufentheorie. Yet it blossomed belatedly with bursts of insight and analytical savvy at the end of the nineteenth century.

Daube’s three chords and the emergence of a function theory Each analytical chord label in the preceding examples corresponds to the position of a favored pitch – bass or root – within a diatonic scale, as befits a theory of scale steps (Stufentheorie). Johann Friedrich Daube takes a different tack: he reduces a key’s harmonic substance to three principal chords (Haupt-Accorden). He explains: We turn now to those chords that one must know in every key when learning thoroughbass. These are the perfect, governing chord, which occurs at the beginning of a composition and also at its close, and its two subordinate chords, namely the second and third chords, which occur over the course of the melody. Their harmony is thoroughly differentiated from the governing chord. This will be explained presently.15

In C Major these chords are constructed using most or all of the following pitches: (1) C-E-G; (2) F-A-C-D; and (3) G-B-D-F. Daube’s perspective is

9

10

Thinking About Harmony

1.8 Rameau: Génération harmonique (1737), ex. X. Rameau’s two examples demonstrate how consecutive numbers within a geometric progression correspond to compositional practice. The chords in the first example are generated by the “triple progression” 1:3:9, wherein 3, the middle number, represents tonic (the son principal) in G Major (sol). The chords in the second example correspond to 3:9:27, wherein 9 represents tonic in D Major (ré). In a geometric progression, each pair of adjacent numbers is in the same proportion: x is to y as y is to z. Whereas 1:2:3 and 1:3:5 are arithmetically arranged, 1:2:4 and 1:3:9 are geometrically arranged. In musical terms, only the geometric progression generates intervals of the same size: 1:2:4 corresponds to octaves, 1:3:9 to twelfths. Observe that Rameau compresses the 1:3, 3:9, and 9:27 twelfths into fifths.

closely allied to some of Rameau’s thoughts on chord progression, though now geared to a more explicitly analytical enterprise through the use of the numerical labels 1, 2, and 3.16 The roots F, C, and G derive from the “triple progression” 1:3:9, a fact that Rameau had exploited [1.8].17 That Daube regards F, rather than D, as his second chord’s root (Grundton) accords with Rameau’s notion of a “chord of the added sixth” (accord de la grande sixte), discussed below (p. 22). Daube’s mature perspective develops out of an earlier formulation, boldly declared in the title of his first treatise of 1756: General-Baß in drey Accorden (Thoroughbass in Three Chords). From that point onward, early formulations of a function theory (Funktionstheorie) offered an alternative to the scale-step (Stufentheorie) approach. Between 1756 and 1770 Daube removed traces of scale-step thinking suggested by his original terminology for the second and third chords: “Accord des 4ten Intervalls” and “Accord der 5 der Tonart,” which reference the fourth and fifth scale degrees. Beginning in 1770 he adheres to the rigorously functional labels 1, 2, and 3. Two years later his septuagenarian compatriot Schröter mimics the conception, employing Roman-numeral labels that advance the dominant to second in rank: C-E-G is “I,” G-B-D is “II,” and F-A-C is “III.”18 On occasion Daube analyzes an extended progression [1.9]. Since this is a novel undertaking he offers a careful explanation:

Chord identification

1.9 Daube: Der musikalische Dilettant: Eine Abhandlung des Generalbasses (1770–71), p. 89. The numbers 1, 2, and 3 serve as labels for the three principal chords of C Major. Additional examples of Daube’s numerical analysis appear in Der musikalische Dilettant: Eine Abhandlung der Komposition (1773), page 26 [Snook, p. 56], and in Anleitung zur Erfindung der Melodie und ihrer Fortsetzung (1797–98), vol. 1, p. 7. The continuation of this example, demonstrating modulation to G Major and then to F Major, appears as 6.5, below.

To facilitate the learning of thoroughbass in the key of C Major we here have marked the bass line with slurs placed below the notes in such a way that one sees exactly how many bass notes are played for one chord, and which of the three chords it is. A practitioner who has correctly understood the three chords can often play the chords as they appear there: the keyboardist may simply observe the number placed inside the slur and accordingly perform the chord which it represents without paying attention to the chords published in music notation. Likewise it does not matter if the keyboardist plays the three chords in another range or configuration from how they are presented here on the upper staff – it yet remains always one and the same chord. It is anyway by no means intended that the practitioner should always perform the chords as they appear here: for these have no other purpose than to demonstrate when and where a chord can be sounded with a bass part, which to a beginner is no small service.19

Koch espouses a similar perspective, though without the numerical analysis that Daube occasionally supplies. In his Versuch einer Anleitung zur Composition (1782) he distinguishes between essential triads (wesentliche Dreyklänge) rooted on tonic and its upper and lower fifths and incidental triads (zufällige Dreyklänge) on the other scale degrees.20 Several authors of later generations group triads in a similar fashion. For example, scale-step advocate Gottfried Weber refers to the “most essential harmonies of the key”

11

12

Thinking About Harmony

En ut mode majeur. ré sol ut si mi la SOL la si UT ré mi FA 2 1 3

En ut mode mineur. ré sol si mi b SOL la b si UT ré mi b 2 1

ut la b FA 3

1.10 Momigny: Entry “Ton” in Framery’s Encyclopédie méthodique, vol. 2 (1818), p. 529. “Other accounts of the fifth scale degree fly in the face of usage by naming this note dominant. Considering its influence and its role in caesuras, through which one may reasonably determine the rank and importance of notes, one must name it the second note of the key, because it is indeed the most meritorious after the tonic, equipped with its perfect chord, just as is the tonic with its. The third note of the key, with regard to importance and merit, is the fourth scale degree, such as C Major’s F. One must observe carefully that each of these notes is the foundation for a major triad in the major mode, and that, in the minor, the dominant is the only one that retains its major quality.” [“C’est abusivement que, dans les autres relations de la cinquième note de la gamme ou de l’octave de la tonique, on appelle cette note dominante. En égard à son influence & aux repos, par lesquels on peut juger avec raison du rang & de l’importance des notes, on devroit la nommer la seconde note du ton, parce qu’elle est en effet la plus digne après la tonique, armée de son accord parfait, comme la tonique du sien. La troisième note du ton, relativement à l’importance & à la dignité, est la quatrième note de l’octave de la tonique; c’est le fa en ut, & l’on doit observer avec attention, que chacune de ces notes porte son accord parfait majeur dans le mode majeur, & que, dans le mineur, la dominante est la seule qui conserve le sien majeur.”]

(wesentlichste Harmonieen einer Tonart) and to the “kindred or appropriate accessory harmonies of the key” (eigenthümliche Nebenakkorde der Tonart).21 The imaginative French author Jérôme-Joseph de Momigny employs the labels 1, 2, and 3 in Daube’s manner (though with Schröter’s ranking) in a single example but does not pursue the notion further [1.10]. And the Bohemian August Swoboda, a Vogler pupil who worked in Vienna, distinguishes between three fundamental harmonies (Grundharmonien) and various derived chords (künstliche Accorde), such as the diminished seventh on the leading tone, that imbue the harmonic progression with “many an unexpected turn” and “furnish greater variety.”22 As with Daube’s chord 2, his fundamental Unterdominante (subdominant) chord may be constructed employing a fifth, a sixth, or both (i.e. in C Major: F-A-C, F-AD, F-A-C-D and their inversions), its principal roles being to create variety (“so that one doesn’t have to listen to the tonic and dominant all the time”) and to serve as intermediary between the other two chords.23 More sophisticated in conception and abundantly illustrated in examples, the functional system of Portmann (whom we have already encountered for

Chord identification

his earlier contribution to analytical notation within the scale-step perspective) comprises six foundational chordal structures (Grundharmonien) from which a large number of chords (Grundaccorde) can be derived. For C Major, these structures are as follows: a f d h g e C 1

f d h g e c A 2

Hauptprimenharmonie

d h g e c a F 3

e c a f d h G 4

Quartenharmonie

Sextenharmonie

h g e c a fis D 5

e c a fis d h G 6

Wechseldominantenharmonie

Dominantenharmonie

Doppeldominantenharmonie24

Each structure’s “dissonant side” extends as far as the thirteenth, though when present in a chord these upper pitches often resolve into lower ones, as in a Dominantenharmonie that proceeds from G-c-e (root-elevenththirteenth) to G-h-d (root-third-fifth). The root, and even the third, may be omitted: e-g-h, a chord of the “second order,” derives from the Hauptprimenharmonie C (with seventh); while h-d-f, a chord of the “second order,” and d-f-a, a chord of the “third order,” derive from Dominantenharmonie G (with seventh, or with seventh and ninth).25 The Wechseldominantenharmonie is of particular interest. This compound noun merges three individual terms, two of which have English cognates. The German verb wechseln has the sense of “exchange” or “change places.” In the context of a major key, the Wechseldominantenharmonie relates to the Dominantenharmonie in the same way that the Dominantenharmonie relates to the Hauptprimenharmonie. (Nowadays this relationship is often described as an “applied” or “secondary” dominant, or as “V of V.”) In a minor key, it takes on a more potent dissonant aspect. In A Minor the Wechseldominantenharmonie is spelled as H dis f a c e g, from which chords containing the augmented sixth – f a dis, f a H dis, and f a c dis – are derived. Portmann uses the numbers 1 through 6, corresponding to the six Grundharmonien, as analytical symbols only in his introductory demonstration [1.11a]. More characteristically he supplies letter names surmounted by various symbols to indicate the Grundharmonie roots and chordal functions [1.11b].26 A little-known treatise proposing a three-chord functional theory much like Daube’s appeared in London in 1850, the work of Spaniards José Joaquín de Virués y Spínola (who died a decade before the work was

13

14

Thinking About Harmony

a

b

1.11 Portmann: Die neuesten und wichtigsten Entdeckungen in der Harmonie, Melodie und dem doppelten Contrapuncte (1798), pp. 20, 123. (Tablature realized in staff notation.) (a) In Portmann’s system the numbers 1, 2, and 3 correspond to Primenharmonien: chords rooted on the tonic (Hauptprime), the sixth scale degree, and the fourth scale degree, respectively; while 4, 5, and 6 correspond to chords with dominant function: the Dominantenharmonie (built on the fifth scale degree), the Wechseldominantenharmonie (built on the second scale degree and including the raised fourth and diatonic sixth scale degrees), and the Doppeldominantenharmonie (used in the context of a pedal point on the dominant and containing elements of both other dominants). (b) In an alternative notational system that he employs more extensively, Portmann places functional symbols above alphabet letters corresponding to the chordal roots. (In what appears to be an almost anorexic obsession for thin symbols, these letters may be followed by raised or lowered commas in lieu of accidentals: for example, c’ stands for cs.) Among the functional symbols are a horizontal line and a curved line (— and ˘) placed above a letter to indicate a Primenharmonie with major and minor quality, respectively; an ascending virgule ( ) to indicate a Dominantenharmonie in a major key and an ascending virgule followed by a dot ( .) for such a chord in a minor key; a double virgule ( ) to indicate a Wechseldominantenharmonie in a major key and a slashed circle (⵰) for such a chord in a minor key. This example shows how a Dominantenharmonie in C Major (g´) becomes a Wechseldominantenharmonie in B Minor (⵰c, = Cs-Es-G-B-D-Fs-A) through the reinterpretation of F as Es. Though Portmann’s conception and symbols contrast Weber’s [1.6], both regard what is nowadays referred to as a “German” augmented sixth chord as the third, fifth, seventh, and ninth of a chord rooted on the prevailing key’s second scale degree.

published) and F. T. Alphonso Chaluz de Vernevil (who brought the work to fruition). Each chord is given a convenient name: “Since the chord hitherto called perfect, and composed of the notes 1–3–5 of the heptachord, takes the name of Cadence; the chord of seventh – sensible, composed of the notes 2–4–5–7 of the heptachord, will henceforth be called the Precadence; and the chord of subdominant, composed of the notes 1–4–6 of the heptachord, which naturally follows the cadence, will take the name of Transcadence.”27 In fact, the authors sometimes work with three functions [1.12a] and sometimes with only two [1.12b]. Hugo Riemann, a distinguished German musicologist whose voluminous theoretical writings span nearly half a century, from 1872 to 1918, is often regarded as the founder of Funktionstheorie.28 Indeed, in his hands the notion took on a sophisticated new life, replete with highly developed

Chord identification

a

b

1.12 Virués y Spínola and Chaluz de Vernevil: An Original and Condensed Grammar of Harmony, Counterpoint, and Musical Composition (1850), pp. 123, 395. (a) This excerpt from an analysis of Paesiello’s Cavatina, “Nel cor più non mi sento,” which continues through 20 measures and includes key shifts from Do to Re and to Sol, displays scaledegree numbers for all pitches: thus 1, 4, and 5 below the “Typometrical Bass” refer to bass rather than to root values (though in these measures the bass and the root pitches coincide). The harmonic analysis is placed above these bass pitches, using abbreviations for the terms Cadence, Precadence, and Transcadence. (b) “Our readers may have inferred that, in music, all consists in going towards or seeking for the tonic, and shunning or flying from the tonic. We have demonstrated that there are no more than two sonorities; viz. the precadence and the cadence. It is obvious, therefore, that they must be the two terms and the two objects of that attraction, as well as that repulsion – of that research, as well as of that flight” (p. 395). Here the word “research” is employed in a now uncommon sense: “The act of searching (closely or carefully) for or after a specified thing or person” (Oxford English Dictionary).

15

16

Thinking About Harmony

(though sometimes dubious) foundational underpinnings and an array of new analytical symbols. That development had repercussions in German scholarship and pedagogy throughout the twentieth century and is being explored anew today. It is curious that, as author of a monumental Geschichte der Musiktheorie im IX.–XIX. Jahrhundert (1898), Riemann barely acknowledges his functional predecessors. Our narrative traces the emergence and development of strategies for harmonic analysis across the swath of territory from the British Isles through Bohemia. The far north (Scandinavia and Russia) and far south (Spain and Italy) remain for the most part spectators to this enterprise. To be sure, some books with progressive contents penetrated these regions (mainly German writings northwards and French writings southwards), and a few works were translated early on. (For example, the erudite Giovanni Battista Martini studied several of Rameau’s treatises in manuscript Italian translations before reporting on the Frenchman’s theories before Bologna’s Accademia delle scienze in the early 1760s.) Yet even confining ourselves to this more limited territory, our plot is sometimes tortuous. Though it might be convenient to regard function theory as essentially a German enterprise, we noted a hint of it from Momigny in France. And how can we explain the aberration of a system much like Daube’s early formulation being offered by two Spaniards, in English no less? Concerning function theory, the relatively obscure Portmann offers the most interesting ideas and analytical methodology to emerge during the era that is our principal focus. Unfortunately he did not have a powerful immediate successor, someone comparable to Gottfried Weber, whose major thrust in Roman-numeral scale-step analysis began just three years after Vogler’s death. Thus the functional perspective lay dormant during much of the nineteenth century. Whether an analyst subscribes to the scale-step or to the function perspective, or simply notates each chord’s fundamental without further analytical observation, achieving a persuasive correlation between the chordal entities of a composition and the foundational entities operative within the theoretical framework is of critical importance. For example, a D-F-A chord in C Major would be interpreted by a practitioner of Portmann’s method as a representative of the Dominantenharmonie, rooted on G. One wonders how persuasive that notion was, particularly to musicians inclined towards the scale-step perspective. Though a larger

Chord identification

number of basic entities – seven roots, some occasionally modified chromatically – are available when scale steps ground the system, even then some chords may be assigned to categories in a way that arouses controversy. Already we have observed disagreement regarding the chord B-D-F. Is its root B, as Vogler would assert? Or G, as Lampe would assert? It is time to take a closer look at practices of assigning chordal roots.

Chordal roots Crafting chord labels for a progression of fundamental pitches within a single key is a mechanical process. Though the symbols employed in a scalestep perspective may vary from analyst to analyst, and though some may pack more information regarding quality, chord components, inversion, and chromatic alteration into their symbols than others, the outcome is predictable. In contrast, determining a chord’s fundamental can be an engaging, challenging occupation. Analysts guided by contrasting basic principles may offer wildly divergent views concerning a chord’s root; or, the same chord may be interpreted in different ways depending upon its context. Recall that Lampe regards a pitch not even present in a chord as its root [1.1]. What justifies such a choice? A chord may in certain contexts be understood as an incomplete or modified representative of some other chord. Gottfried Weber, expanding upon Vogler’s discussion of multiple meaning (Mehrdeutigkeit) in music, presents an apt example: a chord consisting of two Bs and a D. He suggests numerous possible interpretations: it could represent a G chord (G-B-D), or G7 (G-B-D-F); or °h (B-D-F), or °h7 (B-D-F-A), or h (B-D-Fs), or h7 (B-D-Fs-A); or E7 (E-Gs-B-D), or e7 (E-G-B-D); and so on.29 Mendelssohn exploits the multiple meanings of a similarly meager chord in his Song without Words in D Major (op. 102, no. 2), where two Fss and an A (measure 20) may represent fs (Fs-A-Cs) to follow the preceding Cs7 chord or D (D-Fs-A) to inaugurate the return of D Major [1.13]. If a four-note chord can be represented by two of its component pitches, then Lampe’s analysis [1.1], in which three of a chord’s four members are present, may seem less wayward. Yet whereas any chord that contains only two pitches must be analyzed in terms of some imaginative chordcompleting operation, Lampe’s imaginative effort is triggered instead by the theoretical premises of his analytical practice. He simply will not sanction having a diminished fifth above the chordal root: “There are only six Cords which consist of Sounds distinguished to be all natural.”30 (For C Major, he

17

18

Thinking About Harmony

1.13 Mendelssohn: Song without Words in D Major, op. 102, no. 2 (1845), mm. 19–21. Do the pitches Fs and A at beat 2 of measure 20 represent tonic in Fs Minor, tonic in D Major, or both?

1.14a Kirnberger: Die Kunst des reinen Satzes in der Musik (1771–79), vol. 1 appendix, p. II [Beach and Thym, p. 272]. Kirnberger regards the diminished seventh chord to arise “from the first inversion of the seventh chord with the suspended minor ninth” (vol. 1, p. 90 [Beach and Thym, p. 107]). These seventh chords appear on the lowest staff of Kirnberger’s analysis, while the suspended minor ninths are displayed among the figures above the second-lowest staff. For example, the progression’s first chord is: As E G. (Sixteenth-note A is a suspension, resolving to G.) As C(s?) E G. It represents n7 on As, whose complete realization would be: 9 The origin of this chord is 7 on Fs, where G is a suspension: Fs As C(s) E G. s Resolving the suspension, that chord becomes 7s on Fs: Fs As C(s) E Fs.

Chord identification

1.14b Vogler: Handbuch zur Harmonielehre (1802), table IV, ex. l. Vogler takes the diminished seventh chord (beat 2) at face value, interpreting Ds as its root and treating C as an essential chord member. (Kirnberger would analyze C as an incidental dissonance – a suspension – resolving to root B in a chord that spans beats two and three.) Vogler’s progression of roots (Hauptklänge) contains an augmented second. (The German adjective übermäßig means excessive or, in the context of an interval, augmented. Yet the augmented second to which Vogler refers in his caption is that between bass C and soprano Ds on beat 2, not the melodic augmented second that appears among the Hauptklänge.)

displays minor triads on A, D, and E and major triads on C, F, and G.) Thus he is compelled to regard B-D-F as an abbreviation of G-B-D-F, a perspective shared by musical thinkers of many generations.31 Chords such as B-D-F-Ab and B-D-F-A offer additional challenges. As does Vogler [1.4], one could take them at face value, with no imaginative insertions or substitutions. Yet the diminished fifth B-F would again induce some to posit G as root. Rameau regards Ab as a substitute for G: We may accept the diminished seventh chord as long as the fundamental is not destroyed by the transposition of the lowest sound [up a minor second, as in G-B-D-F to Ab-B-D-F]. We must therefore consider this lowest and fundamental sound to be implied in the sound substituted for it, so that the source continues to exist.32

In a related conception, Kirnberger in Berlin juxtaposes the absent root and the ninth, displaying 97 chords beneath diminished seventh chords and resolving their “suspended” ninths to produce conventional seventh chords [1.14a]. The ninths are “incidental” dissonances and therefore can be removed, whereas the sevenths are “essential” dissonances, or bona fide chord members.33 Comparing Kirnberger’s and Vogler’s perspectives [1.14a, b], we observe that the resultant fundamental bass lines are of distinctly contrasting characters: Kirnberger’s is dominated by perfect fourths and perfect fifths, while Vogler’s includes an augmented second.

19

20

Thinking About Harmony

a

b

1.15 Lobe: Lehrbuch der musikalischen Komposition, vol. 1 (1850, 21858), pp. 204, 206. In Lobe’s Jelensperger-inspired notation a dot above an Arabic numeral indicates a minor seventh (here A above root B) and a circle indicates a ninth (here A above absent root G). Similar examples employing Roman numerals, such as one in Friedrich Schneider’s Elementarbuch der Harmonie und Tonse[t]zkunst [1820], p. 28, appear as well.

1.16a Lampe: A Plain and Compendious Method of Teaching Thorough Bass (1737), plate 7, ex. XX (near p. 35). To achieve a perfect fifth above the root, Lampe chooses E as foundation for D-F-A-B despite what may seem a curious alliance with the chord that follows.

Concerning B-D-F-A, Lobe presents a nuanced reading that takes context into account: its root is B if a chord rooted on E follows, but G if a chord rooted on C follows [1.15]. . . Lobe’s “C: 7 3” and “a: 2 5” readings reflect a tolerant attitude towards the diminished triad, B-D-F, as a chord-building component. Certainly its justification does not emanate from B’s overtone series.34 More conservative analysts were compelled to find alternative solutions. Seeking the root of D-F-A-B in the context of A Minor [1.16a], Lampe rejects not only B (because its fifth F is diminished) but also B’s lower third, Gs (because its fifth D is diminished as well). He embraces E, which supports a fifth (5 is absent from his figures), a seventh (7), a ninth (9), and an eleventh (figured as 4). As a result his example displays natural bass E as a shared foundation for D-F-A-B and the E-Gs-B-D chord that follows. Portmann offers a similar interpretation of B-D-F, as “either an incomplete dominant seventh chord in a major key [G-B-D-F], from which the root has been omitted, or

Chord identification

b

c

1.16b Portmann: Die neuesten und wichtigsten Entdeckungen in der Harmonie, Melodie und dem doppelten Contrapuncte (1798), plate 3, figure 35. 1.16c Rey: Exposition élémentaire de l’harmonie [1807], p. 61. (b) Portmann’s example corresponds to a chart (p. 62) that labels the third chord’s D, F, A, and C as the 5th, 7th, 9th, and 11th, respectively, of C Major’s Dominantenharmonie. (See p. 13, above.) Root G and third B are absent, though they arrive later in the measure when the dissonant 9th and 11th resolve to lower elements of the Dominantenharmonie. (c) Rey’s caption for this example is “Emploi de l’Accord de Septième de Seconde” – the use of the seventh chord on the second scale degree. C, the seventh above bass D, is an eleventh (figured as 4) above root G, shown in the unperformed basse fondamentale line. Rey’s “P” indicates dissonant C’s preparation and “R” its resolution.

1.16d Halm: Harmonielehre (1900, 21925), plate XI, ex. 30a. “A subordinate triad can represent one of the two primary triads from which it is constituted, and indeed the one we expect in accordance with the rhythm . . . Consequently [in this example] the subordinate triad VI, on a downbeat and appearing when we expect IV, has the meaning of a suspension chord of this IV; . . . the subordinate triad II arises through a similar substitution: certainly . . . it is meant as a suspension [chord] that delays the arrival of V.” [“Ein Nebendreiklang kann auf einen der beiden Hauptdreiklänge, deren Kombination er ist, bezogen werden, und zwar auf denjenigen, welchen wir dem Rhythmus nach erwarten . . . So hat bei a der Nebendreiklang VI, betont und auf eine Zeit eintreffend, wo wir die IV erwarten, die Bedeutung eines Vorhaltsakkords zu dieser letzteren; . . . demselben Wechsel unterliegt der Nebendreiklang II: er wird . . . schon als Vorhalt auf V bezogen” (pp. 62–63).]

an incomplete dominant ninth chord in a minor key [E-Gs-B-D-F], from which two chord members [root and third] have been omitted.”35 Such interpretations are pursued not only in order to avoid placing diminished triads in foundational roles. Portmann in Germany and JeanBaptiste Rey in France employ a similar strategy even in a major key, where

21

22

Thinking About Harmony

D-F-(A)-C contains no diminished interval [1.16b, c]. The analysis hinges on the question of whether A and C derive from D, or whether they instead displace pitches derived from G. That issue was still generating provocative commentary a century later, in the writings of August Halm [1.16d]. While descending a third or a fifth below the lowest pitch of a chord’s stacked-thirds configuration may restore a missing or displaced root, ascending a third or a fifth above that pitch in quest of the root was practiced as well, especially by Rameau and his followers. Heeding the view of his Italian predecessor Gioseffo Zarlino, Rameau rejects the viability of a chord that extends in thirds beyond an octave above its fundamental. If one extends beyond the seventh to a ninth or an eleventh, “the fundamental of the harmony will then be confused.” By placing the root within, rather than at the bottom of, these stacked-thirds configurations, he also converts the stack’s highest element into a seventh.36 Limiting himself to the third, fifth, and seventh above, his chordal constructions must extend below the fundamental by a third or a fifth as well, in a practice he calls supposition (supposition), or sub-position, because the “added sound will suppose the fundamental, which will be found immediately above it”37 [1.17]. Pitches figured as “9” or “4” above the sounding bass function as “7” above their fundamentals, and at least in theory they will behave as would a seventh. The notion initially found some favor, and was expanded to include the thirteenth in the writings of Rameau’s champions Jean Laurent de Béthizy in France and Friedrich Wilhelm Marpurg in Germany. Yet, as we shall see, even Rameau did not consistently adhere to this formulation. Rameau’s “Irregular cadence” incorporates perhaps the most celebrated instance of a root residing among the interior pitches of a chord’s stackedthirds configuration [1.18]. Whereas the chord F-A(b)-C-D may in some contexts represent an inversion of D7, here F is indicated as basse fondamentale, while D converts the triad into a “chord of the added sixth” (accord de la grande sixte), the sixth serving as a sort of dissonance to propel the chord onward just as a seventh is added to the dominant triad for that purpose. Contrasting these various modes of interpretation, which reduce the number of distinct chord types and eliminate some problematic intervallic relationships between adjacent roots within a progression, is the option of simply embracing all common pitch combinations as chordal and categorizing them according to their stacked-thirds configurations. One particularly robust inventory along these lines appears in Johann Anton André’s Lehrbuch der Tonse[t]zkunst (1832).38 The triangle symbolizes the triad. A number placed within the triangle indicates which of five basic triad types

Chord identification

1.17 Rameau: Traité de l’harmonie (1722), p. 278 [Gossett, p. 296]. Rameau interprets the first chord of measure 2, E-G-D-F, as G7 with supposed third E and the first chord of measure 4, G-G-C-D, as D7 with supposed fifth G. The fundamental-bass progression C–D–G in measures 2 through 4 warrants further explanation, which Rameau was not yet prepared to supply in 1722. Later, in his Génération harmonique (1737), he would promote the concept of “double employment” (double emploi): F-A-C-D (measure 3) could be regarded, upon arrival, as a “chord of the added sixth” (accord de la grande sixte) with root F. Upon departure, D takes over as root. The resulting fundamental-bass progression C–F/D–G emphasizes Rameau’s preferred interval of the fifth and notably eliminates the problematic C-to-D root succession. (The issue of consecutive roots separated by a step will be addressed in chapter 4, below.) Following the model of Génération harmonique (e.g. Example XV), a cursor ( Î ) representing F might be placed below fundamental-bass D at the downbeat of measure 3 to indicate the alternative foundation pitch for this chord.

1.18 Rameau: Traité de l’harmonie (1722), p. 65 [Gossett, p. 74]. These examples display the “irregular” cadence. In his Génération harmonique (1737), p. 72, Rameau employs the term “imperfect” for this cadence type: Cadence imparfaite ou irréguliere. In both examples Rameau indicates that the chordal dissonance (a second or a seventh) occurs between two upper voices, not against the bass. (In this instance the line labeled as basse fondamentale is the sounding bass.) Observe that Rameau’s caption for the first example includes the terms “4me. Notte.” and “Notte tonique,” a model that Lampe would have rendered as “4th. . . . K.”

23

24

Thinking About Harmony

is employed: 1 for major, 2 for minor, 3 for diminished, 4 for augmented, 5 for doubly-diminished (e.g., Cs-Eb-G, upon which augmented sixth chords depend). One or two vertical marks through the triangle’s base indicate first or second inversion, respectively. The square symbolizes the seventh chord. The numbers 1 through 5 again distinguish the triadic foundations from one another, while the seventh’s quality is either minor if no further marking appears, major if a line intersects the square from lower left to upper right, or diminished if a horizontal line runs through the middle of the square. Up to three vertical marks may intersect the square’s base to indicate inversion. Ninth, eleventh, and thirteenth chords appear as triangles (if the seventh is lacking) or squares (if the seventh is present) with one, two, or three thin vertical rectangles appended to the right. Mendelssohn’s thrilling Wedding March was a well-known and beloved staple of musical life in Victorian England. Yet the full orchestra’s first chord – A-C-E-Fs – comes as something of a shock. This combination of pitches was destined to arouse controversy among analysts. We have already encountered analyses of a similar chord in examples by Lampe [1.16a, second chord] and Lobe [1.15, third chord] which, if transposed to Mendelssohn’s context, would pit B against Fs as the chordal root. Mendelssohn goes so far as to utilize this chord, neither consonant nor diatonic within the march’s C Major tonality, to begin the tune’s first phrase. What audacity! And what a challenge to Victorian analysts, who would elicit disdain from the musical public if they branded Mendelssohn as unruly or inept. Though the discussion that follows may seem a tempest in a teapot, it nevertheless conveys the mental processes of two prominent British authors who build upon bits and pieces of existing theory in coming to terms with the Romantic musical heritage, which in the case of Mendelssohn they regarded as their very own.

Mendelssohn’s Wedding March and British harmonic theory During a London visit in the mid-1840s Mendelssohn met with the surgeon and music theorist Alfred Day and his protégé George Alexander Macfarren. Day, the author of a Treatise on Harmony (1845), was intent upon testing his ideas with Mendelssohn. But, as Macfarren relates, Day’s interrogation was unsuccessful, for Mendelssohn displayed a countenance “suggestive of his having taken a dose of nauseous medicine.”39

Chord identification

1.19 Mendelssohn: Wedding March from A Midsummer Night’s Dream (1843), mm. 1–9.

The chord progression that opens Mendelssohn’s Wedding March [1.19] aroused considerable interest among Victorian analysts. The sixth measure appears in John Stainer’s A Theory of Harmony (1871), where a single “ground-note” – B – is assigned to the entire measure.40 Mendelssohn was no

25

26

Thinking About Harmony

longer around to protest, or even to display a chilly countenance. The 6s chord 5 on A is admittedly a surprising intrusion upon the culminating C of the ascending C–E–G–C trumpet fanfare. Its presence at the head of a fourmeasure phrase attracts notice both because it is dissonant and because it is foreign to the key of C Major. Stainer’s perspective echoes Lampe’s discomfort in positioning a diminished fifth above a chordal root. His analysis of both chords in measure 6 as B (dominant root of E Minor) corresponds to Lampe’s analysis of equivalent chords in 1.16a as E (dominant root of A Minor). Alternatively, a succession like that in Mendelssohn’s sixth measure might be understood as two distinct chords with roots a fifth apart: Fs and B. Rameau interprets such a succession in this manner in a fundamental-bass analysis from his Traité de l’harmonie. That analysis reached English audiences in an anonymous partial translation, A Treatise of Musick, Containing the Principles of Composition, published in 1752.41 Similar analyses by many authors, including Lobe a century later [1.15], confirm a widespread adoption of that viewpoint. The diminished quality of the chord’s fifth was not of concern to Rameau, nor to Macfarren, whose Rudiments of Harmony (1860) instructs that “a chord of the 7th may be taken on the second degree [in the minor mode], in which the 5th as well as 7th is a discord.”42 (Though Mendelssohn’s phrase ultimately establishes C Major as tonic, locally Fs serves as the second scale degree of E Minor, within a brief tonicization of the mediant.) Macfarren even presents this chord in 65 position, the exact equivalent of Mendelssohn’s chord. In the context of the Wedding March, one might make a creative application of Rameau’s notion of double employment [1.17] to offset the awkward C–Fs root succession: root C (the trumpet fanfare) would proceed to root A, a chord with added sixth that is reinterpreted as a seventh chord on Fs for continuation to B. Thus Stainer and Macfarren in the nineteenth century perpetuate a difference of opinion evident between Lampe’s and Rameau’s perspectives in the eighteenth. Stainer’s harmonic theory emanates from a “scale drawn out in thirds” in two distinct ways: one manifesting the sense of Tonic, the other the sense of Dominant [1.20a].43 Stainer explains: The simplest and most natural way of arranging chords is evidently to begin with the tonic, and to go on adding thirds from the scale, until the whole of the notes of the scale are exhausted . . . The musical value of the subtonic [leading tone] as a note which has a natural tendency to ascend to the tonic, and which cannot of course be harmonized by the tonic, has involved the necessity for a subtonic harmony or chord. The note in the scale which presents itself at once as best adapted to the accompaniment of the subtonic, is the fifth or dominant.44

Chord identification

a

b

1.20 Stainer: A Theory of Harmony, (1871, 8A Treatise on Harmony, 1884 or later), p. 21. (a) “Having defined a chord as a combination of thirds taken from a scale, it is necessary to exhibit a scale in thirds instead of single degrees, and to give names to the chords formed” (p. 21). (b) “The above diagram shows the chief diatonic chords used in music” (pp. 21–22). Observe that both dominant eleventh chords (Chords 9 and 19) contain the pitches of the supertonic seventh above the dominant root during their initial half notes.

Both of these stacked-thirds configurations contain the same seven pitch classes and may occur in both major- and minor-key colorings. They are abstractions from which the chords of actual music are derived. Stainer forms twenty such chords [1.20b] which, along with their counterparts in keys to which the composer might modulate, provide the grounding for his analytical endeavors. He asserts that “chords on the second, third, fourth, and sixth degrees of the scale are so limited in their growth as to be practically unimportant.”45 Recall that a similar reduction in harmony’s foundations had recently hit British shores in the work of Virués y Spínola and Chaluz de Vernevil [1.12].

27

28

Thinking About Harmony

Stainer’s rejection of independent harmonic status for Mendelssohn’s A-C-E-Fs chord hinges on the fact that it conforms neither to a tonic nor to a dominant rooted on Fs. He specifically addresses the chord’s major-key equivalent: “Fs, A, Cs, E cannot be derived from Fs. If it were a seventh on Fs as the dominant of B, the A would be sharp; if it were on Fs as a tonic, both A and E would be sharp; if it were on Fs as the tonic of Fs minor, the E would be sharp. Therefore Fs cannot be the ground-note.”46 Mendelssohn’s Fs-A-C-E would be prohibited for similar reasons: if it were a seventh on Fs as the dominant of B, both A and C would be sharp; if it were on Fs as a tonic, A, C, and E would be sharp; if it were on Fs as the tonic of Fs Minor, both C and E would be sharp. Stainer instead interprets it as a Chord of the 11th from the Dominant Series of E Minor [1.20b, Chord 19, transposed]. Mendelssohn’s chord is in third inversion: the chordal seventh is the bass. Its root, B, is omitted. As was also the case in Portmann’s analyses [1.11b, 1.16b], two of the higher components of the chord (here the ninth and eleventh) displace lower components, which arrive in the second half of both Mendelssohn’s and Stainer’s measures. Only one issue troubles Stainer in this interpretation: the dominant’s seventh (A, the bass that opens Mendelssohn’s measure 6) “unfortunately” ascends to B. C and E, the chordal ninth and eleventh, “drive out” the root B and third Ds from the measure’s first chord and resolve to those pitches conventionally via descending step in the measure’s second chord. Yet A ascends. This unwonted ascent of the minor seventh so scandalizes some musicians that they promptly deny that the chord is derived from [B]. But as the student proceeds to trace out the progression of chords, he will find that the following may be called a principle of progression. When a chord contains several discords, reckoning from the ground-note, the ear is often satisfied by the resolution of part of them. Thus . . . the downward progression of the eleventh and ninth completes the resolution of two of the three discordant notes, the ear willingly therefore bears with the irregular movement of the remaining one, the seventh.47

Alas, our story does not end so tidily. In his Six Lectures on Harmony (1867) Macfarren again addresses measures 6 and 7 of the Wedding March. Though the passage from his Rudiments of Harmony quoted above might lead us to expect that he will choose Fs as root for the first chord, he now concurs with Stainer, choosing B as root, but for a different reason. The chord here [with bass A] bears somewhat the aspect of a diatonic 7th of which the supertonic [in E Minor] would be the root. That it is not this, is now shown by the non-preparation of either the 7th or the diminished 5th [Macfarren here dis-

Chord identification

a

b

1.21a Mendelssohn: Chorale harmonization (1819), transposed. 1.21b Mendelssohn: Figured bass exercise (1819), transposed. These examples were transcribed by R. Larry Todd and published in his Mendelssohn’s Musical Education: A Study and Edition of his Exercises in Composition (Cambridge: Cambridge University Press, 1983), pp. 118, 109 (transposed). (a) In its larger context, this excerpt spans the major third from mediant to dominant in a minor key, whereas the opening of the Wedding March spans the major third from tonic to mediant in a major key. (b) Note the error in Mendelssohn’s voice-leading (parallel fifths). The figures for the first chord (97) are incorrect; 65 should appear instead. The abbreviations d and m refer to chord quality (dur = major; moll = minor).

regards the E and C of the preceding trumpet fanfare]; whereas preparation is an exceptionless exaction of the strict style for all the discords it includes.48

It is curious that Macfarren instead fosters an interpretation in which three chord members function as dissonances (seventh, ninth, and eleventh above B). Yet in that both the root and third are absent from Mendelssohn’s chord, those dissonant associations do not occur in sound, but instead emerge only in relation to the fifth, Fs. Mendelssohn posthumously challenges Stainer’s and Macfarren’s choice of B as root for the first chord of measure 6 through various surviving exercises completed under the tutelage of the Berlin composer Carl Friedrich Zelter, a pupil of Kirnberger. (Kirnberger had studied under J. S. Bach in Leipzig. Thus through Zelter there is a direct link between the Baroque master and his foremost nineteenth-century advocate.) In a chorale harmonization of 1819 [1.21a] Mendelssohn composes the very progression of chords that opens the Wedding March! Some of his exercises contain a separate staff showing the root progression (Grundbass). Mendelssohn places the second scale degree below a 65 chord on the fourth scale degree [1.21b]. This and other surviving exercises of this type are in major keys, wherein the chord is spelled as Fs-A-Cs-E (thus akin to Chord 9, rather than Chord 19, of 1.20b). Kirnberger’s writings give the same

29

30

Thinking About Harmony

a

b

1.22 Kirnberger: Die Kunst des reinen Satzes in der Musik (1771–79), vol. 1, pp. 113–114 [Beach and Thym, p. 131]. (a) Because this progression is “harsh,” Kirnberger offers example b as an alternative. (b) Adding a 6s to the implied 53 above bass A would result in the distinctive chord progression that Mendelssohn employs in the opening measures of his Wedding March.

status – that of “Essential Seventh Chord” – to its minor-key equivalent, Fs-A-C-E.49 Kirnberger provides a table of thirty progressions offering “the fastest way of modulating from each key to every other key.” His progression for modulating “from the tonic chord to the third, E minor” [1.22a] is accompanied by the following footnote: “This transition from the C chord to the cadence in E minor is harsh. Usually the chord on A [or other possibilities] precedes the dominant, as here [1.22b].”50 Though we understand the example’s second chord to be in the default 53 position, Kirnberger often employs a 65 in the same context.

2

Chordal embellishment

Rameau on suspensions The major triad and its two inversions, our starting point in Chapter 1, represent a primordial harmonic stability that grounds the tonal system. The pitches indicated by the figured-bass numbers 5 and 3 correspond to low partials of the root pitch.1 Thus musicians regard the 53 position as a chord’s most basic state. The numbers 6 in the 63 chord and 4 in the 64 chord represent the inversions of the 53 chord’s 3 and 5, respectively. The pitches that correspond to 6 and 4 are consonant and stable chord members. Most analysts would have concurred with what has been stated thus far. But let us consider a different context for the 64 chord, from two perspectives. E Perspective 1: The bass of a 64 chord (for example, G in GC) may assert itself as a root (as in C Major’s V chord), so that the low partials of G take over as the principal chord members. In that situation the fourth and sixth (regarded by some – for example, by Portmann – as the chordal eleventh and thirteenth to emphasize their dissonant character) typically will yield to the E D third and fifth (GC resolving to GB). This view informs the analytical decisions apparent in 1.5, measure 6, and 1.11b, measure 2. Perspective 2: A 64 chord always represents a 53 chord built from the same pitch classes. Its root is the 5 chord’s bass. Context plays no role in determining the root. What per3 spective 1 proposes to be a dominant harmony not yet fully in place is instead a tonic harmony in second inversion. This view informs the analytical decisions apparent in examples 1.2d, measure 7; 1.3, chord 6; 1.6, chord 7; and 1.9, measures 2 and 8. A serious problem has emerged: incompatible views regarding whether some chordal formations should be perceived as harmonic entities or instead as the embellishment of harmonic entities led to severe disagreements with respect to one of the most basic endeavors of harmonic analysis – determining chordal roots – and resulted in wildly divergent interpretations of certain chords’ roles within their tonal contexts. Whereas the situation concerning the 64 chord, described above, was and remains especially contentious, there are in fact many situations in which some analysts would interpret all of a chord’s members as harmonic, while others would regard the chord as a combination of harmonic and embellishing pitches.

32

Thinking About Harmony

In widely varied terminology,2 four broad categories of embellishment were proposed: the passing note, when one or more subordinate pitches connect two different harmonic pitches; the neighboring note, when a subordinate pitch relates by step to a single harmonic pitch; the suspension, when a pitch lingers beyond the duration of the harmony to which it belongs, clashing with the new harmony; and the anticipation, when a pitch arrives ahead of the chord to which it belongs, clashing with the continuing harmony. The figures in traditional thoroughbass practice are created without consideration of such distinctions. They serve simply as an inventory of what pitches sound above the bass at a particular moment. For example, (n)9 Kirnberger’s 7 notation, which appears three times in 1.14a, provides no s information regarding the roles of the three pitches that it designates. Unlike most of his predecessors, Kirnberger understood the raised third and seventh to be chord members of harmonic stature and the ninth to be an embellishment – an “incidental” dissonance – even if his figures do not convey this conception. He opposed the tendency, endemic to thoroughbass practice, to deal with all chord components together and in the same manner.3 The tension between these two conceptions has persisted within the arena of harmonic analysis to the present day. The figured-bass symbol “7” might occur in two contrasting contexts. A seventh, once sounded, may persist for the duration of a chord (in which 7 case 7 stands for 53), or it may function as a suspension, resolving by descending step to a sixth over a stationary bass (in which case 7—6 would be a char3— — acteristic context). In an embellishment-sensitive perspective such as Kirnberger’s, the pitches indicated by the notation on the upper two staves in 2.1a, measure 1, would be segregated into two groups: A-C-F and G, the latter lingering from the preceding upbeat and playing only an embellishing role. Rameau, in contrast, interprets the measure as two separate entities – A-C-G and A-C-F, the first a realization of A7, the second not an inversion of F53, as we might expect, but instead an incomplete realization of D7 (for reasons unrelated to the suspension, as explained in the caption to 2.1a). The unperformed fundamental bass reflects Rameau’s conviction that a suspension pitch warrants the same sort of harmonic derivation as the other sounding pitches.4 Yet Rameau sometimes adopts a suspension-as-embellishment perspective when other factors are in play. Two examples in his Génération harmonique (1737) show contrasting contexts for the same pitches, E figured as 9–8 in the second measure of each [2.1b]. In the first example, E-G-B-Fs (E9 in the continuo bass) is analyzed in the fundamental bass as G7, with

Chordal embellishment

2.1a Rameau: Traité de l’harmonie (1722), p. 242 [Gossett, p. 261]. “Example of the seventh prepared and resolved in the soprano.” Rameau assigns distinct roots to the preparation, the suspension, and the resolution phases. (Each resolution is preparation for the next suspension.) Complicating matters, he supplies an imaginary root for each “6” chord – for example A6 (A-C-F) in the continuo bass coordinates with D, rather than with F, in the unperformed fundamental bass. By this means the progression of fundamentals proceeds mainly in fourths and fifths (C | A D | G C | F . . .), thereby avoiding the undesirable ascending seconds that otherwise would have resulted over the bar lines (C | A F | G E | F . . .).

2.1b Rameau: Génération harmonique (1737), ex. XXX. In both of these progressions the same figures (9 8) appear over bass E in measure 2. Their contrasting contexts lead to differing analytical interpretations of the ninth: supposition (E below G7) in the first progression versus suspension (Fs above fundamental E) in the second. Rameau appears to favor supposition, for when he instead resorts to a suspension analysis he remarks that he has been compelled to do so (suspension forcee = obligatory suspension).

supposed third E. Supposition, as noted on p. 22, is his typical means of accounting for chords whose stacked-thirds formations extend beyond an octave. It is applied here so that Fs may be justified in the same manner as the other sounding pitches. The following chord, E-G-B-E (E8), is analyzed in the fundamental bass as C7, echoing his analysis of G-B-E as C7 in 2.1a.

33

34

Thinking About Harmony

In this way a root progression in fifths results (though one should note the C–Fs succession between the second and third measures). In the second example, both chords are assigned E as fundamental, impelled by the Ds–E bass succession (yielding the preferred fundamental succession by fifth, B–E, here presented in inversion as a fourth) that leads into measure 2. In this case, Rameau accepts that downbeat soprano Fs is not derived from the same principle as the other sounding pitches. Clearly Rameau’s eye is on the intervals formed by adjacent fundamental-bass pitches: his standards for chordal membership are intentionally wobbly, so that a favorable outcome will result in the fundamental bass.5 In a surprise move, Rameau embraces the embellishment perspective wholeheartedly in a manuscript treatise, “L’art de la basse fondamentale” [ca. 1738–45], where he states that “the suspension is no more than a note of taste, lacking a fundamental bass, which, if supplied, is justified only because it offers the satisfaction of comprehending that the suspended note typically traces its origin to the supposition principle. But since this is of no practical value, it is preferable to disregard the suspension note and, when assigning the fundamental bass, to take into account the consonance that it suspends and that follows directly after it.”6 Though Rameau still prefers a supposition analysis in certain contexts, the rigidity of his earlier formulation appears to have softened considerably. “L’art de la basse fondamentale” served as the foundation for Le guide du compositeur (1759) by Rameau’s student Pietro Gianotti.7 Each of the first two downbeats in one of Gianotti’s examples contains a suspension in the soprano, analyzed as such by Gianotti [2.2]. At the third downbeat, where soprano E–D is situated like C–B and D–C of the preceding measures, the analytical treatment is contrasting. Though D would be an appealing root in this context, Gianotti here takes pains to avoid the fundamental-bass ascent of a second (C to D). In the Traité Rameau states that “whenever it is permissible to have the fundamental bass ascend a tone or a semitone, the progression of a third and a fourth [or their inversions] is always implied.”8 In compliance with that prescription, the fundamental bass for measures 2 and 3 appears as C–A–D. After two downbeats embellished by suspension, Rameau’s theory of supposition is invoked: F97 is analyzed as A7 with supposed F. Jean Laurent de Béthizy, another theorist writing in Rameau’s wake, provides a matter-of-fact description of the contemporary practice: “there are two ways to obtain the chords of the ninth and of the eleventh, namely, supposition and suspension.”9 Gianotti demonstrates that these two strategies may be invoked in close proximity.

Chordal embellishment

2.2 Gianotti: Le guide du compositeur (1759), p. 281 and plate 35, ex. 16. While the unperformed fundamental bass (on the bottom staff) displays Gianotti’s principal analysis, which accords with the bass line supplied on the middle staff, he concurrently offers alternative harmonizations for the soprano via cursors. For example, soprano C at letter A could be supported by C or by D instead of by G, while soprano D at letter C could be supported by G instead of by C.

2.3 Beethoven: Symphony No. 5 in C Minor, op. 67 (1808), mvmt. 1, mm. 33–44.

We care about distinctions such as that between harmonic and embellishing interpretations of suspensions because they affect our perception of musical structure. In the first movement of Beethoven’s Fifth Symphony [2.3] the violin C of measure 34 is a suspension, resolving to Bn in measure 35.

35

36

Thinking About Harmony

a

b

2.4a Structural diagram for 2.3. 2.4b Structural diagram for Beethoven: Sonata in C Minor, op. 13 (1799), mvmt. 1, mm. 11–13. Without its suspensions (displayed as filled-in noteheads), the excerpt from Beethoven’s Symphony in C Minor reveals a kinship with a passage from his Sonata in C Minor (Pathétique).

Violinists should convey this sense of descending resolution, as well as the similar descents from D in measures 36–37 and from the sforzando Eb, F, G, Ab, Bb, and C in later measures. If these pitches are performed as embellishments, a coherent structure emerges [2.4a], one that relates to another C Minor composition by Beethoven [2.4b]. In an analysis that instead invokes Rameau’s principle of supposition, this relationship would be concealed. Certainly Rameau was a force to be reckoned with. Once d’Alembert’s Élémens de musique (1752), an appealing practical digest of Rameau’s basic ideas, appeared in German translation in 1757, circulation east of the French border was extensive. Friedrich Wilhelm Marpurg, d’Alembert’s translator, acted as a defender of the faith, even if his understanding of Rameau’s thought was not reliable. A jumble of Rameauean ideas – from one or another of Rameau’s treatises (which often do not concur with one another), from the 1752 English translation, from d’Alembert’s synopsis, from Marpurg’s translation of that synopsis, or from another author whose outlook was influenced by Rameau – circulated throughout musical Europe. Those ideas did not always garner praise. Examples such as 2.1a raised eyebrows: a simple descending 7–6 sequential pattern, familiar from numerous thoroughbass manuals, requires twelve structural roots in Rameau’s interpretation. Several of these roots contradict the progressive “stacked-thirds” notion of chord-building. Certainly a backlash was to be expected, in the interest of greater simplicity and old-fashioned musical common sense. Kirnberger was a leader in this assault.

Chordal embellishment

a

b

c

2.5 Kirnberger: Grundsätze des Generalbasses als erste Linien zur Composition [ca. 1781], part 1, plate 2, fig. 17; part 2, plate 3, fig. VII/2; part 3, plate 9, fig. XLI. The first example contains only consonances. The second incorporates an essential dissonance (F in the third chord). The third incorporates both an essential dissonance (F in the third chord) and incidental dissonances (Ab in the third and fourth chords, Bn and F in the fourth chord).

Kirnberger’s incidental dissonances In the first volume of his magnum opus, Die Kunst des reinen Satzes in der Musik (1771), Kirnberger asserts that suspensions are “incidental” or “nonessential” (zufällig) in character and thus not harmonic in the way Rameau asserted they were. One must distinguish between these incidental dissonances, which embellish the underlying harmonic formation, and the consonances and “essential” (wesentlich) dissonances that constitute the harmony.10 A chord will fall within one of four distinct categories, which Kirnberger describes as follows: Thus there are altogether four types of chords used in music: (1) the consonant, (2) the dissonant with an essential dissonance, (3) the dissonant with one or more nonessential dissonances, and (4) those resulting from a mixture of types 2 and 3, where nonessential and essential dissonances are combined. The triad with its inversions belong to the first type, the seventh chord with its inversions belong to the next, the suspensions of the consonant chords belong to the third, and the suspensions of the [essential] dissonant chords belong to the fourth.11

Grundsätze des Generalbasses als erste Linien zur Composition [ca. 1781], a little book that Kirnberger wrote as an introduction to his Kunst, illuminates his perspective. The first of its three sections addresses music fundamentals, culminating in the triad and its inversions. The second section addresses essential dissonances, and the third incidental dissonances. Considering an example from each section will reveal how a single harmonic idea fares in the context of Kirnberger’s three-stage pedagogy [2.5]. Kirnberger presents the first of these examples directly after progressions with bass C–G–C or C–F–C. Here he “extends” and “prepares” the cadence.

37

38

Thinking About Harmony

2.6 Kirnberger/[Schulz]: Die wahren Grundsätze zum Gebrauch der Harmonie (1773), pp. 51–52 [Beach and Thym, p. 207]. To eliminate the F–G step of the upper fundamental-bass analysis, Schulz asserts that it would be more correct (richtiger) to reinterpret the F53 chord as an F65 chord with absent D. One may then invoke Rameau’s principle of double employment (double emploi) to generate preferred fundamental-bass intervals (C–F and D–G), shown in the lower fundamental-bass analysis. Modern scholars disagree regarding whether Die wahren Grundsätze, which was published under Kirnberger’s name and was assumed during his lifetime to be by him, is in fact his own work or instead that of Schulz, who declared himself to be its author after Kirnberger’s death. (Dahlhaus calls Schulz Kirnberger’s “ghostwriter.”) Numerous instances of stepwise ascent occur in the fundamental basses of Kirnberger’s Die Kunst des reinen Satzes in der Musik, suggesting that the author of Die wahren Grundsätze was more influenced by Rameau than was Kirnberger himself.

Kirnberger’s claim that the subdominant is the “most natural” triad to precede the dominant contrasts Rameau’s difficulty with stepwise root successions such as F to G, which he rationalizes through double emploi (C–F– G becomes C–F/D–G). Clearly Kirnberger here intends nothing but consonances, not an interpretation of the second chord’s C as an essential dissonance above an imaginary D. Unfortunately Kirnberger’s pupil Johann Abraham Peter Schulz injects this notion into Die wahren Grundsätze zum Gebrauch der Harmonie (1773), his synopsis of Kirnberger’s teachings [2.6]. The second example contains an essential dissonance. Observe the attentive treatment of the dominant’s seventh, F: it is prepared in the preceding chord, and it resolves by descending step in the following chord. This procedure characterizes the strict style, from which composers could assert certain freedoms, such as resolution of a dissonance in another voice, in the galant style. Kirnberger calls the F an essential dissonance because it can resolve only when the chord gives way to its successor. Context is a factor in Kirnberger’s analytical thought process. Not all instances of G, B, and F sounding simultaneously would imply root G. For example, F might instead

Chordal embellishment

displace the E of a 63 chord (G-B-E), in which case E would serve as root and F would function as an incidental dissonance. This 7–6 situation appears in Kirnberger’s Kunst des reinen Satzes in der Musik as an example of “The sixth chord with its suspensions” in a “Table of Consonant Chords with One or More Nonessential Dissonances as Suspensions.” Contradicting that view, an example probably by Schulz in Die wahren Grundsätze displays a series of 7–6 suspensions in which the suspension and resolution phases are given separate roots, mimicking Rameau’s practice [2.1a].12 Kirnberger’s third example likewise employs the fundamental-bass progression C–F–G–C, though here incorporating chordal inversion and presented in the key of C Minor. Kirnberger classifies the third chord’s Ab (above bass D) as an incidental dissonance whose resolution to G is postponed (verschiebet). Though both Ab and F extend beyond this chord and resolve at the same moment, F is an essential dissonance because it cannot resolve above bass D, whereas Ab is an incidental dissonance because it could so resolve, even if in this instance it does not. Because G, though absent, serves as the chord’s root, the seventh formed between Bn and Ab, here inverted to a second, is neither essential nor incidental, but instead unauthentic (uneigentlich; unächt).13 The example’s final measure begins with an abundance of dissonances, all prepared in an exemplary manner. Whereas Rameau might have installed G as the fundamental (with supposed Eb), followed by C in the second half of the measure, Kirnberger would interpret Bn, F, and Ab as incidental dissonances. C – not G – serves as root from beat 1 onward, even if suspension Bn sounds where C belongs for half of the measure. The rift between Kirnberger and Schulz regarding embellishing versus harmonic interpretations of suspensions resulted in an inconsistent treatment of the topic in various works published under Kirnberger’s name. Advocates of either perspective could thus claim both Rameau and Kirnberger as progenitors. An interesting symmetry has emerged with regard to the suspension: Rameau’s harmonic interpretation was moderated to a more embellishment-accommodating conception in his student Gianotti’s treatise (following Rameau’s manuscript “L’art de la basse fondamentale,” which did not circulate widely), while Kirnberger’s embellishment interpretation was nudged in the harmonic direction by his student Schulz.It should thus not be surprising that the determination of just which sounding pitches constitute a harmonic chordal entity remained a contentious issue.

39

40

Thinking About Harmony

2.7 Lobe: Vereinfachte Harmonielehre [1861], p. 75. Lobe here analyzes a passage from Beethoven’s Sonata in C Minor (op. 10, no. 1), mvmt. 2. All embellishing notes are marked and are absent from the display of foundational harmonies (Grundharmonien) placed below Beethoven’s score. The numbers 1 and 2 above the score reference textual comments acknowledging the employment of two embellishing notes concurrently.

To assess how Kirnberger’s perspective developed in the nineteenth century, and how it was integrated with scale-step notation, we move ahead ninety years to an analytical strategy practiced by Lobe, notable not for its employment of numerals to indicate the structural roots (which had by this time become a common attribute of analyses, especially in Germany), but instead for how it deals with embellishing pitches. First, each embellishing note is marked in the score with a special symbol indicating its role; and second, the pitches that constitute the core harmonic fabric are fashioned into block chords, constituting a somewhat crude yet compelling “reduction” of the composition to its harmonic essence. We then apply this method to music by Chopin.

Embellishment in a phrase by Chopin Lobe presents several detailed harmonic analyses in his Vereinfachte Harmonielehre [1861], treating scores by Dürrner, Gänsbacher, Hummel, and especially J. S. Bach and Beethoven. In a passage from a Beethoven Adagio, plus signs (+) and circles (o) indicate embellishing passing notes (Durchgänge) and neighboring notes (Wechselnoten), respectively [2.7]. In other examples Lobe employs a dash (—) for a suspended note (Vorhalt) and a circumflex (^) for an anticipation (Vorausnahme). (Though Lobe acknowledges that a suspension may be either tied over from its preparation or rearticulated, he likely analyzes F at the downbeat of the second measure and Ab at the downbeat of the fourth measure instead as neighboring notes

Chordal embellishment

2.8 Chopin: Étude in E Minor, op. 25, no. 5 (1837), mm. 1–4. This analysis conforms to the procedure of Lobe’s model [2.7]. The essential sevenths E (measure 2) and A (measure 3) are prepared in the preceding chords and resolve by descending step. Kirnberger observes that “whoever wants to take pains to strip the most beautiful arias of all embellishment will see that the remaining notes always have the shape of a well-composed and correctly declaimed chorale” (Die Kunst des reinen Satzes in der Musik, 1771–79, vol. 1, p. 224 [Beach and Thym, p. 234]).

because they do not persist for a full beat.) Below the score, Lobe displays the foundational harmonies (Grundharmonien) as root-position block chords, as well as Arabic numerals indicating the scale degrees of the chordal roots. Four steps are apparent in Lobe’s analytical procedure: (1) mark and eliminate from further consideration all embellishing pitches; (2) arrange all bona fide chord members into foundational harmonies in root position on a separate staff; (3) determine the key in which the passage is composed; (4) label each chord according to the scale degree of its root within the key, making special note of all chord components beyond the three triadic pitches. (Like Jelensperger, Lobe places a dot above the numeral label to indicate the presence of a chordal seventh.) In the opening measures of Chopin’s Étude in E Minor (op. 25, no. 5) [2.8], the inner-voice sixteenth notes are Chopin’s written-out equivalent of standard eighteenth-century embellishments. Carl Philipp Emanuel Bach states in words what Chopin puts into practice: “Appoggiaturas are one of the most necessary of embellishments. They offer improvement to both melody and harmony . . . and vary chords that would have been too plain without them.”14 Measure 1 is an arpeggiation-enlivened proclamation of tonic even if tonic is contradicted at every beat. The second measure’s first chord contains three dissonances. Its B continues the fleeting inner-voice displacements of chord tones. Its G is likewise an incidental dissonance (the middle phase of a preparation/ suspension/resolution cycle), delaying the supertonic 65’s root Fs until

41

42

Thinking About Harmony

the second beat. Concurrently its E functions as the chordal seventh, an essential dissonance resolving (after transfer up an octave) to Ds with the arrival of the dominant in measure 3. Chopin’s dissonant concoction during the last beat of measure 2 includes the third, fifth, and seventh of the prolonged supertonic chord as well as anticipation B, root of measure 3’s dominant chord. G on the downbeat of measure 3 displaces Fs. Whereas Lobe likely would have regarded it as a neighbor to Fs (thus labeled o), an analysis as an accented passing note (+) is also viable. Kirnberger states that “in the free style, passing notes need not always be passed over quickly and lightly as in the strict style.”15 Here it falls on a downbeat – what Kirnberger calls an “irregular” passing note. The G at the end of measure 3 clashes with the other sounding pitches. Kirnberger relates plain melodies to walking and embellished melodies, like Chopin’s, to dancing: “Just as each step in walking can be embellished by various little motions before the foot comes down again, melodic steps can also be decorated by several notes . . . during the time that the downstep would have been held in a simple melody.”16 Chopin’s melody connects the step from Fs to E with an upward kick to G followed by a downward glide that delays the landing until the second beat of measure 4, reminiscent of similar delays in measures 2 and 3.

Rameau’s analyses from the 1720s and 1730s and Lobe’s from the 1860s differ not only in how the harmonic progressions are displayed and in their treatment of embellishment, but also in the fact that Rameau usually deals with artificially fabricated block-chord progressions, whereas Lobe puts his method to the test by applying it to actual compositions. Of course, in the latter strategy a greater density of embellishing pitches may be expected. As it should be: any musician who seeks to develop a perceptive responsiveness to the musical art must be able to deal with it in all its parameters, not only in an artificial world in which the chords are denuded of their teeming vitality. Lobe’s unembellished Grundharmonien, though certainly a part of what the performer and listener should understand about the piece, do not in themselves constitute the artwork. One thread from the opening pages of this chapter – competing interpretations of the 64 chord – is subtly woven into Lobe’s Beethoven analysis [2.7]. Observe that in the third measure two concurrently sounding pitches are marked with a plus sign (+) to indicate their role as passing notes. At that moment, the sounding pitches (Dn, G, and Bb) form a 64. Here it is not the bass Dn that asserts itself as root (as in the cadential

Chordal embellishment

2.9 Koch: Handbuch bey dem Studium der Harmonie (1811), col. 118, fig. 24. Since a key’s Stammakkorde are all arrangements of the same seven pitch classes, it is possible for the same set of four pitches to represent either the C Stammakkord (at a) or the G Stammakkord (at b).

6 4

to 53 formulation), nor is it the fourth G (which resides at the bottom of D the GBb triad that could be derived from the three sounding pitches). Instead, according to Lobe the root remains Bb. Root Bb and third D are stable chord members of the 5 harmony, and the minor third FAb formed by the fifth and seventh is filled in concurrently in both directions, as a b voice exchange (F–G–A ). Lobe asks listeners to interpret the two Gs as Ab–G–F passing, not as harmonic chord members, even though these Gs are held longer than the thirty-second notes F and Ab that follow. Another notion mentioned at the beginning of the chapter is that the fourth and sixth were sometimes interpreted as the chordal eleventh and thirteenth. Let us call upon Koch to offer an explanation.

Koch’s Stammakkord and the dissonant 64 In his Handbuch bey dem Studium der Harmonie (1811) Koch gives “budding contrapuntists” the lesson that context determines function. His fundamental seven-note parent chord (ursprünglich siebenstimmige Stammakkord), akin to Portmann’s Grundharmonien (see p. 13, above), places the seven diatonic pitches in vertical alignment, as stacked thirds. In a playful yet instructive example Koch reiterates the same four pitches on two consecutive downbeats [2.9]. In the first instance they derive from the C Stammakkord, C-E-G-B-D-F-A. D and F are the chord’s ninth and eleventh, respectively. In the second instance they derive from the G Stammakkord, G-B-D-F-A-C-E. Bass C is the chord’s eleventh. These dissonances are prepared and resolved conventionally. The dissonant F in the chord labeled b is of a different type. The C below it, which resolves within the chord, is the main dissonance (Hauptdissonanz); F, which persists until the next harmony, is the subordinate dissonance (Nebendissonanz). The distinction, though not the terminology, stems from Kirnberger.17

43

44

Thinking About Harmony

2.10 Koch: Handbuch bey dem Studium der Harmonie (1811), col. 70, fig. 25. This example triggers two perennially controversial questions: • Is C or G the root of the chord at the downbeat of measure 2? (Koch’s answer: G.) • Is this chord consonant or dissonant? (Koch’s answer: dissonant.)

2.11 Koch: Handbuch bey dem Studium der Harmonie (1811), col. 132, fig. 5. Here C and G alternate as root in one-measure shifts. Hauptdissonanzen on the downbeats of measures 2 through 4 resolve by descending step (marked by slurs).

Because Koch’s abstract Stammakkord contains the full complement of diatonic pitches, it can be used to generate an extraordinarily wide range of chords employed in compositions. One such chord – controversial in Koch’s day as in ours – is the 64 [2.10]. Koch rejects “dissonant 64 chord” (dissonirende Quartsextenakkord) as a suitable label. How could something that is consonant in its initial state (for example, C below E and G) become dissonant upon inversion?18 Koch asserts that the chord is no inversion at all, and though the numbers 6 and 4 might appear in its figured bass, they merely substitute for the true numbers, 13 and 11 – the most extreme components of the G Stammakkord. These dissonances (of the Haupt type) resolve conventionally to the chord’s fifth and third. Koch applies this perspective only when both the thirteenth and the eleventh are prepared in the preceding chord. It coexists with other instances of 64 chords that he identifies as second inversions and as consonant. Taking the argument a step further Koch rearranges the root-position G-C-E configuration (root-eleventh-thirteenth) into inversions: E-G-C and C-E-G [2.11]. All of measure 2 derives from the G Stammakkord. The dissonant thirteenth (bass E) resolves to the fifth, while the dissonant eleventh (alto C) resolves to the third. The alto and bass exchange roles in measure 4.

Chordal embellishment

2.12 Stainer: A Theory of Harmony (1871, 8A Treatise on Harmony, 1884 or later), p. 89. Stainer’s analysis of an excerpt from Beethoven’s Sonata in D Major (op. 10, no. 3), mvmt. 3, highlights the chord marked by an asterisk. The pitch A, though absent, serves as its root. Whereas Stainer accommodates bass F within his harmonic analysis (as root A’s thirteenth), Lobe likely would have placed a circle underneath the F, indicating its role as neighbor to chord member E and freeing him from the need to formulate a Grundharmonie that includes F.

Bass C, a Hauptdissonanz, is not the generator of E and G. Though C-E-G often represent a chord with root C (for example, at beat 4 of measure 3), G serves as root in the context of measure 4. Echoes of Koch’s perspective resonate throughout Stainer’s A Treatise on Harmony. In an example by Beethoven [2.12], bass pitch F is analyzed as a member of a chord he describes as “the sixth inversion of the chord of the minor thirteenth of A.”19 As with Koch, Stainer’s chordal foundation is a stacked-thirds arrangement of seven pitches (see 1.20a, chord 2), here A-CsE-G-Bb-D-F, from which he regards Beethoven’s F-G-Bb-Cs to have derived. Investing so heavily in harmonic explanations unfortunately stifles the sense of pitch hierarchy that Kirnberger’s concept of incidental dissonances had infused into the analytical process. Lobe’s analytical method, with its circles and exes and dashes, accommodates such hierarchy well: only the unmarked notes in 2.7 and 2.8 enter into consideration for the harmonic analysis. Koch and Stainer likely would protest the removal of Beethoven’s Fs (due to their role as neighbors) in 2.12 from harmonic consideration, but only by taking that step is an analyst in a position to observe that voice exchanges between E E the outer voices (Cs ⫻Cs ⫻Cs ) are the controlling factor in Beethoven’s strucE ture throughout this passage.20 Lobe’s Grundharmonien, the unadorned block chords that he places below a musical score, are an outcome of analysis. A score made vibrant through a composer’s varied application of embellishing pitches will often boil down to a surprisingly modest essence. We now turn the tables: from a few modest chords, how can embellishment be applied to form a vibrant musical composition? Though the process of artistic creation defies full explication, perhaps we can be forgiven the whimsy of

45

46

Thinking About Harmony

imagining how a composer such as Beethoven or Schubert might have gone about his business. In most of the analyses presented within this book I inhabit the methodologies of other authors – mimicking Lobe in the analysis of a phrase by Chopin [2.8], for example. For the discussion that follows, however, I wear no mask. The conceptions of thinkers like Kirnberger, Koch, and Lobe gained momentum as the decades passed, going through a major synthesis and transformation under Schenker in the early decades of the twentieth century before being transmitted to the twentyfirst century. Even if analysts working today do not know how the ideas they employ emerged (a defect that this book is intended in part to remedy), much of what we do resonates with ideas that were already in play during the era of Beethoven and Schubert.

A Beethoven/Schubert connection The relation between harmonic and embellishing functions is at the core of composition-building. In the progression from I to V, with intervening IIn (V of V) [2.13a], the initial tonic is particularly susceptible to elaboration. Applying neighboring notes may result in a tonic-prolonging I–V–I (or I–VII–I) progression,21 and a passing note may fill in the bass third from Ab to F [2.13b]. Tonic may be restated in an inversion [2.13c], an event that invites a preparatory dominant [2.13d]. Each added feature makes the model more distinctive, until the boundary between model and composition is crossed. The finishing touches determine just what that composition will sound like. One set of finishing touches leads from 2.13d to 2.14a: • At chord B´ , the placement of Eb above or below the other treble-clef pitches is of little consequence. • At chord D´ , lingering on soprano Eb before descending to Db decreases the harshness of the dissonance. • The connection between chords E and F´ involves the stepwise ascending root succession from Ab to Bb. As we have seen, Rameau and Schulz suggest that such a succession should be understood as Ab–F–Bb. That conception is realized when a chord rooted on F actually occurs: bass F arrives before chord F´ , while the Ab and C of chord E are still operative. • The expanded progression between chords E and F´ invites expanded melodic content. Inner-voice Ab from chord E migrates up an octave for

Chordal embellishment

a

b

c

d

2.13 A harmonic progression and three variants. Just as a painter might first sketch a basic outline and then gradually fill in details, these four examples show how a basic I–IIn–V progression can be fleshed out.

a

b

2.14a Further elaboration of 2.13d. 2.14b Beethoven: Sonata in C Minor (Pathétique), op. 13 (1799), mvmt. 2, mm. 1–4. Chords B´ , D´ , and F´ are altered from the model of 2.13d. An F minor chord occurs between chords E and F´ .

47

48

Thinking About Harmony

a

b

2.15a Further elaboration of 2.13d. 2.15b Schubert: Moment musical, op. 94, no. 6 (1828), mm. 1–8. Chords B´ , C´ , D´ , and G´ are altered from the model of 2.13d. A Bb minor seventh chord occurs between chords A , and B´ .

the chord rooted on F. This migration affects how chord F´ is configured: Bb is placed above Dn, rather than below it. These refinements shape the model into the opening measures of a movement by Beethoven [2.14b]. Another set of finishing touches leads from 2.13d to 2.15a: • Before chord B´ (a variant of V), a II chord is employed. A suspension delays its Bb. • In chord B´ , G-Bb-Db-F substitutes for Eb-G-Bb-Db. F is suspended into chord C´ , delaying the arrival of Eb. • Chord D´ appears in an inversion, enhancing the linear sweep of the bass (Db–C–Bb–Ab–G–F–Eb).22 • The Ab and Dn of chord F are suspended into chord G´ . These refinements shape the model into the opening measures of a movement by Schubert [2.15b].23 Though the relationship between these passages should not be dismissed as mere chance,24 it does not prove that Schubert’s creative process involved a conscious paring down of passages by Beethoven to their bare bones, upon which fresh embellishments could be applied. Schubert’s classmate Johann Leopold Ebner filed the following report in 1858: The very day Schubert finished the song “Die Forelle,” he brought it to us in the Seminary to try out, and we performed it again and again with the most lively

Chordal embellishment

pleasure; all of a sudden Holzapfel exclaimed: “Good heavens, Schubert, you snatched that out of ‘Coriolan’.” To be sure, in the Overture . . . there is a passage that is similar to the piano accompaniment in the “Forelle”; Schubert immediately saw the resemblance and wanted to do away with the song; but we prevented that from happening and thus saved that delightful song from destruction.25

Schubert biographer Brian Newbould proposes the sympathetic assessment that “Schubert’s way of building (possibly subconsciously, who knows?) upon ideas already ‘in the air’ is instructive, the results often a far-reaching, sublime re-creation.”26 We turn our attention now to two musicians living in Paris in 1830: the composer Berlioz and his critic Fétis. Berlioz went on to create a wonderful though perennially underappreciated body of work, while Fétis attained prominence as a musicologist and produced one of the century’s most celebrated treatises on harmony. Fétis, the elder by nineteen years, was a professor at the Paris Conservatory at the time that Berlioz, who was working with a rival teacher, was attempting to break through as a composer. The two men did not get along. Witness now a clash of titans.

Berlioz and Fétis on embellishment Were it possible, it would be immensely interesting to travel back in time to December 5, 1830, for an afternoon concert at the famed hall of the Paris Conservatory. The composer is Hector Berlioz, who at age twenty-six had just been awarded – on his fourth try – the Prix de Rome. First we hear his winning composition, the cantata Sardanapalus,27 and then a new fantastique symphony based not, like Sardanapalus, on ancient legend, but on the composer’s own imagined experiences. (A few members of the audience are aware that the symphony’s story was sparked by the composer’s infatuation with the Irish actress Harriet Smithson.) The performance is a success. Liszt spurs our applause. And though our ears have been receptacles for all sorts of musical experiments that Berlioz’s contemporaries could not have imagined, we discern that the sensibilities of our fellow audience members are being stretched and that the course of instrumental music is at this moment taking a consequential turn. Over the next few years Berlioz went to Rome, wooed and married Smithson, composed Lélio and Harold in Italy, and began work on

49

50

Thinking About Harmony

Benvenuto Cellini. Then, in 1834, Liszt’s piano transcription of the Symphonie fantastique appeared, inviting a detailed exploration of Berlioz’s compositional practice. The following year François-Joseph Fétis, a respected critic, professor of composition, and author on both the theory and history of music, assessed this score in the Revue musicale. First he recounts some earlier encounters with Berlioz: the “harmonic horrors” of his youthful exercises, the orchestra “bursting with laughter” during a rehearsal in 1828. Of the Fantastique only the orchestration receives praise. Otherwise Fétis is severe: “his harmony, formed of aggregates of notes that are often dreadful, was nevertheless dull and monotonous”; “in this drawn out composition . . . there are nothing but harmonic monstrosities, without charm, without stirring effects.”28 Another leading journalist and musician – Robert Schumann – soon came to Berlioz’s defense. His ecstatic and detailed report in the Neue Zeitschrift für Musik counters many of Fétis’s charges. The following is a brief sample from a review that rewards careful reading: If ever something appeared to me incomprehensible, it is the summary judgment by Herr Fétis in the words: ‘I saw that he lacked melodic and harmonic ideas.’ He might, and indeed has, denied Berlioz everything: imagination, invention, originality – but richness of harmony and melody? There is no answer for that. I have no intention to inveigh against this otherwise brilliantly and intelligently written review, for I perceive nothing like personal invective or injustice in it, but frankly blindness, the complete absence of any feel for this sort of music.29

With Fétis’s Traité complet de la théorie et de la pratique de l’harmonie (1844) in one hand and a passage from the Symphonie fantastique [2.16] in the other, let us seek some common ground between these two titans of the Parisian musical world. In their broadest outlines the first two phrases of our Fantastique excerpt (measures 72 through 86) do what almost any tonal composition will do: they progress from tonic to dominant and back. Fétis accomplishes this even in his rudimentary demonstration of melody, harmony, and chord [2.17a]. One of Rossini’s melodies [2.17b], which Fétis describes as “beautiful and meaningful” (belle et significative), is remarkably similar to that in measures 72 through 75 of the Fantastique. Its construction incorporates arpeggiation of the tonic (G–C–E) and neighboring embellishment of 3 (E–F–E) in a syncopated context. Berlioz’s melody shares these features, and after descent to 1 a 4–3 suspension (C–B over bass G in measures 78–79), demonstrated by Fétis in his “harmonie” model [2.17a], occurs. Dominant harmony often affords the opportunity to juxtapose 4 and 7, which form Fétis’s intervalles attractifs of the quarte majeure (augmented

Chordal embellishment

2.16 Berlioz: Symphonie fantastique (“Episode from the Life of an Artist”) (1830), mvmt. 1 (“Dreams, Passions”), mm. 71/72–111.

51

52

Thinking About Harmony

2.16 (cont.)

fourth) and its inversion, the quinte mineure (diminished fifth). Yet in this case F, B’s attractive accomplice, is absent until measure 85, by which time tonic has returned. In the manuscript version of these measures, a diminished fifth in fact does occur.30 In Berlioz’s revised version, tonic reasserts itself sooner than expected – in measure 84.31 (Since in the preceding phrase tonic extends for six measures, followed by a two-measure suspension/resolution on dominant, we expect six measures of dominant followed by a two-measure suspension/resolution on tonic. Measures 84 through 87 would read | G G | F | F | E | V I .) The frenetic arpeggiation of the tonic’s root and fifth in the cellos and contrabasses in measures 84 and 86 resembles bass activity that Fétis encountered in Mozart [2.18]. These C–G fourths are reminiscent of the melody’s initiating interval (G–C), just as the dominant G–D fourths

Chordal embellishment

2.16 (cont.)

(measures 78–79) relate to the second phrase’s initiating interval (D–G in measures 80–81). The revised harmonization of measures 84 through 86 creates a tonic context for the melody’s G–E third, matching that of the E–C third in measures 73 through 77. Both thirds are filled in by a passing note. Berlioz continues by incorporating the upper-neighbor embellishment of the lower third (E–F–E–D–C) in the context of the upper third: G–Ab–G–F–E in

53

54

Thinking About Harmony

a

b

2.17 Fétis: Traité complet de la théorie et de la pratique de la harmonie [1844], pp. 1, 196 (transposed). (a) “Music is the product of successive and simultaneous combinations of sounds.” [“La musique est le produit de combinaisons successives et simultanées des sons.”] The “Harmonie” model includes an example of what Fétis calls “succession retardée,” in which the pitch C, a compound fourth above the bass, functions as a suspension. (b) Rossini, “Serenata” from Les Soirées musicales, quoted by Fétis (original key: Bb Major). Rossini’s work was composed a few years after Berlioz’s.

a

b

c

2.18 Fétis: Traité complet de la théorie et de la pratique de la harmonie [1844], p. 118. (a) Mozart: String Quartet in C Major, K. 465, mvmt. 2, quoted by Fétis. (b) Reduction by Fétis. (c) The fundamental note (note radicale), according to Fétis.

2.19 Fétis: Traité complet de la théorie et de la pratique de la harmonie [1844], p. 47. This example shows the derivation of Fétis’s dominant ninth chord (accord de neuvième de la dominante) via substitution. Fétis explicitly condones modal shifts such as the replacement of A with Ab: “Now, this transformation could give rise to so many different cadences, which will multiply further through changing the major mode into minor, or the minor mode into major.” [“Or, cette transformation pourra donner lieu à autant de cadences différentes, qui se multiplieront encore en changeant la mode majeur en mineur, ou le mineur en majeur” (p. 179).]

Chordal embellishment

2.20 Fétis: Traité complet de la théorie et de la pratique de la harmonie [1844], pp. 124–125. Fétis demonstrates how Beethoven should have employed pedal point in his Pastorale Symphony. He faults the grand artiste for delaying the tonic pedal F until the dominant harmony (measure 5) instead of allowing it to take hold during the preceding tonic, a correction that Fétis does not hesitate to make. Though Beethoven’s transgression (faute) at first caused astonishment (étonnement) and a painful sensation (sentiment pénible), Fétis reports that his contemporaries eventually accustomed themselves to it. (A typographical error – E instead of C at the downbeat of the penultimate measure – has been corrected.)

a

b

c

2.21 Structural diagrams for 2.16, mm. 73–103. (a) The thirds E–C and G–E and the sixth E–C (shown in open noteheads connected by slurs) occur in a tonic context. The third B–G occurs in a dominant context. The A–Fs third occurs during a sequential passage that comes between the tonic and dominant. (b) The extension of the final third (B–G) to F in measure 101 results in a melodic presentation of the intervalle attractif B–F, which Berlioz answers with a melodic presentation of its resolution, E–C. (c) This sketch shows the ascending contour of measures 73 through 103.

measures 86 through 90. A dominant ninth chord [2.19] over a tonic pedal supports the neighbor. Though Fétis’s example of tonic pedal [2.20] is leaner than Berlioz’s concoction, his examples of dominant pedal reveal a great tolerance for jarring combinations of pitches, such as Ab-C-Eb-Fs against bass G.

55

56

Thinking About Harmony

2.22 Fétis: Traité complet de la théorie et de la pratique de la harmonie [1844], p. 70. In this example of succession retardée (suspension), the dominant chord’s B, D, and F extend into the domain of the tonic that succeeds it.

a

b

2.23a Fétis: Traité complet de la théorie et de la pratique de la harmonie [1844], p. 129. 2.23b Structural diagram for 2.16, mm. 108–110. (a) “The sustained sounds of pedal point are also sometimes employed in the middle and upper voices.” [“Les sons soutenus en pédale sont aussi quelquefois employés dans les parties intermédiaires ou supérieures.”]

The G–A(b)–G–F–E motive works its way upwards: starting on A in measure 94 and on B in measure 98 [2.21a]. The bass follows suit, reaching D in measure 98 and E prematurely in measure 100. Berlioz prevents B–G from unfolding as fifth and third of III, providing instead a context in which the interval is understood as third and root of V (measure 101). The descent extends to F. Finally a legitimate intervalle attractif (B–F) [2.21b], denied us in measure 85! In the following measure, finally a suspension resolution, denied us in measure 86! (Fétis could have created his example of multiplepitch suspension [2.22] by consulting Berlioz’s measures 101 and 102.) The c3 in measure 103 caps an upward arpeggiation of the tonic pitches: e2 in measures 73 (itself the goal of the melody’s local g1–c2–e2 arpeggiation), g2 in measure 84, and finally c3 in measure 103 [2.21c]. Diatonic and chromatic passing notes connect the tonic chords of measures 102 and 106. The cellos and contrabasses fill in the ascending third from E to G, while the violas fill in C to E. Fétis provides an apt model for Berlioz’s procedure [2.23a]. The dominant chords of measures 108 and 110 follow suit in the descending direction, with three active voices [2.23b]. Even

Chordal embellishment

a

b

2.24a Structural diagram for 2.16, mm. 102–111. 2.24b Sechter: Die Grundsätze der musikalischen Komposition (1853–54), vol. 2, p. 276 (transposed). (a) The pitches of | I | V7 | I | appear as open noteheads. Each filled-in notehead is a passing note (diatonic or chromatic), a neighboring note, or a suspension. Regarding the analysis of measure 110, see 2.24b. (b) Though the melody of measure 110 spans a diminished fifth, it is analyzed in 2.24a as F-E-D two integrated thirds. Using Schenkerian terminology, D-C-B (the analysis) “unfolds” to become F-E-D (the melody). A similar conception is lacking in Fétis’s Traité complet. Yet this intriguing D-C-B analysis by Simon Sechter, published a decade later, strongly supports such an interpretation: the melodic thirds F-Eb-D and D-C-Bn (the first five pitches of his melody) represent – appear statt F-D (instead of) – the harmonic thirds D-Bn , shown in the chordal version on the right.

wilder things were displayed in harmony treatises long before Berlioz wrote his symphony. For example, Antoine-Joseph Reicha, whose students included Berlioz, Liszt, and Franck, published a succession involving chromatic descent of a diminished seventh chord in all four voices in his Cours de composition musicale [1816].32 An extension of the G–A–G–F–E motive [2.24a] coordinates with these chromatic lines. G–A occurs in the second violins in measures 103–104. The A is picked up by the flutes and first violins in measure 105 and then suspended over tonic in measure 106. Its resolution pitch G is delayed until measure 108, over dominant harmony, followed by F in measures 109 and 110. Contrasting the motive’s typical closure on E, the line now leads to C in the context of a perfect authentic cadence. In essence, the original E–F–E–D–C motive and its G–A–G–F–E offspring here merge into G–A–G–F–E–D–C.

57

3

Parallel and sequential progressions

Parallel motion in thirds or sixths Strategies for determining chordal roots, symbols for indicating a chord’s position within a key or function within a progression, and procedures for segregating embellishing pitches from harmonic chord members are all important components of the analytical process. Yet these techniques do not tell us much about how and why one chord follows another. In fact, they may inject a bias into our analytical deliberations, for they were developed with certain chordal behaviors in mind. The contrasting behaviors characteristic of progressions that we explore in this chapter will not only alert us to some of the lacunae in early analytical procedures, but also expand our vista to include alternative analytical responses triggered by this broader range of chordal motions. Johann Georg Albrechtsberger, a distinguished composer who counted Beethoven among his pupils in Vienna, launches two fast-paced lines in coordinated ascent, each spanning an octave [3.1a, beat 1 to beat 3]. Their overall effect is to reinforce the tonic chord articulated at the endpoints. Though scale-degree harmonic analysis is not employed in Albrechtersberger’s thoroughbass manual, his more progressive German contemporary Portmann places the analytical Arabic numeral 1 (representing tonic in his scale-step theory) below the start of a similar ascent in eighth notes.1 Observe that the tonic-chord pitches in Albrechtsberger’s progression do not always align [3.1b]. Alternative interpretations, with a change of harmony at beat two [3.1c–d], seem forced, at least when sixteenth notes are involved and when articulation slurs are not provided. Gottfried Weber makes similar observations concerning a pair of parallel descending lines [3.1e]. The nonalignment of P and Q within his progression reflects the unevenness of tonic-chord pitch distribution. With the choice of allowing the nonalignment to persist or altering some of the notes (for example, converting Weber’s Bs and As into eighth notes) to form more ideal convergences, composers would often elect the former. The harmonic label I in 3.1b – suggesting that, despite the variety of other pitch combinations that Albrechtsberger’s ascent offers,

Parallel and sequential progressions

a

3.1a Albrechtsberger: Kurzgefaßte Methode den Generalbaß zu erlernen [ca. 1791], p. 6.

b

c

d

3.1b Structural diagram for 3.1a, opening. 3.1c An alternative to 3.1b. 3.1d Another alternative to 3.1b.

e

f

3.1e Weber: Versuch einer geordneten Theorie der Tonse[t]zkunst (1817–21, 31830–32), vol. 3, ex. 168 [Warner, p. 580]. 3.1f Harbordt: “Lehrbuch der Harmonie, Melodie und des doppelten Contrapuncts” [late eighteenth century]. (e) Weber’s preferred analysis concurs with 3.1b: he marks the tonic-chord pitches in each line (Prinzipal, Terz, and Quinte) and refers to the other pitches as non-harmonic (harmoniefremd). In a parenthetical remark he suggests something akin to 3.1c: “unless indeed we choose to consider [the F and A] as essential intervals of a transient F-harmony” (vol. 3, p. 242). That he does not also propose a “transient G-harmony” akin to 3.1d likely results from his progression’s prolonged bass C, alien to the G-harmony’s B and D. (f) Harbordt, a pupil of Portmann (whose functional analytical terms and symbols were introduced in 1.11, above), penned this example about two-thirds through his manuscript treatise, housed at the Library of Congress. (The pages are unnumbered.) Merging ascending and descending lines in thirds, it nevertheless amounts to no more than a prolonged C Primenharmonie.

59

60

Thinking About Harmony

tonic prevails as the harmonic focus of the entire passage – concurs with Gottfried Harbordt’s tonic interpretation of an even more varied concoction of simultaneous ascending and descending lines in thirds [3.1f]. Though none of the chords interior to Harbordt’s progression correspond to tonic, and though they could be separately labeled – D-F-B-D an inverted Dominantenharmonie with absent root, E-G-A-C an inverted Sextenharmonie with seventh, F-A-G-B an inverted Dominantenharmonie with seventh and ninth, etc. – Harbordt eschews that analytical strategy. His label c¯ emanates from a potent alternative perspective, one based on the conviction that not every chord corresponds to a distinct harmonic event. Like his contemporaries Albrechtsberger and Portmann, Daube is fascinated by progressions in thirds. He comments on the use of parallel thirds in the vocal improvisational practice of the population at large: That the Greeks are said to have had no other harmony than just the unison, octave, fourth and fifth is difficult to believe, since progressions of thirds are so natural and effortless in singing that frequently one hears people singing who have not studied music at all and nevertheless know how to sing in thirds.2

Though Albrechtsberger’s parallel progression in 3.1a is more virtuosic in character, it stems from the same improvisational impulse. Not all intervals are equally viable within a parallel progression. Momigny’s explanation is characteristically colorful. Posing the question, “At what intervals may two melodies proceed together?,” he first displays examples of two lines moving successfully in octaves, in thirds, and in sixths. Then he presents lines moving in fifths (mauvais – bad), in fourths (plus mauvais – worse), in sevenths (détestable – wretchedly bad), and in seconds (affreux – ghastly)!3 Of course, all this was enshrined within the extant thoroughbass tradition. Long before the principal manuals of the eighteenth century (such as those by Johann David Heinichen and C. P. E. Bach) had appeared, Gottfried Keller, a German musician working in England, penned parallel progressions of 63 chords [3.2]. Keller understands that placing thirds and sixths above successive bass pitches achieves rich sonorities while avoiding parallel fifths, which he prohibits.4 To reposition the notes of Keller’s 63 chords to form fifths and thirds would seriously compromise the progression, as Momigny attests. Such parallel progressions fit uncomfortably within the emerging

Parallel and sequential progressions

3.2 Keller: A Compleat Method, for Attaining to Play a Through [sic] Bass [4ca. 1715–21], p. 5. “Composers (especially in few voices) may Compose as many Sixes either Ascending or descending by degrees as they think fit.”

3.3a Rameau: Traité de l’harmonie (1722), p. 112 [Gossett, p. 126]. “If the two upper parts are inverted, we would find as many fifths as there are fourths. The insipidity of several fifths is so diminished by inverting them, however, that we should not attribute to the fourth that which affects only the fifth and the octave.”

harmonic perspective of the eighteenth century. Cognizant of the natural order provided by the series of partials, Rameau asserts that adjacent fundamental pitches should relate by fifth or third, or their inversions (corresponding to the partials represented by the low-integer ratios 2:3, 3:4, 4:5, 5:6, 5:8, etc.) – not by second (8:9, 9:10, 15:16).5 The musician Rameau understands that parallel progressions cannot simply be banished, so the theorist Rameau contrives an explanation that falls within his system’s purview, despite its awkwardness. In a progression similar to Keller’s, Rameau analyzes the second and fourth chords straightforwardly as inversions [3.3a]. For example, E appears in the fundamental bass below the chord G-B-E. In contrast, the first, third, and fifth chords are analyzed as comprising the thirds, fifths, and sevenths of chords with phantom roots that are exposed only through analysis. For example, A-C-F is understood not as derived from F53, but instead from D7. In this manner what would otherwise be for him a frightful progression of descending fundamentals (F–E–D–C– B–A) is moderated at least in part. The ascending seconds (D–E, B–C) that

61

62

Thinking About Harmony

3.3b Sechter: Die Grundsätze der musikalischen Komposition (1853–4), vol. 1, p. 86. Whereas Rameau avoids the stepwise descent of fundamental-bass pitches F–E–D–C–. . . by interpreting some 63 chords as incomplete seventh chords [3.3a], Sechter here avoids the unpalatable analysis A–G–F–E by interpolating an additional root between each pair of chords. The sounding pitches become the fifth, seventh, and ninth above an imaginary root, integrated into the progression via a chain of fifths (A–D–G–C–F–. . .).

appear in his fundamental bass are interpreted as examples of the Cadence rompuë (broken cadence), his oft-invoked justification for ascendingsecond successions. The chordal “sevenths” (C in measure 1, A in measure 2, F in measure 3) are unprepared dissonances. Even scholars sympathetic to Rameau’s perspective may find this analysis to be “contorted” and admit that Rameau “cannot fit [the progression] into his cadence-oriented notion of harmony.”6 The motivation that fed Rameau’s imagination was still reaping analytical consequences in the Viennese theorist Sechter’s influential Die Grundsätze der musikalischen Komposition (1853–4) [3.3b], where descending seconds are interpreted as a contraction of two descending fifths: A–G in place of A– D–G, for example. The contrast between Sechter’s and Harbordt’s [3.1f] analyses epitomizes the extreme disparities that one may encounter among nineteenth-century analytical views: five chords with eight labels versus eight chords with one label. Alternatives to Rameau’s view appeared on various fronts. On the one hand, Vogler blithely proceeds in determining the fundamentals in a parallel progression strictly according to the stacked-thirds configuration of each chord [3.4a]. I–VII–VI–V is for him a forthright and informative analysis. On the other hand, Crotch leaves the internal chords of a similar progression unlabeled [3.4b]. Reicha offers a particularly intriguing analysis [3.4c] that both sifts out numerous pitches within a parallel progression of six 63 chords and realigns those that he retains, a strategy consonant with the relationship between 3.1a and 3.1b proposed above. Crotch’s and Reicha’s examples demonstrate the two principal roles of such progressions: to connect two different harmonies (such as Crotch’s do and sol – or, I and V in C Major) or to prolong a single harmony (such as Reicha’s B-major dominant in E Major). Aware of the diversity of views on this topic, Gottfried Weber endorses them all in his analysis of a progression like Vogler’s:

Parallel and sequential progressions

a

b

3.4a Vogler: Handbuch zur Harmonielehre (1802), table XII, fig. 4. 3.4b Crotch: Elements of Musical Composition (1812), plate 18, ex. 253. (b) “In the species of faburden [sic], called in this work a Succession of Sixes, the bass may ascend or descend throughout the octave, in the major key, every note being accompanied with a sixth and a third. . . . Such a succession is not considered as an inversion of triads” (21830, pp. 29–30).

c

3.4c Reicha: Cours de composition musicale [ca. 1816], p. 269 [Bent, Music Analysis in the Nineteenth Century (1994), vol. 1, p. 52].

I

°VII

VI

V

versus

I

V

versus

I

VI

V.

He advises the analyst to select “that mode of explanation which may be the most natural, in the given circumstances.”7

63

64

Thinking About Harmony

3.5a Beethoven: Sonata in C Major, op. 2, no. 3 (1795), mvmt. 4, mm. 1–8. Observe Beethoven’s subtle intervention at the end of measure 2. The stepwise ascent of a tenth might outline an interval of tonic, as in c2–e3 or e1–g2 (beginning of measure 1 to the end of 2), or it might not, as in g1–b2. Beethoven reinforces the tonic thrust of these measures by substituting c3 for b2 at the end of measure 2. No such alteration is required in measures 3 and 4 because the dominant’s seventh appears in the chord. Root–third, third–fifth, and fifth–seventh outlines (all expanded into tenths) occur. The same sort of dominant prolongation (B7 in E Major) occurs in the first measure of 3.4c, where the connection is by descending sixths rather than ascending tenths (B down, rather than up, to Ds, etc.).

3.5b Analysis of 3.5a, mm. 0/1–2 and 4/5–6.

Adopting the perspective of Crotch, Reicha, and Weber’s second option to analyze a passage by Beethoven [3.5a], we observe that a large number of chords are employed to project a few individual harmonies. Beethoven’s melody arpeggiates the pitches of tonic (G–C–E) and of dominant (D–G–B) [3.5b]. The C–E and G–B thirds are expanded into tenths, with passing notes and their chordal support filling in the gaps. A harmonic interpretation of these parallel progressions – for example, Vogler might analyze the first measure as I VII I II III IV – is just one among several ways of interpreting such motions. A repudiation of Vogler’s perspective did not need to await Schenker’s arrival on the scene a century later, though his condemnation of such thinking was indeed particularly vituperative and consequential.

Parallel and sequential progressions

Discerning analysts of Beethoven’s own time – here represented by Crotch in England, Reicha in France, and Weber in Germany – sought alternatives to a harmony-saturated perspective. A parallel progression has a purity and no-nonsense simplicity that can be very appealing if not overused. Of course, such motion is not exactly parallel: though uniform interval sizes are usually retained throughout such a progression, qualities generally will conform to the prevailing tonality. (For example, both major and minor thirds and sixths appear throughout the parallel passages in the phrase by Beethoven examined above.) A somewhat more complex sort of motion propels a sequence. Though usually some of the voices will proceed by step as in a parallel progression, at least one voice will engage in a contrasting trajectory, in a cycle that repeats at a different pitch level every two chords. Sechter coincidentally displays the relationship between parallel and sequential progressions in 3.3b. If treated as an actual four-voice sequential progression, the example’s upper three voices would proceed in parallel motion, with the bass alternating descending fifths and ascending fourths. I call upon Sechter again to launch our investigation of the familiar circle of descending fifths sequence (or chain of fifths, to borrow Sechter’s more poetical term). Once we get our bearings, we will proceed by considering the following notion: that diatonic sequences may have held a certain fascination for Baroque musicians, but by the nineteenth century this interest had waned. (Or, more precisely, composers of the first rank would shun the unadorned sequences that still appeared regularly in theory manuals.) Composers would often elect to modify a sequential progression in some way, both to forestall tedium and to demonstrate exceptional skill and creativity. Extending beyond an explanation of how the chain of fifths operates, I will show how composers such as Schumann, Chopin, and Liszt made of it something unique and wonderful – even to the extent of transforming it into what may appear to be a parallel progression of forbidden intervals.

Chains of descending fifths Parallel progressions of 63 chords cover relatively small spans of musical terrain. A chain (Kette) of descending fifths, in contrast, cannot persist beyond a few chords without exceeding the normative range of composition.

65

66

Thinking About Harmony

3.6 Sechter: Die Grundsätze der musikalischen Komposition (1853–54), vol. 1, p. 13. ”We now mention the possibility of letting the seven triads of the major scale progress in an ordering similar to the cadence, where the fundamental leaps about by fifth downward or by fourth upward, namely: Triad of the 1st scale step, that of the 4th, the 7th, the 3rd, the 6th, the 2nd, the 5th, the 1st scale step.” [“Und nun ist die Möglichkeit gegeben, die sieben Dreiklänge der Dur-Tonleiter in einer dem Schlussfall ähnlichen Ordnung, wo das Fundament um eine Quint abwärts oder eine Quart aufwärts springt, folgen zu lassen, nämlich: Dreiklang der 1ten Stufe, jener der 4ten, der 7ten, der 3ten, der 6ten, der 2ten, der 5ten, der 1ten Stufe.”]

Thus such chains are generally realized as an alternation between descending fifths and ascending fourths [3.6]. Several types of creative modification are possible. In one of Sechter’s models a diatonic seventh is added to each chord [3.7a]. Gottfried Weber (borrowing from Kirnberger) instead employs inverted dominant seventh chords [3.7b]. Both authors provide a Romannumeral analysis. Sechter’s progression employs diatonic pitches only, and thus his numerals correspond to the scale degrees of each chord’s root within the operative key. Weber analyzes his chromaticism-intensified progression as a series of thwarted dominants, each interpreted in a different key. He finds continuity principally through his key choices: A Minor, D Minor, and G Major are all closely allied to C Major. Analysis in A Major and D Major would more accurately reflect what actually occurs (A major and D major chords appear in Weber’s second model, after all), but those keys do not reinforce the concluding tonic C Major. Because Sechter’s examples contain only diatonic chords, the chain’s weak link, dissonant F–B, is called into service. Henri-Montan Berton, for many years a professor at the Paris Conservatory, pursues the opposite priority: employing only perfect fourths and fifths, whatever the consequences may be [3.8]. That, combined with a determination to make every seventh chord a dominant seventh, results in chromatic lines falling in half-steps for an entire octave. Tonic closure would be impossible without temperament.8 Bass Dbb must coincide with C. If, instead, perfectly tuned intervals (descending fourth, ratio 3:4; descending fifth, ratio 2:3; ascending fourth, ratio 4:3) are employed, the ratio of the initial bass C and the concluding Dbb would be 131072:531441, which exceeds a double octave. (A perfectly tuned fifteenth would be perceptibly smaller, with ratio 1:4, or 131072:524288.)

Parallel and sequential progressions

3.7a Sechter: Die Grundsätze der musikalischen Komposition (1853–54), vol. 1, p. 19. “The chain of all the major scale’s seventh chords in succession is founded likewise on the natural ordering of the cadence-emulating steps. One begins with the best of the seventh chords, namely with that of the 5th scale step, and allows it to progress to the seventh chord, instead of to the triad, of the 1st scale step, which is novel only in that the third above the 5th scale step does not ascend, but holds over as the seventh of the 1st scale step. The seventh chord of the 1st scale step will then proceed to the seventh chord, rather than the triad, of the 4th scale step. Then follows the seventh chord of the 7th, then that of the 3rd, then that of the 6th, then that of the 2nd, then that of the 5th scale step, which finally resolves itself in the triad of the 1st scale step, concluding the protracted restlessness. 7 V

7 I

7 IV

7 VII

7 III

7 VI

7 II

7 V

3 I.

With the exception of the initial seventh on the 5th scale step, which has the freedom to enter without preparation, all the subsequent sevenths in this chain are prepared and resolved properly, as can be seen in the following example in five voices.” [“Die Kette aller Septaccorde der Dur-Tonleiter nach einander beruht auch auf der natürlichen Ordnung der dem Schlussfall ähnlichen Schritte. Man beginnt mit dem besten der Septaccorde, nämlich mit jenem der 5ten Stufe, und lässt statt des Dreiklangs den Septaccord der 1ten Stufe folgen, wozu weiter nichts Neues gehört, als dass die Terz der 5ten Stufe nicht steigt, sondern als Sept der 1ten Stufe bleibt. Der Septaccord der 1ten Stufe wird sodann statt in den Dreiklang der 4ten, in den Septaccord derselben Stufe übergehen. Dann folgt der Septaccord der 7ten, dann jener der 3ten, dann jener der 6ten, dann jener der 2ten, dann jener der 5ten Stufe, welcher sich nach langer Unruhe nun in den Dreiklang der 1ten Stufe auflöset. 7 V

7 I

7 IV

7 VII

7 III

7 VI

7 II

7 V

3 I.

In dieser Kette sind ausser der ersten Sept auf der 5ten Stufe, welche die Freiheit hat, unvorbereitet einzutreten, alle folgenden Septen gehörig vorbereitet und aufgelöset worden, wie man in folgendem fünfstimmigen Beispiele sehen kann.”]

Rameau cautions: “We should not . . . stray too far from the initial key, and as soon as an occasion to return arises, we should take advantage of it.”9 The impetus that generates Berton’s progression need not persist to the end. A chain of descending fifths may enter the terrain charted by Berton but then, as Rameau advises, veer back to its diatonic foundations [3.9a]. The location of the weak link (diminished fifth or augmented fourth) may shift as a result, or even be skipped over [3.9b]. This latter version corresponds to a passage from Schumann’s Sonata in Fs Minor [3.10a]. The concluding links, C–Fs–B–E–A, contract to become C–E–A. Rudolf Louis and Ludwig

67

68

Thinking About Harmony

3.7b Weber: Versuch einer geordneten Theorie der Tonse[t]zkunst (1817–21, 21824), vol. 3, table 35, fig. 313 [Warner, p. 544]. Juxtaposing two versions of the same progression, Weber displays how passing notes (marked in the second example) can take over the full time value of their measures. Consequently the pitch that resolves the preceding measure’s leading tone is elided. (This procedure is characteristic only of the free style – not the strict style.) The pitches of Weber’s example, though not the analysis, are from Kirnberger’s Die Kunst des reinen Satzes in der Musik (1771–79), vol. 1, pp. 89–90 [Beach and Thym, p. 108]. Other eighteenth-century authors, including Rameau, Marpurg, and Béthizy, likewise were fascinated by this progression.

3.8 Berton: Traité d’harmonie [1815], p. 134. In Berton’s chain of descending fifths, each dominant seventh chord (7eme D:) except the last proceeds not to its tonic but, like Weber’s in 3.7b, to another dominant seventh chord, through successive interrupted perfect cadences (suites de Cadences parfaites interrompues). The progression had long fascinated musicians. For example, it appears in Giorgio Antoniotto’s L’arte armonica; or, A Treatise on the Composition of Musick (London, 1760), plate 33, canon 48. Antoniotto’s version is not accompanied by analysis, however, and he avoids Berton’s provocative double-flat spellings by executing the enharmonic shift at Gb/Fs. Georg Friedrich Lingke does employ these spellings in his Kurze Musiklehre (1779), p. 78. Sechter presents a similar progression in Die Grundsätze der musikalischen Komposition (1853–54), vol. 1, p. 206. In his version, minor chords and major-minor seventh chords appear in alternation: a

D7

g

C7

f

Bb7

ds

Gs7

cs

Fs7

b

E7

a.

Each minor chord is understood initially as a tonic, but is reinterpreted as a supertonic (of minor, rather than diminished, quality) in the minor key a whole step lower. Louis and Thuille follow a similar strategy in 3.10b.

Parallel and sequential progressions

a

b

3.9a A chain of descending fifths. 3.9b A variant of 3.9a, constructed to conform to 3.10a. (a) This progression’s opening closely resembles the first six chords of Berton’s model [3.8]. Its bass and inner-voice lines are transpositions of the model’s bass and soprano lines, respectively. After the bar line the progression no longer corresponds to Berton’s model (which would continue with bass notes F, Bb, Eb, Ab, . . .). Instead roots Fs, B, and E lead back to tonic A. Observe that the chromaticism shifts the location of the bass diminished fifth from its diatonic position, D–Gs (4–7), to Cn–Fs. (b) Though 3.9a is presented as an abstract model derived from Berton, its construction was guided by a passage from Schumann’s Sonata in Fs Minor [3.10a]. Here further refinements that reveal Schumann’s distinctive stamp are incorporated. One chord is added (in measure 120) and two chords are deleted (in measure 123). Anticipations and chromatic passing notes, shown as filled-in noteheads, embellish the basic structure.

Thuille, working in Munich at the beginning of the twentieth century, analyze this music [3.10b] with a saturation of dominants rivaling Berton’s. Because not all of these chords contain sevenths, the primary analysis shows only one key change per measure. The major-to-minor shifts in measures 121 through 123 provoke these modulations. The bracketed bottom line of analysis increases the density of dominants, responding to the chromatic alterations at the end of measures 121 and 122 so that, for example, the EbG-A-Cs augmented sixth chord (measure 121) is interpreted as a supertonic.10 That makes the following D-Fs-A come across as V. Honoré François Marie Langlé, another member of the Paris Conservatory faculty, shows how, through careful attention to chordal inversion, the chromatic lines we observed in Berton’s model [3.8] can be positioned strategically in both outer voices [3.11a]. Charles-Simon Catel,

69

70

Thinking About Harmony

3.10a Schumann: Sonata in Fs Minor, op. 11 (1835), mvmt. 4, mm. 120–125.

3.10b Louis and Thuille: Harmonielehre ([1907], 41913), p. 364. Louis and Thuille’s analysis presents a sophisticated application of the notion, also present in the examples by Weber and Berton above, that successive chords within a chain of descending fifths may each function as a dominant. The bracketed G Minor and F Minor segments never achieve their tonics; the parenthesized Bb Major (German B) segment never achieves even its dominant.

also employed at the Conservatory, ups the ante, showing how descending chromatic lines may occur simultaneously in all four voices [3.11b]. Here the resolutions are modified not only by elision [as in 3.7b] but also by the substitution of diminished sevenths for dominant sevenths [3.11c]. Given such precedents, it is not surprising that composers boldly expanded the contexts in which chromaticism might flourish. Both Chopin and Liszt employ ear-opening chromatic progressions that derive ultimately from the same chain of descending fifths, in ever more imaginative transformations. Three operations transform the rudimentary chain of 3.12a into 3.12b: (1) incorporating the passing seventh into the initial statement of each chord (as did Weber in 3.7b); (2) adding chordal ninths in the second chord of each measure, thereby transforming the melody’s whole steps into successions of half steps; and (3) adding chromatic passing notes in the tenor register. In 3.12c the dissonant ninths are

Parallel and sequential progressions

3.11a Langlé: Traité de la basse sous le chant [ca. 1798], p. 138, ex. 69. Among numerous examples of chromaticized sequences in Langlé’s treatise is this alternation of 6 - and 42-position dominant seventh chords, with parallel chromatic lines in the outer voices. 5

3.11b Catel: Traité d’harmonie [1802], p. 54. By substituting diminished seventh for dominant seventh chords, Catel brings new life to the chain of descending fifths. A similar progression, without fundamental-bass analysis, appears with attribution to J. S. Bach in Kirnberger’s Die Kunst des reinen Satzes in der Musik (1771–79), vol. 1, p. 132 [Beach and Thym, p. 148]. Compare Catel’s analysis with that of Macfarren [3.11d].

softened through the suppression of the roots (shown in parentheses), while each chromatic passing note (shown as a filled-in notehead) takes over the time value of its diatonic predecessor (compare with 3.9b). This selection of pitches (root, third, fifth, and seventh of the first chord of each measure;

71

72

Thinking About Harmony

3.11c Three stages in the development of 3.11b, measure 2. By eliding bass C and substituting Db for inner-voice C, two diminished seventh chords related by half step occur in succession. They represent the fundamental-bass succession of a descending fifth: G–C.

3.11d Macfarren: Six Lectures on Harmony (1867), p. 137. Macfarren pursues a chromatic descent in diminished sevenths for nearly a full octave. Only three spellings occur: all inversions of Fs-A-C-Eb are supertonic (s), all inversions of B-D-F-Ab are dominant (d), and all inversions of E-G-Bb-Db are tonic (t) chords in C Major. The roots D, G, and C, respectively, are all suppressed until the final cadence. The Arabic numbers indicate which chord components (with reference to the absent roots) appear in the bass.

third, fifth, seventh, and ninth of the second chord of each measure) corresponds to a passage from a mazurka by Chopin [3.12d]. A different selection of pitches (root, third, and fifth of the first chord of each measure; fifth, seventh, and ninth of the second chord of each measure) corresponds to a passage from a composition by Liszt written a year or two later [3.12e]. Chopin’s example is both astonishing and dangerous: dangerous because it appears to open the floodgates for parallel progressions of traditionally prohibited intervals. (Recall that Momigny, also a resident of Paris, characterized progressions of fifths as mauvais – bad – and of sevenths as détestable – wretchedly bad.) Its meticulous derivation from the chain of fifths counters that reading. The Cn that appears above bass Fn in the excerpt’s first measure, like Kirnberger’s ninths [1.14a], is an incidental pitch, substituting for B, whose third, Ds, Chopin spells as Eb (compare with 3.12c); while the Fn is a chromatic passing note that asserts itself

Parallel and sequential progressions

a

b

c

3.12a A chain of descending fifths. 3.12b Variant of 3.12a. 3.12c Variant of 3.12b. (c) The interpretation of a seventh chord as a ninth chord with absent root is frequently encountered in analyses, as in 1.6, chord 6; 1.11b, chord 3; 1.14a, passim; 1.15, chord 5; 2.5, chord 11; and 3.11d, passim.

d

3.12d Chopin: Mazurka in Cs Minor, op. 30, no. 4 (1837), mm. 129–132. Schenker addresses the mazurka’s voice leading both in Kontrapunkt (1910–22; book 1, ex. 184) and in Der freie Satz (1935, 21956, figure 546). He recomposes the passage to display his view of its essence, as follows: Cs Fs 5,

Cn Gb 4 –

— Fn 5,

B Fn 4 –

— E 5,

Bb E 4 –

— Eb 5,

Though all but one of these pitches appear in 3.12b, Schenker endorses the opposite hierarchy. For example, he regards the second chord’s elided Gb (Fs) as a bass suspension delaying a structural Fn, rather than Fn as a chromatic passing note following a structural Fs.

73

74

Thinking About Harmony

3.12e Liszt: “Il penseroso” from Années de Pèlerinage, Deuxième Année: Italie (1838–39), mm. 17–19.

within the chord, rather than in its conventional position after the chord sounds. These concurrent creative adjustments transform the normative BF# perfect fourth [3.12a] into an Cn perfect fifth. The Fn also forms a minor Fn seventh with Eb. But, as mentioned above, Eb is an enharmonic respelling of Ds, while Fn occurs in place of Fs. Thus the minor seventh Eb is a substiFn D# tution for a major sixth F# [3.12a]. Though Liszt’s example is less extreme – there are no sevenths, and the judicious use of chordal inversion prevents the direct succession of fifths – it too partakes of the chromatic intensity that was so boldly proposed by theorists such as Berton [3.8] earlier in the century.

One can almost imagine the expatriates Chopin and Liszt spending an afternoon together in Paris, taking turns at the Pleyel churning out wilder and wilder transformations of the humdrum circle of fifths progression. By then the notion that a chord could function with an absent root – or even an absent root and third – had been bandied about for nearly a hundred years [1.1, 1.6, 1.11b, 1.14a, 1.15, 1.16a, 1.16c]. These forwardlooking composers certainly put that idea to the test, bending the sequential principle so far that their progressions become indistinguishable in sound from parallel progressions. Analysts who advocated Roman- or Arabic-numeral scale-step analysis tended to apply numerals to all the chords of a sequence, while those who did not tended simply to display a variety of sequential possibilities in music notation, often including figured-bass numbers and perhaps adding some brief commentary. The numeral analyses were often peculiar. Labeling thirteen consecutive chords using the same symbol, as does Berton (or even four consecutive chords, as does Weber) may be modestly informative concerning each individual chord’s tendency, yet the larger question – where is this sequence leading us? – is left unanswered.

Parallel and sequential progressions

Because sequential progressions are governed by a repetitive pattern, their individual chords resist cogent analysis either according to scale degree or function. But whereas in parallel progressions a numeral-saturated analysis [3.4a] seemed so obviously out of kilter that many eschewed labeling each chord, a sequence usually contains elements, such as a succession by descending fifth within each cycle, that mimic nonsequential harmonic activity, thereby inducing a liberal application of labels, sometimes with about as many key changes as chords [3.7b, 3.10b]. Of course, in the post-Schenkerian era alternatives to such saturation labeling and key-changing are more widely practiced and encouraged, making some of the more extreme of the early analyses seem more bizarre now than they would have seemed to musicians of the nineteenth century. Just as artists generally kept drawings and engravings on hand as models for a variety of visual compositional elements, composers benefited from theory manuals that displayed a wide range of sequential possibilities. At the turn of the nineteenth century, Langlé distinguished himself as an especially resourceful and creative guide in this domain. Though his models may extend to the point of tedium, the skilled composer would know where to snip. We ask Langlé to lead us as we investigate sequential progression by ascending fifths.

Langlé’s Tours de l’harmonie The excitement of taking a tour is not limited to physical travel. Literature, drama, and painting give audiences panoramic impressions of a wider world. In music the tour de l’harmonie, an occasional feature in eighteenth-century treatises, offers the opportunity to visit the various regions that constitute the world of pitch. No one published more extensive itineraries for such tours than did Honoré François Marie Langlé, a native of Monaco who trained in Naples and eventually became a professor of harmony at the Paris Conservatory. A progression of ascending perfect fifths touches on all twelve tonal regions before returning to the initial tonic. Though few composers would elect to follow such an exhaustive course to its end, Langlé demonstrates that it is feasible [3.13a]. As with physical travel, one soon forgets about home, even if the itinerary ultimately leads back to where it starts. The bass succession must proceed without deviation. Altering the B–Fs perfect fifth (the third and fourth bass notes) and the corresponding chords to diatonic B–F would shorten the journey while limiting its scope to closely allied regions.

75

76

Thinking About Harmony

a

b

c

d

3.13a–d Langlé: Traité d’harmonie et de modulation [ca. 1797], p. 57, ex. 4; p. 82, ex. 41; pp. 84–85, ex. 48 (two versions). (a) Had Langlé not undertaken an enharmonic shift (Eb minor substituting for Ds minor) the final chord would appear as GS–Bs–DS rather than as A–C–E. Compare Langlé’s model with Berton’s progression of descending fifths [3.8], where the enharmonic day of reckoning is postponed until the end. (b) Here the twelve major keys are interspersed among the twelve minor keys, in alternation. (c)–(d) The antiseptic character of the preceding progressions is here disguised through the insertion of cadences. These accretions, while making the progressions more palatable, expand the models to such length (25 chords and 73 chords, respectively) that their viability for unabridged application is compromised.

Langlé instead forges ahead to the end of the world, from which return is possible only if sharp notes are metamorphosed into flat ones. Langlé offers an expanded itinerary encompassing both minor and major tonal regions in alternation [3.13b]. Each melodic fifth of the earlier bass is here replaced by two thirds. Langlé persists through the

Parallel and sequential progressions

3.14a Reicha: Cours de composition musicale [ca. 1816], p. 50. Reicha’s modulations correspond to three steps within Langlé’s progression of ascending thirds: from E Minor (Mi mineur) to G Major (Sol), from G Major to B Minor (Si mineur), and from B Minor to D Major (Ré). Reicha marks the dominant chords that instigate these shifts with a plus sign (+). (Note the typographical error in the second dominant chord: the upper sharp should appear beside the A notehead.) The fourth dominant leads directly back to E Minor.

3.14b Weber: Versuch einer geordneten Theorie der Tonse[t]zkunst (1817–21, 21824), vol. 2, table 11, fig. 185 [Warner, p. 340]. Weber pursues the progression of ascending thirds to its sixth chord, though with less regimentation than does Langlé. Weber proceeds from D through fs, A/a (!), C, and e to G. Langlé’s itinerary would have led to the more distant key of Gs Minor (via the route D–fs–A–cs–E–gs).

twenty-fifth chord, visiting every minor and every major tonal region along the way. Though these examples may prove their point, they do so with dubious musical interest. That fault can be mitigated by fortifying each arrival point with a cadence [3.13c–d]. Though Langlé here limits his commentary to a caption stating “with common final cadences” (par des cadences finales simples), other authors supply greater analytical detail in similar progressions. For example, Reicha reports each shift of key, while Gottfried Weber additionally offers a detailed Roman-numeral analysis [3.14a–b].

77

78

Thinking About Harmony

a

b

3.15a Beethoven: March from Fidelio, op. 72 (1805–14), act 1. 3.15b Chords 64 through 70 of 3.13d. (b) These seven chords from 3.13d (within the region marked by an ellipsis) are an expansion of three chords from 3.13b, namely, Bb major, D minor, and F major. Keeping this perspective in mind will help avert disorders in performing Beethoven’s March. Though positioned at a downbeat, the A major chord of measure 4 should not be projected as an arrival point. It resolves to the midmeasure D minor chord. Likewise the C major chord in measure 5 resolves to the F major chord.

Since each of Langlé’s examples encompasses either twelve or twenty-four keys, it is of no consequence where one begins. In every case the sequential progression, if pursued for long enough, will return to its chord of origin. As Reicha and Weber demonstrate, however, even music theorists had little patience for such a tedious endeavor run to its conclusion. They employ segments of the total progression to whisk them off to a new tonal region but return via a quicker strategy. In Beethoven’s stylish March from Fidelio, the chordal activity in measures 3 through 5 connects more stable regions in Bb Major and F Major at the perimeters of the phrase [3.15a]. The chord choices are almost exactly what Langlé’s tour de l’harmonie prescribes [3.15b]. (Beethoven’s Bn in

Parallel and sequential progressions

measure 4 is a chromatic inflection of Langlé’s Bb.) Like Weber [3.14b], Beethoven devotes some time to establishing his initial key before proceeding on his journey. Whereas Langlé’s model places the roots of the ascending thirds (or descending sixths) in the bass (Bb–D–F), Beethoven places ascending thirds (linking the fifths of the Bb, D, and F triads) in the soprano: F (measures 2 and 3), A (measure 4), and C (measure 5). This frees his chords to assume a wider range of inversional configurations. Beethoven exploits that potential by creating a bass line that descends by step, countering the soprano melody’s ascent.

Straightforward and predictable patterns like those presented by Langlé were a part of the composer’s craft throughout the tonal era. In Beethoven’s March a tour de l’harmonie segment serves as the guiding principle for several measures, after which an autonomous harmonic progression (F Major: I6–VI–II6–V7–I . . .) seamlessly takes over, prolonging the goal key. Despite – or perhaps because of – their inherent repetitive nature, composers will often intervene when traversing a tour de l’harmonie. None of this chapter’s sequential progressions from compositions have pursued their course without modification: Schumann injects chromaticism into several chords in 3.10a, Chopin and Liszt selectively omit chordal members to create memorable voice-leading in 3.12d–e, and Beethoven employs a chromatic inflection (Bn) and creatively refashions the outer-voice lines in 3.15a. Yet in each case a basic contour established at the outset guides the continuation. This security and relative predictability contrast the dynamic of an autonomous harmonic progression, our topic in chapter 4. Before proceeding to that discussion, let us consider one more category of sequence, the ascending 5–6, which Schubert employs in a breathtaking way in “Aus Heliopolis II.” Like Chopin in the mazurka discussed above, Schubert in his lied so modifies the basic workings of the sequential progression that it eventually comes to resemble a highly unorthodox parallel progression.

Schubert’s transformation of the ascending 5–6 sequence In a diatonic context the ascending 5–6 sequence will proceed on a gradual upward course, with each diatonic scale degree serving as bass for both a 53 and a 63 chord, until the tonic triad returns. The complete tour de l’harmonie

79

80

Thinking About Harmony

3.16a Langlé: Traité de la basse sous le chant [ca. 1798], p. 208, ex. 20 (top). Langlé pursues the sequential progression from tonic C through dominant G, after which a cadential progression concludes the example.

3.16b Langlé: Traité d’harmonie et de modulation [ca.1797], p. 83, ex. 46 (transposed). In Langlé’s unabridged example, the sequential progression traverses an entire octave – twentyfive chords in all – and is followed by a four-measure cadential progression.

thus contains fifteen chords, a length that risks tedium. Composers often employ an abridgement of the full sequence. Langlé demonstrates its use in traversing the path from tonic to dominant [3.16a]. Perhaps even more common is the span from I to I6, a six-chord segment. In the major mode the six-chord segment possess an assertive momentum and appealing brevity. IV follows naturally, and at that point the sequential operation will often give way to an autonomous harmonic progression. In contrast, this span of six chords is rather problematic in the minor mode [3.16a, chords 1 through 6]. First, the third chord is of diminished quality, dampening the momentum a sequence is designed to achieve. (We will see later how Lampe substitutes the lowered second scale degree in the bass to alleviate this awkward moment [6.1].) Second, the fourth and fifth chords so strongly signal a mediant arrival that the sixth chord, if terminal, may seem more an appendage of III than the return of I. Langlé shares Lampe’s instinct, mentioned parenthetically above: he senses that bass C in the second chord of 3.16a could justifiably proceed to Db instead of to D. (Whereas D preserves the diatonic integrity of the key, Db taps the potential for C-Eb-Ab to behave locally as a dominant.)

Parallel and sequential progressions

Unlike Lampe’s modest overhaul, however, Langlé’s revision is substantial: the half-step motion from C to Db becomes the template for each sequential cycle [3.16b]. Thus every pitch in the chromatic scale (in the soprano) appears in two consecutive chords, and the complete tour de l’harmonie is thereby expanded to twenty-five chords. (Langlé unfurls the 63 chord of the basic sequence cycle of 3.16a into the corresponding 53 chord in 3.16b: thus C5–6 appears as C53 to Ab53. This is principally a voice-leading matter – the prevention of parallel octaves – that in no way affects the overall pitch content or upward thrust of the sequence.) Traversing this sequence requires frequent enharmonic adjustments in the chordal spellings, without which the twenty-fifth chord would be spelled Abbbbbbbbb-Cbbbbbbbbb-Ebbbbbbbbb rather than C-Eb-G. Probably independently of any treatise, Schubert modifies an ascending 5–6 sequence in a manner similar to Langlé’s model for deployment in his “Aus Heliopolis II” (D. 754), a setting of a text by Mayrhofer [3.17].11 In fact, he ups the ante: whereas Langlé employs consonant Ab-C-Eb to lead into Db (the second and third chords of 3.16b), Schubert adds the chordal seventh: C-Eb-Gb-Ab (3.17, measure 30). As is the case in Langlé’s progression, Schubert’s Db chord is of minor quality: Db-Fb-Ab in measures 31 through 34. The sequence then continues its upward course in half steps with Db-FbAbb-Bbb (enharmonically respelled by Schubert as Cs-E-G-A) leading to D-F-A (measures 35 through 38). Then something unexpected happens. Langlé’s sixth chord in 3.16b is spelled Bb-D-F. Schubert concurs, again adding the minor seventh and presenting the pitches in 65 position: D-F-Ab-Bb (measure 39). But the expected succession to Eb-Gb-Bb does not occur. Things begin to run amuck: one 65 chord leads into another. Despite some hesitation in measure 40, 65 chords on D, Ds, and E occur in succession (measures 39 through 41), the last of these finally resolving normatively to IV, which prepares the phrase-ending V. Having initiated a sequential progression that is inherently plodding, Schubert must confront a potential disaster: tedium is on the horizon. His response is both assertive and ear-opening: he jettisons some of the sequential chordal content, as follows: m.

26–28 29–30 31–34 35–36 37–38 39 C53 C65 Db53 Cs65 D53 D65

x 39 x 41 5 Ds3 D#65 E53 E65

As a consequence of eliding the 53 components of these last cycles, what remains appears to have morphed into a parallel progression of dissonant 65 chords, parallel fifths included! The poetic text, which offers a set of prescriptions for leading a worthy life, is well served by a sequence that starts

81

82

Thinking About Harmony

3.17 Schubert: “Aus Heliopolis II” (D. 754), mm. 26–47. Text by Johann Mayrhofer.

its ascent slowly and methodically. But as does a life that is thriving through honorable pursuits, eventually the arduous becomes a joyous and energetic striving ever upwards, and in the ethereal atmosphere of that higher order of existence, the friction of earthbound life dwindles.

Parallel and sequential progressions

3.17 (cont.)

From a broad perspective, we understand that the sequential progression connects the C minor tonic chord of measure 26 and the inverted C major chord with minor seventh (nowadays often called V65 of IV) in measure 41. Despite the chromatic inflections, the addition of dissonance, the ascent via half-steps, and the eventual breakdown of the sequential cycles, Schubert is nevertheless following a long tradition of pursuing the sequence through the diatonic model’s sixth chord. Yet Schubert’s creative impulse will not subside. As mentioned above, the progression leads to V as goal in measure 42. Another initiative must commence to lead through V to I. At its outset (measure 43) Schubert backtracks, but not all the way back to the root-position tonic (as in measure 26). Instead he reinstates measure 41’s E65 chord, the modified tonic. He then proceeds not to IV, as before, but instead traverses the next two 65 chords in the elisionridden sequence: E65 F65 Fs65 (measures 43–45). This Fs65 (nowadays often called V65 of V) leads to V, which this time heralds the goal tonic of measure 47. It was important for composers to understand the basic workings of sequences and their variants. Langlé’s treatises and others like them were a

83

84

Thinking About Harmony

convenient source of information and ideas. Yet the models presented in textbooks are not in themselves works of art. The analyst, whose familiarity with sequential progressions should rival that of the composers, must not only sense which basic model grounds a sequential progression, but also be cognizant of how the composer incorporates the progression, both in terms of what part of the unabridged sequence is included and how it has been altered. Certainly a composer of Schubert’s talent could extract such patterns directly from existing scores without recourse to theoretical abstractions. But that was just the first step: giving a sequential progression a personal stamp through creative modification appears to have been as vital to Schubert’s artistic expression as it was to Chopin’s and Liszt’s. As a result, we are the beneficiaries of compositions that are both astonishing and memorable, unlike anything one could find in a harmony treatise.

4

Harmonic progression

The artistic progression of harmonic triads Sorge, writing around the middle of the eighteenth century, claims that “one gradually comes to understand that all music is nothing but an arrangement of one harmonic triad after another; and all that occurs therein is focused principally on its harmonic progression.”1 For those who shared Sorge’s view, attempts to clarify the principles governing harmonic progression would constitute a primary goal of musical speculation. Composers, who daily confronted the task of shaping cogent harmonic progressions, were a primary audience for such efforts,2 though elite performers, who often put notes together themselves in the form of improvisations, cadenzas, or their own compositions, would likewise be receptive to clear prescriptions that might enhance their artistry. The extent to which any set of guidelines for harmonic progression could succeed was itself a subject of dispute. In the early nineteenth century Momigny asserts that the “genius” is guided by a “natural and almost divine instinct . . . in the absence of written laws”3 and suggests that if the music examples in a harmony treatise are of high quality it is likely because they were composed by a fine musician, not because that musician’s rules are particularly discerning. Such rules are “almost always feeble or false.”4 A century later Heinrich Schenker, in “Rameau or Beethoven? Rigidity or Spiritual Vitality in Music?,” charged Rameau and those who had built upon his foundations with misguided and detrimental notions of harmony: There was something mechanical already in Rameau’s basic musical outlook, because he turned away from dynamic voice-leading principles; and from that initial wrong turn a host of mechanical ideas has ensued . . . Where organic musical coherence ought to have reigned there were only mechanical successions: Motives came and went, . . . musical tones flitted by without being certified through composing-out (Auskomponierung). Indeed, the feeblest cookbook promises more coherence in its recipes than do composition texts based on Rameau’s musical outlook in theirs.5

If, following Schenker’s precedent, many modern practitioners of analysis integrate harmonic thinking within a broader conception of musical

86

Thinking About Harmony

structure, basic questions of harmonic progression nevertheless remain at the forefront of our pedagogical and analytical enterprises, and notions propagated centuries ago echo still today. One wonders, though, how common it was for practitioners to map out in any systematic way a harmonic perspective for compositions under consideration. We must be cautious to read a historical treatise as documentation of what its author suggested his readers should think rather than as confirmation of what they did think.6 And, as Schenker reminds us, the gap between the thinking of a Beethoven and that of a treatise author may be wider than that between the author and his readers. As Dahlhaus muses, “how musical works are interpreted analytically . . . is a process that never achieves closure, in that the current state of composition inspires the detection of technical facts that do not cease to be facts even if none of the composer’s contemporaries noticed them.”7 Compared with parallel and sequential progressions, autonomous harmonic progressions are characterized by considerably greater variety and unpredictability, and thus greater challenge to the composer and analyst. From any point within such a progression, many continuations are possible. This state of affairs could lead to creative composition of a very high order, at least among Momigny’s genius composers. Yet potent theoretical explications were not so readily forthcoming. In fact, in the early nineteenth century discussion of chord progression usually amounts to little more than the consideration of two-chord successions. The prescriptions for proper chord succession explored below suggest that fledgling composers could find some sensible advice, if they knew where to look. But unwieldy or indifferent formulations were on hand as well. In addition, we must keep in mind that our notion of nineteenthcentury repertoire is not a representative sampling of what actually was heard at the time. For example, a number of harmony instructors at the Paris Conservatory were prominent composers of operas. Their theories probably coordinate much better with the Parisian fare of their time than it does with the more rarefied repertoire that now constitutes early nineteenth-century music for many serious music lovers.

Rankings of chord successions The enterprise of harmonic analysis asks practitioners to make judgments concerning the merits of various successions. For example, encountering

Harmonic progression

an ascending-second root succession, such as G–A in C Major, might induce more analytical flurry than encountering a descending-fifth root succession, such as G–C. Though both may function in cadential roles, only G–C follows a descending path (from third to second partial) within the Nature-ordained harmonic series. How an event is processed depends upon the operative analytical precepts. G–A might be regarded as motion by ascending major second, where the interval between roots is the critical factor. Or, it could be regarded as motion to a triad that shares no common tones, perhaps inducing the insertion of an imagined linking chord within the analysis. Or, as motion from scale degree 5 to scale degree 6, which might be viewed more favorably than some other ascending-second motions. Notions of harmonic sense emanated either from abstract theorizing (much of it acoustically derived) or from observation of compositional practice. From the latter, Gottfried Weber concludes that “no class of harmonic successions admits of being pronounced good or bad universally, none can be approved or reprobated in the gross.”8 He posits that there are in all 6888 possible successions, and that the bad effect of some could be mitigated by employing a “somewhat slower grade of time; for, in this case, the ear has more time to comprehend, digest and reconcile itself to the succession, though the latter be in itself rather foreign and unnatural.”9 Berton, in contrast, presents a systematically arranged collection of two-chord successions, each awarded the rating bon (good) or mal (bad), in a voluminous supplement to his Traité d’harmonie [1815].10 He evaluates motion from one chord in 53 position to another chord in 53 position, with stationary bass or with bass ascending or descending by second, third, or fourth. (All of these are bon.) Then he repeats the procedure for a chord in 53 position followed by one in 63 position. Then every other chord in his firmament serves 5 4 as the second chord: 46, 45, 25, 47, 9, 70 (= doubled root, third, and seventh), 60, 59 and on and on. Once that cycle is complete each other chord takes its turn at the head of the succession. On occasion Berton specifies a preferred pair of scale degrees for the succession (e.g., “Chiefly from the 6th to the 5th degree” [“Surtout du 6eme au 5eme dégré”]), thus softening the rigidity of his crude thumbs-up/thumbs-down evaluation system. The effect is daunting, suggesting that acquiring harmonic sense requires a monstrous task of memorization and that the purview of such thinking need never extend beyond two adjacent chords. Other authors focus on the more limited number of scale-step successions, without the added dimensions of inversion and dissonant chordal constructions: for example, from a chord rooted on the fourth scale

87

88

Thinking About Harmony

degree, where might one proceed? Crotch, in 1812, starts from a foundation of six “Simple Diatonic Successions” (up or down a fourth, third, or second). He may rule out a succession either if the continuation chord is dissonant (as in an ascending fourth from the fourth scale degree) or if a succession is “peculiar to ancient music” and thus to be avoided unless “writing professedly in the church style” (as in an ascending third or a descending second from the fourth scale degree).11 Crotch ends up endorsing only IV–I, IV–II, and IV–V (translating his symbols into Roman numerals). Two decades later Jelensperger offers a more variegated (though still manageable) perspective to his French and German readers. First he divides all root successions into two basic classes: Successions of the First Order:

Successions of the Second Order:

Ascending Fourth (Descending Fifth) Ascending Fifth (Descending Fourth) Ascending Sixth (Descending Third) Ascending Second (Descending Seventh) Ascending Seventh (Descending Second) Ascending Third (Descending Sixth)

Jelensperger then proceeds to rank all seven successions of major-key diatonic chords within each of his six diatonic categories [4.1]. 5–1 is preeminent among the Ascending Fourth successions, while 7–3 is least favored. 2–1 (his example shows supertonic followed by what many now call a cadential 64) leads the list of Ascending Seventh successions, which concludes with 7–6. The grid’s diagonal construction positions the fortytwo entries within twelve horizontal bands, thereby correlating successions of varying sizes. For example, the successions 4–2, 4–1, and 2–5 appear side by side, indicating an equal ranking. After devoting special attention to 1–2 and 6–1, he suggests: “For the other successions above the center, the realization is arbitrary enough, but for those below, they are very fragile and demand almost always, and particularly those of the second order, that their second chord be in the first inversion.”12 Jelensperger notes with satisfaction that one of his examples contains six successions of an Ascending Fourth, four of an Ascending Fifth, and one of an Ascending Second—ten successions from the First Order and one from the Second Order [4.2].13

pa ua rq

"

/

"

rte

"

su c /= seco cess == n io == d o ns d == rdr e == e /\

"

ns io

cc Su

s p ucc /= rem essi == ier on == or s d == dre e == /\

Harmonic progression

re

e

"

te six

p su

te in qu

"

"

"

"

--

"

--

"

--

pt se

"

e " nd co e se ièm

/

"

---

e rc tie

--

5–1

1–5

--

4–2

1–4 4–1

2–5

-

"

---

4–5

---

2–1

6–1

1–6 5–6

6–5

5–2 6–4

1–2

6–2 2–6

5–3

3–6 6–3

4–7

-----------------------------------------------2–4

5–4

3–5

3–4

4–3 4–6

3–1

2–3 3–2

1–3

7–4

7–5 7–1

1–7 5–7

7–3

3–7 2–7

6–7 7–6

7–2

4.1 Jelensperger: L’harmonie au commencement du dix-neuvième siècle (1830, 21833), p. 30 [Häser, p. 22]. All forty-two diatonic successions are ranked both among successions of the same interval (read from upper left to lower right) and in relation to successions of other intervals (read horizontally).

4.2 Jelensperger: L’harmonie au commencement du dix-neuvième siècle (1830, 21833), pp. 25, 31 [Häser, pp. 17, 23]. Jelensperger’s practice of indicating the scale degrees of chordal roots below the bass is here supplemented by an indication of the interval formed by each adjacent pair of roots. (All intervals are calculated as ascending.)

89

90

Thinking About Harmony

Whether we think in terms of Weber’s 6,888 or Jelensperger’s forty-two chord successions, certainly the more different entities a system accommodates, the more complex the task of assessing their possible interactions becomes. Though some authors are so intrigued by chordal inversions and added dissonances that they become mired in their myriad categories, any scale-step perspective inherently must come to terms with a considerable number of chord successions: at the very least, forty-two, as in Jelensperger’s chart of the succession from each of the seven scale degrees to the other six [4.1]. A functional perspective has an advantage in this regard. With a greater variety of chords falling within a single category, the analyst needs to account for fewer successions from one category to another. Portmann’s system, based on four diatonic and two chromatic Grundharmonien (introduced on pp. 12–13, above), includes particularly elegant and useful remarks on chord succession. Because the scale-step system’s III falls within the same functional category as I, and because VII and even II fall within the same category as V, the number of distinct diatonic successions is quite limited in Portmann’s system – to just twelve successions, nine of which are wholeheartedly endorsed, two permitted with restriction, and one forbidden. (Readers familiar with Riemann’s functional system should note some interesting differences, especially the alignment of diatonic scale-step II with the dominant rather than the subdominant.) Formulated in the 1780s and 1790s, Portmann’s no-nonsense rules are much easier to absorb than Jelensperger’s multi-tiered chart. They demonstrate that he took the task of establishing normative patterns of chords succession far more seriously than did Weber, whose bandying about of the number 6,888 may seem impressive, though ultimately it fails to account for the norms of harmonic practice in his era. We thus turn our attention now to Portmann’s sage advice. Because his chord names and their complete pitch content may seem daunting, a simplified table of chord relations using modern terminology is provided opposite as a guide for the following discussion.

Portmann’s rules of succession In that Portmann’s collection of functional harmonic entities (see pp. 12–13, above) differs from that of scale-step analysts, we should expect from him a similarly novel treatment of harmonic succession. Whereas Jelensperger’s seven diatonic chords generate forty-two possible successions, Portmann’s

Note:

a

Tonica Tonic Tonic

Permitted to:

only when both chords are consonant.

Tonic Submediant Subdominant Dominant V/V V/V over V pedal

From:

Submedianta Submediant

Submediant

Subdominant Subdominant

Dominant Dominant

Dominant Dominant Dominant

V/V V/V V/V V/V

V/V over V pedal V/V over V pedal

92

Thinking About Harmony

harmonic universe is more compact. Jelensperger’s 1 and 3 are both manifestations of Portmann’s Hauptprimenharmonie, while 5, 7, and even 2 correspond to his Dominantenharmonie. Thus Portmann can focus on the twelve successions of only four diatonic entities. His two remaining Grundharmonien both contain the raised fourth scale degree, placing them decisively within the orbit of the dominant. Portmann’s prescriptions concerning harmonic succession may be summarized as follows.14

From the Hauptprimenharmonie [e.g., C Major: C e g b d f a; A Minor: A c e gs b d f] A succession to a chord of the Sextenharmonie is always possible, as is one to a chord of the Quartenharmonie, Dominantenharmonie, or Wechseldominantenharmonie. A chord of the Doppeldominantenharmonie is not a suitable successor.

From the Sextenharmonie [e.g., C Major: A c e g b d f; A Minor: F a c e gs b d] A succession to a chord of the Hauptprimenharmonie is generally avoided, though an exception can be made if both chords are consonant. That to a chord of the Quartenharmonie, Dominantenharmonie, or Wechseldominantenharmonie is always possible. A chord of the Doppeldominantenharmonie is not a suitable successor.

From the Quartenharmonie [e.g., C Major: F a c e g b d; A Minor: D f a c e gs b] A succession to a chord of the Hauptprimenharmonie is always acceptable, but not to a chord of the Sextenharmonie, though an exception can be made if both chords are consonant. A chord of the Dominantenharmonie is a suitable successor, as is a chord of the Wechseldominantenharmonie. A chord of the Doppeldominantenharmonie is not a suitable successor.

From the Dominantenharmonie [e.g., C Major: G b d f a c e; A Minor: E gs b d f a c] A succession to a chord of either the Wechseldominantenharmonie or the Doppeldominantenharmonie is possible, as is that to a chord of the

Harmonic progression

Hauptprimenharmonie or the Sextenharmonie. A chord of the Quartenharmonie is not a suitable successor.

From the Wechseldominantenharmonie [e.g., C Major: D fs a c e g b; A Minor: B ds f a c e g (in inversion only)] This chord corresponds to “V of V” in major keys and the augmented sixth chords in minor keys. A succession to a chord of the Dominantenharmonie or to a chord of the Doppeldominantenharmonie is possible. A chord of the Hauptprimenharmonie, Sextenharmonie, or Quartenharmonie is not a suitable successor.

From the Doppeldominantenharmonie [e.g., C Major: G b d fs a c e; A Minor: E gs b ds f a c] This chord merges components of the Dominantenharmonie and Wechseldominantenharmonie. It is employed chiefly during a pedal point. The principal goal of succession is to a chord of the Dominantenharmonie. Neither a chord of the Wechseldominantenharmonie, the Hauptprimenharmonie, the Sextenharmonie, nor the Quartenharmonie is a suitable successor. An instructive example of how such prescriptions affect analytical practice occurs in 1.11b. After an initial tonic-to-dominant succession (c¯ g´), G-B-D-F is reinterpreted as an augmented sixth chord (øc , = Cs-Es-G-B-D, with absent root) in B Minor. As a representative of the minor-key Wechseldominantenharmonie, the dominant – but not tonic – is a suitable successor. When Fs-B-D in fact occurs next, Portmann rejects tonic as its analysis, instead regarding Fs, B, and D as the root, eleventh, and thirteenth ., of the Dominantenharmonie (f ) with B and D resolving to As and Cs, respectively, later in the measure. We depart the domain of Funktionstheorie, with its clear and sensible perspective on chord succession (at least as articulated by Portmann), for the more variegated and less easily codified terrain of Stufentheorie. While acknowledging that nineteenth-century conceptions are of limited scope and imperfectly reflect the practices of composers, we nevertheless undertake a brief survey to assay the state of affairs during that auspicious era of composition, taking for granted that the most able practitioners would transcend any textbook prescriptions. We proceed

93

94

Thinking About Harmony

according to the three traditional categories of motion: by fifth, by third, and by step. The elite status of the fifth is announced in its qualitative designation: perfect. When representing the fifth, the fourth shares in that status. Thus an ascending or descending fourth may appear in place of a descending or ascending fifth in a progression without altering its harmonic meaning. In such contexts both intervals function as consonances. In contrast, the fourth that precedes the third in a 4–3 suspension is dissonant. Though we generally use the label “perfect fourth” in both contexts, recall that Portmann and Koch regard the latter not as an inversion of a fifth or as a consonance, but as a dissonant eleventh above the root. The low-integer ratios of the fifth and fourth (2:3 and 3:4, respectively) were regarded by many as Nature’s endorsement of their primary roles in musical composition. Such assurance, such conviction of rightness and inevitability, was retained throughout the eighteenth and well into the nineteenth century. In that context, Weber’s assertion that any chord may lead to any other chord likely struck some as heresy. Thus the paeans to motion by fifth, to which we now direct our attention, sometimes take on a zealous character. Roots separated by fifth offered a tried-and-true formula for compositional development that none of the authors cited could have imagined would be so thoroughly undermined in a later phase of music’s history.

The privileged fifth In acoustically oriented approaches to chord succession, root motion by fifth enjoys a favored status. Only the octave is more confirmative in Nature’s scheme. (Momigny in fact labels the descending octave as a cadence complétive ou confirmative.) Yet the 2:1 octave produces merely the continuation of an existing harmony, rather than a succession from one harmony to another. The 3:2 ratio of the perfect fifth suggests that the most basic harmonic means of intensifying musical activity is through root motion of an ascending fifth, while a step towards closure is through root motion of a descending fifth. Though I–V and V–I represent the prime instances of these tendencies, the principle is applicable elsewhere within the tonal landscape as well: for example, V–II leads away from closure, while II–V leads towards closure. Though initially Rameau was unaware of partials, he became cognizant of the order they impart through experiments with vibrating strings, from which the numerical ratios of acoustics can be formulated empirically. (For

Harmonic progression

example, if a string is divided in half, the segment will vibrate twice as fast as the entire string and thus sound an octave higher; likewise the second partial – or first overtone – vibrates twice as fast as the fundamental.) He announces his perspective at the outset: Music is a science which should have definite rules; these rules should be drawn from an evident principle; and this principle cannot really be known to us without the aid of mathematics. Notwithstanding all the experience I may have acquired in music from being associated with it for so long, I must confess that only with the aid of mathematics did my ideas become clear and did light replace a certain obscurity of which I was unaware before.15

Just as some authors sought irrefutability through an alliance with God,16 Rameau invokes the god of Science. Though he asserts that the fundamental-bass succession of a descending fifth (or ascending fourth), forming a cadence parfaite, should be used to end a progression, Rameau otherwise endorses a range of possibilities: “We should now be able to compose a bass in whatever manner we judge appropriate; as long as it begins and ends with the note Do, it may proceed by any consonant intervals at all . . . The note Si should be avoided in the bass, however . . . The arrangement of the bass depends only on fancy and taste.”17 Rameau becomes more prescriptive when assessing the impact of chordal dissonances: “Remember that after a seventh chord the fundamental bass should always descend a fifth.” In this way the dissonant chord “dominates the chord which follows it.” The major dissonance (the chordal third) and minor dissonance (the chordal seventh) propel the motion. Clearly Rameau favors motion by descending fifth: “This bass should contain as many perfect cadences as possible.”18 (The term “cadence,” in Rameau’s usage, is not restricted to the succession that ends a phrase.) The reverse – motion by ascending fifth – characterizes the cadence irréguliere. (See 1.18.) Here, too, dissonance propels the progression, as in F-A-C-D proceeding to C-E-G, with fundamental bass F–C.19 In this case the dissonance is the sixth, and its normative resolution is upward: D to E. Dissonance, sometimes assumed when not literally present, is thus a pervasive and powerful force in Rameau’s conception of harmonic succession. In an example in which only the fifth and its inversion occur between adjacent pitches of the fundamental-bass progression [4.3], every bass F supports dissonance D, which resolves upward by step; and every bass G supports major dissonance B, which resolves upward by step, and minor dissonance F, which resolves downward by step. The fifth, the favored interval within chords, is also the favored interval between roots.

95

96

Thinking About Harmony

4.3 Rameau, Traité de l’harmonie (1722), p. 222 and Supplement, p. 14 [Gossett, p. 243]. Whereas the Basse-Continue (the second-lowest staff) moves by step, the analytical Basse-Fondamentale (lowest staff) is a progression of fourths and fifths.

Lampe privileges motion by fifth as well: The Scholar . . . should now learn how to proceed from one Cord to another and properly to vary their Harmonies, and to do this, he must learn in what manner Cords are related to one another, the sixth Example [4.4a] shews what different Relations a Cord may have. . . . and in like Manner are all other Cords related to one another by Thirds or Fifths; therefore the Scholar must be taught, how to distinguish what the first and nearest Relation to a ground Note is, which is the fifth Note of any Cord . . . I think I need make no farther Explaination, therefore let him now learn to move the Parts regularly, when these relative Cords succeed one another, and for this Purpose, let him practise the Seventh Example [4.4b].20

Though Lampe’s chart of relatedness [4.4a] would seem to place thirdrelated triads as “first and nearest” to a given triad, he suggests that the fifth, not the third, is the closest relation. (In fact, revisiting this topic in The Art of Musick (1740), he revises his example to show only the F, C, and G triads.21) Some hint of his motivation comes from his music example [4.4b], wherein motion by fifth occurs without thirds, but motion by third occurs only in a context that also includes fifths. The two fifth-related chords that flank the tonic are among the “principal” harmonies of a key: “Here the Cord of the fourth Note to the Key makes as well a principal Harmony to its

Harmonic progression

a

b

4.4a, b Lampe: A Plain and Compendious Method of Teaching Thorough Bass (1737), plate 4 (adjacent to p. 21), exs. VI and VII. (b) Lampe presents these progressions in other versions as well, varying the starting positions of the melodic lines.

Key, as the Cord of the Fifth Note to the Key, because the Relation of the Key and its fourth Cord is of the same Nature as the Relation of the fifth Cord to its Key Cord.”22 Lampe’s first keyboard Lesson for practice is the succession Key note . . . 4th . . . K . . . 5th . . . K, presented in eleven major and eleven minor keys.23 His penchant for fifth-related roots extends beyond this domain, however. For example, it controls the behavior of the chord on the second scale degree: “Here it may be seen, that the Cord of the second Note to the Key, is succeeded by its nearest related, the Cord of the fifth Note to the Key, to which it is a preceeding Fifth Cord, and therefore is sounded with the Seventh, and for which Reason the Figures of 65 are placed over the fourth Note to the Key.”24 Kirnberger is of the same opinion: “Two successive chords can have a close association by the relationship of their roots. We know that every note carries with it the feeling of its fifth, and that in general the transition from one note to another is easier the better these notes harmonize with one

97

98

Thinking About Harmony

another. Thus the progression from one root to another is easiest through consonant leaps, i.e., fifths, fourths, and thirds.”25 He demonstrates how motion from dominant to tonic (the “final cadence” or “principal close”) and, in a “somewhat less perfect” guise, from subdominant to tonic are particularly suited to cadential effects at the end of a composition. In fact, when the latter follows the former, a “double cadence” results. In a similar formulation, Vogler regards the three principal cadences as V–I, I–V, and IV–I.26 The first two are suitable for use in minor keys as well, so long as the dominant’s third is raised. Sechter inaugurates his discussion of harmonic succession by extending the descending-fifth principle from V–I to all other positions in the key. Among ascending-fifth successions, he sanctions only three in major keys: I–V, IV–I, and VI–III. VII–IV is faulty because VII’s dissonant fifth does not resolve. (A common tone would occur instead.) Sechter’s conception of II as dissonant27 likewise prevents motion to VI, for II’s fifth would lack resolution. III–VII and V–II are faulty because the dissonant fifths of VII and II are not prepared. Next we consider succession by third. Our examples thus far, admittedly not a random sampling, contain few such successions. Some of these, such as C–A in the fundamental bass of 2.1a or F–D in that of 2.6, are analytically generated rather than part of the sonic experience of the progression. Whereas these analyses add third-successions when they do not actually sound, Portmann’s functional system tends to delete some third-successions: the distinct tonic and mediant chords of the scale-step system both fall within Portmann’s Hauptprimenharmonie category, while the dominant and leading tone chords fall within his Dominantenharmonie category. (See p. 13.) That analysts could add or delete a third-succession at will suggests a non-assertive character, contrasting the more distinctive and dynamic connections of root motion by fifth and by second.

Succession by third Momigny’s distillation of cadential harmonic motion is represented numerically by his “sacré quaternaire” (sacred quaternary): 4 3 2 1. The 4:3 ratio (descending fourth) corresponds to the cadence imparfaite (Rameau’s cadence irréguliere), the 3:2 ratio (descending fifth) to the cadence parfaite, and the 2:1 ratio (descending octave) to the cadence complétive ou

Harmonic progression

4.5a Asioli: Trattato d’armonia e d’accompagnamento [1813], p. 37. Asioli’s use of T for “Tonica” is akin to Lampe’s use of K for “Key Note” [1.1]. The diminished chord at 7a. is tolerated (tollerati).

4.5b Sechter: Die Grundsätze der musikalischen Komposition (1853–54), vol. 1, p. 13. Though descending thirds are employed freely, the fifth plays a critical role at the cadence (Schluss).

comfirmative. Only with the number 5 does succession by major third (5:4) emerge, while 6 is required for the minor third (6:5). These numbers are too far up the series to produce strong cadential effects, yet not so far as to be problematical for lesser harmonic motions. Though lacking the special cachet of motion by fifth, motion by third generally was regarded in a favorable light. In fact, Momigny sanctions progressions of nothing but thirds: C–E–G–B–D–F–A–C

or

C–A–F–D–B–G–E–C,

thereby omitting a cadence derived from his sacré quaternaire. A similar demonstration by Bonifazio Asioli includes both fundamental-bass and numerical analyses [4.5a]. Sechter, in contrast, caps such a progression with a more conventional close [4.5b]. Sechter’s stance accords with that elaborated by Rameau more than a century earlier: “Since the fifth is constructed of two thirds, the bass, in order to hold the listener in an agreeable state of suspense, may be made to proceed by one or several thirds, and consequently by the sixths which represent these thirds. All cadences, however, are reserved for the fifth alone and for the fourth which represents it. Thus, the entire progression of the

99

100

Thinking About Harmony

fundamental bass should involve only these consonances.”28 Motion by third inevitably results in multiple common tones between chords [4.4a]. The art of chord progression balances the greater continuity between adjacent chords that results from progression by thirds with the greater cadential force that results from progression by fifths. With thirds, the direction of motion is a more significant factor than with fifths or seconds. Crotch banishes ascending-third motions to the domain of “ancient music.”29 In Jelensperger’s chart [4.1], both ascending fifths and descending fifths (ascending fourths) are ranked as first-order successions and both ascending seconds and descending seconds (ascending sevenths) as second-order successions. In contrast, the ranking of the descending third (ascending sixth) does not correlate with that of the ascending third. In fact, 6–1 is the only ascending third that manages to poke above his dotted line separating the more common successions from those that warrant special attention (such as presenting the second chord in inversion) when employed.

Only when one proceeds upwards into the next octave of partials does one encounter seconds, which are well represented from the eighth partial onwards. (Their diverse sizes are smoothed out when equal temperament is employed. For example, the ratios 9:8 and 10:9 both correspond to major seconds. The former interval is shrunk a bit and the latter is expanded a bit when each half-step is defined as one-twelfth of an octave.) Compared with fifths and thirds, seconds are remote from the fundamental. That should make them less common in usage than successions by third. But that is not the case. How could successions as common as I–II, IV–V, or V–VI be regarded as inferior? Since that was out of the question, a new analytical project emerged: how can one justify successions by second, despite their seemingly weak pedigree? This is a topic about which many had something to say. Let’s listen in.

Succession by second Unlike chords separated by a fifth or a third, two triads a second apart lack the kinship of common tones. Succession by second involves the concurrent shift of all chord components, a situation that might warrant its avoidance or, at least, some mental maneuvering to recast the succession as something other than what it appears to be. Rameau propounds the aesthetic ideal that

Harmonic progression

4.6 Rameau: Traité de l’harmonie (1722), p. 212 [Gossett, p. 232]. Rameau’s example is based on an ascending and descending octave scale in the bass (bassecontinue). His selection of fundamental-bass pitches generates two chordal sevenths that do not sound in the actual music: G (seventh against imagined A) in measure 2 and C (seventh against imagined D) in measure 3. Curiously, neither of these sevenths resolves downward by step, whereas all of the chordal sevenths within the sounding progression do: F in measure 1, C in measure 2, F in measure 4, C in measure 6, F in measure 7, and F in measure 8.

“each sound will . . . harmonize with the sound preceding it.”30 Succession by second lacks such harmoniousness. Rameau reminds his readers of Zarlino’s prescription regarding bass progressions: “the composer should make [the bass] proceed by movements which are rather slower and more separated, i.e., more spread out, than those of the other parts.”31 Rameau transfers this prescription from bass to fundamental bass. Justification for ascending-second motion, when it does occur, takes one of two forms. First, one may interrupt a perfect cadence, creating a cadence rompuë (broken or deceptive cadence). Without disturbing the upward resolution of a dominant’s leading tone or the downward resolution of its seventh, the resolution chord’s sixth may sound instead of its fifth. For example, A may sound in place of G in the C chord of a G7–C succession. C remains the “true fundamental sound,” Rameau asserts, assuring his readers that “there is nothing harsh in this alteration.”32 Second, one may mentally interpolate a bass pitch between second-related roots.33 An ascent from C to D may be understood as C descending to A, then A ascending to D [4.6, measure 2]. In a related strategy, what may seem to be a stepwise succession G–F–G [4.6, measures 3 and 4] may be interpreted as G–D7–G, with D7 represented by its third, fifth, and seventh.

101

102

Thinking About Harmony

a

c

b

d

4.7 Kirnberger: Die Kunst des reinen Satzes in der Musik (1771–79), vol. 1, pp. 62, 66 [Beach and Thym, pp. 82, 85]. Each seventh above a sounding bass pitch in these examples is “unauthentic” because the bass does not move by descending fifth. (See page 39, above.) In each case the seventh is formed by the third and ninth of a chord rooted a third below the sounding bass. These ninths are “incidental” dissonances because they could resolve within the same chord, even if (as in 4.7a, c, d) they do not. Root succession by ascending second (such as F–G in 2.5, C–D in 4.7c, and D–E in 4.7d) is unproblematic for Kirnberger so long as it does not coincide with the resolution of a dissonance.

Kirnberger’s conception, though related to Rameau’s, is more nuanced in its treatment of dissonance. When a dominant resolves to tonic (for example, G7–C), the dominant’s seventh (F) is an essential dissonance whose resolution pitch (E) occurs in the succeeding chord. When the submediant substitutes for tonic (seemingly G7–A) [4.7a], the pitch that appears to be the dominant’s seventh (F) is instead an “incidental” dissonance, a ninth above an imagined root a third below the sounding bass. (Thus G7–A stands for E97–A.) This conception prevails regardless of whether that incidental dissonance does [4.7b] or does not [4.7a] resolve before the submediant chord arrives. Other examples confirm that Kirnberger’s central concern is not root succession by second, which he employs freely, but resolution of dissonance via root succession by descending fifth [4.7c, d]. Kirnberger’s influence can be discerned in the work of his German compatriot Augustus Frederic Christopher Kollmann, whose career unfolded in London. His two “general rules on which all fundamental progressions depend” single out not only dissonance resolution but also motion by second as special concerns:

Harmonic progression

Rule I. The fundamental concord may proceed to a fundamental discord, on the same, or on any other degree of the diatonic scale; but it may proceed to a fundamental concord only by a consonant progression [root succession by third or fifth], and not by the dissonant progression of ascending or descending, a second, or seventh. Rule II. The fundamental discord, has only the one real progression, of descending a fifth, (or ascending a fourth) to a fundamental concord or discord. For its progression to those chords, one degree higher, as in the interrupted cadence, is only a contraction of the former progression with a nearly related one.34

The notion that a progression might represent something other than what it appears to be was taken up by Vogler’s pupil Friedrich Dionys Weber. Presenting the outer-voice progression F D

F G

E Fs

D G,

which appears to contain root successions of descending and ascending minor seconds, Weber suggests an interpretation as F D

F G

E C

Fs

D G,

a conception that eliminates the G–Fs second.35 The Fs–G second that remains echoes Vogler’s own analytical practice, as in the fifth cadence of 1.4. Rameau’s solution to the ascending-second dilemma is reprised over a century later by Simon Sechter: “One must know that, in the progression from IV to V or to V7, II or II7 is actually employed between them, or imagined there (and treated accordingly), through which the following chord progressions arise: 7

I IV II V I

or

I IV II V I

7

or

7

I IV II V I .”36

Moritz Hauptmann likewise employs mediating chords to justify successions of ascending or descending seconds [4.8a]: Two triads lying wholly outside each other (such, namely, as have no common connecting note whose transformation into another meaning might give the understanding of the passage), require to be mediated by that triad, lying between the two, of which the first of the two unconnected triads contains two notes, and the other one note. And the passage from the first into the second cannot take place otherwise than in so far as the first has already this preponderance of community with the intermediate triad, and may therefore be put for it. Or, the progression from the first of the unconnected triads to the second is the same as it would be from the mediating triad to the second.37

103

104

Thinking About Harmony a

b

4.8a Hauptmann: Die Lehre von der Harmonik (1868), p. 41. 4.8b Jadassohn: Lehrbuch der Harmonie (1883, 131911), p. 54. Hauptmann’s parenthetical chords connecting C and D in 4.8a reveal in music notation the mental maneuvering he suggests as justification for an ascending-second progression. Jadassohn transforms the mental into the actual in measure 4 of 4.8b, an example of dubious artistry.

Unfortunately Hauptmann’s silent mediating chords are elevated to fundamental harmonic entities in his pupil Salomon Jadassohn’s harmony textbook [4.8b]. Linking tonic and supertonic on the downbeats of measures 4 and 5 are the very chords that Hauptmann prescribes for mediation, with full Roman-numeral analysis! To most musicians the roster of august authorities relegating motion by second to an inferior status likely was persuasive. Yet there were other voices to be heard. Lampe displays none of Rameau’s reserve, reasoning that since the fourth and fifth notes of the scale are the “nearest related to the Key Note,” their chords may well be juxtaposed. He issues but one caution: “But whenever the fourth Note immediately succeeds the fifth Note, or the fifth Note the fourth Note to the Key, each being accompanied only with their own Harmony, . . . the Scholar must move the higher Parts contrary to the Motion of the Bass, otherwise the Effect would be harsh and disagreeable, or the Parts want Variety . . .”38 His examples demonstrate the progressions

Harmonic progression

Key note Key note Key note Key note

4th 5th 3rd 7th

5th, 4th, 4th 6th

5th 5th

6th, 4th.39

and

Though Sorge also permits motion by ascending or descending second, he suggests that no more than two in a row should occur, for example: F

G

A

and

A

G

F

in C Major, and

D

s E

F

(but not

F

s E

D)

in A Minor.40

Kirnberger employs ascending seconds when the resolution of dissonance is not a factor.And in Vogler’s pioneering Roman-numeral analyses of 1778, four of the ten model cadences contain ascending-second root successions [1.4].

“In the beginning was the Tonic” would be a promising opening for the gospel of tonality. Though the tonic pitch may be the origin and goal of harmonic progression, in itself it offers no diversity, no motion. Choosing A as a primordial tonic, harmonic activity dawns with the emergence of E, the only non-tonic pitch among A’s lowest partials, as the dominant’s root. A–E–A exemplifies the most fundamental of progressions. Though its unique role in tonal practice was later acknowledged through Schenker’s expression “sacred triangle,” its foundational status was understood by early practitioners of music analysis [4.4b], even if some would regard A–D–A as a model of equivalent import. An expansion into four chords could result in the progression A–B– E–A, where B relates to E as E relates to A. This dual relationship may obey tonal constraints – with minor B chord and major E chord, in conformity with the A Major key signature—or it may be shaped into an exact parallelism by raising the B chord’s third. (The modified B chord is now often called “V of V” to acknowledge its transformed state.) Yet the adjacent roots A and B form a major second, a problematic interval for succession because no common tones link the two chords. Since Rameau’s time a routine means of averting that problem has been to imagine, or to pursue, the circuitous route of a descending third followed by an ascending fourth, which both assures common tones and E C s Fs A(s) D(s)). The progression thus has grown welcomes chromatic inflection (Cs A Fs B to A–Fs–B–E–A. Successive roots form a descending third and three descending fifths, all favored intervals.

105

106

Thinking About Harmony

Let’s now watch as Schubert takes this evolved progression into his masterful hands. Something extraordinary occurs: he allows the fifths to pierce through the boundary of the diatonic tonality. From Fs to B to E to A normally would be the extent of the progression, with tonic’s return serving to terminate the cascade of fifths. Yet Schubert proceeds downwards beyond the tonic, from A to D to Gn. In the resulting progression, A F#7→B E7→A D7→Gn, what begins as an autonomous harmonic progression with a high density of descending fifths is eventually overpowered by those fifths. A sequential progression (the chain of descending fifths) results. Though accurately recreating Schubert’s thought process of course is not possible, we can at least explore some of the alternatives that he might have considered. That investigation will help us to understand just what was at stake in his progression and to better appreciate why his solution is so brilliant.

Koch’s model: Schubert’s composition Consider an example by Koch [4.9a]. Its uninspired craftsmanship could not be mistaken for the writing of a gifted composer. Its chords fulfill the task of supporting the melodic descent from 5 to 1 without fuss, without the creative imagination that could make this musical statement unique and memorable. It is constructed in compliance with a musical grammar that many understood, but which few could use to shape something of enduring interest. Consider now an example by Schubert [4.9b]. Its inspired artistry could not be mistaken for a textbook exercise. And yet its creation represents a careful selection and amplification of ideas that were discussed in pedagogical writings from around Schubert’s time. A comparison of Koch’s and Schubert’s creations illuminates the distinction between craft and art.

Embellishment Schubert’s harmonic progression is enlivened by non-harmonic elements. Sechter (the teacher to whom Schubert, in his final year, applied for instruction in counterpoint) demonstrates alternative positionings of figuration [4.10a]. Schubert similarly redeploys the upper neighboring notes of measure 11 in measure 13 [4.10b]. The D-Fs-A simultaneity that begins measure 13 is neither IV in A Major nor III in B Minor, but instead is built from tonic A’s root and the upper neighbors of its third and fifth. Neighbor

Harmonic progression

4.9a Koch: Handbuch bey dem Studium der Harmonie (1811), col. 124, fig. 36 (transposed). Koch wrote this example to demonstrate the simultaneous occurrence of a third and an eleventh above the bass (D and E in the second chord). The progression’s continuation is straightforward, with a harmonization that supports the descent from 5 to 1:

A Major:

5 I

4 II

V

3 I

2 II

V

1 I

The measure numbers placed above Koch’s example correspond to Schubert’s composition [4.9b].

4.9b Schubert: Quintet in A Major for Pianoforte, Violin, Viola, Violoncello and Contrabass (“Trout”), op. 114 (1819), mvmt. 5. The violoncello and contrabass share the same staff. The contrabass (downward stems) sounds an octave lower than notated.

107

108

Thinking About Harmony

a

b

4.10a Sechter: Die Grundsätze der musikalischen Komposition (1853–54), vol. 1, p. 95 (transposed). 4.10b Models corresponding to 4.9b, mm. 11 and 13–14. (a) Embellishment of the dominant chord in B Minor may be positioned at various locations within the texture. (b) Upper neighbors embellish the A Major tonic’s third Cs and fifth E in two contexts. In chapter 5 we will encounter Jelensperger’s comparison of neighboring motions undertaken at various speeds [5.4]. Given Schubert’s Allegro giusto tempo indication, Jelensperger likely would have regarded D and Fs as incidental notes (notes accidentalles) in both contexts.

D is doubled in the contrabass, where it both arrives and departs by leap. The model shows the resolution of these neighbors before As, which connects the tonic and supertonic roots, arrives. In Schubert’s composition E Cs’s tendency towards II is strengthened these two events converge, and As through the addition of root Fs. The neighboring-note strategies displayed in 4.10b recur in alternation every two measures throughout the excerpt.

Root motion by second Many analysts of Schubert’s time would have interpreted the ascendingsecond root succession that inaugurates Koch’s harmonic progression [4.9a] as a truncation of A–Fs–B. Schubert affirms that predilection by actuD D C# ally composing A–Fs–B [4.9b, measures 11–14]. Koch’s AE– B– E– A outer-voice structure has greater momentum in Schubert’s composition both through the impact of bass Fs and inner voice As against soprano E in measure 13 and through the expanded progression of fifths in the bass (Fs–B–E–A). By employing chromatic As, Schubert establishes a relationship between the Fs and B chords that will be echoed not only by E and A in measures 17–18 (and 25–26), but also by D and Gn in measures 21–22.41

G Major in A Major Schubert’s measures 19 through 22 could have been more conservatively constructed. A less resourceful composer might have modeled them after measures 11 through 14, since the root progression A–Fs–B functions just as well for soprano Cs–B as for E–D [4.11a]. Yet that version, especially the

Harmonic progression

a

b

4.11 Alternatives to Schubert’s measures 19 through 22.

repetition in measure 19 of the tonic from measure 18, seems tedious. Schubert rambunctiously brings in the Fs7 chord in measure 19 (rather than measure 21, as in 4.11a). What does this move portend? Perceptive listeners might develop several hypotheses: (1) Because the Fs chord resembles the one heard in measure 13, likely the most common initial interpretation would be that measures 19 through 22 will turn out to be a variant of measures 11 through 14. Three structural chords occur in the earlier passage: A–Fs7–B. Because measure 18 supplies an A chord, Schubert could proceed directly to Fs in measure 19. As a result measures 19 through 22 would incorporate only the second and third of the three chords of measures 11 through 14 [4.11b]. This hypothesis ultimately must be rejected, however, since measures 21 and 22 do not fulfill these expectations. Why did Schubert not follow this course? Perhaps it was that three consecutive four-measure units would repeat transpositions of the same V7–I material: E7–A (measures 15–18), Fs7–B (measures 19–22), and then E7–A again (measures 23–26). (2) Superficially measures 19 and 20 may sound like a transposition of measures 11 and 12 to Fs Major. Though the C# fifth that begins measure 19 F# corresponds to the EA fifth of measure 11, the transposition is not exact. Why, for example, does the pitch D, rather than Ds, occur twice in measure 19? And why is E present in the chord? Were a harmonic progression like that of measures 11 through 14 to emerge from this shaky foundation, a problematic juxtaposition of D and Ds might occur in hypothetical measure 21 [4.12a]. (3) Because neither of the first two hypotheses adequately accounts for Schubert’s handling of measures 19 through 22, a fresh idea – one not likely to emerge until one hears measure 21 – is called for. The two preceding

109

110

Thinking About Harmony

a

b

4.12 More alternatives to Schubert’s measures 19 through 22.

four-measure units employ prominent fifth-relationships: Fs7→B, E7→A. Given how measures 19 through 22 conclude, the fifth-relationship that warrants consideration here is D7→Gn. Though a direct succession from an A chord (measure 18) to a D7 chord would be feasible [4.12b], Schubert instead divides the descending-fifth bass [4.13a] into two thirds [4.13b] and adds a bit of chromatic spice [4.13c]. The quirkiness of this passage stems from the fact that a chord we are inclined to regard as an applied dominant (Fs7 poised to resolve to B as “V7 of II,” as in measure 13) ultimately functions as a connector between A and D.42 An analogous situation occurs in a contemporaneous example by Justin Heinrich Knecht [4.13d]. As does Schubert, Knecht here divides a descending fifth into two thirds. And like Schubert’s interior chord, which we are tempted to perceive as the dominant of B, Knecht’s augmented F chord (which he labels as III.) possesses an untapped tendency: to resolve to Bb (D Minor: III. VI.; or Bb Major: V. I.). Knecht demonstrates that resolution on the same page. How the internal chord does behave – as opposed to how it might have behaved – reflects the controlling force of the boundary fifth. Major-mode tonality is not a symmetrical system. The chain of diatonic perfect fifths ascending from tonic is long, whereas that descending from tonic is short. For A Major, the diatonic perfect fifths are arranged as follows: D

A

E

B

Fs

Cs

Gs

From this perspective the non-diatonic pitch that is closest to tonic is Gn, achieved by descending two perfect fifths from tonic: A–D–Gn. Descending fifths are a defining feature in measures 13 through 18 of Schubert’s composition: Fs–B–E–A. The piano continues that trajectory beyond the diatonic confines of the key, with D–Gn. A chain of descending fifths (one of the sequential progressions introduced in chapter 3) takes control.

Harmonic progression

a

c

b

d

4.13a–c Dividing a descending fifth into two descending thirds. 4.13d Knecht: Elementarwerk der Harmonie (21814), table XVIII, fig. 4a (transposed). A major triad with minor seventh [second chord of 4.13c] and an augmented triad [second chord of 4.13d] both hold the potential to function as dominants. When that potential remains untapped, should such chords be labeled as dominants? Knecht thinks not.

Whereas the Fs7 chord (measures 19–20) might have steered the progression onto a more normative harmonic trajectory (Schubert’s dressing of the VI chord in “applied dominant seventh” garb was of course purposeful and intentionally misleads the listener), the continued descent to D7 (and the correction of wayward As to An) followed by Gn asserts the priority of descending fifths in this region, despite the extension beyond the diatonic realm. Sequential progression has sabotaged harmonic progression.

Return to A Major Those who wander into remote tonal regions need to know how to get themselves out. Schubert was exceedingly precocious in this regard, of course. As we have seen, fifths and thirds are the favored intervals of harmonic motion. Though complete cycles of fifths or of thirds are feasible [3.6, 4.5a], they can quickly become tedious. A combination of thirds and fifths has the advantages of variety and a shorter trajectory. Because phrase-building depends upon the V–I cadence, the path from the initial I to the cadential V is the site of most harmonic creativity. An especially appealing and prevalent filling of that space employs one descending minor third and two descending perfect fifths. Three positionings of the third among the fifths are possible:

111

112

Thinking About Harmony

I I I

VI IV IV

II II bVII

V V V

Schubert utilizes the I–VI . . . option (chromaticized as I–VIs) in his first phrase. And though he seems for a moment (measures 19 and 20) to be repeating this idea in the second phrase, ultimately the option pursued is I–IV–bVII . . . The voice-leading connection between I and VIs is exactly the same as that between bVII and the V that follows, though the tonal relationship is reversed: whereas I–VIs leads into chromaticism, bVII–V leads out of chromaticism, with the subtonic pitch reverting to the leading tone. Though Koch’s prosaic progression might have offered an adequate model for Schubert’s composition, the excursion to bVII, so unexpected and yet so logical, offers listeners a compelling and memorable musical experience.43

5

Chordal hierarchy

Passing note, passing chord The third is a highly favored interval in chord construction. Consequently its diatonic filling-in – connecting root and third, third and fifth, or fifth and seventh – is encountered frequently. Any third may be expressed melodically as two consecutive seconds, either ascending or descending. The internal pitch of such a line clashes with its context: it “passes” between pitches that have a more secure footing within the immediate chordal framework. A passing note occurs least obtrusively in a weak metrical position. Yet it may be emboldened in various ways. In filling in an F–D third, Friedrich Wilhelm Marpurg places passing note E in a relatively strong metrical position, against a change of bass from G to B [5.1a]. An eighth-eighth-quarter rhythm for F–E–D would have resulted in the juxtaposition DB, a consonant element of the G-B-D-F chord. Marpurg’s quarter-eighth-eighth rhythm instead places bass B against passing E. As a result, a dissonant fourth follows a dissonant seventh. The interpretation of this situation is especially delicate because traditional dissonance-resolution strategy mandates that the F of a G7 chord should resolve to an E. Yet according to Marpurg it is not this E that fulfills that role, but instead the E on beat 3. The language he uses to express this idea in 1757 is clear and persuasive: It is wrong to think that a dissonance could resolve properly on a passing note. That might at best happen only in a figurative sense. For who could understand harmony and not realize that in the example [5.1a] the resolution of the seventh is artfully delayed through the inversion of the harmony, and occurs not on the eighth note marked by a stroke, but only on the final half note E?1

Now consider an example published by Koch in 1811 [5.1b]. Here the melodic line F–E–D occurs in a context that compels the listener to hear a direct resolution from F to E. The tendency of the diminished fifth FB is fulfilled by the major third CE .2 Koch’s next example [5.1c] brings to the fore one of the most controversial issues of harmonic analysis: passing chords. Two contrasting interpretations of the melodic line F–E–D are possible: either E passes between F and

114

Thinking About Harmony

a

b

c

5.1a Marpurg: Handbuch bey dem Generalbasse und der Composition (1757), vol. 2, table III, fig. 16 (transposed). 5.1b, c Koch: Handbuch bey dem Studium der Harmonie (1811), col. 237, figs. 1 and 2. By juxtaposing regular and exceptional (ungewöhnlich) resolutions Koch hopes to strengthen the case for regarding the G-C-E chord of 5.1c as functionally equivalent to C-C-E in 5.1b. In contrast, a passing-chord proponent might argue that a more apt juxtaposition would be that between 5.1c and 5.1a.

D in the manner of 5.1a, in tandem with C passing between D and B in an inner line; or E resolves the dissonant seventh F in the manner of 5.1b. Much is at stake in how such a question is answered. Koch is an advocate of the conservative, literalist stance: When in the strict style the diminished fifth . . . functions as the structural dissonance of the diminished triad, it is obligatory that it be prepared and resolved. In this case the resolution is most often into the third, provided that the bass concurrently ascends by step, as in [5.1b]. Yet it tolerates the following exceptional resolutions as well, namely, 1) into the sixth, when the bass moves down a third, as in [5.1c] . . .3

Though many harmony treatises promoted the sort of analysis Koch endorses (the alleged moment of resolution in 5.1c typically would be labeled “I64” during the nineteenth century), a number of voices rose in opposition to that perspective. Schulz, writing under his teacher Kirnberger’s name, addresses the issue as follows in 1773: In harmony there are passing chords that are not derived from any fundamental harmony; they are to be understood in the same manner as passing notes in the melody, and they come into being from them, when multiple voices engage in passing motion . . . Consequently passing chords are mediating chords in which one or more voices pass via a stepwise and usually consonant motion from the preceding to the following foundational chord. They always come between two foundational chords that are either the same or at least follow very naturally one after the other . . . One recognizes them further by the unnaturalness of their harmonic

Chordal hierarchy

5.2a Rameau: Génération harmonique (1737), ex. XXVIII. D, the analytical fundamental bass, persists while passing (marchent) notes E and G fill in two of the dominant’s thirds, D–Fs and Fs–A, respectively. Though soprano C is a dissonance, it temporarily becomes consonant at letter A.

progression, in which either some dissonance possibly remains unresolved, or, despite appearing to be a conventional fundamental chord, it nonetheless would impede the natural progression of the fundamental harmony.4

By definition a passing chord (in contrast to a passing note) results from at least two moving voices. In that the dominant seventh chord contains three thirds, several varieties of passing chord between statements of the dominant are possible. Whereas 5.1c employs concurrent seventh–fifth (F to D) and fifth–third (D to B) stepwise descents, Rameau chooses root– third and third–fifth ascents to prolong a D dominant seventh chord in G Major [5.2a]. This model displays perhaps the most widely used of all passing chords, itself subject to an array of variants: the belated addition of the dominant’s seventh [5.2b], inversion [5.2c], and application in the context of tonic [5.2d] and other [5.2e] chords. The French, German, and Bohemian authors cited uniformly resist asserting a harmonic role for the chord formed during the passing motions. Simultaneous passing motions may occur in opposing rather than parallel directions. Sechter shows how a GB ⫻GB voice exchange may be embellished by means of a passing A in both directions without affecting the harmonic meaning of the passage [5.3a]. In another example Sechter indicates the progression of fundamentals, asserting that passing chords have no harmonic import [5.3b]. When three voices are active, parallel and contrary passing motions can be combined, as in an example that Gottfried Weber quotes from Mozart [5.3c]. Here Weber refrains from labeling the second chord of the first measure as II7. In a similar example Lobe takes apart Beethoven’s prolongation of a dominant seventh chord E-Gs-B-D and puts

115

116

Thinking About Harmony

5.2b Savard: Cours complet d’harmonie [1853], vol. 1, pp. 76–77. “One observes in fact . . . that the 63 chord positioned on the sixth scale degree (la) – the first inversion of the triad of the fourth scale degree (fa) – does not bring about a sense of cadence, but functions as a transitional chord leading to another chord that resembles the first. In this same example the bass of the dominant progresses to rest on the tonic, in the process merely gliding over the intervening scale degrees; . . . the two extreme points alone bear chords expressing a full harmonic meaning.” [“On voit en effet . . . que l’accord de sixte place sur le la ci qui est le premier renversement de l’accord parfait de fa ne forme plus un sense arrête, mais devient un accord de transition menant à un autre accord en rapport avec le premier. Dans ce même exemple la basse partie de la dominante va se reposer sur la tonique, en ne faisant qui glisser sur les degrees intermediaries; . . . les deux points extremes portent seuls des accords exprimant un sens harmonique complet.”]

5.2c Louis and Thuille: Harmonielehre ([1907], 41913), p. 81. “As a rule the resolution of the dominant seventh chord into the subdominant is only apparent, like the succession V–IV in general; that is, it arises from suspension or passing-note structures, in which . . . the subdominant appears between two forms of the same dominant harmony as an interpolated chord, as an incidental structure without fundamental.” [“Die Auflösung des Dominantseptaccords in die Unterdominant ist, wie überhaupt die Folge V–IV, in der Regel nur scheinbar, d. h. sie entsteht durch Vorhalts- oder Durchgangsbildung, indem . . . zwischen zwei Formen der Dominantharmonie bei liegenbleibendem Fundament der Dominante die unterdominant als eingeschobener Accord, als fundamentfremde Zufallsbildung auftritt.”]

Chordal hierarchy

d

e

5.2d Reicha: Cours de composition musicale [ca. 1816], p. 75. 5.2e Sorge: Vorgemach der musicalischen Composition [1745–47], part 3, table XI, fig. 1. (d) “[This example] is remarkable for the long duration of its passing notes.” [“Le cas suivant est remarquable en ce que les notes de passage peuvent y avoir une grande valeur.”] Reicha’s example echoes numerous eighteenth-century models, including those by Rameau (Génération harmonique, 1737, ex. XXVIII), Sorge (Vorgemach der musicalischen Composition [1745–47], part 3, table XI, fig. 1), Marpurg (Handbuch bey dem Generalbasse, 1757, vol. 2, table IX, fig. 19), and Kirnberger/[Schulz] (Die wahren Grundsätze zum Gebrauch der Harmonie, 1773, p. 34 [Beach and Thym, p. 191]). (e) Sorge’s example occurs in the context of a chapter entitled “Concerning the Passing Seventh,” rendered both in German (Von der durchgehenden Septime) and in Latin (septima transitoria).

a

b

5.3a, b Sechter: Die Grundsätze der musikalischen Komposition (1853–54), vol. 1, pp. 38, 94. (a) Voice exchange (Vertauschung) and passing notes (Durchgängen) are successively applied to a basic progression. In all three cases the succession of fundamentals is G–C. The third beat of Sechter’s third example, like the third beat of 5.2c, is “merely passing” (nur ein Durchgang) and “does not belong to the essence” (gehört nicht zur Wesenheit). (b) Sechter’s progression contains eleven chords but only five fundamentals.

117

118

Thinking About Harmony

5.3c Weber: Versuch einer geordneten Theorie der Tonse[t]zkunst (1817–21, 21824), vol. 3, table 47, ex. 313 [Warner, p. 248]. Here Weber analyzes a passage from Mozart’s Don Giovanni. Elsewhere he displays a similar passing chord occurring on a downbeat (3vol. 3, p. 119 [Warner, p. 621]). This plate reveals some of the hazards that may be encountered when viewing music examples from historical treatises: the numeral V was inadvertently omitted in the third measure, and the illegible caption above the example is not some vital information but instead merely Mozart’s text (“Doch in Spanien schon Tausend und drei”).

5.3d Lobe: Lehrbuch der musikalischen Komposition, vol. 1 (1850, 21858), pp. 162–163. This example is based on a passage from Beethoven’s String Quartet in A Major (op. 18, no. 5), mvmt. 1. In the first model Lobe shows the migration of the dominant seventh’s pitches among the lower three parts. Through the gradual addition of passing notes (marked with exes), Beethoven’s composition is eventually fully reconstructed (the fourth model). A stroke marks bass pitch A, which may be regarded either as a passing note (the fourth model) or as the root of a tonic chord (the fifth model).

Chordal hierarchy

a

b

c

5.4 Jelensperger: L’harmonie au commencement du dix-neuvième siècle (1830, 21833), p. 108 [Häser, p. 120]. “When one gives certain embellishments a long duration, they function as essential notes, whereas with a short duration the ear prefers to interpret them as incidental notes, since it is not possible to comprehend such hurried chordal alteration. [Compare Example b and Example a.] If one performs the mediating notes of [Example a] slowly, one perceives all the chords in succession. At a moderate speed, the ear often is left undecided [Example c]. In that case it seems unimportant whether one considers the embellishing notes as essential or as incidental.” [“Quand certaines broderies se fout avec de grandes valeurs, elles deviennent notes réelles, tandis qu’avec de petites valeurs l’oreille aime mieux les prendre comme notes accidentelles, ne pouvant saisir un changement d’accord trop précipité [compare b with a]. En transformant en grandes valeur les médiaires de la [a], on obtient successivement tous les accords. Avec des valeurs moyennes, l’oreille reste souvent indécise [c]; alors il semble indifférent de considérer les notes qui brodent comme réelles ou comme accidentelles.”] (a) The abbreviation “m.” stands for médiaire (something in the middle).

it back together again [5.3d]. Beethoven’s structure gradually emerges out of bare arpeggiation. Though not tempted towards harmonic interpretation by the notes E-A-Cs in the third model or Fs-A-Cs-E in the fourth model, he does offer a harmonic interpretation of the notes A-Cs-E later in the fourth model, calling this moment ambiguous (zweideutig): “the pitches marked as passing may also be accepted as a chord.”5 Neighboring notes likewise may generate chords without harmonic meaning. Jelensperger alternates between G-B-D and G-C-E in C Major at fast, slow, and moderate speeds [5.4]. At the slow speed he regards G-C-E as tonic, while at the fast speed he does not. When a moderate speed is employed he offers alternative analyses and claims not to care which option is selected. Of course, the examples assembled here are not a representative sampling. . The very chord that Reicha marks as passing in 5.2d is labeled 2 by Jelensperger.6 This reversal – the assertion that C functions as a dissonant harmonic seventh above root D rather than D as an non-harmonic passing note below root C – brings to mind Schulz’s remark, quoted above, concerning a dissonance remaining unresolved. Jelensperger sidesteps this dilemma by asserting two categories of resolution: whereas in the succession . 2–5 the supertonic chord’s seventh descends by step in a “resolution of the . first order,” 2–1 constitutes a “resolution of the second order,” in which the seventh persists as a common tone.

119

120

Thinking About Harmony

a

b

5.5a Durutte: Esthétique musicale (1855), pp. 146–147. 5.5b An alternative analysis of the second segment of 5.5a. (a) Durutte’s use of figured-bass numbers is reminiscent of Vogler’s [1.4]: the numbers between the staves correspond to the chords as written, while those above the lines below the bass correspond to the root positions of the chords. The full-sized numbers below these lines, like those of Jelensperger and Lobe, correspond to the scale degrees of the chordal roots, while the superscript numbers appended to the right indicate the inversions. The abbreviation “q. r.” notes that A, the chordal fifth (quint), has been suppressed (réprimer). (b) In my analysis, which explores notions not mentioned in Durutte’s commentary, the pitches represented by filled-in noteheads embellish the pitches that constitute the I and IV harmonies. In this interpretation the two instances of D-F-(A)-C have contrasting roles. In the first case it occurs within a presentation of the tonic, where only its C is stable (displayed by open noteheads); in the second it occurs within a presentation of the subdominant, in which its F, A, and C are stable.

A most instructive example by François Camille Antoine Durutte, whose analytical work extends the French Jelensperger tradition and consequently does not embrace the passing-chord perspective, displays three contrasting deployments of the very D-F-(A)-C chord about which Reicha and Jelensperger had disagreed earlier in the century [5.5a]. The first instance, in the example’s second measure, shows a supertonic seventh chord in third inversion (23) followed by a dominant seventh chord in first inversion (51). In this context most scale-step analysts (excepting some we encountered in 1.16, above) would agree with Durutte’s harmonic interpretation. A few measures later the same notes (this time with A omitted) recur with bass D. . Here Durutte’s label 72 corresponds to Jelensperger’s 2, thus countering Reicha’s view.7 Like Jelensperger, Durutte is concerned enough about the

Chordal hierarchy

non-resolution of the seventh to comment on it: “Its resolution may be achieved through the prolongation of the sound when it has been prepared by the same note.”8 Passing-chord adherents (such as Reicha, 5.2d) would instead regard D and F as non-harmonic in function, filling in tonic’s C–E and E–G thirds [first segment of 5.5b]. Two measures later in 5.5a the third instance of the D-F-A-C chord occurs. Though Durutte likely would assert that he was simply repeating what had occurred earlier, but in a different inversion (11 21 12 instead of 1 2 11), an analyst who embraces (even in the context of half-notes) the neighboring interpretation of 5.4 and the passing interpretation of 5.2e’s second measure might suggest instead that these measures represent a fusion of two separate embellishing initiatives: lower neighbors of IV’s root and third, followed by passing motions connecting the root–third (F–A), third–fifth (A–C), and fifth–octave (C–F) intervals of IV [second and third segments of 5.5b]. In this interpretation an elision occurs: instead of soprano D sounding after the neighboring motions of the lower voices conclude, its arrival coincides with the return of F and A below. The determination of a chord’s root thus again proves to be a controversial aspect of the analytical process. In that the pitch content of a passing chord may be identical to that of a chord that (in a different context) functions harmonically, analytical investigation requires a vigilant assessment of just which pitch combinations warrant consideration as harmonic entities. Our examples confirm that a number of thoughtful musicians of the eighteenth and nineteenth centuries did not regard all chords as harmonic in intent. Their analytical symbols – whether Roman numerals, Arabic numerals, letter names, or music notation – are placed below some chords but not others, revealing a keen awareness of the distinction between structural harmonic entities and the various forms of embellishment that may enliven them. A chord succession from Bb-D-F-G to C-F-A occurs in measures 6 and 7 of Beethoven’s Piano Sonata in F Major, movement 1 [5.6a]. Analytical curiosity should be aroused: the first chord’s F, a seventh if G functions as root, does not resolve by descending step. In a harmonic interpretation we would need to adopt a perspective akin to Jelensperger’s “resolution of the second order,” which permits the maintenance of a common tone. Lobe, who adopted many of Jelensperger’s notions, shows that perspective in action [5.6b]. (Compare the chords with bass A, Bb, and C in 5.6a and 5.6b.) The resolution issue becomes moot if one instead regards F as root amidst concurrent F–G–A (passing), A–Bb–C (passing), and C–D–C (neighboring) motions connecting the downbeats of Beethoven’s measures 6 and 7 or Lobe’s measures 1 and 3. In that perspective, tonic persists for several chords (including both 63 and 64 positions), with a shift to subdominant at measure

121

122

Thinking About Harmony

a

b

5.6a Beethoven: Piano Sonata in F Major, op. 10, no. 2, mvmt. 1, mm. 5–8. 5.6b Lobe: Vereinfachte Harmonielehre [1861], p. 140, transposed. The similarity between Beethoven’s third through fifth chords and Lobe’s first through third chords provides a clue regarding how nineteenth-century musicians might have interpreted the Beethoven excerpt. (Recall that Lobe employs a dot above an Arabic numeral to indicate the presence of a chordal seventh.) Alternatively some analysts would have acknowledged the persistence of tonic until the arrival of the subdominant in each excerpt’s final measure.

8 (or measure 4 of Lobe’s 5.6b).9 Whereas the one-chord/one-label methodology held an appeal – especially in elementary pedagogy – due to the simplicity of its execution, the concept of passing chords nevertheless retained a footing within more nuanced analytical discourse from the eighteenth century onwards. Though a consideration of chronology and geography often helps one to understand trends in harmonic analysis, the notion of passing chords defies categorization according to when or where a particular author was writing. A significant number of German authors of the eighteenth and nineteenth centuries embraced the passing-chord concept, so articulately enunciated by Schulz in 1773, though perhaps an even greater number did not. Few French writers say much about passing chords, and those who do did not match the variety of contexts that their German counterparts explored. But the idea was alive from Rameau onwards. The British caught wind of the idea principally as an import, since works by several of the German authors we cite in this chapter were available in English translation.

Chordal hierarchy

Consequently any analysis from the eighteenth or nineteenth century is strongly colored by its author’s individual stance regarding chordal hierarchy. Whereas differences among various symbol systems (Roman versus Arabic numerals, indication of chordal qualities and inversions, etc.) are relatively superficial, different outcomes when determining a passage’s progression of roots – which depends upon the analyst’s perspective on what constitutes a harmonic entity – go to the core of the analytical process. The passing-chord dilemma has been more persistent and more problematic to the analytical enterprise than Rameau’s briefly fashionable supposition perspective for suspensions or the petty disagreements regarding whether the diminished chord on the leading tone . should be labeled as vii° (or 7 or VII) or as an incomplete V7 (or 5). Only in the twentieth century did the passing-chord perspective achieve hegemony, at least in analytical discourse beyond the elementary level. A significant step away from the one-chord/one-label approach was taken by the Munich team of Rudolf Louis and Ludwig Thuille in their Harmonielehre [1907]. Around the same time Schenker was beginning his potent transformation of the analytical enterprise in Vienna. Though the term“reductive analysis”now may seem synonymous with Schenkerian analysis, its use to describe methodologies practiced by several nineteenth-century authors is not far-fetched. Faced with progressions of chords that seemingly defy rational explication via existing harmonic precepts, these men pursued the urge to simplify and in consequence to reveal a more essential progression underlying the complexity at the musical surface. Even Ernst Friedrich Richter, Schenker’s bête noire, was a creative force in this experimental agenda. Lobe countered with indignation concerning these developments emerging in his midst.Yet, as we now know, these tentative notions could not easily be contained. I call upon Beethoven’s student Carl Czerny to lead us into this domain.

Reductive analysis in the nineteenth century In his School of Practical Composition (ca. 1848?), Carl Czerny pursues a reductive form of analysis: reductive to the extent that the sixty-two noteheads in four measures of a Clementi sonata are represented by twelve noteheads [5.7]. The excerpt’s second and third measures each contain the sort of voice exchange (DF ⫻DF) that Sechter examines [5.3a, b]. Yet in both cases an additional element of activity creates a situation of greater interest and complexity.

123

124

Thinking About Harmony

a

b

5.7 Czerny, School of Practical Composition [ca. 1848?], vol. 1, pp. 53, 55. (a) Czerny quotes this passage from Clementi’s Sonata in D Minor, op. 40, no. 3, mvmt. 1. (b) Czerny employs three chords to convey the essence of 5.7a. Not all of his contemporaries would have resisted positing a more robust harmonic content for the passage. In particular, the B-D-F-Gs chord at the beginning of Clementi’s third measure likely would have generated some analytical flurry, perhaps including enharmonic reinterpretations.

In measure 2 the voice exchange begins amidst an unstable chordal situation: A is a suspension, resolving to Gs just as the passing notes (E in the soprano and tenor registers) emerge to traverse the F–D and D–F thirds. Czerny employs only Bb, D, and Gs in his reduction [5.7b]. Though F warrants inclusion as well, apparently he preferred to neglect the note (as did Clementi at the end of the third measure) than to blemish his reduction with bald parallel fifths (FBb–E ). –A The voice exchange of measure 3 likewise competes with instability, now coming from the bass, whose Bn forms a diminished seventh chord with the upper parts. Where is the progression heading? Which of the many possible implications of the diminished seventh chord is intended here?10 It turns out that no new harmonic intent is realized. The Bn bows out unfulfilled, returning to the Bb from whence it came. Czerny remains silent concerning the incident, encouraging us to interpret measures 2 and 3 as Bb-D-Gs even if only one-third of their time value is devoted exclusively to these pitches (for the most part including F as well). Richter’s account of passing chords, published in the following decade, focuses on passages that resist explanation via the conventional norms of harmonic progression, thus hinting that some other principle may be operative. For example, pondering the implications of the 64 chord in the first

Chordal hierarchy

a

b

c

d

5.8a, b Richter: Lehrbuch der Harmonie (1853, 211897), pp. 130–131. 5.8c Lobe: Vereinfachte Harmonielehre [1861], p. 144. 5.8d Tiersch: Elementarbuch der musikalischen Harmonie- und Modulationslehre (1874, 21888), p. 148. Each of these examples begins with descending motion in the right hand against ascending motion in the left hand. Only Lobe (5.8c) is inclined to find harmonic meaning in all the vertical combinations that result. Tiersch’s analytical bass with figures (5.8d, bottom line) amounts to a reductive analysis that accounts for thirty-one of the forty-seven noteheads.

measure of (5.8a), he suggests that “the peculiar occurrence of the six-four chord in the example . . . is accounted for only through the ensuing stepwise progression of all voices to their next goal (the chord on the downbeat of the following measure) in the manner of passing notes.”11 Supplementary examples [5.8b] show the descending and ascending motions that merge to create 5.8a. Opposing Richter’s stance, Lobe includes 5.8a in one of his own treatises. Quoting Richter’s commentary (presented above), he adds an exclamation

125

126

Thinking About Harmony

point in parentheses to register his astonishment that such an idea was being promulgated.12 His alternative analysis dutifully labels each chord [5.8c]. Despite Lobe’s protests, composers and analysts continued to explore passing contexts for chordal progressions. For example, Otto Tiersch uses Richter’s idea of 5.8a as the starting point for his own exuberant progression, strewn with cross marks indicating the abundant diatonic and chromatic passing motions [5.8d]. With authors like Tiersch, an instructor at the Stern Conservatory in Berlin, pursuing a highly selective notion of what constitutes a harmonic entity, the diversity of possible interpretations for common musical events expanded, likely to the general bewilderment of students. Consider his Gs-B-D-F chord [5.8d, measure 1]. Now, in addition to disputes regarding whether III (or IIIs) in C Major, or instead V or VII° in A Minor, offers the best analysis, some authorities urge the elimination of such chords from harmonic consideration altogether! Whereas many analysts likely would not want to venture a harmonic label for the extraordinary concoction Tiersch places at the end of the example’s second measure (with bass Fs), fifth-related chords (measure 1, beat 4 to measure 2, beat 1; measure 2, beat 2 to beat 3) present no similar challenges to interpretation, and the absence of a harmonic label in such cases thus was strongly provocative, especially at a time when analysis using Arabic or Roman numerals had become pervasive. In fact, the assertion of a hierarchical relationship between fifthrelated chords has a rich history. The analyses we sample below, from a wide spectrum of German and Austrian authors spanning a century, vindicate Tiersch from his apparent negligence. Though none pursued the perspective to the level Schenker took it in the twentieth century, clearly there was a strong tradition among German musicians to seek harmonic meaning somewhere beyond music’s immediate surface.

Hierarchy in fifth-related chords Jelensperger, starting with dominant G-B-D, undertakes concurrent B–C–B and D–E–D neighboring motions [5.4] and ponders whether G-C-E represents a harmonic event (tonic) or an embellishment of dominant. Sechter, starting with tonic C-E-G, undertakes concurrent C–B–C and E–D–E neighboring motions [5.9a, b] and ponders whether G-B-D

Chordal hierarchy a

b

c

5.9 Sechter: Die Grundsätze der musikalischen Komposition (1853–54), vol. 1, pp. 158–160. (a) Sechter’s original progression is eight measures in length: C–G–E–A–F–D–G–C. Each variation likewise pursues this full course, for which we provide an adequate sampling of three measures in 5.9b through 5.9e. (b) “First variation, whereby every triad becomes tonic for a measure, in the midst of which its own dominant harmony is heard, which however must not be considered as a subordinate harmony (Nebenharmonie) within the core C-Major progression of fundamentals.” [“Erste Veränderung, wodurch jeder Dreiklang während der Dauer des Tactes zur Tonica wird, und dazwischen seine eigenthümliche Dominantenharmonie gehört wird, welche aber als Nebenharmonie nicht zur eigentlichen Fundamentalfortschreitung in der C dur Tonleiter gerechnet werden darf.”] (c) “Second variation, where the subdominant of every triad, understood as a tonic, is heard during the measure, though not regarded as a part of the core progression of fundamentals.” [“Zweite Veränderung, wo man die Unterdominant jedes einzelnen Dreiklangs während des Tactes, wo er als Tonica angesehen wird, hören lässt, welche abermals nicht zur eigentlichen Fundamentalfortschreitung gerechnet wird.”]

represents a harmonic event (dominant) or an embellishment of tonic. Both authors present nuanced analyses. For Jelensperger, the speed of motion affects the extent to which the internal chord registers as a harmonic entity; for Sechter, the internal chord has a local harmonic effect without participating in the broader harmonic progression. The G-B-D chords in measures 1 and 2 of 5.9b belong to different hierarchical planes; only the latter warrants the label “G.” Then Sechter replicates Jelensperger’s

127

128

Thinking About Harmony

d

e

5.9 (cont.) (d) “Third variation, where in the midst of each subordinate tonic (Nebentonica), as with the primary tonic, the corresponding subdominant, 2nd scale step, and dominant are heard, but likewise not regarded as a part of the core progression of fundamentals.” [“Dritte Veränderung, wo zwischen jeder Nebentonica, so wie bei der Haupttonica, deren eigenthümliche Unterdominant, 2te Stufe und Oberdominant gehört werden, aber auch nicht zur eigentlichen Fundamentalfortschreitung gerechnet werden.”] (e) “Without first going through all possible variations, one can finally install in each measure all of the roots of the main theme as subordinate roots, as can be seen here.” [“Ohne erst alle möglichen Veränderungen vorzunehmen, kann man endlich in jedem Tacte alle Fundamente vom Hauptthema als Nebenfundamente anbringen, wie hier zu sehen.”]

initiative, employing upper neighbors of chordal thirds and fifths [5.9c]. His measure 2 approximates 5.4c. In his view G-C-E has no affiliation with C Major – certainly not as its tonic. It instead functions as subdominant in G Major. Such dominant and subdominant relations – upper and lower fifths of a given chord – are musical events for which full-fledged harmonic analysis often seems overblown. Just as Sechter registers only the deeper layer of root progression in 5.9b and c, Gustav Schilling displays one fundamental (C, F, Bb, . . .) for every three chords in an “Infinite Chord Progression” (Reihe . . . Unendliche) [5.10]. In these examples, a local dominant or subdominant is sandwiched between two statements of a more elemental chord. Or, a dominant may herald a more elemental chord. A progression by Johann Adolph Scheibe [5.11] includes not only chords with roots C, D, and E (in measures 1, 3, and 5, respectively) that resolve by ascending fourth into the succeeding chords, as do those of Schilling in 5.10, but also chords inserted on weak beats just before the arrival of more elemental chords. The chords on E in measure 2 and on Fs in measure 4 play no role

Chordal hierarchy

5.10 Schilling: Polyphonomos, oder die Kunst . . . sich eine vollständige Kenntniß der musikalischen Harmonie zu erwerben (1839), p. 11. Each group of three chords in Schilling’s “Infinite Chord Progression” (Reihe . . . Unendliche) shares a single fundamental. The internal chord among each group functions as a local dominant, with no impact upon the larger progression. Thus the first and fifth chords of the progression (both C-E-G) are unrelated. The former functions as tonic in C Major, while the latter functions within the realm of F Major, as dominant. (Compare with the C chords in measures 1 and 2 of 5.9c.)

5.11 Scheibe: Über die musikalische Composition (1773), p. 159. “One could proceed from the primary tonic (Haupttone) first to its subdominant, that is, to the key (Tonart) of the fourth [scale degree], and from there to the minor key of the second [scale degree], and then to the major key of the fifth [scale degree], after that to the minor key of the third [scale degree], and finally to the minor key of the sixth [scale degree], and from here again quite easily back to the primary tonic (Haupttonart).” [“Man könnte aus dem Haupttone zuerst in seine Unterdominante, nämlich, in die Tonart der Quarte gehen, aus dieser in die weiche Tonart der Sekunde, ferner in die harte Tonart der Quinte, alsdann in die weiche Tonart der Terz, und endlich in die ebenfalls weiche Tonart der Sexte, aus dieser aber wieder ganz bequem zurück in die Haupttonart.”]

129

130

Thinking About Harmony

5.12 Weber: Versuch einer geordneten Theorie der Tonse[t]zkunst (1817–21, 21824), vol. 3, table 44, fig. 254 [Warner, p. 619]. “It is especially worthy of notice, that, in many cases, we have the choice whether we will consider such combinations as transitions to intervals of the following, or of the present harmony. In [5.12], for example, we may, if we will, regard the combination [g¯ ¯b g= ] as a mere apparent chord, if we assume that the g¯ [sic: should read g= ] is only a transition to a=, ¯b a transition to c=, and g¯ to f¯. In this point of view, the passage would consist of only two harmonies: C and F. – We may then assume, in particular, that the C-harmony continues on to the third chord, and that during this C-harmony the tones g¯ , ¯b, and g= are transitions to the intervals f¯, c=, and a= of the following F-harmony, as indicated in k. – Or else we may assume that the F-harmony commences at the combination [g¯ ¯b g= ] as is indicated in l, where, consequently, the transition-tones g¯, ¯b, and g= relate to intervals of the F-harmony, during which they sound as transitions.”

within the broader progression, which Scheibe indicates using dotted halfnotes and capital letters above the sounding bass. Instead, they are dependent upon the chords to which they resolve: E (inversion of A7) within D Minor, and Fs (inversion of B7) within E Minor. Swoboda calls such chords “leading dominants” (führende Dominante).13 Tiersch’s progression [5.8d], discussed above, employs leading dominants of A and of F. Though less common, a fifth-related chord may follow rather than precede the chord it serves [5.12]. Gottfried Weber first presents a neutral, arhythmic progression of three chords, with G poised ambiguously between C and F (his example i). He then explores contexts, distinguished by contrasting rhythmic positionings, in which G may be perceived either as a trailer – upper fifth – of C (his example k) or as an antecedent of F (example l). In both scenarios the basic progression is analyzed as C to F. The same hierarchical precepts that guide the subordination of a single chord may be extended to encompass several chords. Sechter, continuing the example quoted above, gradually increases the content of each local progression to the point where it replicates in miniature his example’s largescale progression of fundamentals [5.9d, e]. Likewise Portmann betrays a hierarchical perspective in his guidelines for composing a chorale prelude. First he numbers the six chords of a chorale phrase [5.13a]. Then he shows

Chordal hierarchy

a

b

5.13 Portmann: Musikalischer Unterricht (1785), example supplement, pp. 17–18, figs. 24–25. In Portmann’s expansion from chorale (a) to chorale prelude (b), the interpolation of dominants of the numbered chords, third-relations, dominants of the third-related chords, and alternation between 53 and 63 configurations all occur, in accordance with his commentary.

where these chords reside within several elaborations, including that of 5.13b. His comments are as follows: The second type of prelude [of the three types described] is composed by inventing some melodic ideas and integrating them with the existing chorale, interpolating the appropriate dominant chords between the chorale’s adjacent fundamental chords or even, for a triad of a major key with its dominant, allowing a closely related minor triad with its dominant to follow – or by presenting a chord in 63 rather than 5 position. Example [5.13a] shows a phrase from the chorale “Sünder willst du sicher 3 seyn.” In Example [5.13b] the dominants of these successive fundamental chords have been interpolated.14

Indeed we observe that the dominants of chords 1 through 5 all appear, generally preceding their tonics. The excursion from Ab major to C minor in measures 7 and 8 exemplifies Portmann’s instruction about interpolating a closely related minor triad and its dominant. Though unmentioned by Portmann, the reverse – from minor to major – occurs as well: an excursion from C minor to Eb major in measures 3 and 4. In this example it is more the listener’s assumed familiarity with the chorale [5.13a] that justifies the assertion of hierarchical relations among third-related chords than any inherent structural logic that could be extracted from 5.13b alone.

131

132

Thinking About Harmony

The development of strategies for harmonic analysis in the eighteenth and nineteenth centuries thus occurred in the midst of profound disagreement concerning just where the harmonic dimension of music resides. Is harmony restricted to music’s surface layer, shaping the chordto-chord progression? Or does it reside somewhere deeper within the texture, with non-adjacent chords shaping the principal harmonic progression? Or does it function in different planes concurrently? This awkward state of affairs is vividly demonstrated in an analysis by Siegfried Dehn, an erudite teacher, author, and editor who was active in Berlin around the middle of the nineteenth century. Within his detailed analysis of an excerpt from a Beethoven string quartet we shall witness both a plodding examination of adjacent chord pairs and a willingness to propose daring connections between non-adjacent chords. In the discussion that follows I will prod him to think more broadly when he becomes mired in minutiae, and remind him of a harmonic relation he may be overlooking when he rushes ahead too quickly.

Dehn on Beethoven Siegfried Dehn addresses the challenging, potentially baffling Introduction to Beethoven’s String Quartet in C Major (op. 59, no. 3) [5.14] in his Theoretisch-praktische Harmonielehre (1840).15 Though his analysis contains traces of a conservative perspective, its audacious moments are astonishing.

Measures 1 through 11 Dehn’s assessment of the first six measures echoes the manner of Vogler’s groundbreaking analyses from the 1770s.16 Vogler analyzes a progression much like Beethoven’s opening measures [5.15]: D with seventh: Ds with diminished [seventh]: E with perfect fourth and minor sixth: F with seventh:

the fifth [V] of G. the seventh [VII] of E Minor. an inversion, in which the fifth [scale degree] of A Minor lies in the bass. the fifth [V] of Bb.17

Dehn’s analysis of the opening chords from Beethoven’s Introduction follows suit:

Chordal hierarchy

5.14 Beethoven: String Quartet in C Major, op. 59, no. 3 (1806), mvmt. 1, mm. 1–30. The score from which Dehn worked contains an error. Beethoven wrote b’ as the second-violin pitch of measure 9, where Dehn’s score instead reads c’’.

133

134

Thinking About Harmony

5.15 Vogler: Gründe der Kuhrpfälzischen Tonschule in Beispielen [1778], table XXX, fig. 2 [reproduced in Wason, Viennese Harmonic Theory (1985), p. 17]. This excerpt is from an example constructed on a circular system – an infinite loop of music. A triangle is inscribed within the circle, dividing its fifteen measures into three five-measure segments, each devoted to demonstrating one of the three basic diminished seventh chords. For example, the Ds-Fs-A-C chord above appears as Fs-A-C-Eb, A-C-Eb-Gb, and Bs-Ds-Fs-A in succeeding measures. The fifth measure of each segment segues into the next segment.

Measures 1 and 2: Measures 3 and 4: Measure 5: Measure 6:

the diminished seventh [VII] of G Minor. the dominant [V] of Bb Major or Bb Minor. an A minor chord in 64 position. the dominant [V] of G Major or G Minor, followed by its third inversion.18

Dehn twice invokes the notion of “deceptive succession” (Trugfortschreitung) in discussing these chords: to explain why a G minor chord does not follow the first chord; and why a Bb major or Bb minor chord does not follow the second chord. His view of the passage is concordant with Adolf Bernhard Marx’s more general description: “the harmony loses its way and gropes about unsteadily as if in pitch-darkness.”19 While Dehn and Marx focus on what they regard as irregular harmonic successions, practitioners of a hierarchical perspective would seek illumination by limiting the extent to which harmony is assigned the burden of explanation. In one example by Sechter the D–Fs third of a D7 chord is traversed simultaneously in ascending and descending motions [5.16a]. When the E passing notes in the lower voices sound along with the prolonged A and C above, a chord “of no consequence” results. In another example an Fs–D third, already filled in by passing note E in the diatonic context, is further enriched by the chromatic pitches Fn and Eb [5.16b]. These additions do not affect his harmonic analysis. Applying the chromatic filling-in of Sechter’s second example to both of the moving lines of 5.16a results in a distinctive progression, recently dubbed the “classical omnibus” [5.17a].

Chordal hierarchy

a

b

5.16 Sechter: Die Grundsätze der musikalischen Komposition (1853–54), vol. 1, pp. 38, 132 (transposed). (a) “In this example . . . the chord that happens to fall between the first and third beats should be regarded as of no consequence.” [“In allen diesen Beispielen sind die zwischen dem Anfang des ersten und dem Anfang des dritten Viertheils des Tactes erscheinenden zufälligen Accorde als unwesentlich zu betrachten.”] (b) Observe that Sechter does not place the letter A below the A-E-A-C confluence on beat 3.

a

b

5.17a 5.17b 5.17c 5.17d

c

d

A classical omnibus. Analysis of 5.14, mm. 1–6. A prolongation of D7, incorporating all four of its positions. Analysis of 5.14, mm. 6–7.

(c) The relationship between this model and its expansions [5.17b and 5.17d] is similar to the relationships shown in 5.3d. (d) This model associates pitches that occur in different instruments. For example, first-violin A in measure 6 is linked to second-violin B and C in measure 7. Beethoven’s slurring in measures 6 and 7 (C to A, D to Fs, Fs to C) counters the notion that V42 resolves to I6 (bass C to B).

Beethoven would have encountered similar progressions in a number of eighteenth-century works.20 Whereas Dehn proposes a potential harmonic implication for each chord, he fails to comprehend any broader order. The tension between potential harmonic function and actual connective function is at the heart of Beethoven’s strategy [5.17b], which is both deformed (Eb substitutes for the D of the model’s first chord) and truncated

135

136

Thinking About Harmony

5.18 Analysis of 5.14. The 143 noteheads in the first twenty-nine measures of Beethoven’s quartet are here represented by 34 noteheads, about the same level of reduction as that employed by Czerny in 5.7. At measure 9 the likely initial interpretation of Ab-F-B-D would be as representative of G-F-B-D, in which case Ab, rather than B, would be written as a grace note in the reduction. Ultimately this hypothesis must yield to the continuation that Beethoven in fact pursues, in which Ab-F-B(Cb)-D represents Ab-F-Bb-D. This does not imply that Beethoven was unaware of the implications his writing might have elicited, which in fact may in part account for the belated D–G root succession of measures 18 through 20.

(the full-chromatic model’s fourth chord is absent), as well as being presented at a breathtakingly slow pace – even slower than the passing-chord model that elicited Reicha’s comment on long duration [5.2d]. From this perspective, the first chord’s resolutional tendency is yet to be fulfilled in measure 6. Measure 1’s diminished seventh and measure 6’s major–minor seventh are phases of a single harmonic thrust towards G. Whereas Dehn hears the chords of measure 6 resolving to G major in measure 7, a further application of Sechter’s perspective would suggest a prolongation of the D7 chord through the end of measure 7 [5.17c, d]. At first the diminished seventh chord of measures 8 and 9 appears to fulfill the role of resolution. (Second-violin C functions as a suspension.21) Indeed we might expect that Ab will descend to G (cello Ab–G instead of second-violin Cb–Bb in measures 10 and 11), creating a V7 that could lead directly to the Allegro vivace’s C Major. Beethoven had other plans, however. Any diminished seventh chord is inherently mehrdeutig – capable of being interpreted in multiple ways. (The term will recur in our exploration of modulation in chapter 6.) Because preceded by D7, it is tempting to interpret B-D-F-Ab (measure 9) as a representative of G-B-D-F, which the proposed Ab-G bass motion would confirm. Yet Beethoven’s enharmonic respelling in measure 10 suggests a different interpretation: D-F-Ab-Cb as representative of Eb’s dominant Bb-D-F-Ab. The ensuing chords confirm the Bb–Eb succession. A compilation of fundamental chords in a manner inspired by Czerny [5.7] and Sechter [5.3b, 5.9] would thus include only two entries thus far: not D7 to G7, as initially supposed, but instead D7 to Bb7 [5.18].

Chordal hierarchy

Measures 12 through 17 In his analysis of measures 12 through 17 Dehn takes a bold step away from Vogler’s style of harmonic analysis, offering three distinct perspectives from which his readers might choose. In the manner of his analysis of the preceding measures he first provides a standard interpretation of each chord, despite the absence of normative resolutions. For example, the chord of measure 14 could be regarded as an inversion of the leading tone seventh (G-Bb-Db-F) in Ab Major. In a second view he proposes that bass F in measure 14 be regarded as a suspension. The chord of measures 14 and 15 would then function as a diminished seventh (E-G-Bb-Db) on the leading tone in F Minor, though again the expected resolution does not occur. His third view, a remarkable departure from his conventional practice, is that the leading tone chord in measure 13 (Bn-D-F-Ab in 43 position) resolves to C minor in measure 17 (C-Eb-G in 63 position) and that the three distinct chords between them are “interpolated postponements” (eingeschobene Verzögerungen) of the resolution.22 The Bn-D-F-Ab diminished seventh chord thus functions in the manner of Swoboda’s “leading dominant,” totally dependent upon its goal chord. The fundamental chords that result from this reading of measures 12 through 17 – namely, from Eb at the outset to goal C – are duly recorded in our model [5.18].

Measures 18 through 29 In that Dehn is diligent in considering the harmonic implication of each chord to this point, it is surprising that his treatment of the Introduction’s final measures lacks a comparable fastidiousness. He declares first-violin C in measures 18 and 19 to be a suspension, with no suggestion that D-F-Ab-C (measure 19) should resolve to Eb major. Measure 18 contains “melodic non-harmonic notes” (melodische harmoniefremde Noten) in the inner voices. And in measure 21 two concurrent melodic passing notes (C in both the first-violin and cello lines) connect the diminished seventh chords of measures 20 and 22. Perhaps Dehn has become a bit excessive in his reductive thinking. Could D-Fs-Ab-C in measure 18 represent a harmonic entity, a “French” augmented sixth chord in root position?23 In that the succession of fundamental chords D–G in measures 1 through 9 turned out to be an illusion, it is fitting for D to return in measure 18, so that the root progression D–G–C may now serve as the path to the Allegro vivace [5.18]. This is the extent to which we might reasonably suggest such a reductive analysis would be

137

138

Thinking About Harmony

pursued during the nineteenth century. Certainly a twenty-first-century analyst might go further, asserting that Eb5–6 (measures 12 through 17) is a temporary displacement of D, and that the D chord of measures 1 through 6 returns – as yet unresolved – in measure 18 (its fifth now lowered). In this reading, D–G–C serves in the broadest sense as the foundation for measures 1 through 29. Though some might assert that Beethoven conceived these measures according to that model, it would go too far to suggest that Dehn or any other analyst could have formulated such a notion around 1840.

6

Modulation to closely related keys

An analytical pioneer: Lampe In 1737, fifteen years after Rameau’s novel conceptions concerning harmony were launched in Paris, Lampe published in London an extraordinary analysis displaying a rich panorama of responses to chromatic pitches [6.1]. Though Lampe charts the progression of chordal roots occasionally (as in 1.1), here he instead documents the positions of individual bass pitches within one or more keys. The “or more” aspect of Lampe’s analysis is its most striking feature. Though G, A, B, and D are preceded by their leading tones and thus are analyzed as temporary “Key notes” (tonics), each also receives an analytical label acknowledging its position within the original key. The leading tones of G and D are themselves dually analyzed. In all, Lampe’s analysis reveals six distinct analytical responses: (1) Bass Gs and As (measure 2)

Analysis in the context of a temporary key only

(2) Bass Cs (measure 3)

In addition to analysis in the context of a temporary key, analysis in the original key

(3) Bass Fs (measure 1)

Though diatonic in the original key, analysis in a non-tonic role in the context of a temporary key

(4) Bass Ds (measure 4)

Acknowledgement of the major mode’s leading tone in the context of the parallel minor key (pertains also to the As of measure 2 in the context of the temporary key B Minor)

(5) Inner-voice Cs Acknowledgment of altered pitches (here (measure 2) and resulting in the subdominant and dominant of Ds (measure 5) the parallel major key) by means of conventional figured-bass notation (6) Bass Fn (measure 1)

Unresponsiveness to a chromatic event (in this case, an F major chord preceded by its leading tone)

140

Thinking About Harmony

6.1 Lampe: A Plain and Compendious Method of Teaching Thorough Bass (1737), plate 59, Lesson XV (near p. 39). These measures are from an exercise whose first half is a pedestrian traversal of the scale: a sequential progression of 5–6 motions above bass notes E, Fs, G, A, B, Cs, and Ds lead to E, with analysis K [key note] . . . 2d. . . . 3d. . . . 4th. . . . 5th. . . . 6th. . . . 7th. . . . K. The second half (presented above) is a variant of the first half, retaining the 5–6 pattern in the midst of abundant chromaticism, followed by a cadential progression. The principal analysis, resembling that of the first half, retains E as the key note. Below it Lampe designates four other pitches as temporary key notes. Rameau’s term “Notte sensible,” which Gossett translates as “leading tone,” appears in the 1752 English translation of the Traité as “Leading-note, or sharp Seventh.” In this example, which antedates that translation, Lampe uses the “sharp Seventh” symbol (7) consistently for the leading tone. Yet it seems that the stroke through the 7 merely acknowledges that a sharp (from the key signature or as an inserted accidental) affects the notehead. Compare with 6.3b, where no stroke appears when the leading tone falls on a natural pitch. Concerning the F major chord in measure 1, see p. 204, below.

A large share of the ink devoted to issues of chromaticism in the eighteenth and nineteenth centuries reflects one or another of the analytical strategies that Lampe here employs. A key change of long duration generally does not generate widely divergent responses. More insight into the varied ways in which modulation was employed in analysis can be gained by exploring the context of minimum provocation: a single chromatic pitch. Will it trigger analysis in a temporary key (Lampe’s Gs and As)? Or will its effect be absorbed within the original key (Lampe’s Ds)? Or will analysis in two keys simultaneously (Lampe’s Cs) juxtapose these viewpoints? Historically the term “modulation” has referred to two distinct harmonic procedures. Swoboda alerts his readers to the confusion that may ensue, counsel worth repeating here: “In a general sense the word modulation refers to the progression of diverse harmonies [within a single key]. But in a particular sense one nowadays understands by modulation the art of passing – smoothly, freely, sometimes surprisingly and often even abruptly – from one harmony into another [region] that differs from the first by one or more accidentals.”1

Modulation to closely related keys

To be in a key means to segregate the twelve pitch classes into two categories: seven pitch classes residing within the key, the other five residing outside. Each pitch class is a member of fourteen of the twenty-four keys. Though the exact roster of keys for each pitch class may vary from analyst to analyst depending upon exactly how the minor keys are formulated (7 being especially contentious), each pitch class is both member and non-member in the same proportion. The pitch class C is a member of most of the most common keys, while Fs/Gb is a member of most of the least common keys. For example, C’s membership list is C Major, C Minor, Bb Major, Bb Minor, A Minor, Ab Major, G Major, G Minor, F Major, F Minor, E Minor, Eb Major, D Minor, and Db Major. Once a key is established, the occurrence of a pitch from outside its diatonic realm will have a novel effect. The analyst is faced with the task of justifying its presence within the composition. Certainly the most facile explanation will rely upon the fact that the pitch in question belongs to fourteen diatonic keys, one of which may be called into service as a temporary tonic. Yet at the moment of its first sounding, the listener does not know what the event heralds. Does it launch a major thrust in a new key? Or is the occurrence merely episodic – a ruffle within the expanse of the principal key? Analytical responses to such pitches fall into two broad categories. Either they trigger a shift (either temporary or for a longer duration) of the tonal center, or they are absorbed as a separate class of pitches within the original key. We explore in turn how both of these perspectives were practiced, beginning with that in which the key shifts as needed to keep each chord within a diatonic context.

Chromatic pitches as modulatory triggers As does Lampe, Rameau on occasion analyzes a harmonic succession with reference to bass pitches rather than fundamentals [6.2]. A single chromatically inflected pitch – Fs in place of F – prompts a reassessment of the tonal center: G becomes a tonic note. The brevity of the example reinforces Rameau’s assertion that what follows the G chord is irrelevant to its interpretation. It is solely “by means of the difference between the progression of a tone and a semitone ascending to the note bearing the perfect chord (accord parfait)” that one forms an analytical response. Once that perfect chord sounds, the composer may choose to – but is not compelled to – resume composition in the original key, “since after a perfect chord we are free to pass

141

142

Thinking About Harmony

6.2 Rameau: Traité de l’harmonie (1722), p. 208 [Gossett, p. 228]. “The composer is thus free to make the bass proceed by a tone or by a semitone, even if he should be in a key in which the semitone is not appropriate; for since the dominant can be treated as a tonic note, it may be approached using all those sounds which naturally precede a tonic note.”

6.3a Rameau: Traité de l’harmonie (1722), p. 253 [Gossett, p. 272]. Rameau’s brackets delineating regions in C Major (Ut), G Major (Sol), and again C Major admit no overlap. At one later point in the example Rameau interprets the same chord successively in two keys (writing whole note G twice within the same measure): the first G closes a region in G Major; the second opens a region in D Minor.

wherever we desire.” Though Rameau’s analytical notation does not convey both interpretations simultaneously, his prose acknowledges the chord’s dual meaning: “we may still continue after this dominant (which would then appear to be a tonic note) in the original key.”2 A more extended example later in the Traité displays clear boundaries between keys [6.3a]. The C chord of measure 1, analyzed in C Major (Ut), lies outside the domain of the following dominant region (Sol), while the G chord of measure 2 plays no role in the restored tonic region that follows. Lampe’s analytical practice is suppler [6.3b]. His E6 chord (measure 2), unlike Rameau’s second chord, relates both backward to the key of C and forward to the key of G. Daube’s analytical response to the raised fourth scale degree conforms to Rameau’s.3 In an example that begins and ends in D Major, Daube interprets

Modulation to closely related keys

6.3b Lampe: A Plain and Compendious Method of Teaching Thorough Bass (1737), plate 17 (near p. 31). The notion of what we now call a “pivot” chord – the same event interpreted simultaneously in two keys – is amply demonstrated in Lampe’s analysis. Observe also that Lampe employs the symbol “7th.” for pitches such as E and B, and (“7th.”) for pitches such as Fs and Cs. The stroke through the 7 reflects a mere happenstance of music notation and not a distinction between diatonic and chromatic. That is, each 7th is diatonic in the key in which it functions as the seventh scale degree.

6.4 Daube: General-Baß in drey Accorden (1756), pp. 70–71. “In [this] example one observes how through the addition of a single s this chord of the fourth scale degree in D Major [G-B-D-E, a chord with added sixth] can be transformed into the chord of the fifth scale degree in A Major [inversion of E-Gs-B-D], and how one may reattain D Major by applying a 7 to the A-Major tonic chord.” [“Bey ersterem Exempel siehet man, wie durch Beysetzung eines einzigen s dieser 4ten-Accord von D dur könne in den 5ten-Accord von A dur verwandelt werden: und wie man durch die 7 auf dem Grundtons-Accorde A dur wiederum in D dur zurück gelangen könne.”] Recall from chapter 1 that Daube pursues a functional analysis focused on just three chords, all of which are invoked in this explanation.

Gs in the context of A Major [6.4], just as Rameau had interpreted Fs in G Major [6.2]. Later, in the first volume of Der musikalische Dilettant (1770), Daube inaugurates the practice of numbering his “three chords” using the digits 1, 2, and 3 [6.5].4 Though only one digit appears beneath each bass note (or group of notes bound by a slur), his commentary is more nuanced. In fact his explanation concords with the notion of Mehrdeutigkeit (multiple meaning) that would dominate later accounts of key shifts. Koch explores the implications of approaching the dominant via the raised fourth scale degree in the first volume of his Versuch einer Anleitung zur Composition (1782–93). Once this chromatically targeted dominant arrives, the composer is at a crossroads (Scheideweg). If the original tonic is restored, then the modulation is classified as “incidental” (zufällig) or “a brief discretionary modulation” (eine kurze willkührliche Ausweichung).

143

144

Thinking About Harmony

6.5 Daube: Der musikalische Dilettant: Eine Abhandlung des Generalbasses (1770–71), pp. 89–91. This example is a continuation of 1.9. The numbers 1 through 3 refer to Daube’s three principal chords, introduced in chapter 1, above. The + or m symbol placed beside a number indicates interpretation in another key. The label “1+” for the second chord of measure 11 is misleading. Either “1” or “2+” was perhaps intended. Though it is tantalizing to speculate that Daube’s manuscript read “1 2+” and that this novel juxtaposition was botched during publication, it is unlikely that Daube actually created such a “pivot-chord” numerical analysis: had he, he would have labeled the G chord in the second half of measure 12 as “1+ 3.” Daube’s commentary reads as follows: “The numbers below the staff marked by a plus sign (+) denote the modulation into the most closely related key, here G Major. This occurs on beat two of measure eleven. Here one finds the 1 chord, namely the tonic C chord, and since this perfect concord functions also, as explained above, as the 2 chord of G Major, the modulation into another key is most opportunely accomplished at this point. The 3 chord of G Major follows, after which the melody returns again to C Major after a few notes. Now at this point this chord must once again sustain a dual role: namely, it should simultaneously also function as the harmony of the 3 chord of F Major, as we have put forward and amply demonstrated above. Now the melody is in the second most closely related key to C Major, namely in F Major. This is indicated by the double m symbol. But here it goes immediately back again into C Major, which occurs over stationary bass F, a member of the 3 chord in C Major, and since it appears here in the bass, the 3 chord of C Major is in third inversion.” [“Die untenstehende Ziffern, die neben sich ein einfaches + haben, bedeuten die Ausweichung in die nächst anverwandte Tonart, welches hier G dur ist. Diese geschiehet im eilften Tackt bey der zweyten Viertelsnote. Hier ist der erste Accord, nämlich der herrschende Accord C, und weil diese ganze Harmonie zugleich auch, nach der vorhergehenden Erklärung, im zweyten Accord von G dur befindlich ist; so findet die Ausweichung in eine andere Tonart die beste Gelegenheit auf dieser Stelle. Auf diesen Accord folget der dritte Accord von G dur, worauf diese Melodie nach etlichen Noten sich wider zurück in C wendet. Hier muß nun dieser Accord aufs neue eine zweyfache Stelle vertretten, nemlich er soll zu gleicher Zeit auch die Harmonie des dritten Accords von F dur versehen, wie wir dieses oben mit mehrern erwiesen und vorgelegt haben. Nun steht die Melodie in der zweyten anverwandten Tonart von C dur, mithin in F dur. Dieses wird durch ein doppeltes m angezeiget. Hier aber geht sie gleich wider zurück in C dur, welches durch die Liegenbleibung des Basses geschiehet, als welches F auch im dritten Accord von C dur sich befindet, und da es hier im Baß erscheinet; so stellt es die dritte Umwendung oder Verkehrung des dritten Accords von C dur vor.”]

Modulation to closely related keys

But if the succeeding progression reinforces the dominant key, then the modulation is “essential” (notwendig). In 1787 Koch revises his terminology and expands to three classifications: “incidental” (zufällig), “passing” (durchgehend), and “structural” (förmlich).5 In examples that follow Koch employs a chromatic pitch to reinforce chords on the second, third, fourth, fifth, and sixth scale degrees of C Major, asserting that these alterations are pertinent not to the foundational key itself, but instead to these “related keys” (verwandten Tonarten).6 Ernst Wilhelm Wolf reaffirms Koch’s selection of “auxiliary keys” (Nebentonarten) for a major tonic. He goes astray in minor, however. Though he correctly asserts that the third, fourth, fifth, sixth, and seventh scale degrees constitute the Nebentonarten of a minor tonic,7 his analysis of a passage from Händel’s Alexander’s Feast proceeds from B Minor ultimately to Cs Minor, a turn of events for which he provides no rationale beyond a comment that passing cadences may target goals that are generally avoided.8 Fortunately this and other aspects of his analysis come into better focus by taking a broader view of the work’s tonal context [6.6]. The nineteenth century thus inherited both a perspective concerning which keys were most suitable as goals for modulation and a notion that some modulations are more consequential than others, judging from how long the alternative key persists and the means by which it is confirmed (its leading tone being a principal factor in the latter). In the early nineteenth century Antoine-Joseph Reicha, a Bohemian who lived for a time in Bonn and Vienna before settling in Paris, distinguishes between “conventional” (régulière) modulation and “modest transitory modulations” (petites modulations passagères) in his Cours de composition musicale [ca. 1816]. A ten-measure example in C Major touches on most of the same keys that Koch employs. Reicha provides brief commentary below the score, as follows: A passing modulation from C Major into D Minor. Return [to C Major]. From C Major into F Major. From F Major into G Major. Return to C Major. From C Major into A Minor. From A Minor into D Minor. Return to C Major. and comments that “these transitory modulations are so brief that the ear does not lose the impression of the key of C Major, and they have moreover

145

146

Thinking About Harmony

6.6 Wolf: Musikalisicher Unterricht (1788), plate 28, ex. Qqq, with commentary paraphrased from pp. 51–52. Wolf ’s abbreviated score for a passage from Händel’s Alexander’s Feast includes figured-bass numbers instead of written-out chords. His harmonic analysis (paraphrased below the score, above) is rendered within a textual commentary. (The original German is provided below.) In measure 4 he omits a chordal seventh E above Fs, present both in Händel’s score and in a printing of an excerpt in Johann Friederich Reichardt’s Kunstmagazin (vol. 1, 1782, p. 140), to which Wolf makes reference. He offers three different labels for the cadence that, in his view, occurs at that point: half, Phrygian, and plagal. Two questions on key choice arise from a study of Wolf ’s analysis. First, why does Cs Minor occur prominently in the context of B Minor? And second, why does Händel not include a modulation to G Major? Händel’s key choices would make better sense if Wolf had indicated that the aria from which the passage is extracted is in A Major. As the chart below reveals, Händel’s key choices within this passage (measures 72 through 82, about two-thirds of the da capo aria’s middle section) are more closely aligned with A Major than with B Minor.

Modulation to closely related keys

6.6 (cont.) Tonic and auxiliary keys of B Minor: Tonic and auxiliary keys of A Major: Händel’s key choices:

b b b

cs cs

D D D

e E e

fs fs fs

G

A A A

Wolf ’s commentary reads as follows: “So wie es hier steht, geht es mittelst des Quartensprungs im Basse zuerst in h moll; beym dritten Viertheil im ersten Takte macht es mittelst des kleinen Septimenenakkords auf der Dominante von fis eine durchgehende Kadenz, oder einen Gang in fis moll; im zweyten Takte, vermöge des kleinen Septimenakkords auf der Dominante von e, eine unterbrochene und durchgehende Kadenz in e moll; im dritten Takte mittelst des Septimenakkords auf der Dominante von d, eine durchgehende Kadenz in d dur, und alsdann bis zum vierten Takte, eine halbe – oder phrygische Kadenz in die Dominante von h moll; (diese Kadenz wird sonst auch eine plagalische Kadenz genennet;) im fünften und sechsten Takte, mittelst der Quartensprünge, eine durchgehende Kadenz in h moll, eine in a dur, und im siebenden Takte, mittelst eines Sextensprungs und eines Septimenfalles im Basse, eine Ausweichung in die Dominante von fis, die sich vermöge des kleinen Septimenakkords in die zwote Verwechselung des Dreyklangs von fis moll auflöst; im achten Takte ergreift der Baß den Unterhalbenton von cis, und modulirt durchgehend in cis moll; im neunten Takte eine Fortschreitung in die Dominante von cis, und schließt im eilften Takte in cis moll.”

the benefit of enlivening a musical phrase which, without them, would often turn out to be routine.”9 Though Gottfried Weber maintains that “many digressive modulations are so very transient that they scarcely deserve the name”10 and that “the ear, after imperfect digressive modulations, is inclined of its own accord to resume again its state of attunement to the yet scarcely quitted principal key,”11 the analyses of block-chord progressions in his Versuch einer geordneten Theorie der Tonse[t]zkunst emphasize key shifts at the expense of continuity.12 Chromatically reinforced chords will inevitably appear to be the most significant in his analyses. In one example he calculates the intervals between adjacent tonicized keys: C Major to D Minor is an ascending major second (2•); D Minor to F Major is an ascending minor third (•3); F Major to C Major is an ascending perfect fifth (5•); and so on [6.7]. Thus C–d–F–C is highlighted at the expense of G (the eighth chord), which, though lacking a preparatory Fs, plays a vital role within the progression – arguably more vital than either d or F.13 Weber’s analytical system had a wide influence. It became routine for nineteenth-century analysts to extract a chord containing an altered pitch from its tonal context and to assign it a temporary home key for diatonic interpretation.14 This preoccupation with diatonic identity – matching the components of every chord to one of the twenty-four pitch collections of the tonal system – proliferated at the expense of connectedness. In a progression that begins in C Minor, Jadassohn interprets Fs-A-C-Eb in G

147

148

Thinking About Harmony

6.7 Weber: Versuch einer geordneten Theorie der Tonse[t]zkunst (1817–21, 31830–32), vol. 2, p. 193 [Warner, p. 411]. Weber indicates interval quality by the left/right positioning of a bullet beside an Arabic numeral: minor/major for imperfect intervals, perfect/augmented for fourths, and diminished/perfect for fifths. Chord quality is indicated by the size of the Roman numeral.

6.8 Jadassohn: Die Kunst zu moduliren und zu präludiren (1890), p. 175. Compare Jadassohn’s treatment of two successive diminished seventh chords here with that of Momigny [6.11, mm. 12–13]. Though Momigny does not analyze the harmonic progression, he marks the chromatic elements (in the context of C Major) with filled-in noteheads and asserts that the progression occurs entirely within the key of C Major. Jadassohn instead indicates a diatonic context for each chord, neglecting to provide a rationale for the succession from one chord to the next.

Minor15 even when the resolution is to G-Bn-D (which, in any event, he analyzes in neither G Major nor G Minor) [6.8]. And a surprising tierce de Picardie is rendered humdrum by his shift to C Major before even the preceding dominant. Jadassohn seems blithely indifferent concerning the progression of two consecutive diminished seventh chords and the apparent unconventionality of the dissonance treatment.16 The progression sits at the boundary between what he regarded as cogent and what was considered to be beyond concrete appraisal from a harmonic perspective. Concerning a longer progression of diminished sevenths, Weber comments: “If moreover a really equivocal chord be followed by still others which are themselves also equivocal . . . the ear must at last entirely lose the thread of modulations so very complicated and can really no longer know where it should be, but is obligated as it were to fluctuate hither and thither between several keys to which the different harmonies occurring might belong.”17

Modulation to closely related keys

As we saw in chapters 3 and 4, an extended progression of chords was often understood in terms of its component two-chord harmonic successions. This narrow view of chordal interaction is conducive to a similarly narrow focus concerning chromatic chords. A chord’s role within its broader context often is not considered. Instead its immediate implication, based upon a diatonic interpretation of its pitch content, is the decisive factor, and consequently the key will shift whenever the chordal pitch content asserts elements that contradict the prevailing key. Thus we observe Jadassohn freely juxtaposing two °7 chords [6.8], or Weber four V7 chords [3.7b]. Yet one wonders whether the musical passages they analyze actually “fluctuate hither and thither,” as Weber claims, or if instead their analyses give the false impression that they do. If the latter is the case, then alternative analytical strategies would be welcomed. An opposing camp indeed did emerge early on, rejecting the modulatory stance or in some cases juxtaposing broad one-key and narrow multiple-key perspectives, as does Lampe [6.1]. Consequently there was no simple answer to the simple question: What key are we in? At issue is whether a pitch that is external to the prevailing key’s diatonic collection should be interpreted as diatonic in another key, or instead as a chromatic element within the prevailing key. Though the dilemma persists to the present day, one can take comfort in the fact that both modulating and non-modulating modes of analysis have been practiced since the eighteenth century. We now focus on the latter perspective.

Non-modulatory analysis Despite the appeal of the modulatory practices described above, another of the strategies we observed in Lampe’s pioneering analysis – that of retaining a focus in the original tonic key despite chromatic elements – persisted as well. In his Essay towards a Rational System of Music (1770), Holden expands upon an example in G Major from Lampe’s A Plain and Compendious Method of Teaching Thorough Bass [6.9]. Whereas in this case Lampe interprets all chords containing a chromatic pitch in an “occasional key” only (targeting A Minor, B Minor, C Major, D Major, and E Minor18), Holden supplies a second row of numbers to track the locations of the bass pitches within the original tonic key. He explains that Lampe did not “pursue the imitation [marked by brackets] but one step further” to the bass progression

149

150

Thinking About Harmony

6.9 Holden: An Essay towards a Rational System of Music (1770), plate VII, ex. LI (facing page 88). The upper row of numbers and letters below the staff is by Holden, while the lower row is derived from Lampe. K represents the “Key note,” whereas k stands for an “occasional key.” The figure 7# above E in measure 4 (present in Lampe’s treatise) was inadvertently omitted in Holden’s version.

6.10 Kirnberger: Die Kunst des reinen Satzes in der Musik (1771–79), vol. 1, p. 111 (n.) [Beach and Thym, p. 129 (n.)] Though chords rooted on G (measure 2), D (measures 3 and 6), and A (measures 4 and 5) are all either preceded or followed by their major dominants, the lack of further confirmation induces Kirnberger to retain C as tonic throughout, despite the abundant chromaticism.

C–Fn–G–C \ 5 k) 5 k) / because F falls outside the “system of G.”19 Kirnberger stresses the importance of a pitch “foreign to the former key” – one that “erases” its effect – in establishing a new key.20 But if that new key is not given a substantial confirmation, he advocates absorbing such chromaticism within the initial key: “Although thirds taken from outside the scale of a given key (which are indicated by accidental sharps or flats) usually indicate a modulation, this is not always the case. Often no modulation takes place . . . For if one does not actually go to the announced key, or if one abandons it immediately, no modulation has occurred. Thus the following period is entirely in C Major [6.10].”21 Toward the end of the 1770s Vogler, in early experiments using Roman numerals for harmonic analysis, makes surprising accommodation of chromatic pitches [1.4]. In C Major, the numeral IV appears below both F-A-C and Fs-A-C-E, while in A Minor, II is used for B-Ds-F-A, IV for Ds-F-A, V for E-Gs-B, and VII for Gs-B-D-F. By the time of his Handbuch zur Harmonielehre (1802), he incorporates a sharp as a component of Romannumeral labels corresponding to chords with raised root: IVs and VIIs.22

Modulation to closely related keys

(As in his earlier analyses, the accompanying figured-bass symbols acknowledge alterations affecting other chord members.) In this way Vogler’s system embraces not only some of the“occasional”inflections to which others might respond by changing key, but also chords in which chromatic alteration produces the interval of a diminished third or its inversion, the augmented sixth. To justify his procedure Vogler asserts the necessity of the leading tone in minor keys: “The cadence from the chord on the fifth scale degree to that on the first, and that from the first to the fifth, are usable . . . in a minor key as well; so long as the minor third above the fifth scale degree is raised, the harmony will thereby be conclusive and . . . cadential.”23 Through analogy, and through recourse to acoustics,24 he justifies raising the fourth scale degree as well: What the seventh scale degree in a major key or the raised seventh scale degree in a minor key is to the first or eighth scale degree, the raised fourth scale degree is to the fifth. That one may bring about a cadence on the fifth scale degree that, if not complete, nevertheless functions cadentially at a subordinate level, has been . . . established and confirmed through examples. But if one investigates the fourth scale degree in the harmonic series, as 1/11 . . . it is closer to B than to Bb in F Major, closer to F# than to F in C Major. Consequently the fourth scale degree can be raised even apart from the analogy with the seventh scale degree.25

Yet in at least one case he prefers that the raised fourth scale degree be perceived as a leading tone in the dominant key: The cadence from the chord on the second scale degree to that on the fifth scale degree occurs only in the minor mode, since in the major mode, as soon as one wants to join a major third to the second scale degree, it would no longer be the second scale degree but most assuredly the fifth scale degree of another key, for example:

II ia II if II iD II in C

a fs D V in G.26

In other cases he allows two alternative analyses to coexist (Zweideutigkeit). Fs-A-C may be analyzed as IVs in C or as VII in G, and B-Ds-F may be analyzed as II in A or even as V in E.27 In France, Momigny ardently endorses the chromatic and enharmonic expansion of a key’s pitch palette. In the flat direction C Major’s seven diatonic pitches (B E A D G C F) are followed by five chromatic pitches (Bb Eb Ab Db Gb) and five enharmonic pitches (Cb Fb Bbb Ebb Abb). Likewise in the

151

152

Thinking About Harmony

6.11 Momigny: La seule vraie théorie de la musique [1821], pp. 77–78. “Example entirely in the key of C Major with the employment of chromatic pitches.” Nine of C Major’s ten chromatic pitches are employed: Cs, Db, Ds, Eb, Fs, Gs, Ab, As, and Bb.

sharp direction the seven diatonic pitches (F C G D A E B) are followed by five chromatic pitches (Fs Cs Gs Ds As) and five enharmonic pitches (Es Bs FS CS GS).28 Like Vogler he endeavors to replicate common cadential formulas through exact imitation (imitation exacte). Thus G-B-D-F to C-E-G serves as model for D-Fs-A-C to G-B-D, or for C-E-G-Bb to F-A-C, all within the key of C Major. The allure (appat) of the half-step and our natural love of symmetry sanction these chromatic adjustments. In comparison, their diatonic counterparts would seem savage (sauvage), suited to barbaric music (Musique barbare). Momigny recognizes that his is a minority view: “This Fs is in the key of C and not in G, as is generally believed.”29 And he is certain that he is correct: the title of his treatise is The Only True Theory of Music (La seule vraie théorie de la musique). Perhaps irked that Reicha, and not he, had been appointed to a professorship at the Paris Conservatory, he quotes an example from Reicha’s Cours de composition musicale [ca. 1816] only to condemn all its modulations (petites modulations passagères, to be sure). Reicha’s tonic in D Minor is, for Momigny, the second of C Major, while Reicha’s tonic in G Major is, instead, the dominant of C Major.30 In a provocatively crafted example Momigny highlights the abundant chromaticism with filled-in noteheads or the abbreviation “ch.” [6.11]. Whereas Momigny seems antagonistic towards those for whom chromaticism routinely induced modulation, Jelensperger’s analytical practice is eclectic, with occasional juxtapositions of modulating and non-modulating

Modulation to closely related keys

6.12 Jelensperger: L’harmonie au commencement du dix-neuvième siècle (1830, 21833), p. 51 [Häser, p. 48]. Chromatic alterations are acknowledged by symbols beside or through the Arabic numbers in Jelensperger’s single-key analysis. (See 1.7, above, for an explanation of these symbols.) His multiple-key analysis leads from G Major (Sol) through A Minor (la), B Minor (si), C Major (Do), D Major (Ré), and E Minor (mi) – the same keys Lampe and Holden employ in 6.9.

analyses of the same progression [6.12]. His procedure is methodologically similar to Holden’s [6.9], though it treats more sophisticated chromaticism. In the upper line of analysis frequent key shifts facilitate a diatonic interpretation of each chord. This conception echoes Gottfried Weber (though without Weber’s preoccupation with chord quality) and demonstrates Jelensperger’s command of a methodology then rarely practiced with such vitality in France. (In fact, it so aptly captured German tendencies that within three years of its appearance in Paris, Breitkopf & Härtel published a translation of Jelensperger’s treatise in Leipzig.) This analysis amounts to chordal juxtaposition rather than progression: note the three consecutive “5” labels and the two consecutive “1” labels in 6.12. But Jelensperger’s treatment extends further: a second row of analytical numbers relates each chord to the original tonic key, G Major. Though Momigny had embraced this notion in principle, he did not implement it with such a profusion of symbols. One may wonder which method Jelensperger prefers. His answer: “Whenever the distinction between half and full modulation is uncertain, it is of no consequence whether one indicates a different tonic [full modulation], or writes with parentheses [half modulation]; in all such cases one chooses the sort of representation which appears to be the simplest.”31 Lobe, who spent part of his career teaching and composing in Weimar (where A. F. Häser, Jelensperger’s translator, served as a choral conductor), was strongly influenced by Jelensperger’s treatise. (Jelensperger had died at a young age during the three-year period between the French and German editions.) Even so he rejects non-modulatory analysis, though he finds its practice to be sufficiently prevalent among the progressives as to warrant comment:

153

154

Thinking About Harmony

a

b

6.13 Lobe: Lehrbuch der musikalischen Komposition, vol. 1 (1850, 21858), pp. 241, 243. (a) × marks chords analyzed in a manner that Lobe endorses. (b) × marks chords analyzed in a manner that Lobe rejects.

Modern theorists do not want to interpret chords such as those at a. x and b. x in [6.13a] as true modulating chords, but as altered chords within the key. Why? Because the sense of the prevailing key is not supplanted through such interpolated chords . . . It is as if [the chord] were putting in an appearance here wearing a disguise, so to speak.32

Lobe endorses the altered-chord strategy only for cases where a chord is formed using pitches for which a single source key does not exist. For ° example, he approves of the label 2 for chords that incorporate an augmented sixth [6.13b].33 Yet he marks most of the so-called “altered chords” in this example with an “x” to indicate that he rejects the novel analysis that he displays.

Modulation to closely related keys

As the century progressed, and as chromaticism became ever more prominent in contemporary music, the clash between adherents of the two stances continued unabated. Josef Schalk, defending the altered-chord viewpoint, sums up the situation as follows: The notions of chromatic progression and actual change of key (modulation) generally have been so indiscriminately applied that it has become very difficult to distinguish between them. Above all the scope of a key must be understood in a broader sense than formerly. As a result it should not be necessary to go through constant modulatory transitions when nothing more than chromatically altered chords appear, and true modulation can be reserved for those situations where a second key is operative with true independence for one or more periods or sections.34

Just as a pitch plays multiple roles in various keys, so do chords. The German term Mehrdeutigkeit (multiple meaning) is used to designate this capacity, as when C-E-G could represent I in C Major or V in F Major, or when C-E-G-Bb could represent V7 in F Major or (understood as C-E-G-As) a German augmented sixth chord (a modified II9 with absent root) in E Minor. On the one hand, multiple interpretations of a single chord provide an expedient means of moving from one key into another. On the other, when each chord under consideration can be interpreted in a variety of ways the aptness of an analysis may come into question: if C-E-G can function diatonically as I in C Major or IV in G Major, or chromatically as bII in B Minor or bVI in E Major, when is an analysis neglecting important information by omitting some of these (or other) choices? Or, once the analysis of how a chord does behave comes into focus, what is one to make of the alternatives that a listener may have contemplated (how the chord might have behaved)? Ultimately every analysis is a conjecture, including some and omitting other potential interpretations of the varied chords that parade past. Lobe asks us to hear the Neapolitan sixth as a diatonic 4 chord in the prevailing key’s submediant key [6.13a, example a]. If we do not hear it that way, are we not hearing nineteenth-century music the nineteenthcentury way? Or is Lobe’s analytical practice at odds with how composers of his time conceived of chromatic chords? One pursues harmonic analysis despite such nagging questions. Ultimately one develops a set of convictions, accepting the fact that clashes (such as modulating versus non-modulating modes of analysis) are inevitable. In the discussion of Mehrdeutigkeit that follows we will explore, in the context of a Mazurka by Chopin, what happens when

155

156

Thinking About Harmony

analysis is carried out concurrently in two keys – with some chords that are diatonic in one interpreted as chromatic chords in the other, in equal measure. Though this may seem an equitable and creative response to the Mehrdeutigkeit dilemma, ultimately it leads to interpretive indifference. The most effective analysis probably lies somewhere between strict diatonicism, in which the key shifts whenever triggered by a modification in the pitch content, and free chromaticism, in which so many altered chords are accommodated within a single key that two different keys may seem equally viable for an entire progression.

Multiple meaning The arithmetic is telling: just twelve major triads, twelve minor triads, and twelve diminished triads are the building blocks for the diatonic harmonies of all twenty-four keys. So, as Vogler observes, A-C-E may play the role of I (in A Minor), II (in G Major), III (in F Major), IV (in E Minor), V (in D Minor), or VI (in C Major).35 His term for multiple meaning – Mehrdeutigkeit – expands the notion of zweideutig: ambiguous, equivocal. The concept is applied not only to chords of stable spelling (Vogler’s “type two” Mehrdeutigkeit), but also to chords amenable to enharmonic reinterpretation (“type one” Mehrdeutigkeit), a topic we defer until chapter 7. Just as Lampe provides dual interpretations of individual bass pitches in 1737 [6.3b], many later analysts provide dual interpretations of chords – Crotch’s “doubtful” chords, our “pivot” chords – as a means of negotiating a modulatory transition [6.14]. Gottfried Weber suggests that the meaning we assign to the chords of a harmonic progression, or even the key we choose for analysis, will shift upon repeated hearings. Once aware that a modulation is about to occur, we anticipate it in how we perceive the preceding chords.36 Chromaticism complicates and enriches the environment in which such analytical assessments are made. Whereas Vogler analyzes a brief progression with the conviction that a major key contains only three major triads, modulating from A Major to E Major in response to the pitch Ds [6.15a], other analysts might regard such a chord as rooted on the initial key’s second scale degree (as demonstrated in 1.7, 6.9, and 6.12 in their respective keys).37 Choosing the key for analysis thus becomes a selective act of interpretation as modulation becomes more often an option than an imperative. If a key indeed possesses the mix of diatonic, chromatic, and enharmonic pitches catalogued by Momigny, then each key is far less exclusive than previously

Modulation to closely related keys

6.14a Crotch: Elements of Musical Composition (1812), plate 35, ex. 364. “Gradual modulation signifies such as is effected by doubtful chords, or chords common both to the original key, and to that into which the modulation is made” (p. 87).

6.14b Savard: Cours complet d’harmonie [1853], vol. 1, p. 100. The route from C Major (UT majeur) to Eb Major (MIb majeur) passes through C Minor (UT mineur), since C Minor’s submediant (sus-dominant) is Eb Major’s subdominant (sous-dominant).

conceived, and the total pitch content of a passage under analysis will more likely fit within one key.38 Eventually some responded to this situation by pursuing analysis in multiple keys simultaneously, an enterprise that even Vogler explores in a diatonic setting [6.15b] but whose potential expands when the chromatic floodgate is opened [8.22]. In Chopin’s Mazurka in A Minor (op. 7, no. 2) the middle section, governed by a three-sharp key signature, opens with eight measures during which D major and A major chords, preceded by their respective dominant sevenths, take turns in filling the mazurka’s potent second beat [6.16]. In all, nine of the twelve pitch classes occur within each two-measure cycle. An analysis offering a diatonic interpretation of each chord would need to draw upon the pitch collections of three keys: measure: bass: D:

33 A V7

D------I a: ii°6 A:

34 E

A, etc.

V7

I

157

158

Thinking About Harmony

a

b

6.15 Vogler: Handbuch zur Harmonielehre (1802), table III, fig. 2; table IV, ex. x. (a) Without visual signal Vogler switches from analysis in the context of A Major to analysis in the context of E Major between the third and fourth chords. (b) This progression employs only the six pitch classes shared by C Major and F Major. Vogler weakens his case for interpretation in F Major by constructing the C chords with doubled E (F’s leading tone).

Such an analysis suffers from the malady of unconnectedness, a concern mentioned in connection with 6.8 and 6.12. In this composition the question of whether D or A is the controlling tonic is especially problematic, in part because the progression loops back upon itself again and again. Simultaneous analysis of the principal chords in both keys, acknowledging chromatic coloration where warranted, leads to equivocal results: bass: A

D

7

D:

V

A:

I

I

7n

IV

E

A

7 s

8–7

II

V

7

8 – 7n

V

I

D

E

A

7 s

8–7

I

II

V

IV

V

D... I...

7

I...

Is Chopin teasing us, in a musical equivalent of the familiar diagram that could represent either an ornate vase or facing profiles, depending on which part is regarded as solid? In his Harmonielehre (1900), August Halm presents a progression containing, like Chopin’s, two seemingly equivalent segments: statement (Vortrag) and answer (Antwort) [6.17]. Its ambiguity results from the succession of two competing descending-fifth bass motions – Halm’s “axiom of movement” (Axiom der Bewegung).39 The abandonment of traditional

Modulation to closely related keys

6.16 Chopin: Mazurka in A Minor, op. 7, no. 2 (1832), mm. 31–40. The eight measures that open the middle section of the work (measures 33-40) are shown here preceded by the close of the opening section, with a cadence in A Major during the second ending.

6.17 Halm: Harmonielehre (1900, 21925), plate I, ex. 3a (transposed). The example, presented by Halm in C Major, is here transposed to A Major. In contrast to Chopin’s mazurka, Gn (the pitch that might erase the effect of A Major) does not occur.

voice-leading draws attention to the descending contour. Because tonic’s authority is challenged in the statement, its return in the answer results in a deeper affirmation of the key. Between the two halves lies a fissure (Kluft), indicated by double vertical strokes. Halm regards the subdominant as a mere pseudo-tonic, fostered by the legitimate tonic’s behavior as a

159

160

Thinking About Harmony

dominant (I–IV functioning as V–I, emphasized by Chopin with Gn above A). We might perceive a caesura, but not a cadence, at IV. This threat to tonic motivates the continuation: V follows IV to steer the progression back to I. The subdominant and dominant chords bear no affinity. In fact, Chopin’s intervening diminished 63 (D-Fn-B) mitigates the potential harshness of the succession from one to the other. (Compare with Rameau’s notion of double emploi [1.17].) For Halm, “tonic is the king of the key.”40 Yet identifying tonic when chromaticism-fortified keys compete for supremacy can be challenging. Are A Major and D Major indeed equally viable candidates for tonic in this region of Chopin’s mazurka? Certainly not. Churning out dual labels for each chord is lacking in illumination because it evades the very judgments that would give focus to the passage. These judgments are influenced by consideration of the melody’s shape – alternating ascending A major triads (A–Cs (–E)) and descending E dominant seventh chords (D–B–Gs–E) – and of the chromatic inner-voice descent that recurs once every two measures: A (Gs) | Gn Fs Fn | E. These features establish the priority of A-Cs-E over D-Fs-A, a point that could be missed in analyses focused either on establishing a diatonic legitimacy for each chord through frequent modulation, or on the opposite – regarding all chords as functional in all keys. A number of our recent examples have displayed a mehrdeutig relation between tonic in the initial key and dominant in the subdominant key [6.3b, 6.5, 6.9, 6.14a, 6.15b, 6.16]. Whereas a chord such as Bb-D-F is neutral – it perfectly fulfills the requirements of tonic in Bb Major and of dominant in Eb Major – the case of Bb-D-F-Ab is less equivocal. The urge towards Eb is strongly felt, and the diatonic pitch collection of Bb Major is violated. We conclude this chapter by considering how a chord such as Bb-D-FAb may be regarded as a tonic, despite its minor seventh. To represent the contrasting, strictly diatonic perspective, I call upon the pedagogue and textbook author Ebenezer Prout. In one of his analyses published in 1903, we note that such a minor seventh would trigger modulation to the subdominant key. (His symbols allow this to be displayed in two different ways, one less decisive than the other.) For the alternative view – that in some contexts the presence of the tonic root is so vital to the harmonic initiative that the chord’s tonic role is embraced despite an errant seventh – I call upon four authors, all of whom published a harmony treatise between 1906 and 1911: the Munich team of Rudolf Louis and Ludwig Thuille, and the Viennese luminaries Heinrich Schenker and Arnold Schoenberg.

Modulation to closely related keys

6.18 Prout: Analytical Key to the Exercises in “Harmony: Its Theory and Practice” [1903], p. 28. The variegation of Prout’s Roman numerals to indicate major, minor, and diminished qualities stems from Gottfried Weber. The letters b, c, and d correspond to first through third inversions, respectively. (This is a British phenomenon. Compare with 6.19c.) Prout interprets all 64 chords harmonically as second inversions.

Prout’s modulatory practice As the nineteenth century was drawing to a close the industrious Ebenezer Prout churned out a new textbook or supplement almost every year. His Analytical Key [1903] offers solutions to the exercises in the revamped sixteenth edition of his Harmony: Its Theory and Practice, first published in 1889. Prout’s readers were expected to be industrious as well: they were asked to supply a Roman numeral and indication of inversion for every chord of each exercise, in addition to composing three upper lines to realize the given figured bass [6.18]. They also grappled with the implications of chromatic pitches, invoking one of two analytical responses: modulation (e.g., Fs in measure 2 triggers a move to G Minor); or “transitional dominant”41 (e.g., Bn in measure 3, En in measure 5, and Ab in measure 5 trigger the analysis of a single chord in the key of its successor).42 The G minor chords in measures 1 and 2 are analyzed twice, in the contexts of the keys that precede and follow. They are what Prout calls “ambiguous” chords, yet another term to describe what others refer to as “mehrdeutig,” “doubtful,” “intermediate,” or “pivot.” Though Prout’s analysis might appear to be in order, the symbols do not add up to a compelling vision of how the example is fabricated. For example,

161

162

Thinking About Harmony

G Minor in measure 2 seems unduly favored, as the focus of the exercise’s only modulation. Is it not, however, just a step along the path between tonic and supertonic? Were its dominant not preceded by a 64 (measure 2, beat 1), Prout likely would have analyzed it via a transitional dominant, as he did the supertonic in measure 3: m. Bb:

1

2 vi (g: V)

vi.

Moreover the half cadence in measure 4, which divides the progression into two four-measure phrases, has received no special analytical notice. A more selective Roman-numeral analysis, conceivable at about this time from Louis and Thuille in Munich or Schenker in Vienna, could better convey the similarity between the two phrases, both of which contain a bass line that extends from Bb through G to Eb on the way to F.43 In Prout’s notation, such an analysis might appear as: m.

1 I

2 vi

3 iib

4 5 V, I

6 IVb

7 iib V7

8 I.

An especially revealing detail of Prout’s analysis occurs at measure 5, beat 3. Viewed locally, these pitches indeed do form a dominant seventh chord in Eb Major, in a way described a century earlier by John Callcott as a “partial modulation”: Whenever the Dominant and Tonic of a new Key are employed without the Subdominant Harmony, such change constitutes a partial modulation. One change of this kind arises when the Seventh of the Major Mode is flattened [e.g., Ab in 6.18, measure 5], and the Modulation returns again through the Leading Tone to the Tonic.44

The analytical symbols for Prout’s transitional dominant vividly convey the “partial” nature of the modulation: only the chord containing the chromatic pitch is interpreted in the temporary key; the goal chord retains its position within the original key. Prout thus accommodates the modulatory practice that was on display in recent German publications by Lobe and Jadassohn [6.19a, b] while attempting some commonality with his British predecessor Alfred Day, who rejects modulation in this context [6.19c]. Prout’s notion is appealing and, in less cumbersome notation, survives as the “secondary” or “applied” dominant chord in modern harmony textbooks. Yet Louis and Thuille provide a more compelling analysis of a similar passage by extending a horizontal line from Roman numeral I, fostering the notion of multiple meaning – that even with an added minor

Modulation to closely related keys

a

b

6.19a Lobe: Lehrbuch der musikalischen Komposition, vol. 1 (1850, 21858), p. 159 (transposed). 6.19b Jadassohn: Lehrbuch der Harmonie (1883, 131911), p. 98 (transposed). (a) The dot above the 5 acknowledges the chordal seventh. (b) Prout’s bass (measure 4, beat 3, through measure 6, beat 1, of 6.18) corresponds to Jadassohn’s soprano.

6.19c Day: Treatise on Harmony (1845), p. 77 (transposed). “The seventh on the tonic may also be followed by the common chord of the subdominant . . . This is not a modulation into the subdominant.” The letters A and B indicate root position and first inversion, respectively.

6.19d Louis and Thuille: Harmonielehre ([1907], 41913), p. 383. In this analysis of an excerpt from Brahms’s “Variations on a Theme by Händel” (op. 24), beat 3 of measure 1 is analyzed dually as tonic in Bb Major (“B”) and as dominant in Eb Major (“Es”).

163

164

Thinking About Harmony

6.20 Three perspectives on tonic’s prolongation (Prout’s measures 4 and 5) In the models above, bass Ab and soprano D form an augmented fourth whose resolution tendency targets the subdominant chord, thereby strengthening tonic’s inherent propensity to lead to IV. Prout’s dominant (measure 5, beat 2 of 6.18) is hierarchically dependent upon the Bb chords that precede and follow it, even if an elision (bass Ab arriving with rather than after Bb) taints the succeeding tonic. Kirnberger displays similar instances of such elision in Die Kunst des reinen Satzes in der Musik (1771–79), vol. 1, pp. 89–90 [Beach and Thym, p. 108], suggesting that resolving bass A to Bb before moving to Ab would be characteristic of the strict style. Prout’s version (A–Ab in measure 5) could occur, according to Kirnberger, in the free style. See also 3.7b, in which Weber’s Roman numerals accord with Prout’s interpretation.

6.21a Schenker: Harmonielehre (1906), p. 428, ex. 366 [Borghese, p. 326, ex. 295].

seventh, the subdominant’s dominant retains a tonic role [6.19d]. Thus just as the submediant and the supertonic in Prout’s first phrase are extended via their dominants (or dominant “derivative,” the leading tone chord), in measure 5 tonic is extended via its F major dominant, even if the tonic chord contains an added seventh, Ab, upon its return. Prout’s analytical notation makes it difficult to come to this reasonable conclusion [6.20]. A similar construction occurs in Chopin’s Prelude in Db Major [6.21]. Chopin fills in the tonic triad’s lower third (Db–Eb–F) in the soprano

Modulation to closely related keys

6.21b Schoenberg: Structural Functions of Harmony (1954), p. 122, ex. 128. In their analyses of an excerpt from Chopin’s Prelude in Db Major (op. 28, no. 15), both Schenker and Schoenberg regard the Dbb7 chord, which Prout would analyze exclusively in the context of Gb Major, as a representative of tonic in Db Major.

(measures 8–9) while descending from tonic chromatically (Db–C–Cb) in an inner voice. (Compare with soprano Bb–C–D and bass Bb–A–Ab in Prout’s measures 4 and 5.) Both Schenker and Arnold Schoenberg label the Db-F-(Ab)-Cb chord at beat 4 of measure 9 as tonic. Schenker indicates with an Arabic numeral and accidental that the minor seventh is utilized. He also suggests, parenthetically, that the chord produces the effect (Wirkung) of a dominant in Gb Major. (Compare with 6.19d.) Schoenberg acknowledges Chopin’s use of “substitute tone” Cb by placing a horizontal line through the Roman numeral I. In this case tonic functions as an “artificial dominant seventh chord” leading to IV. Prout asserts that “the value of a thorough analysis to the student who wishes for an intelligent mastery of his subject can hardly be overrated.”45 Though we may heartily support him in principle, we must acknowledge that his analytical practice lacks the sophistication and artistry that was emerging around this time especially in Munich and Vienna.

165

7

Chromatic chords: diminished/augmented

Chords via “licence” The diminished seventh and the augmented sixth are among music’s most intriguing intervals. An example by the Scotsman John Holden puts them in the spotlight [7.1]. Chords containing these intervals are products of “licence”: the “substitution” of a special pitch for a conventional one.1 E Minor’s dominant root, B, is replaced by the sixth scale degree, C (measure 2, beats 1 through 4); and its fourth scale degree, A, by a chromatic variant, As (measure 3, beats 2 and 3). These transformations, in various inversions, appear in the thorough bass and the upper voices (represented by the figures), while the analytical fundamental bass presents the progression without substitutions. Measure 2 bears the imprint of Rameau [7.2], whose Traité de l’harmonie had recently appeared in an abridged English translation. Each of the chord’s four members serves in turn as bass in Holden’s progression. In accordance with the conventions of a “regular cadence,” the resolution is to the “perfect chord of the key” – E minor – on the downbeat of measure 3. The two chords that precede the cadential dominant of measure 3 contain an “extreme sharp” (augmented) sixth or an “extreme flat” (diminished) third, again derived via substitution. The other inversional possibilities, for which stepwise resolution to the dominant root is impossible, are not shown. Holden mentions in passing that the chord on beat 2 “has been called the Italian sixth; probably because they first introduced it.”2 Though the versions of the chord that Holden presents correspond to what we now regard as the “French” and “German” varieties of the chord, his comment confirms that a special nomenclature for augmented sixth chords was in use among the British by 1770.3 Because Rameau’s Traité de l’harmonie does not account for augmented sixth chords, Holden was acting without that authority in choosing A as their fundamental pitch. He correlates the situations in measures 2 and 3 of 7.1: C a half-step displacement of fundamental B; As a half-step displacement of fundamental A. Rameau incidentally had offered a perspective on

Chromatic chords: diminished/augmented

7.1 Holden: An Essay towards a Rational System of Music (1770), plate IX (facing page 98), ex. LXV. The caption “Substitution” refers to C in measure 2 (substitute for B) and As in measure 3 (substitute for A). Unfortunately the example’s concluding measures were squeezed into a limited space at the bottom of a plate, severely compromising their legibility. Holden’s commentary confirms that the second chord of measure 3 might contain either the pitches As Fs E C

or

As G E C

(that is, either 4 or 5 with raised 6 and 3), while the third chord might contain either the pitches G E C As

or

Fs E C As

(that is, either 7 or 6 [with 5 and 3]). The symbols above fundamental bass pitch A likewise are potentially confounding. They apparently imply that either a 6th Fs or 7th G belongs with the first chord (along with 5th E [and 3rd C]), and either a 7th G or 6th Fs belongs with the second chord (along with 5th E [and 3rd C]). In both cases the fundamental pitch is A. (As in Rameau’s theory, where scale degree four is the site of the accord de la grande sixte, this 65 chord is in root position. Holden, like Rameau, regards a sixth and a seventh as alternative forms of dissonance that may be applied.)

7.2 Rameau: Traité de l’harmonie (1722), p. 282 [London (1752), p. 100]. “We say that the Chord of the extreme sharp [augmented] Second and its Derivatives are borrowed Chords, by reason that the Governing-note [dominant] lends her Fundamental to the sixth Note of flat Keys, from whence this Chord of the extreme sharp Second and its Derivatives proceed.” 6

the 43 chord in sources that Holden would not have known. Contrasting Holden’s fundamental A, altered to As and supporting “added sixth” Fs, in the Mercure de France Rameau shows a derivation from the half-diminished seventh chord on Fs, scale degree 2 [7.3a]. That perspective recurs in his

167

168

Thinking About Harmony

a

b

7.3a Rameau: “Lettre de M. à M. sur la Musique,” Mercure de France (September 1731), plate 1 (transposed) [reprinted in The Complete Theoretical Writings of Jean-Philippe Rameau (1967–72), vol. 6, p. 64]. 7.3b Durutte: Esthétique musicale (1855), p. 191. (a) Rameau displays first A and then As above bass C in the example’s third and fourth chords. Fundamental Fs is displayed below both chords. Holden applies this transformation to the second of Rameau’s chords as well [7.1]. Rameau’s example was published in C Minor with a two-flat key signature, here transposed to an E-Minor equivalent to facilitate comparison with Holden’s example. The abbreviations s, q, si, and t beside basse continue and basse fondamentale pitches indicate scale degree 2 (seconde note du ton), scale degree 4 (quatrième note du ton), scale degree 6 (sixiéme note du ton), and tonic (note tonique), respectively. (b) An echo of Rameau’s analytical notation is found over a century later in Durutte’s Esthétique musicale. Durutte’s second chord corresponds to Rameau’s fourth chord. Like Rameau’s “s” beside fundamental bass note Fs, the lowest 2 in Durutte’s analytical label indicates that scale degree 2 serves as root. (The superscript 2 indicates that the chord appears in second inversion.) 7 7 Rameau’s figures s5 and Durutte’s +5 are equivalent. (Compare with the last of Vogler’s ten cadences [1.4].)

Code de musique pratique (1760)4 and has persisted as a viable interpretation [1.4 (cadence 10); 5.18 (measure 18); 7.3b]. Though Marpurg regarded himself as Rameau’s stalwart champion in Germany, he apparently knew as little about Rameau’s thoughts on the augmented sixth chords as did Holden. He presents them as an intermixing of diatonic elements from two keys. They belong to a special category of chords that he calls “mixed” (gemischte) or “fantastic” (fantastische).5 Two triadic formations ground his augmented-sixth derivation: • “major diminished” (harte verminderte) • “diminished diminished” (verminderte verminderte)

B-Ds-F Ds-F-A

These chords employ A Minor’s diatonic F, E Minor’s diatonic Ds, and A or B, diatonic in both keys. Upon inversion, the latter becomes F-A-Ds [modern “Italian”]

Chromatic chords: diminished/augmented

Adding a seventh to the two triadic formations and inverting them, the following derivatives result: • “43 chord with the augmented sixth” (Terzquartenaccord mit der übermäßigen Sexte) • “augmented 65 chord” (übermäßige Sextquintenaccord)

F-A-B-Ds [modern “French”] F-A-C-Ds [modern “German”]

Marpurg rejects the employment of the root-position forms (Stammaccorde), asserting that in practice they occur in only one of their generative keys (A Minor for the spellings above) and in only one position (scale degree 6 in the bass). Marpurg’s “major diminished” chord corresponds to Sorge’s “Triade manca,” which Sorge permits on either scale degree 2 or 5 of a minor key. In A Minor these chords are B-Ds-F and E-Gs-Bb, which generate the augmented sixths Ds , poised towards a dominant resolution, and Gs , poised F Bb towards a tonic resolution. Adding the seventh, he shows B-Ds-F-A [“French”] resolving to E-Gs-B. His examples display bass B leaping to E, bass Ds or F resolving by step to E, and bass A resolving by step to Gs.6 Vogler’s initial foray into Roman-numeral analysis in 1778 includes two augmented sixth chords [1.4, the last two cadences]. He shows the raised fourth and the second scale degrees as their foundational pitches, mirroring Marpurg’s view. The use of Roman numeral IV for F-A-Ds in A Minor probably reflects the imprecision of an analytical methodology in its infancy rather than any commonality with Holden’s perspective [7.1]. By the time of his Handbuch zur Harmonielehre (1802), he had adopted the label IVs, clearly indicative that the raised fourth scale degree serves as the root, rather than as a substitute for a diatonic root. An elaborate circular music diagram in Gründe der Kuhrpfälzischen Tonschule in Beispielen enlivens Vogler’s discussion of four-note chords used in cadences. The diagram is comprised of fifteen wedges that display seemingly every possible spelling these chords might utilize in any key. Each wedge shows arpeggiations of four closely related chords [7.4], with Roman numerals marking the chordal roots. Single half-step alterations have a dramatic effect upon the cadential focus. Spelled as G-B-D-F, the chord functions as V and resolves to tonic C Major or C Minor. Changing G to Gs, the chord functions as VII and resolves to tonic A Minor. Changing one more note – B to Bb – directs the progression not to a tonic but instead to a dominant, that of D Minor. The chord is IV [our “German” augmented sixth].

169

170

Thinking About Harmony

7.4 Vogler: Gründe der Kuhrpfälzischen Tonschule in Beispielen [1778], table XXVII. “If one wants to cadence, then I can follow only after V and after VII, and V after IV and II.” [“Will man aufhören: so darf nur nach dem fünften und nach dem siebenten der erste, und nach dem vierten und zweiten der fünfte Ton folgen” (Vogler’s Tonschule, Tonwissenschaft und Tonse[t]zkunst: Kuhrpfälzische Tonschule [1778], p. 174.)] In his Handbuch zur Harmonielehre (1802), Vogler employs the symbols VIIs and IVs (in place of VII and IV) for chords with a raised root. This wedge is from an elaborate circular diagram that can be read both vertically (as shown above) and horizontally. For example, to the left of GV-B-D-F is Ab-BVII-D-F, and to the right is G-B-CsII-Es.

Yet another half-step transformation (F to E) produces II [our “French” augmented sixth], which also resolves to D Minor’s dominant. Diminished seventh and augmented sixth chords figure prominently in the tables of foundational chords that were a common feature of nineteenth-century treatises. In the “Tableau des Accords simples” in AlexandreÉtienne Choron’s Principes de composition des écoles d’Italie [1809], Ds-F-A [“Italian”] is ranked as one of the four “Accords de premiere classe” (along with C-E-G, A-C-E, and B-D-F), while Gs-B-D-F [diminished seventh], B-Ds-F-A [“French”], Ds-F-A-C [“German”], and B-Ds-F-A-C [!]7 are

Chromatic chords: diminished/augmented

7.5 Sechter: Die Grundsätze der musikalischen Komposition (1853–54), vol. 1, p. 191. The chromatic version of the succession exemplifies Sechter’s “hybrid-chord” (Zwitteraccord), here an uncommon inversion of the chord nowadays often labeled as a “German” augmented sixth at the end of the first measure. The gradually evolving pitch content incorporates elements of diatonic harmonic successions from three keys: VI–II in F Major, V–I in G Minor, and II–V in C Minor. At the middle of the first measure the chordal ninth Eb (diatonic in G Minor and C Minor) arrives, by which point root D is no longer sounding.

ranked as four of the eight “Accords de seconde classe” (along with G-B-DF, B-D-F-A, G-B-D-F-A, and E-Gs-B-D-F).8 Yet not all analysts regarded such distinctions as necessary. Holden’s substitution explanation persisted: diminished seventh and augmented sixth chords continued to be analyzed as modifications of diatonic chords, as examples by Catel [3.11b], Weber [3.14b], and Sechter [7.5] confirm. Vogler had put his finger on something important: the dominant seventh, diminished seventh, and augmented sixth chords are all closely related [7.4]. Moving one pitch by a half-step changes the nature of the chord, though not necessarily its resolutional tendency. Adjusting one detail of Vogler’s presentation may help clarify the relationship among these chords. In his version, the uppermost of the four chord arpeggiations is poised towards resolution to C, whereas the other three would resolve to A (either as a tonic or as a dominant). By deriving the diminished seventh chord from an E dominant seventh rather than a G dominant seventh, all of the chords would resolve to A. My revised and expanded table appears as follows: In A Minor B-D-E-Gs B-D-F-Gs

7

V V9 or VII7

In D Minor B-D-E-Gs B-D-F-Gs Bb-D-F-Gs Bb-D-E-Gs

II7 II9 or (s)IV7 “German” “French”

171

172

Thinking About Harmony

The left side of the table displays chords in A Minor. The choice of E or F as a chord member is of little consequence. Though some would regard B-D-F-Gs as built on the dominant (with root suppressed) and others as built on the leading tone, the chords both lead to A as tonic. On the right side of the table these same chords are displayed in the context of D Minor, in which they would precede the dominant. Nowadays many analysts regard these chords as applied or secondary dominants, with labels such as “V/V.” (As we have seen, Prout calls them “transitional” dominants [6.18].) By altering the B of these two chords to Bb, we derive the two principal forms of the augmented sixth. (The “Italian” version – Bb-D-Gs – is derivable from the others. Alternatively, one could expand the table to include the three-note chord B-D-Gs (VII) and its Bb-D-Gs mutation.) From this perspective the “German” augmented sixth chord is to the “French” exactly what the leading-tone diminished seventh is to the dominant seventh. In that many analysts would regard both of the latter to be rooted on E, so also could both of these augmented sixth chords be regarded as E-rooted: a modified II leading to V. Though occasionally an augmented sixth chord will resolve to tonic, their placement only in the table’s right column corresponds to conventional practice in the early nineteenth century. The pitch Bb is diatonic in D Minor and easily achievable through a modal shift in D Major, but it is uncommon in A Minor or A Major except in the context of the Neapolitan chord, which is a different phenomenon. Though the relationships displayed on this table are both subtle and intriguing, they represent just one component in a yet more complex web of chordal relations. Consider the table’s diminished seventh chord, B-DF-Gs. In this spelling four of the twenty-four keys can easily be attained (A Minor or A Major directly, and D Minor or D Major via their dominant). Yet through enharmonic reinterpretation any one of the chord’s four pitches may be understood as the leading tone: not only B-D-F-Gs, but also B-D-F-Ab, Cb-D-F-Ab, and B-D-Es-Gs. Thus sixteen of the twenty-four keys can be attained from a single diminished seventh chord – either directly, or indirectly via their dominants. Through halfstep mutation(s) any dominant seventh or augmented sixth chord can be transformed into its corresponding diminished seventh, and then that diminished seventh can be reinterpreted enharmonically to access a wide range of potential keys for continuation. Fétis explores enharmonic reinterpretation in terms of both the mechanics of chord progression and in terms of aesthetics. Thus we are in good hands if we allow him to guide us through the practice of enharmonic modulation involving the diminished seventh chord.

Chromatic chords: diminished/augmented

7.6 Fétis: Traité complet de la théorie et de la pratique de la harmonie [1844], p. 179. Though these six progressions cadence in major keys, Fétis suggests that the parallel minor keys would be feasible goals as well. The first bass pitch of Progression 4 was printed in error as D in the first edition and was later corrected.

Enharmonicism When Vogler first employed a Roman numeral as a chord label in print, in his Tonwissenschaft und Tonse[t]zkunst (1776), it was to demonstrate enharmonicism: If one wants to go from C Minor, with a three-flat signature, into A Major, with a three-sharp signature, or likewise into A Minor, in which Gs, the major third above the fifth scale degree, remains indispensable, one need only convert the chord on the seventh scale degree in C Minor into that on the seventh scale degree in A Minor. VII in C VII in A

B b and then b mode can lead to an ordinary cadence in A.9

d d d

f f E

ab Gs gs in either

The word was out: diminished seventh chords are modulation-facilitators. In 1821 Momigny states what had by then become obvious: “Since the keyboard has only twelve keys per octave, there are tangibly only three different diminished seventh chords, each of these chords utilizing four keys, and three times four making twelve.”10 Fétis presents six progressions as a demonstration of enharmonic modulation [7.6]. Each begins with the same diminished-seventh sonority, written in one of four contrasting spellings. In a simple setting one of these progressions might be preceded by other chords in the same key and thus conclude without modulation. Fétis’s point, however, is to suggest ways of

173

174

Thinking About Harmony

a

b

c

7.7 Fétis: Traité complet de la théorie et de la pratique de la harmonie [1844], pp. 16, 21, 179. (a) Normative resolution of the quarte majeure. (b) Normative resolution of the quinte mineure. (c) Inward and outward resolutions of the same intervallic sound made available through enharmonie.

moving rapidly from one key into another. For example, the diminished seventh chord could follow after a passage in the key of C Major and continue as in Progression 6, cadencing in the key of Fs Major. The pairing of the fourth scale degree with the seventh scale degree (the note sensible) creates the interval of an augmented fourth (quarte majeure) or its inversion, the diminished fifth (quinte mineure). The attractive force of these pitches determines their resolution tendencies [7.7a, b]. These resolutions are obligatory in the ordre transitonique, Fétis’s term for the sort of music that was introduced by Monteverdi and that persisted through much of the eighteenth century. (It had gradually displaced the ordre unitonique of earlier composers such as Palestrina.) Transitonique modulation is accomplished by setting up an appropriate intervallic attraction to target a new tonic. The dominant seventh chord, whose adoption Fétis attributes to Monteverdi, is a crucial component of such modulation, due to its potent interval content. Fétis credits Mozart with inaugurating the next era of musical expression by exploiting enharmonic equivalence (enharmonie), the defining feature of the ordre pluritonique. For example, since the sound of the augmented fourth is indistinguishable from that of the diminished fifth, resolution may follow either of two contrasting trajectories [7.7c]. The diminished seventh chord is extraordinarily compelling in this regard because all of its intervals are susceptible to enharmonic reinterpretation. Since Fétis derives the chord from the minor mode’s dominant seventh chord in 65 position (e.g., Bn-DF-Ab substitutes for Bn-D-F-G),11 each diminished seventh chord in his example [7.6] represents, in accord with its spelling, a specific dominant seventh chord. Through substitution the dominant seventh chord in one key can be replaced by a diminished seventh chord, and in resolving, that diminished seventh chord can be reinterpreted enharmonically to represent the dominant seventh in a different key. Fétis’s six progressions appear without extensive commentary. He merely displays how “identical-sounding” chords can herald diverse “tonal destina-

Chromatic chords: diminished/augmented

tions,” without revealing much about how the progressions are constructed. Thus some belated remarks are in order: (1) Three of the progressions incorporate straightforward resolutions of the diminished seventh chord. In Progression 1, both the diminished fifth F and diminished seventh Ab above leading tone B resolve by descending step, in coordination with B’s ascent to the tonic pitch. In the enharmonically respelled (and, as a result, inverted) diminished seventh chord in Progression 5, these tendencies are taken over by D and F, respectively, against leading tone Gs. All resolutions are conventional. Bass B’s ascent to Cs precludes the questionable voice-leading of B–A with the F–E above. In Progression 6, the enharmonic respelling endows B and D with downward tendencies against leading tone Es. (2) Whereas the 7, 65, and 43 positions of the diminished seventh chord resolve to favored 53 or 63 sonorities, the 42 position does not. In Progression 3, bass Cb follows its normative tendency, resulting in a resolution chord in 64 position. (Here Fétis leads the augmented fourth DAb to Eb perfect fourth Bb , resulting in a doubling of the bass pitch Bb.) As in Progressions 1, 5, and 6, this tonic (in second inversion) is then confirmed by a V7–I cadence. (3) The 64 chord in Progression 2 should be understood differently from that in Progression 3. (Observe the prolonged F, functioning as a suspension, in Progression 2.) Here the diminished seventh chord targets the dominant seventh of the emerging key – that is, B not to C as tonic, as in Progression 1, but instead to C as dominant. The resolution of B-F-AbD is C-E-Bb-C. The intervening 64 chord embellishes the dominant, in a manner similar to a 64 usage Fétis discusses earlier in the Traité [7.8]. Progression 4 follows the same strategy as Progression 2. Here the bass descends to the dominant’s root, rather than ascending, because the diminished seventh chord is now in 65 position. (4) Why only six progressions, rather than eight? Fétis resolves a diminished seventh chord to a dominant only when that dominant is in root position, both to facilitate embellishment by a 64 and to produce a cadence proceeding from dominant root to tonic root.12 Only the 7 and 6 positions of a diminished seventh chord resolving to the dominant 5 achieve that outcome.13 Thus diminished seventh chords in 43 and 42 positions are presented in only one progression each. If the diminished seventh of Progression 3 had resolved to Eb as dominant (perhaps adding Db to the 64 to create a V43), the key of Ab Major could be achieved; if the diminished seventh of Progression 6 had resolved to Fs as dominant (perhaps adding E to the 63 to create a V65), the key of B Major could

175

176

Thinking About Harmony

7.8 Fétis: Traité complet de la théorie et de la pratique de la harmonie [1844], p. 79. “Sometimes the dissonance of the 65 chord, instead of resolving immediately, continues over the 64 chord built on the dominant, and descends only to the third of the following 53 chord. This delay of the resolution is not lacking in charm.” [“Quelquefois la dissonance artificielle de l’accord de quinte et sixte, au lieu de faire immédiatement sa résolution, se prolonge sur l’accord de quarte et sixte de la dominante, et ne descend que sur la tierce de l’accord parfait suivant: cette suspension de la résolution n’est pas dépourvue de grâce.”]

be achieved. With this completion of Fétis’s strategy, and taking into account that all cadences could be replicated in their parallel minor keys, sixteen of the twenty-four keys are accessible from one diminished seventh chord: all except Bb Major/Minor, Cs Major/Minor, E Major/Minor, and G Major/Minor.14 This demonstration of what was possible should not be equated with what was often done. Though C Major and Fs Major can be linked with lightning speed by reinterpreting B-D-F-Ab as B-D-Es-Gs, two enharmonic shifts are required. Many composers of the era would have resisted such a strident move. Others, including Liszt, were fascinated by the possibilities that Fétis reveals and undertook experiments in his fourth and final stage, the ordre omnitonique, in which all expectations concerning pitch behavior are confounded.15

Fétis formulated his four categories of musical practice without necessarily endorsing them all. The ordre omnitonique represented a challenging unknown. How composers might further develop the potentialities of the tonal system remained an open question. “The music of the future” (Zukunftsmusik, a term associated with mid-century progressive composers, including Liszt) had yet to be written. Complicating matters is the variety of compositional strategies that may interact with one another. With the diminished seventh chord, resolution of dissonance is a central concern, complicated by the potential for enharmonic reinterpretation. Yet at the same time composers were experimenting with strategies for the prolongation of a harmony. We have

Chromatic chords: diminished/augmented

seen how Lobe grapples with an A-Cs-A-E chord residing between two dominant chords, Gs-B-B-E and B-D-Gs-E in A Major [5.3d]. He cannot with certainty answer the question of whether the A chord resolves the first dominant and consequently represents tonic, or instead serves as a link between the dominant chords. Despite a diminished seventh chord’s greater resolutional force, it too can be prolonged via passing chords. We have seen how the diminished seventh that opens Beethoven’s String Quartet in C Major [5.14] can be understood as extending for seven measures (eventually transformed from diminished seventh – or incomplete dominant ninth – into dominant seventh). So, in addition to the quandary regarding which of several possible resolutions will occur, the listener must also consider the possibility that a chord following a diminished seventh is no resolution at all, but instead a link to another statement of the diminished seventh. In the analysis of music from Carl Maria von Weber’s Euryanthe that follows, I emulate Lobe by offering two contrasting views: one in which the diminished seventh chords resolve, and one in which they are linked in a nine-measure prolongation. The latter reading results in a harmonic progression of just three basic chords: tonic (extended through motion to its upper third), major supertonic (or V/V, represented by its third, fifth, seventh, and ninth – the diminished seventh chord), and dominant. Though I show how various nineteenth-century analysts concur with one or another of the assertions I make in the latter analysis, I know of no nineteenth-century analysis that integrates all these components in this way. That situation was to change dramatically by 1930, of course. Whereas my analysis in 7.16 bears some resemblance to Sechter in 5.3b or 5.16a, a few stems, beams, flags, and a “3” and a “2” would turn it into something akin to a Schenkerian graph.

Diminished seventh chords in Weber’s Euryanthe The Largo section from Carl Maria von Weber’s Euryanthe Overture [7.9] is an island of calm emerging from a sea of faster notes. In Act One this material will support Euryanthe’s retelling of words that had been whispered to her and to her beloved Adolar by the ghost of Adolar’s sister, Emma. The recipient of Euryanthe’s retelling is Eglantine, who also loves Adolar and, unrequited, is set on revenge. As the opera unfolds Eglantine makes Adolar believe that Euryanthe has been intimate with Lysiart. Though Euryanthe pleads her innocence, Adolar abandons her.

177

178

Thinking About Harmony

7.9 Carl Maria von Weber: Euryanthe (1823), Overture, mm. 129–143. This material from the Overture is employed again, in a somewhat extended form, during the third scene of Act One (number 6), where it supports the following text: “You who, heart to heart, so blissfully shed love’s tears, listen to me! Once this golden light also shone on me, for my Udo loved me tenderly and devotedly. He was killed in bloody battle! Since my life was no longer worth living, I imbibed death from a poison-filled ring. Woe unto this deed, which has separated me from the light! Isolated from Udo I wander through the nights! O cry for me! I will not find peace until this ring, from which I drank death, is moistened by innocent tears in deepest grief, and fidelity atones for the murderer’s monstrous deed!” [“Die ihr der Liebe Thränen Herz an Herz so selig weinet, hört mich an! Auch mir strahlt’ einst dies goldne Licht, mein Udo liebte mich zart und treu. Er fiel in blut’ger Schlacht! Da war mein Leben mir kein Leben mehr, aus gifterfülltem Ring sog ich den Tod! Weh dieser That, die mich vom Hell geschieden! Getrennt von Udo irr’ ich durch die Nächte! O weint um mich! Nicht eh’ kann Ruh’ mir werden, bis diesen Ring, aus dem ich Tod getrunken, der Unschuld Thräne netzt im höchsten Leid, und Treu’ dem Mörder Rettung beut für Mord!”]

Chromatic chords: diminished/augmented

7.10 Analysis of 7.9, mm. 129–134. The critical word Schlacht (battle), the event that precipitates both Udo’s and Emma’s deaths, coincides with the arrival of the D Major chord when this music recurs during Act One.

The text conveys two contrasting sentiments. First Emma compares the love between Adolar and Euryanthe with that which she shared with Udo. But then she recounts its unraveling: Udo’s death in battle and her consequent self-poisoning. Now she must wander (irren) through the nights until redeemed by the suffering of an innocent being. Euryanthe will be that innocent one, preceding her reconciliation with Adolar.

From bliss to despair Emma’s love had lost its object: Udo was no more. Torn from the state of bliss, she entered the realm of despair – an oppressive earthly torment followed by an action (suicide) that merely transferred the torment to the ghostly realm. In musical terms Weber conveys this unhappy turn of events by transforming tonic (B-D-Fs in measure 129) into a diminished seventh chord (B-D-F-Gs[Ab] in measure 134). Emma first tells of her love for Udo. B minor is transformed into B major in measure 130,16 followed by an incandescent ascending glide to D major in measure 132 [7.10]. But just as B minor expands to B major, D major contracts first to D minor (measure 133)17 and eventually to a diminished seventh chord (measure 134). This chord might be interpreted either as a tortured D chord (D-F-Ab-Cb) or as a tortured B chord (B-D-F-Ab). In fact, its resolution alternatives will engage the listener during the remainder of the Largo, paralleling the forlorn Emma’s wanderings. The diminished seventh chords of measures 129 and 130 behave in a conventional fashion. The first, an inversion of As-Cs-E-G, comes between the minor and major B chords; the second, Bs-Ds-Fs-A, triggers the motion to a Cs major chord, which glides between B major and D major (measure 132) in an evocation of Emma’s blissful state of love. The Cs and D chords appear in inversion, averting parallel fifths and enhancing the ethereal effect.

179

180

Thinking About Harmony

7.11 Vogler: Handbuch zur Harmonielehre (1802), table VII, fig. 4.1. Each of the diminished seventh chord’s four pitches serves in turn as leading tone. Vogler’s analytical symbol “VIIs” signifies that the chord’s root is the raised seventh scale degree in the minor key in which it is interpreted. (He does not specify the keys of analysis: A Minor, C Minor, Eb Minor, and Fs Minor.)

The treatment of the diminished seventh chord of measure 134 is more adventuresome.18 Weber’s teacher, Georg Vogler, advises: In order to bring about more distant modulations, one must seek the benefits which the diminished seventh . . . afford[s]. For Gs b d f can be heard as ab B d f gs b d Es ab cb D f These are the same keys on the organ, and yet Gs could be the seventh scale degree of B Es D

A Minor C Fs Eb19

Vogler demonstrates all four of these resolutions within a single music example [7.11] in his Handbuch zur Harmonielehre (1802). Weber, depicting Emma’s wanderings, likewise suggests all four of these resolutions within measures 134 through 143. Considering its spelling, the diminished seventh chord of measure 134 should resolve to A minor. That is what seems to occur at beat 3 of that measure [7.12a]. Yet immediately thereafter the progression leads instead to a C-major dominant of F minor [7.12b]. Fétis would document such a resolving-to-a-dominant strategy. (See Progression 2 of 7.6, above.) But Weber has more in store: the diminished seventh chord returns, respelled, in measure 138 and resolves to Eb minor [7.12c]. In its next appearance, in

Chromatic chords: diminished/augmented

a

b

c

d

7.12 Carl Maria von Weber: Euryanthe (1823), Overture. This extraction of chords from Weber’s composition is strikingly similar to an example Fétis would publish in France twenty-one years later. (See 7.6, Progressions 5, 2, 3, and 6.) Within the limited context of a), the pitch A seems to perform the role of chordal root, heralded by leading tone Gs; whereas within the broader perspective of b), it instead embellishes a C major dominant chord’s fifth, G. (Employing a 64 – rather than a 63 – on C would be a more typical construction, but it would lack the momentary A minor resolution potentiality that Weber may have been seeking to achieve.) Without the embellishing A, the diminished seventh chord in this context might have been spelled as D-F-Ab-B.

measure 142, it resolves to Fs major [7.12d]. Weber thus accomplishes, with infinitely greater artistry, the same feat that Vogler displays in his example [7.11].

Losing one’s way When Euryanthe and Adolar encounter her, Emma is doomed to “lose her way” (irren20) in wanderings through the nights, an invitation for Weber to exploit harmonic wanderings. Not only are diverse resolutions of the same diminished seventh chord explored, as described above; in addition, diminished and half-diminished seventh chords are juxtaposed in measures 135 and 136, with no apparent resolutional intent. These seventh chords occur in the context of a neighboring chord and inversional shifts [7.13]. Gottfried Weber explores the neighboring-chord concept: lower neighbors embellishing the third, fifth, and seventh of a C7 chord [7.14a]. He argues against a harmonic interpretation of the resulting diminished seventh chord. He also presents an example containing the downward slithering of diminished seventh chords [7.14b]. In the context of Euryanthe (measures 135 and 136), a similar reliance on copious Roman numerals to reveal multiple meanings is countered by the fact that, when dealing with the diminished seventh chord, ascending or descending three half-steps in each voice results in a chord equivalent to the initiating chord [7.14c]. Yet perhaps composer Weber had something akin to theorist Weber’s imposing collection of keys and Roman numerals in mind as a fitting depiction of Emma’s wanderings.

181

182

Thinking About Harmony

7.13 Analysis of 7.9, measure 134, beat 4, through measure 137, beat 1. The passage begins and ends with a C7 chord in 42 position, embellished by means of three lower neighboring notes that, together with the prolonged root C, form a diminished seventh chord (1). This diminished seventh chord is prolonged by means of inversional shifts: down a minor third and then back (2). Passing chords of diminished or half-diminished quality fill in the descending minor third (3).

a

7.14a, b Gottfried Weber: Versuch einer geordneten Theorie der Tonse[t]zkunst (1817-21, 31830–32), vol. 3, p. 124 (transposed); (1817–21, 21824), vol. 2, table 1212, fig. 204q [Warner, pp. 624, 373]. Compare this model and the second measure of 7.13. Gottfried Weber comments as follows: “In [this example] the combination [C Fs A Ds] perfectly resembles the chord of B7 with the fundamental tone omitted and an added small [minor] ninth . . . The ear, however, does not receive it as such; because it is evidently much simpler to regard the notes [Fs, A, and Ds] of the three upper voices as mere transitions [lower neighbors]; for, then the whole measure appears to rest on the principal fourfold chord C7, while, otherwise, we should have to assume three fundamental harmonies for this measure, viz. first C7, then B7 . . . with small ninth, and then again C7, – which would give, for this measure, the following far less simple harmony succession: F:

V7

===

e:

V7

===

F:

V7 .”

Competing hierarchies The strategies generally employed to analyze progressions such as those in 7.12 would dictate that the dissonant diminished seventh chords resolve as indicated by the arrows. A nineteenth-century analyst would be inclined to create a string of modulations, with a variety of pitches taking a turn as the local tonic, leading ultimately to Fs Major (major dominant of the Largo’s B Minor tonic) in measure 143. Could one possibly imagine the opposite: that the diminished seventh chord first presented in measure 134 holds up against less dissonant chords that prolong rather than resolve it?21 Vogler offers an

Chromatic chords: diminished/augmented

b

7.14 (cont.) Compare the fifth through eighth measures of this model and the fourth measure of 7.13. Rey (1806), Reicha (1816), and Asioli (1832) also include examples of successive diminished sevenths in their treatises, though without elaborate Roman-numeral analysis. Gottfried Weber comments as follows: “If, moreover, . . . many combinations of tones . . . are equivocal on their first appearance, yet such combination of tones . . . still acquires in many cases from the subsequent portion of the musical phrase and of course afterwards, a more definite meaning.”

7.14c Hasel: Die Grundsätze des Harmoniesystems (1892), p. 352. Compare the second measure of this model and the fourth measure of 7.13. Hasel positions fundamental bass pitch E below the first diminished seventh chord and draws a horizontal line, thereby asserting that only the first and fourth chords (with identical spellings) in the progression of four chromatically ascending diminished sevenths play a role in the larger harmonic structure.

intriguing model for such an analysis. In a creative circular example, he devotes one measure each to the twelve pitches within the octave, supplying appropriate letter names as captions [7.15]. C (measure 1), which will lead to F (measure 2), is prolonged by means of passing and neighboring notes connecting chord members. For example, A in the alto and bass registers connects G and Bb (or Bb and G), while F is neighbor to E. Vogler here refrains from labeling the chord on beat 3 as F.22 Pursuing the same line of reasoning in the context of Weber’s Largo results in an extended prolongation of a diminished seventh chord [7.16]. (Enharmonic spellings are employed freely to clarify this reading.) In Weber’s composition some of these passing chords are themselves prolonged. That of measures 134–137 has been discussed above, while that of measures 139–141 employs strategies that echo measures 129–130.

183

184

Thinking About Harmony

7.15 Vogler: Gründe der Kuhrpfälzischen Tonschule in Beispielen [1778], table XXIX, fig. 1 (excerpt). The diagram from which these measures are excerpted is circular. Vogler’s caption for the entire diagram reads: “Circular progressions from any note back again via fifths through all the others” [“Zirkelmässige Fortschreitungen von einem willkührlichen Tone in alle andere Fünftenweis zurück”]. There are in all twelve measures, corresponding to the chords C, F, Bb, Eb, Ab, Db, Fs, B, E, A, D, G, then back again to the initial C.

7.16 Analysis of 7.9. This example explores the hypothesis that the diminished seventh chord of measure 134 does not resolve until measure 143. In this interpretation, a progression of three chords (B–Cs–Fs) forms the essential harmonic fabric.

Modern ears, stretched by more radical tonal (and atonal) experiments, will never quite recapture the extraordinary impression this music must have made upon its initial audiences. Though Euryanthe did not receive the critical acclaim that had greeted Der Freischütz, it fulfilled another role very well, for passages like the Largo were as much a textbook on modern harmonic procedures for “pupils” such as Schubert, Liszt, and Wagner as any tome written by a pedagogue. Chords containing an augmented sixth inevitably have appeared in some of our earlier examples. Though we did not focus upon them at the time, mention was made of how Portmann accommodated such chords within his minor-key Wechseldominantenharmonie category (see p. 13

Chromatic chords: diminished/augmented

and 1.11b, above). Examples show how Vogler uses the numerals IV and II [1.4], Weber the numeral °II7 [1.6], and Lobe the numeral 2° [6.13b] to label augmented sixth chords. Their incorporation within the purview of harmonic analysis was both early and pervasive, a contrast to the difficulties surrounding the Neapolitan sixth chord (a topic of chapter 8). From many quarters it was asserted that the second or (raised) fourth scale degree grounded the augmented sixth chords. (In addition to the examples mentioned above, see those introduced earlier in this chapter: 7.1 (Holden), 7.3a (Rameau), 7.3b (Durutte), and 7.4 (Vogler).) A contrasting perspective was offered by Adolf Bernhard Marx, a prominent scholar working in Berlin around the middle of the nineteenth century. His criticism of the prevailing view is enlightening, and the alternative he presents would warrant adoption at least in part were other views not now so entrenched.

Marx on diminished thirds (augmented sixths) The standard English terminology for the augmented sixth chords seems beyond hope of revision. The colorful labels Italian, French, and German are arbitrary23 and distracting and are rarely encountered in analytical writings published outside of Great Britain until the twentieth century. It is refreshing to go back to Germany in 1841, when the University of Berlin professor Adolf Bernhard Marx, criticizing the recently published Harmonielehre of Siegfried Dehn, voiced opposition even to the word “augmented” (übermässig) being used in the chords’ names.24 Marx is both exhaustive and contrary in his approach to these chords [7.17]. He presents all eleven possible bass positionings for B-Db-F, G-BDb-F, and B-Db-F-Ab. His resolutions are to tonic – not dominant. Countering Dehn and others he rejects the label “übermässige Sext-Akkord” because the root positions of all three chords lack augmented intervals. Though B appears above Db in seven of Marx’s eleven models, a redistribution of the upper voices could eliminate the augmented sixth in all but three – examples 38b, 39f, and 40i. Db replaces D to create these sonorities just as Ds replaces D to create the augmented dominant triad G-B-Ds. He suggests that the triad B-Db-F might be called a “double-diminished triad, if we were in want of a new name.”25 Following this reasoning, B-Db-F-Ab would be a triple-diminished seventh chord. Marx wonders why one would name any of these chords using an adjective that applies only in the context of inversion.

185

186

Thinking About Harmony

7.17 Marx: Die alte Musiklehre im Streit mit unserer Zeit (1841), p. 127 (fn.), exs. 38, 39, 40. Marx presents the three basic chords first in their root positions (examples 38a, 39d, and 40h). Then the other pitches of each chord take a turn as bass. Wilhelm Tappert, in his study “Die übermässigen Sexten-Accorde” (Allgemeine musikalische Zeitung 3 (1868), p. 275), expands upon Marx’s “Mozart” annotation (example 40i) as follows: “Mozart has more than once resolved the augmented 6/5 chord directly and thus – produced parallel fifths; he has done this so often that one can speak of ‘Mozartean fifths’ ” [“Mozart hat mehr als einmal den übermässigen QuintSexten-Accord direct aufgelöst und also – Quinten gemacht; er hat das so oft gethan, dass man von ‘Mozart’schen Quinten’ reden darf ”].

Marx’s discontent concerns not only the adjective “augmented” (or “superfluous” in Saroni’s English translation), but also the noun “sixthchord.” In English the term “augmented sixth chord” is ambiguous: does it imply a chord containing the interval of an augmented sixth (an “augmented-sixth chord”) or a sixth chord whose quality is augmented (an “augmented sixth-chord”)? The German “übermässige Sext-Akkord” is unambiguous. In fact it is even more specific than English-speakers might realize. “Sext-Akkord” is one of several German terms, such as “QuintsextAkkord” and “Terzquart-Akkord,” that correspond to specific figured-bass 6 6 symbols – 63, 53, and 43, respectively, for these three terms. Though all three sets of figures contain the number 6, “Sext-Akkord” is correctly employed only for the inversion of a triad (not of a seventh chord) and thus corresponds to only one of Marx’s eleven examples – 38b. Riemann describes the use of the term in other contexts as “uncalled-for, . . . unsystematic, misleading, and inadequate.”26 Though terms such as Tonika and Dominantakkord appear occasionally

Chromatic chords: diminished/augmented

in Marx’s prose, his abundant music examples seldom show figured bass and never a Roman-numeral harmonic analysis, in stark contrast to the practice of Gottfried Weber, whose Versuch einer geordneten Theorie der Tonse[t]zkunst (1817–21) had given a strong impetus to Roman-numeral usage among German-speaking musicians. As does Marx, Weber presents all eleven configurations of the three augmented sixth chords.27 Whereas Marx’s chords resolve to tonic, Weber’s chords precede dominant E-Gs-B in A Minor.28 He employs the symbol °7 for all of these configurations. In A Minor the supertonic’s pitches, including its ninth, are B

D

F

A

C.

Through selective omission (including possibly the root) and modification of the third Weber achieves the three standard spellings B

Ds Ds Ds

F F F

A A A

C

[modern “French”] [modern “Italian”] [modern “German”].

Weber demonstrates contexts for °II7 in longer progressions, including exit voice leading to I64 (our “cadential 64”) and the potential for enharmonic reinterpretation [7.18a, b]. His disciple Philipp J. Engler adds the number 9 when the supertonic’s ninth is a chord member [7.18c]. Marx’s discussion of these chords in his Die Lehre von der musikalischen Komposition (vol. 1, 1837) occurs in a chapter on the passing note (“Der Durchgang”), where he examines the “elevation” and “depression” of the dominant’s fifth in turn.29 A chromatic passing note that follows after or even substitutes for its diatonic precursor may generate a distinctive chordal variant. Chopin’s Mazurka in C Minor (op. 56, no. 3) demonstrates what Marx has in mind. In measures 78 through 81, in the key of Bb Major, a half cadence on dominant F is followed by a return to tonic Bb, which begins a consequent phrase [7.19a]. The dominant’s soprano C (= 2) in measure 79 is in the same register as the D (= 3) that initiated the phrase’s melody in measure 73. For the consequent phrase, Chopin employs the D an octave higher (measure 81). The Cs that precedes it (measure 80) is “elevated” in two senses: it is a compound augmented fifth above root F (Marx’s meaning), and it is positioned an octave higher than its diatonic precursor. Later, in measures 201 through 205, D (now 2 in C Minor) is modified [7.19b]. Here the “depression” to Db in the B-Db-F-Ab and G-B-Db-F chords corresponds to Marx’s examples 40l and 39d, respectively [7.17]. In both chords Chopin’s configuration incorporates a diminished third, not an augmented sixth: melodic Db–Bn (with intervening passing note C, all over

187

188

Thinking About Harmony

a

b

7.18a, b Weber: Versuch einer geordneten Theorie der Tonse[t]zkunst (1817–21, 3 1830–32), vol. 2, table 111⁄2, ex. 192i; vol. 2, p. 137 [Warner, pp. 346, 356]. (a) Weber analyzes the “augmented sixth” chord in measures 2 as a diminished supertonic, indicated by a degree symbol (°) above a small II. Though rooted on B, only the chord’s raised third (Ds), diatonic (diminished) fifth (F), seventh (A), and ninth (C) are present. Weber’s chord corresponds to Marx’s example 40i [7.17]. The third measure’s 64 offsets the parallel fifths that Marx allows on the authority of Mozart. In fact, Weber’s table of augmented sixth resolutions includes a parallel fifth resolution as well (vol. 1, table 8 (opposite p. 255), ex. 123s [Warner, p. 210]). (b) Here Weber reveals the potential for enharmonic reinterpretation. Though the spelling and resolution of the third chord (bass Es) might justify analysis as °II7 in B Minor (German “h”), his label corresponds to how one likely would hear the chord when preceded by G-Bb-D: as a dominant seventh (G-Bn-D-F) in C Minor rendered in 42 position.

7.18c Engler: Handbuch der Harmonie (1825), p. 18. The example’s first two “augmented sixth” chords, in G Minor and F Minor, respectively, include the supertonic’s raised third, diatonic fifth, and seventh. The third “augmented sixth” chord, in C Minor, includes the supertonic’s ninth as well.

tonic pedal C) in measure 202 and harmonic Db in measure 204. Though Bn joining Db and Bn within such close quarters may be exceptional, Chopin appears to have had no reservations in doing so.30 He might have been chastised by Marx [7.20a], though not by Knecht [7.20b].

Chromatic chords: diminished/augmented

a

b

7.19 Chopin: Mazurka in C Minor, op. 56, no. 3 (1844). (a) Measures 78–81 and analysis. (b) Measures 201–205 and analysis.

So who, then, are the contrarians – Marx and Chopin or modern textbook authors?31 Are augmented sixth chords actually diminished in quality? Should they be regarded as chromatic variants of the V–I succession, or of a similar succession applied to V? Though one may find Marx’s answers to these questions intriguing or even persuasive, probably for as long as tonal harmony textbooks are published in English there will be little change in the chapter on the “Italian,” “French,” and “German” “augmented” “sixth chords.”

189

190

Thinking About Harmony

a

b

7.20a Marx: Die Lehre von der musikalischen Komposition, vol. 1 (1837), p. 259, ex. 499. 7.20b Knecht: Elementarwerk der Harmonie (1792–97, 21814), table XVIII, fig. 6. (a) “The passing chord Ds-F-A is well employed in examples a and b, but spoiled in example c due to the positioning.” [“So ist der Durchgangs-Akkord dis-f-a hier . . . bei a und b wohl angebracht, bei c aber durch die Lage verdorben.”] (b) In transforming the triad B-Ds-Fn into a chord, Knecht does not hesitate to place Ds and Fn in close proximity. In that the plate on which these examples were engraved contains several other oddities of Roman-numeral employment and alignment, it is probable that the omission of V between II and I is an oversight.

Each of Marx’s augmented sixth chords is focused on a particular goal [7.17]; Fétis’s one diminished seventh chord is not [7.6]. Yet even Fétis’s roster of resolutions is far from complete. Consider Gottfried Weber’s example of C-Fs-A-Ds leading to C-G-Bb-E [7.14a]. This usage is of an entirely different nature from those assembled by Fétis. Due to the common tone C, its CFs augmented fourth does not expand outwards as Fs–G convention would dictate (C–B(b) ). As a result the chord functions as an embellishment of – certainly not the dominant of – its successor. Note 14 in the midst of the Fétis discussion earlier in this chapter credits Swoboda with demonstrating a variety of interesting strategies for diminished seventh resolution. It is now time to follow up on that hint. Music by Liszt analyzed according to theoretical principles enunciated by his friend Carl Weitzmann provides a fruitful vehicle for our exploration of cutting-edge diminished seventh usage.

Weitzmann on diminished sevenths Franz Liszt maintained close ties with his native Hungary throughout his life. Funérailles is his response to the news that Hungary’s prime minister and thirteen generals had been executed on October 6, 1849. Over the next decade Carl Friedrich Weitzmann published several

Chromatic chords: diminished/augmented

treatises that assess the practices of composers such as Liszt and his progressive contemporaries. Der übermäßige Dreiklang (The Augmented Triad) was published in 1853; Der verminderte Septimen-Akkord (The Diminished Seventh-Chord), dedicated to Liszt, appeared the following year. In 1860 his Harmoniesystem won a competition sponsored by the Neue Zeitschrift für Musik to honor the work that best elucidated recent advances in composition. Lobe and Liszt were the competition’s judges. Measures 89 through 108 of Funérailles [7.21] conclude a section in Ab Major, the mediant of the work’s F Minor key. The Ab chord, initially a stable tonic in Ab Major, is eventually destabilized to become dominant in Db Major, whose tonic arrives in measure 109. The sudden shift of Liszt’s notation to sharps at measure 100 is of no structural importance: notation in flats is restored in the bass at the end of measure 108 and continues thereafter. Weitzmann classifies many dissonant chords as Vorhalte. The term conveys the sense of “suspension chord” – something that delays the arrival of what follows, either a consonant chord or another Vorhalt. The diminished seventh chord of measure 89, which resolves to tonic Ab in measure 90, is a Vorhalt conforming to one of Weitzmann’s models [7.22a]. Whether one, a few, or all pitches move to resolve a Vorhalt is not a factor. All such chords are Vorhalte as long as the resolution pitches are not already present in the chord.32 The same pitch classes, with B transformed into Cb, recur in the second half of measure 95, resolving to dominant Eb in measure 96 to end the phrase. Because the dominant’s seventh, Db, is present, the Vorhalt’s consonant resolution [7.22b] is averted: a “deceptive succession” (Trugfortschreitung) occurs, with one Vorhalt leading to another.33 Suspensions F and Ab and chromatic passing notes An and Bn embellish the Eb chord. At no point do the dominant seventh’s four component pitches sound at the same time.34 Liszt’s traversal of the span between tonic Ab and dominant Eb in measures 92 through 96 is accomplished via what Weitzmann likely would have regarded as a progression of seventh chords (Septimenakkordfolge). Weitzmann’s models in Der verminderte Septimen-Akkord employ diatonic, dominant, or diminished sevenths.35 Liszt’s version is a hybrid progression, with dominant seventh and diminished seventh chords in alternation [7.23]. Following the model exactly, measure 95’s second bass note would be spelled Ebb. By employing Dn instead, Liszt provokes an enharmonic reinterpretation. The upward resolution to Eb terminates the Septimenakkordfolge, and the phrase concludes in a half cadence. The new phrase that begins in measure 97 has much in common with its predecessor. Its first three measures are nearly identical to measures 89

191

192

Thinking About Harmony

7.21 Liszt: Funérailles (1849), mm. 89–108.

through 91. In addition, both phrases contain a bass descent to a diminished seventh chord with bass Dn (measures 95 and 102). Yet the chords associated with these descents and the resolutions of the diminished sevenths are contrasting. When Ab is tonic, the tonic/dominant axis from Ab to Eb guides the tonality. A descent to Dn is an ideal means of targeting the dominant, because Dn

Chromatic chords: diminished/augmented

7.21 (cont.)

is Eb’s leading tone. On the other hand, when Ab is dominant (thinking ahead to measure 109), the tonic/dominant axis is Db/Ab. Descending from Ab to Dn does not have the same effect in this case. The chord of measures 103 and 104 is the Phrygian II or Neapolitan (Ebb-Gb-Bbb) in Db Major.36 It follows its normative role for this context, leading the way (back) to the dominant, Ab7 (spelled as Gs7) in measures 105 through 108. (The Neapolitan appears in its normative 63 position in measures 103 and 104.) Due to the abundant embellishment, all of the dominant chord’s members sound together only during the second half of measure 108, and that due only to the retention of the left-hand pitches by the pedal. How Liszt deploys diminished seventh chords in this phrase illustrates their capacity for enharmonic reinterpretation, a concept distinct from the additional complication of their notation in sharps. The second halves of measures 97, 99, and 102 contain the same four pitch classes. In each case the resolution follows the strategy of 7.22a: one of the Vorhalt’s pitches is

193

194

Thinking About Harmony

a

b

c

7.22a, b Weitzmann: Der verminderte Septimen-Akkord (1854), pp. 13, 33 (transposed). 7.22c Lobe: Vereinfachte Harmonielehre [1861], p. 58. (a) The resolution of this diminished seventh chord to tonic, employed in measures 89 and 90 of Funérailles, corresponds to that of Gottfried Weber in 7.14a (there resolving to a dominant seventh chord). Compare the Weber/Weitzmann view with that of Lobe [7.22c]. (b) Weitzmann shows how the enharmonic equivalent of 7.22a’s diminished seventh chord may resolve to an Eb chord. (c) Lobe’s analysis of an excerpt from Beethoven’s Sonata in C Minor (op. 10, no. 1) juxtaposes the keys of Eb Major and G Minor, an analytical strategy that Weber had disparaged [7.14a].

retained as the root of the resolution chord. Each resolution is to a different chord, in a progression of ascending minor thirds: Ab–Cb(B)–Ebb(D) [7.24]. Thus in terms of their chordal content, the two phrases are quite different: the first gradually descends, whereas this latter phrase ascends in minor thirds to achieve D. (By placing the Cb chord first in 64 position – with bass Gb (Fs) – in measure 100 and then in 63 position – with bass Eb (Ds) – in measure 102, Liszt nevertheless achieves a descending bass line reminiscent of that in the preceding phrase.) In both phrases the diminished seventh Vorhalt on Dn is decisive: in measures 95–96 it resolves to Ab Major’s dominant, Eb; in measures 102–103 it resolves to Db Major’s Neapolitan, Ebb (Dn). The juxtaposition of Ab, Cb, and Ebb [7.24] demonstrates Weitzmann’s perspective on chord progression, as articulated in his Harmoniesystem: “Any consonant chord may follow after any other consonant chord.”37 Weitzmann likely would have interpreted Liszt’s measures 99 and 100 as a Vorhalt-intensified equivalent of one of his examples demonstrating the succession from a major tonic to its lowered mediant (Ab–Cb) [7.25a]. Measures 102 and 103 repeat the succession starting on Cb (Bn) [7.25b].38 The combined span of a diminished fifth (Ab–Ebb) is characteristic of the

Chromatic chords: diminished/augmented

a

b

c

7.23 Analytical models for 7.21, mm. 89–96. Examples (a) and (c), based on models by Weitzmann, present descending Septimenakkordfolgen that employ dominant seventh and diminished seventh chords, respectively. Example (b), which corresponds to Funérailles, incorporates elements from both (indicated by arrows). At the downbeat of measure 95 inner-voice G occurs instead of Gb, forestalling a continuation into increasingly flat domains. The Funérailles melody departs from the model of measures 93 and 94 by means of incomplete upper neighbors: C–Db, Bb–C in place of C—, Bb—.

relationship between the dominant and Neapolitan chords. When root Ab returns (Gs, measure 105) and is destabilized by its seventh Gb (Fs, measure 107), its role as dominant is confirmed. Weitzmann’s Vorhalt principle thus aptly responds to chordal behavior in works by progressive nineteenth-century composers. Whereas Rameau is justified in interpreting a diminished seventh chord as a dominant seventh with one pitch altered via substitution (B-D-F-Ab representing G-B-D-F, for example), the array of resolution strategies for the chord expanded greatly thereafter. Many of Weitzmann’s (or Liszt’s) resolutions do not readily accommodate a root-oriented conception.39 For example, a fundamentalbass reading of 7.22a would yield a bizarre outcome, G–Ab. Weitzmann bypasses thorny questions of roots and their succession by placing a Vorhalt within the domain of its resolution chord.

195

196

Thinking About Harmony

a

b

c

7.24 Three diminished seventh chords from 7.21 and their resolutions. Here Weitzmann’s resolution model of 7.22a is replicated at other pitch levels. These successions are fundamentally different from those presented by Fétis [7.6] in that the diminished seventh chords and their resolutions share a common tone. In common with Fétis’s models, they illustrate the diminished seventh chord’s capacity for enharmonic reinterpretation. Liszt’s notation in sharps (measures 100 through 108) allows him to avoid the cumbersome notation Ebb and Bbb. Because the Ebb chord functions as Neapolitan in Db Major (whose tonic arrives in measure 109), the flat-key spellings are reinstated above to foster a meaningful analytical understanding of the passage.

a

b

7.25a Weitzmann: Harmoniesystem [1860], p. 18 (transposed). 7.25b The progression of 7.25a transposed up a minor third. (a) This model is a transposition of one of twenty-three examples created by Weitzmann to demonstrate the direct succession from a C major chord to the eleven other major chords and to all twelve minor chords. (b) The succession from Ab to Cb is replicated a minor third higher in the succession from Cb to Ebb.

Yet there is a danger: the Vorhalt principle’s imposition of hierarchy can be perfunctory. For example, is the Dn diminished seventh chord in measure 95 of Funérailles merely a local embellishment of the following dominant? Or is it instead part of an important and extended harmonic initiative between tonic and dominant? A different hierarchy, one that forges a relationship between Bb-Dn-F-Ab in measure 94 and Dn-F-Ab-Cb in measure 95, deserves consideration here. Countering the notion of Septimenakkordfolge [7.23b] – a sequential progression – is the potential interpretation of the passage as a harmonic progression [7.26], wherein some chords play harmonic roles and others play connective roles. A more complex hierarchy may be operative, as follows: m. 89–92 bass: Ab root: Ab

93 G ()

Gb F

94 95 96 F Fb Eb Dn Eb Bb –––––––––––––––––––––––– Eb

Chromatic chords: diminished/augmented

7.26 Analysis of 7.21, mm. 89–96 (in three states of development). Viewed as a sequential progression [7.23], the potential harmonic implications of the phrase’s internal chords are not called into service. In contrast, the harmonic view displayed above depends upon two hierarchical assertions: (1) that the chord in the first half of measure 93 performs a connective role between the preceding Ab and following F chords, the latter of which is significantly altered (the score’s soprano Db functions as a neighbor to C); and (2) that the BbD-F-Ab (measure 94) and D-F-Ab-Cb (measure 95) chords are connected by means of two passing chords. (Compare Liszt’s bass F–Fb–Eb–D and the analysis above with Hasel’s bass B–C–Cs–D and his analysis in 7.14c, measure 2.)

In this view the major supertonic (IIn or V/V) plays its role as fulcrum between tonic and dominant. Thus we confront yet again the question that emerged in our analyses of Beethoven’s String Quartet in C Major [5.14] and of Weber’s Euryanthe [7.9]: namely, whether a diminished seventh chord functions only within its local context or instead participates in a broader prolongation, relating functionally to another diminished seventh chord or to a dominant seventh chord, from which it is separated by intervening passing motion.

197

8

Chromatic chords: major and minor

bII: the strategy of denial The chord we call the “Phrygian II,” “bII,” or “Neapolitan sixth” was too conspicuous a presence in compositions to be overlooked by nineteenthcentury analysts. Yet among their diverse responses was a tendency by some to regard the lowered second scale degree as a half-step substitution: for example, as a chromatic neighboring note or suspension displacing diatonic 1, the minor subdominant chord’s fifth. Whereas the similar half-step substitutions that result in the diminished seventh and augmented sixth chords add dissonant intensity, out of context the sound of the Neapolitan is consonant. Yet in context the lowered second – a minor sixth above the fourth scale degree – may be perceived as a “wrong” note within what should be a minor IV chord. From that perspective the Neapolitan does not register as a harmonic entity in its own right, with root on the lowered second scale degree, but instead as an embellishment of the subdominant. Just as a diminished seventh chord (the dominant’s third, fifth, seventh, and ninth) may never settle into a dominant seventh (with the dominant’s ninth resolving to the octave), the Neapolitan may never settle into the subdominant (with the sixth resolving to the fifth). When pursuing harmonic analysis one identifies – and eliminates from further consideration – pitches that perform a non-harmonic role. The remaining pitches are then arranged to form meaningful combinations. How one analyzes the harmonic progression in two measures from Réminiscences de Don Juan [8.1a], Liszt’s bravura rendering of popular numbers from Mozart’s Don Giovanni, depends upon just which combinations of pitches one accepts as harmonic. Charles Rosen offers a vivid yet misleading account: “Bernard Shaw called the variations on the duet conventional, but they contain passages harmonically in advance of their time and which predict the Richard Strauss of Der Rosenkavalier. . . A delicate suggestion of the harmonies of G major and B flat major laid over A major is purely coloristic.”1 By granting harmonic status to G major (near the end of measure 84) and Bb major (after the D major chord that opens measure 85), Rosen confronts

Chromatic chords: major and minor

a

b

c

d

8.1a, b Liszt: Réminiscences de Don Juan (1841), mm. 84–85, 58–59. 8.1c The foundational chords of 8.1a and 8.1b. 8.1d Catel: Traité d’harmonie [1802], p. 56 (transposed). (b) These measures from the Duetto theme are the model for Liszt’s variation in 8.1a. (c) This straightforward harmonization of the chromatic melodic descent from A to E resembles models by Jadassohn [6.19b], Day [6.19c], and Catel [8.1d]. If accepted as the foundation for 8.1a, then our appreciation of Liszt’s writing in this passage should focus on his command of non-harmonic procedures (what is absent from this example) rather than harmonic ones. (d) Catel’s example, intended to demonstrate “Pédale” (pedal point), coincidentally contains a melodic/harmonic framework similar to Mozart’s.

the need to assess their roles. The description “purely coloristic” is a disappointment. Rosen seems to deny the possibility that the Bb chord might function as a Neapolitan. (It is followed by A Major’s dominant in the second half of measure 85, a typical Neapolitan context.) But a more basic

199

200

Thinking About Harmony

a

b

8.2 Vogler: Handbuch zur Harmonielehre (1802), table IV, figs. 4 and 5. Vogler’s examples demonstrate contexts for the diminished sixth and the augmented third. (His first example is adapted from one in C. P. E. Bach’s Versuch über die wahre Art das Clavier zu spielen (1753–62), vol. 2, p. 54 [Mitchell, p. 216].) Vogler regards Bb as a Vorhalt, a pitch that “delays the entry of the essential, harmonic tone” [“der wesentliche, zur Harmonie gehörige Ton seinen Eintritt verzögert”] (p. 11).

concern is whether the pitch combinations G-B-D and Bb-D-F form harmonic entities in the first place. Comparison with Mozart’s opera or an earlier passage from Liszt’s Réminiscences [8.1b] suggests that E and Cs – not B and D, which in this view function as accented passing notes2 – harmonize soprano G at the end of measure 84. (Thus measure 84 is akin to the progression examined in 6.19 and 6.20.) And Bb might be perceived as a chromatic neighbor to A, with D serving as root for the entire first half of measure 85 [8.1c]. Instead of coming up empty-handed in assessing these chords’ harmonic roles (à la Rosen), one may instead question whether they warrant a harmonic interpretation at all. Though certainly many analysts would acknowledge the presence of a Neapolitan here (with A and Cn on the third eighth note of measure 59 and sixth sixteenth note of measure 85 functioning as passing notes connecting Bb–Gs, and D–B, respectively), others would assert that the subdominant persists through a chromatic neighbor (A–Bb–A), a modal shift (Fs–Fn), and the addition of the dissonant seventh (D–Cn). Rosen’s stance is idiosyncratic: he both declares the Bb major chord to be harmonic and neglects to regard it as a Neapolitan. Vogler stumbles upon a potential bII (DBb or DBb in A Minor) in the process of demonstrating some uncommon intervals [8.2]. His commentary suggests that he does not regard Bb as harmonic at all, but instead as a displacement of A. Thus the progression is from IV to V, even if by the time IV’s A arrives, its D has undergone chromatic mutation. In his Die Grundsätze der musikalischen Komposition (1853–4), Sechter argues that chromaticism emanates from a diatonic foundation. Juxtaposing diatonic and chromatic formulations, he challenges his readers to hear beyond the intense dissonances of key-bending chromaticism and pitch displacements to a straightforward underlying progression [8.3]. His diatonic model is uncomplicated, even drab.3 Its only dissonant moment is at measure 3, where root D fulfills the utilitarian role of averting the stepwise succession of fundamentals F and G.

Chromatic chords: major and minor

8.3 Sechter: Die Grundsätze der musikalischen Komposition (1853–4), vol. 1, pp. 155–156.

Much has changed in the first of his five chromaticism-enhanced progressions. Sechter offers a harmonic explanation for each alteration without employing Roman numerals, which have been constructed below from his commentary and in his manner.

201

202

Thinking About Harmony

Measure 1: E, G, Bb, and Db are four of the five pitches that constitute F Minor’s dominant ninth chord. Root C is suppressed. This could be displayed as measure: C Major: F Minor:

1 I

2 V

I

Measure 2 and the first half of measure 3: Though measure 2’s chords assert tonic in F Minor, the first chord of measure 3 contradicts that key (which would require Db) but is diatonic in C Minor. This could be displayed as measure: F Minor: C Minor:

2 I IV

3 ––– –––

II

The second half of measure 3: Fs, An, C, and Eb are four of the five pitches that constitute G Minor’s dominant ninth chord. Root D is suppressed. When G arrives, the chord’s quality is major. This could be displayed as measure: C Minor: G Minor: G Major:

3 II

4 V I

Measure 4: G’s status as a tonic is contradicted by F. The G7 chord instead should be interpreted in C Major. This could be displayed as measure: G Major: C Major:

4 I

5 V

I

Though there is no “bII” situation as yet, the requisite pitch Db, diatonic in F Minor, has been introduced. In the second chromaticism-enhanced progression, two pitches are suspended: Db (measure 2) and C (measure 4). Sechter’s analysis (capital letters below the bass) is not affected by these modifications: “bII” does not register as a harmonic event, even though F, Ab, and Db sound together for half a measure. Instead, the Db displaces the C acknowledged in the notation “F” (for F-Ab-C) below the staff. In addition, the F-D-Ab-C chord of measure 3’s downbeat is elided. Sechter consequently interprets measure 2’s F minor chord as a representative (Stellvertreter) of D7. D is retained as fundamental for the Fs-A-C-Eb chord in measure 3.

Chromatic chords: major and minor

In the third chromaticism-enhanced progression, even the F-Ab-C chord is elided. The Db suspension’s resolution coincides with activity in the other voices, leading away from F Minor to form G’s dominant.4 The suspension Db has resolved to C first before and then with the arrival of Fs, Eb, and An. In the fourth chromaticism-enhanced progression, it resolves after those other pitches arrive. D is indicated as the chord’s fundamental even though Db is sounding: the lingering ninth of F Minor’s dominant mingles with pitches from G Minor’s dominant. Whereas in the fourth chromaticism-enhanced progression F Minor’s Db sounds against G Minor’s Fs, in the fifth progression F Minor’s F lingers as well (measure 2). Despite the complexity of the sonority at this moment, each pitch performs a specific role. That is for Sechter the exemplary state in which chromaticism should flourish. In none of these contexts does the pitch combination Db-F-Ab register as harmonic. After the first bar line, Db functions as a displacement of C, the perfect fifth above fundamental F. That status persists in Sechter’s thinking even when an unadulterated F chord fails to materialize in the actual sound of the composition.

Thus at least some of the contexts in which a “Neapolitan” chord might appear result from the behavior of a wobbly note: scale degree 1. It joins a family of wobbly chords: V7: II7: II7: IV:

G-B-D-F D-F-A(b)-C D-F-A(b)-C F-A(b)-C

versus versus versus versus

Ab-B-D-F (diminished seventh) D-Fs-Ab-C (“French”) Eb-Fs-Ab-C (“German”) F-Ab-Db (“Neapolitan”)

(If II7 or IV appears in a major key, then A is among its wobbly pitches.) Though the issue was and remains contentious, one of the principal justifications for some of music’s most striking chromatic chords hinges upon their relationship with simpler dominant, supertonic, or subdominant chords. An obvious alternative is to take the “Neapolitan sixth” chord at face value, as the inversion of a stacked-thirds triad emanating from the pitch a minor second above tonic. Yet how should one contextualize its root? As with other events that extend beyond the key’s diatonic pitch collection, analysts were sharply divided regarding whether that pitch should be interpreted chromatically within the original tonic key, as its lowered second scale degree, or diatonically within a subsidiary key. For example,

203

204

Thinking About Harmony

a Db major chord in C Minor might be interpreted as the subdominant within C Minor’s submediant key, Ab Major. Though a phenomenon common in music since the eighteenth century, the Neapolitan’s analytical acceptance within a key’s society of chords was slow in coming. Well into the nineteenth century trepidation and indecisiveness typify discussions of the Neapolitan chord. Our exploration of the topic, below, traces some of the high points in the chord’s struggle for recognition on an equal footing with the diatonic chords. One brave commentator, Loquin, goes so far as to remove any presumption of diatonic hegemony from his analytical notation.

bII: strategies of inclusion Our introduction to modulation drew upon an example from 1737 by the German-trained, London-based author John Frederick Lampe in which five different scale degrees take turns as the “key note” [6.1]. Its first measure contains an unlabeled major chord built on Fn, the lowered second scale degree of E Minor. Lampe seems not to know what to make of it: the absence of analytical notation hints of a discomfort with the situation, an unwillingness to sanction something so deviant with a legitimizing label. Since the diatonic triad on E Minor’s second scale degree (Fs-A-C) is unstable, a modification is particularly welcome here. The two viable adjustments are: Lower Fs to Fn 5 – 6 5 – 6 E

E

Fn

5

Fs | G

5 – 6s s

E

Es

Raise C to Cs 5s – 6 Fs

5

Fs | G

In lowering Fs to Fn Lampe may be condemning the commotion of moving from E-G-B to Es-Gs-Cs (on the way to Fs-A-Cs) more than endorsing the lowered second as a root.5 In eighteenth-century German theory the lowered second scale degree has its place among the “Chordæ elegantiores” of a minor key. Fn, As, C, and D are the “graceful” pitches in E Minor, according to Johann Mattheson.6 Daube suggests that chords such as A-C-Fn in E Minor would delight lovers of exotic harmony (die Liebhaber fremder Harmonie).7 The elderly Rameau appears to concur, for in his Code de musique pratique (1760) he fearlessly provides an extraordinary fundamental bass, A–Bb–E–F, for a progression rendered in modern analytical notation as A Minor: I–bII6–V7#–VI.8

Chromatic chords: major and minor

8.4a Langlé: Traité de la basse sous le chant [ca. 1798], p. 164, ex. 95. Only through enharmonic reinterpretation does this chromatic progression retain an affiliation with the diatonic pitches in C Major. Left untended it would proceed via bass C–Ab–Db–Bbb–Ebb– Cbb to Fbb and beyond, ultimately reaching Abbbbbbbbb rather than C at its twenty-fifth measure.

8.4b Momigny: La seule vraie théorie de la musique [1821], pp. 78–79. Momigny’s caption asserts that the entire progression is in the key of C Major (“UT majeur”). Enharmonic reinterpretation (e.g., Db = Cs) plays a crucial role.

Certain sequential progressions endow the lowered second scale degree with an inevitability unmatched in conventional harmonic progressions. Langlé passes through both the lowered and diatonic second scale degrees in quick succession [8.4a]. Momigny’s commentary on a variant of the same progression [8.4b] asserts his anti-modulatory stance: Although the octave span here would seem to affirm Db as tonic in the key of Db Major, Db nevertheless is merely the chromatic lowered second of the key of C Major, taking into account that the establishment of C Major has preceded it and that the remainder of the progression conforms. Likewise, and for the same reasons, the octave span Cs B A Gs Fs E Ds Cs is not in Cs Minor, but in C Major. To conceive of each octave span in this example as if it were the set of diatonic pitches in a different key is the misunderstanding of those who know nothing about the chromatic genus.9

Berton’s circle of descending fifths (C–F–Bb–Eb–Ab–Db–Gb–Cb– . . .) effortlessly touches upon the lowered second in a sequential progression that persists to the point where enharmonic shadows dwell [3.8]. More cautious souls, sensing danger ahead, would be more inclined to breach

205

206

Thinking About Harmony

a

8.5a Förster: Anleitung zum General-bass [1805], examples appendix, p. 14, ex. 126a. For analysts who chart bass rather than root progressions (see 1.2b), the succession 4–5 corresponds to a broad range of possibilities including, as here, a 4 surmounted by a minor sixth (the lowered second scale degree) and a 5 surmounted by a sixth and a fourth.

b

c

8.5b, c Crotch: Elements of Musical Composition (1812), plate 30, exs. 328, 331. In addition to the two successions shown, Crotch displays successions from the Neapolitan sixth to a diminished seventh on the raised fourth scale degree (also labeled fa) and to a 64 on the fifth scale degree (labeled sol). Each of these successions is displayed in both major- and minor-key contexts.

the pattern than to enter territories populated by such eerie shapes, in some cases placing the lowered second and the dominant in direct succession. Weitzmann, for example, displays the progression C–F–Bb–Eb–Ab– Db–G–C.10 In that a bass, as opposed to root, orientation to chord progression (as in 1.2) persisted in some quarters well into the nineteenth century, several early attempts at labeling the chord do not distinguish it from the subdominant. For Langlé it consists of a “minor sixth on the fourth note of the key,” a license that he permits only in the minor mode and only when its altered sixth and the dominant’s diatonic fifth are not juxtaposed in adjacent chords, but instead separated by a 64 (his cadence double).11 Förster employs the Arabic numeral “4” in his bass-oriented analysis [8.5a]. Crotch employs the label “fa” [8.5b, c], explaining: “The Neapolitan sixth is a minor third and a minor sixth to Fa, and is never inverted.”12 Accepting the chord at face value – as an inversion of a major triad rooted a minor second above tonic – triggers a concern for what Lobe calls nahe Beziehung: the close relationship between successive roots.13 1– b2 and b2–5 hardly qualify. Vogler, who sometimes fails to acknowledge the Neapolitan

Chromatic chords: major and minor

8.6 Jelensperger: L’harmonie au commencement du dix-neuvième siècle (1830, 21833), p. 40 [Häser, p. 34.] “We shall use the term half modulation when one only touches upon another key in passing, with just one or a few chords, and without making a cadence.” [“On appellera demi modulation, celle où l’on ne touche à un autre ton que passagerement, avec un ou quelques accords seulement, et sans y faire de cadence.”] This example is paired with one that begins in the same way but cadences in F Major, creating a full modulation (modulation entière).

[8.2], also employs a Roman-numeral strategy in which this foreign (fremd) chord is interpreted not in the prevailing key but instead in a closely related key. The labels IV (in F Major) and V (in A Minor) are juxtaposed:

bass: root:

6b D Bb IV of F

5n 3s E V [of A]

3n A I14

The keys F Major and A Minor are related in a sort of nahe Beziehung even if the roots Bb and E are not. The ear’s confidence in the progression results from a “certain elevated taste” (gewisser haut gouˆt).15 Thus Vogler justifies, through a shifting focus of the tonal center, the freedom of succession that Weber would later espouse: “there is not a single harmonic succession which we should be able absolutely and unconditionally to forbid.”16 Though Bb and E are “antipodes” (Antipoden), they follow one another without incident.17 Jelensperger concurs with Vogler’s perspective in an example whose captions assert that despite a “half modulation” to accommodate the foreign chord, the phrase as a whole is in a single key [8.6]. Around mid-century authors began to speak openly of the chord as an altered supertonic in the prevailing key. In his Esthétique musicale (1855), Durutte employs the symbols

207

208

Thinking About Harmony

bF 21

and

b5 b21

(conveying the sense of a first-inversion chord on the second scale degree of a minor key with lowered fundamental (bF), and a first-inversion chord on the lowered second scale degree of a major key with lowered fifth, respectively) to represent a harmony that is “very beautiful and often employed.”18 In 1862 Anatole Loquin relates, “this is, properly speaking, a diminished chord on the supertonic, in first-inversion, in which the supertonic pitch has been lowered by a half step.”19 Lobe took up his pen in battle against the trend: “In other words, Bb-D-F [in A Minor] is not Bb-D-F, but B-D-F!”20 A few years later George Alexander Macfarren defines it matter-of-factly as “a chromatic major common chord of which the minor 2nd of the key is the root, . . . employed with admirable effect in both minor and major keys.”21 Given such a variety of explanations, the status of the chord remained unsettled. John Stainer seems inclined to embrace all views simultaneously. Within the first two pages of his six-page exposition on the chord, he accomplishes all of the following: • Employs the term “chord of the flattened supertonic” • Derives the chord from scale degrees 1, 3, and 6 of the minor subdominant key • Employs the term “Neapolitan Sixth” • Resolves the chord to a cadential 64, to the dominant, and to tonic • Permits continuation from the dominant to either a major or a minor tonic • Derives the chord from two roots: for example, the minor seventh (F) and minor ninth (Ab) of G plus the minor ninth (Db) of C • Permits construction in any of its three positions.22 Accepting the Neapolitan chord and its succession to the dominant as normative events within a key encouraged the accommodation of other chords and chord successions as well. Loquin’s analytical notation in L’harmonie rendue claire et mise à la portée de tous les musiciens (1895) is designed to be minimally restrictive in this regard. He dispenses with traditional diatonic/chromatic distinctions altogether, naming chords according to their positions within the chromatic scale.23 In C Major his premier son, second son, and sixième son represent not C, D, and A (the first, second, and sixth diatonic pitches), but instead C, Db, and F (the first, second, and sixth chromatic pitches). In contrast to Sechter’s notion that chromaticism emanates from a diatonic foundation, Loquin’s terms and symbols grant no

Chromatic chords: major and minor

a

b

8.7a, b Loquin: L’harmonie rendue claire et mise à la portée de tous les musiciens (1895), pp. 27, 148. In Loquin’s system each chord type (taking into account both interval content and inversion) is assigned an individual number. (For example, his chart of “Chords containing three tones” consists of thirty entries labeled using numbers ranging from 16 through 60.) Such numbers appear below the chords in his analyses. Relations between adjacent chords are indicated by capital letters interspersed between these numbers. For example, the letter T corresponds to a descending perfect fifth, while the letter G corresponds to an ascending augmented fourth. (a) The number 35 corresponds to a minor triad in root position (état 1), while the number 36 corresponds to a major triad in first inversion (état 2). Loquin describes this succession as “From the premier son to the second son.” (Ascending chromatically from tonic, C = 1 and Db = 2.) (b) Additional numbers and letters account for the more varied chord types and relationships of this example, which demonstrates the use of the second son in root position.

favoritism to any pitch combination or succession beyond placing tonic (premier son), root position (état un), and major quality (1e espèce) ahead of all the remaining chordal permutations. His analyses are fascinating in their idiosyncrasy [8.7].

Expansive tendencies are apparent in both the music and in the analytical tools of the late nineteenth century. Though extreme, Loquin’s transformation of scale-step theory from a seven-entity into a twelve-entity enterprise asserts a universality that extends well beyond the Neapolitan. His second son is no mutant of a diatonic chord, but instead a legitimate, independent player in an analytical system no longer rigged to favor the diatonic. As with chord relations, likewise with key relations. With respect to modulation the eighteenth century was surprisingly accommodating in theory, though certainly composers at first did not utilize the options proposed as fully as their successors would. As we expand now beyond

209

210

Thinking About Harmony

modulation to closely related keys (our focus in chapter 6) to consider more distant relations, we should note especially any advice offered regarding which keys are more and which are less accessible, as well as regarding how their connection may be accomplished – directly, or via one or more intermediate keys.

Non-diatonic goals of modulation Introductory demonstrations of modulatory practice favored a small set of “closely related” keys: those whose pitch collections overlap with the original tonic’s to a large extent. Even so, the existence of “extraordinary” or “strange” modulation was acknowledged in the eighteenth century and its potentials explored. In his Vorgemach der musicalischen Composition Sorge quotes Andreas Werckmeister’s invocations of Nature and of God in defense against “eccentrics” (Kautze) who might lead from C to Fs.24 Though Kirnberger grumbled about how “unpleasant” and “contrary to our sensibilities”25 the rapid key changes of some of his contemporaries were, his three-tiered system nevertheless accommodates all possibilities:

Major keys (C Major as model) Direct modulations (in ranked order): From C Major:

G

a

e

d26

F

Distant modulations: First level: Second level:

From C Major via F Major: Bb From C Major via G Major: D From C Major via F Major and Bb Major: From C Major via G Major and D Major:

g b Eb c A fs

Modulations to remote keys, via direct modulation from the dominants of the original tonic’s directly-related keys: From G Major (dominant of C): From D Major (dominant of G): From E Major (dominant of a): From B Major (dominant of e): From A Major (dominant of d):

b D E B A

D fs fs cs b

A gs ds cs

b A E D

B Fs E

cs gs fs

The remaining remote keys achieved via modulation from one of these keys.

Chromatic chords: major and minor

Minor keys (A Minor as model) Direct modulations (in ranked order): From A Minor:

e

C

d

G27

F

Distant modulations: First level: Second level:

From A Minor via D Minor: g From A Minor via E Minor: b From A Minor via D Minor and G Minor: From A Minor via E Minor and B Minor:

Bb D c Eb fs A

Modulations to remote keys, via direct modulation from the dominants of the original tonic’s directly-related keys: From E Major (dominant of a): From B Major (dominant of e): From G Major (dominant of C): From A Major (dominant of d): From D Major (dominant of G):

E B b A D

fs cs D b fs

gs ds

A E

B Fs

cs gs

cs A

D b

E

fs

The remaining remote keys achieved via modulation from one of these keys.28 Kirnberger’s and similar schemes are pre-compositional plans, expedient routings for harmonic journeys either commonplace or exotic. Instruction manuals featured circular diagrams incorporating all the keys, inviting compositions that Kirnberger dismisses as “only a curiosity and . . . of no use otherwise.”29 Tables of twenty-three modulations from any tonic, such as that to which Daube devoted over seventy pages in his General-Baß in drey Accorden (1756), were published as well.30 Rarely are rankings such as Kirnberger’s invoked in a harmonic analysis. For example, though Weber occasionally displays a precise measure of the distance between adjacent tonics [6.6], he does not concurrently affirm that these are close relationships. Jelensperger does address this issue, drawing upon his own segmentation of all key relationships into three classes [8.8]. Momigny documents how, in modulating from C Major to Gs Minor, an intermediate key can mitigate to some extent the brusqueness of the transition [8.9]. The Gs of measure 1 is understood initially as a chromatic pitch within C Major. Only with the Cs of the following chord is the listener inclined to abandon C as tonic and to interpret the new chord in A Major. Likewise the As that follows is understood at first as a chromatic pitch

211

212

Thinking About Harmony

8.8 Jelensperger: L’harmonie au commencement du dix-neuvième siècle (1830, 21833), pp. 43–44 [Häser, p. 39.] This example displays the relationship between A Minor (la) and Ds Minor (res ), designated as a modulation of the third class (3.e ordre). Jelensperger’s division of key relationships into three classes is as follows:

from C Major: from C Minor:

First Class G F Ab aced Eb C Ab Bb G gf

Second Class Eb E fg F Db d bb

Third Class Db A B D Bb Fs b fs db bb ab eb D Gb B A E eb e a ab b db gb

In comparison with Kirnberger’s system, the relationship between C Major and C Minor is favored, as is the minor mode’s major dominant (G). Also more favored are the major mode’s flat submediant (Ab), major mediant (E), and minor subdominant (f). Conversely a number of relationships are positioned lower than in Kirnberger’s ranking. The modulation from A Minor to Ds Minor in Jelensperger’s example corresponds to the very last relationship displayed in his chart: C Minor to gb.

within A Major. But the Ds that follows opens the way for Gs Minor. To prevent offense, Momigny recommends that modulations of this nature be undertaken only at a very slow tempo.31 Finlay Dun, writing in The Harmonicon in 1829, agrees with Momigny’s procedure, though he does not share Momigny’s enthusiasm for the practice: Tables of modulation . . . often put a dangerous weapon in the hand of inexperience. The frequent use of abrupt and surprising modulation, has, for half a century past, been a besetting sin of ambitious composers; but in the present day, the rage for this species of writing, and also for chromatic harmonics and accompaniments, has infected the style and composition to a remarkable degree. This practice has undoubtedly been resorted to by the best masters, but only on fit occasions, and even then sparingly . . . In modulating from a tonic to a non-related or remote key – from C major to F-sharp major, for instance – the ear must be made to lose gradually the impression of the original key; and be led to a satisfactory reception of that which is to be established. This is effected by means of intermediate chords. These form the links which connect a series of keys and of musical ideas together. The art of modulation will be found, therefore, to consist in the selection and application of these intermediate chords.32

Chromatic chords: major and minor

8.9 Momigny: La seule vraie théorie de la musique [1821], p. 96. “In order to ascend an augmented fifth.” [“Pour monter d’une quinte superflue.”]

Poor Finlay Dun! Already in 1829 he was sounding the alarm, and yet he lived nearly a quarter century more, enduring further developments that some regarded as music’s future and others as its downfall. The Wagner/Brahms split was taking shape by 1860. Wagner’s successors eventually succeeded in abandoning tonality as Dun had known it, while Schenker declared Brahms to be the last of the great composers. But that takes us beyond our purview. Let us return to 1829. Rossini was the rage in Paris, where Jelensperger was writing his treatise on harmony in the early nineteenth century (L’harmonie au commencement du dix-neuvième siècle), for which he undertook a mammoth statistical analysis of key relationships in music recently performed in Paris, including the 1829 hit, Guillaume Tell.

Rossini and the major mediant In the ballet music from the first act of Rossini’s Guillaume Tell, two measures securely positioned in F Major are followed by two measures in which the pitch Cs occurs as a chord member [8.10]. Since it falls outside the diatonic pitch collection of F Major, analysts must decide whether to interpret Cs as a chromatic event within F Major or as a diatonic event in some other key. The pitch content of measure 3 and the first half of measure 4 invites modulation to D Minor, wherein Cs functions conventionally as leading tone. In Jelensperger’s notation, an analysis of these chords might appear as follows: . 5 1 5 ré A facile analysis of this sort employs a key shift as often as new pitch content warrants, resorting to an “altered-chord” (chromatic) explanation only when no diatonic collection proves accommodating.33

213

214

Thinking About Harmony

8.10 Rossini: Ballet music from Guillaume Tell (1829), Act I. Cs in measures 3 and 4 may or may not be grounds for a modulation. But if so, to what key: D Minor or A Major?

Rossini’s triumphs in Paris occurred just after Momigny’s pleas for the acceptance of a broad spectrum of chromatic and enharmonic pitches within a single key.34 In this view F Major is home both to C and to Cs, and thus modulation is not a mandatory response to a few chordal Css. Jelensperger’s notation, in which a right parenthesis indicates the shift of a chord’s quality to major, easily accommodates Rossini’s progression without a full-fledged modulation: . 3) 6 3) Fa In the context of Momigny’s fortified keys the considerable overlap of pitch content among the various keys requires a considered choice regarding which candidate key best supports the content of the music at hand. The pitches of measure 3 and the first half of measure 4 – A, Cs, D, E, F, and G – might represent not only D Minor (with leading tone Cs) or F Major (with chromatic Cs), but also A Major (with chromatic F and G). The choice of A Major for Rossini’s ballet music would give a plagal flavor to the cadence at measure 4. Using Jelensperger’s notation, in which a left parenthesis

Chromatic chords: major and minor

indicates the shift of a chord’s quality to minor, an analysis in A Major would appear as: . 1 (4 1 La Jelensperger’s L’harmonie au commencement du dix-neuvième siècle, issued in 1830, draws from his analysis of over 31,000 measures of music selected from compositions performed in Paris during the preceding fifty years: Haydn’s Creation, Mozart’s Don Giovanni, Beethoven’s Fifth Symphony, and works by Auber, Boieldieu, Cherubini, Hummel, Reicha, Spontini, and Weber. Rossini is represented by Guillaume Tell. Among the fruits of Jelensperger’s labors are two ordered lists of the twenty-four tonal regions – one list for compositions in a major key [8.11], another for those in a minor key. From these lists readers could determine which regions were employed frequently, and which rarely. The nebulous character of what Jelensperger measured compromises his enterprise, despite the formidable exertion. Though measures 3 and 4 of the ballet music from Guillaume Tell are among those that helped shape these statistics, it is impossible to reconstruct exactly how he interpreted them. Were they understood in the key of F Major (57.0%), D Minor (4.4%), or A Major (0.7%)? Among possible modulations from F Major, Jelensperger ranks D Minor as one of seven relationships of the “First Class,” while A Major is one of four relationships of the “Second Class” (outranking twelve relationships of the “Third Class”).35

The case for D Minor Choosing D Minor as a modulatory goal would be the logical course for musicians with a conservative outlook on chromaticism. Choron describes a progression akin to F–A7–D in measures 2 and 3 as viable only as a means of attaining the relative minor key.36 Lobe demonstrates that even when the A chord lacks a seventh it may target D Minor [8.12a]. Yet the D chord of measure 3 has a less robust impact than is typical of a tonic. If a modulation to D Minor in fact occurs, then dominant-to-tonic successions pervade the entire period: in F Major (measures 1, 2, 5, and 6), in D Minor (measure 3), and in C Major (measure 7). Had measure 4 continued the pattern of measure 3 (as in A7→d | G7→C), a transitory modulation to D Minor might be persuasive. As it stands measures 3 and 4 articulate a voice-leading formulation and metrical positioning that subordinate the

215

216

Thinking About Harmony

Jelensperger’s key symbol

I V  IV  III VI     VI III VII II  II  VII   I

V IV

Sample key name (based on F tonic)

Number of measures

F Major C Major F Minor Bb Major D Minor Ab Major Db Major G Minor A Minor C Minor Bb Minor D Major A Major Eb Major G Major Eb Minor Gb Major E Minor E Major Ab Minor Db Minor Fs Minor Cb Major B Minor

13844 2659 1260 1089 1075 946 790 625 392 369 317 209 171 117 81 62 61 48 42 41 37 28 16 4

Statistic converted into percent 57.0 10.6 5.2 4.5 4.4 3.9 3.3 2.6 1.6 1.5 1.3 0.9 0.7 0.5 0.3 0.3 0.3 0.2 0.2 0.2 0.2 0.1 0.1 0.0

8.11 Jelensperger: L’harmonie au commencement du dix-neuvième siècle (1830, 21833), p. 42 [Häser, p. 36] (cols. 1 and 3), with explanatory additions (cols. 2 and 4). Jelensperger’s statistics show that, at least in the repertoire that he analyzes and given the analytical methods that he employs, some of the traditionally close relationships, such as from F Major to G Minor or A Minor, occur with less frequency than some that involve fewer common tones, such as F Major to F Minor, Ab Major, or Db Major. (This data is reflected in his ranking of modulations [8.8].) A Roman numeral’s size distinguishes between the major and minor keys on that scale degree. A diagonal line through the numeral indicates a chromatically raised ( ) or lowered ( ) tonic. In Häser’s German translation the diagonal lines are replaced by acute and grave accents placed above the Roman numerals. The second and fourth columns amplify Jelensperger’s data. A typographical error of the French edition has been corrected: IV in the fifth row should read VI, as it does in the German edition.

Chromatic chords: major and minor

a

b

c

8.12 Lobe: Lehrbuch der musikalischen Komposition, vol. 1 (1850, 21858), pp. 241 and 244 (transposed). (a), (b) Cs might induce modulation to D Minor or to A Major. (c) This example appears without analysis. It demonstrates the sort of progression that Lobe’s opponents would analyze entirely within one key, regarding the second chord as “altered” (alterirt). (Perhaps hinting at the nationality of some of these opponents, Lobe here employs a term derived from the French word altérer – to adulterate or corrupt.) In Lobe’s view an A major chord is “foreign” (fremd) to F Major and requires the establishment of a temporary diatonic context: perhaps “d: 5” or “A: 1,” as in the A-Cs-E chords of (a) and (b).

a

b

8.13a Türk: Kurze Anweisung zum Generalbaßspielen (1791), p. 33 (transposed). 8.13b Schenker: Der freie Satz (1935, 21956), Anhang, p. 38, ex. 795 [Oster, Supplement, ex. 795] (transposed). In both the originals and in these transpositions, the prevailing key signatures suggest that the authors regard the chords that conclude their examples as tonic.

members of the D chord to those of the A chords that surround it [8.13], weakening the case for D Minor as tonic.

The Case for A Major Typically A Major would be confirmed via its dominant, as Lobe demonstrates [8.12b]. Here A Major is confirmed, if at all, via its minor subdominant.37 This reading of measures 3 and 4 is appealing, even if the initial tonic contains a lowered seventh (Gn), pulling towards A’s subdominant. Part of the appeal is that, unlike our reading in D Minor (above), here the D chord is dependent upon the A chord. Yet the D subdominant’s quality is minor. If the key is in fact A Major, then it is an A Major in which vestiges of its predecessor, F Major, linger.

217

218

Thinking About Harmony

8.14 Jelensperger: L’harmonie au commencement du dix-neuvième siècle (1830, 21833), p. 62 [Häser, p. 61] (transposed). This example contains, as does Rossini’s ballet music, a major triad on the initial tonic’s third scale degree. Jelensperger does not establish a diatonic context for the Cs in the final chord but instead retains continuity with the initial tonic, F. His label – 3) – indicates a major triad on the third scale degree of F Major. In both the French and German editions this chord’s sharp is positioned incorrectly beside the middle upper-staff notehead.

Gn–Fn in measure 3 (Violin II) reiterates a motive of measures 1 and 2, here extended a step to E in measure 4. Both versions could be regarded as truncations of longer, chord-defining descents: G–F

abbreviates A–G–F,

connecting scale degrees 3 and 1 of F Major G–F–E abbreviates A–G–F–E, connecting scale degrees 8 and 5 of A Major.38 This A major chord weakly asserts itself as a tonic. Both melodically and harmonically, its trappings remain allied to F Major.

The case for F Major Upon encountering an A major chord surrounded by diatonic chords of F Major, Lobe would modulate out of F and then back in again [8.12c]. In the same circumstance, Jelensperger likely would remain in F Major throughout [8.14]. By accepting chromatic pitches such as Cs as chord members within F Major, broader issues of phrase construction, such as the substitution of I–IIIs for the conventional I–V formula in Rossini’s phrase, come to the fore [8.15] and make Lobe’s painstaking scrutiny of diatonic pedigrees seem fussy. A frustrating aspect of harmonic analysis is the diversity of responses a passage may elicit among commentators. Some matters, such as Arabic versus Roman numerals, or all-capital Roman numerals versus a mix of

Chromatic chords: major and minor

a

b

c

8.15a A model for antecedent/consequent phrase construction. 8.15b A variant of 8.15a, corresponding to 8.10. 8.15c Pitches of 8.15b migrating to a lower range. Though an antecedent phrase will typically cadence on the dominant (a), the major mediant provides an interesting variant (b). The label IIIs (indicating a chord on the third scale degree with diatonic root and fifth and sharped third) possesses a neutrality that other labels imputing a dominant function (V of VI; D Minor: V) lack. In comparing (b) with Rossini’s composition, observe the migration of pitches to a lower register (c). The models’ foundational soprano and bass pitches are displayed in open noteheads.

capital and small Roman numerals, are of little significance. Yet it would seem that something as critical to the analytical process as the assessment of what key a passage is in ought to result in a unified response. But it does not. Lobe exuded an “I’m right” attitude every bit as potent as Momigny’s, and yet clearly they could not both be right on many areas of contention. (Of course there were no exchanges between them: Momigny died before Lobe’s first treatise appeared in 1850. Singled out on account of their especially vivid prose and the persistence of their endeavors, they serve as representatives of two opposing tendencies that persisted throughout the century.) We shift now from Paris to Vienna, where Schubert’s candle had gone out in 1828. On the one hand, we lament his early departure from life and the resultant loss of compositions from one of music’s most sensitive and prolific voices; on the other hand, one wonders if the profundity of his late works would have been achieved had he not been condemned by an incurable disease to torment, to unfulfilled interpersonal relationships, and to the certain prospect of a reduced lifespan. Though the brief illness that killed him did so unexpectedly, catching his friends by surprise,

219

220

Thinking About Harmony

Schubert knew that his health was beyond repair. The last years of his life were an uninterrupted winter journey. In chapter 2 we explored a Beethoven/Schubert connection. Passages from works by those composers were shown to be constructed along similar lines. Is it possible that Schubert also was an attentive reader of music theory treatises, using modest modulating examples from a work by Ignaz Ritter von Seyfried as the impetus for one of the Winterreise songs? Alas, that is another question that we cannot answer with certainty. In any event, let us consider the evidence.

Seyfried’s and Schubert’s modulations A year or two before the Vienna publisher Tobias Haslinger issued the first part of Schubert’s Winterreise in February 1827, he offered a weighty theoretical set called J. G. Albrechtsberger’s sämmtliche Schriften über Generalbaß, Harmonie-Lehre, und Tonsetzkunst, compiled by Albrechtsberger’s pupil, the distinguished Kapellmeister Ignaz Ritter von Seyfried. Albrechtsberger had died in his early seventies in 1809. It is probable that much of the pedagogical material on harmony for this work was constructed by Seyfried. “Auf dem Flusse,” the seventh lied in Winterreise, opens with a progression that leads from E Minor to a cadence in Ds Minor (measure 12) [8.16]. These keys are not closely related: their signatures differ by five sharps. In line with Kirnberger’s strategy, E Minor and Ds Minor find common ground in E Minor’s dominant, B major (measure 8).39 Schubert’s friend Anselm Hüttenbrenner, writing in 1854, recounts an exclamation made by Schubert during his study of scores by Händel: “Ah, what do you think of these for bold modulations! Such things could not have entered our heads even in a dream!”40 From a minor tonic the major key a whole step lower would be a natural and conventional goal [8.17]. Roots descending by perfect fifth (such as A–D–G in 8.17, measures 7–9) lead straightaway to a new and happier domain, one that might endure or might lead onward to the mediant. The sentiments of Schubert’s text do not warrant such a benign turn of events. Ds Minor, alien to E Minor, is a more suitable choice. The opening seven measures of Seyfried’s progression [8.17] closely resemble Schubert’s introduction, which in turn serves as model for the initial vocal/piano material (measures 5 through 8), where the accompanying bass twice ascends from E to G (inverting the descending sixth of measures 1 and 2) on its way to B, while the dissonant second Fs (from the E supertonic 65 of measure 3) occurs above the dominant root. The melodic

Chromatic chords: major and minor

You who so gaily rushed, you clear, turbulent river, How still you have become, you give no farewell!

8.16 Schubert: “Auf dem Flusse” from Winterreise, D. 911 (1827), mm. 1–13. Text by Wilhelm Müller.

8.17 Seyfried, ed.: J. G. Albrechtsberger’s sämmtliche Schriften [ca. 1825], vol. 1, p. 152. Intended by Seyfried to demonstrate modulation from A Minor to G Major, the example begins with a chord progression similar to that which opens Schubert’s “Auf dem Flusse.” Ludwig Stoffels, in Die Winterreise; Band 2: Die Lieder der ersten Abteilung (Bonn: Verlag für systematische Musikwissenschaft, 1991, p. 222), juxtaposes Schubert’s opening progression with an excerpt by G. P. Telemann. The Seyfried–Schubert connection is more compelling, however.

221

222

Thinking About Harmony

8.18 Seyfried, ed.: J. G. Albrechtsberger’s sämmtliche Schriften [ca. 1825], vol. 1, p. 162. This example is one of forty-six presented by Seyfried to demonstrate how, “through skillful turns,” modulation from C Major to all other keys and from C Minor to all other keys can be achieved.

a

b

8.19a Model for 8.16, mm. 7–12. 8.19b Model for 8.18 (transposed). Schubert’s composition (a) and Seyfried’s model (b) share a number of distinctive features.

third G–A–B is presented prominently: in the bass of measures 2–3 and in the vocal line of measures 5–6 and 7–8. Its chromaticized retrograde – bass B–As–Gs in measures 8–11 – triggers the modulation to Ds Minor, while its diatonic restoration (in both directions), embedded within the keyboard texture of measure 13, signals the return to E Minor. Seyfried had just published an extraordinary modulation from C Minor to B Minor [8.18]. Schubert’s move from E Minor to Ds Minor follows a very similar path [8.19]. In fact, Schubert’s is a bit tamer than Seyfried’s: Schubert employs diatonic Gs for Ds Minor’s IV7 chord (measure 11), proceeding by whole step to the dominant root (Gs–As); whereas Seyfried approaches the dominant via its leading tone. By consulting Seyfried’s model as a hypothetical plan for Schubert’s phrase, we appreciate how beautifully the word still is set. In tandem with extraordinary sehr leise and ppp performance indications, the passing note As connecting B and Gs stalls for two measures, representing the frozen, lifeless river.41

Chromatic chords: major and minor

8.20 Seyfried, ed.: J. G. Albrechtsberger’s sämmtliche Schriften [ca. 1825], vol. 1, p. 29 (transposed). Compare Seyfried’s E–A–Dn–B root progression with Schubert’s E–As–Ds–B (measures 1–7, 11, 12, and 13). Though Seyfried’s third chord, D Major, lies outside the diatonic realm of E Major, it is attained easily via a chain of descending fifths (E–A–D).

The foreignness of Ds Minor to E Minor may raise concerns regarding how or when tonic might return. Schubert’s strategy is quite simple, however: he does with Ds Minor exactly what was commonly done with D Major [8.20]. The subtonic-to-dominant succession requires that the leading tone replace the subtonic pitch. In E Minor, that would be followed by

B

D Ds

Fs Fs

A A

[8.20, measure 3] [8.20, measure 6].

Seyfried in fact supplies an intermediate step, B

D

Fs

[8.20, measure 4].

With Ds Minor instead of D Major, As is the pitch that must move, as in followed by

B

Ds Ds

Fs Fs

As B

[8.16, measure 12] [8.16, measure 13].

It is indeed tempting to speculate that Schubert modeled these measures of “Auf dem Flusse” on Seyfried’s examples. Perhaps that was the case. Yet perhaps Schubert and Seyfried shared a common source: the music performed in Vienna during the century’s opening decades, with Seyfried responding by assembling a theory text, now remembered principally by scholars, and Schubert by synthesizing what he saw and heard to create some of the most sublime works in the lieder repertoire. As our study draws to a close, we turn to two composers whose careers dominated the latter half of the nineteenth century: Wagner and Verdi. Though their most characteristic and celebrated works are from beyond the century’s midpoint (the topic for another book), we should find some rapport between their early style and the analytical apparatus developed for works of their immediate predecessors. First Wagner.

223

224

Thinking About Harmony

Readers likely need no reminder that Wagner’s music is saturated with chords that possess specific resolutional tendencies, generated through the chromatic modification of a triadic chord member, the addition of a dissonant pitch, or both; and that often a tendency chord’s expected resolution does not occur. Sometimes a tendency is generated even without dissonance. For example, a major chord rooted on F followed by a major chord rooted on B is so characteristic of bII–V that we may expect the progression to continue to E (I). An example from Lohengrin (to be explored below) contains such a succession, which in fact does not so resolve. Two contrasting analytical agendas will be juxtaposed in our discussion: first, a label- and modulation-intensive analysis that maximally accounts for each chord’s potential tendencies, pursued even when confirming resolutions do not occur; and second, a perspective that absorbs the chromaticism of individual chords within the broader C Major tonality and that asserts a chordal hierarchy resulting in a nonharmonic interpretation of some of the chords. Though a large share of the Wagner analysis published since the mid-nineteenth century pursues the first approach, I hope to show that the second approach also develops out of ideas current during the era of Wagnerian hegemony. Thus its further exploration and application is especially warranted.

A Wagnerian antipodal conundrum F and B are antipodes, maximally distant positions within the tonal system. That fact does not prevent an occasional interaction between them. They are co-members of two diatonic pitch collections: as 6 and 2 they appear together in A Minor’s supertonic chord, for example, and as 4 and 7 they appear together in C Major’s dominant seventh chord (often borrowed for use in C Minor as well).42 Beyond the diatonic realm their most common interaction occurs in the succession from the Neapolitan to the dominant: in E Major or E Minor, Neapolitan root F is followed by dominant root B.43 An antipodal succession – from F major to B major – occurs in “Athmest du nicht mit mir die süssen Düfte?” from Wagner’s Lohengrin [8.21, measures 4–6]. It attracts our attention not only because F and B are juxtaposed, but also because a B major chord occurs rarely in C Major. The various examples of historical analysis we have explored up to now fall into two basic categories: those that hold all chordal activity to be harmonically generated; and those that regard chordal activity as an interplay between harmonic and connective functions. In that chordal density and

Chromatic chords: major and minor

Don’t you breathe, with me, the sweet fragrances? Oh, how so pleasingly intoxicating to the senses they are! 8.21 Wagner: “Athmest du nicht mit mir die süssen Düfte?” from Lohengrin (1848), Act III, Scene 2.

chromatic daring in music increased as the nineteenth century progressed, advocates of the former viewpoint found themselves grasping for small spans of continuity, sometimes subdividing coherent-sounding phrases into an incoherent array of snippets in a range of keys. We will consider our example from Wagner first from this intensely harmonic perspective, but then will broaden our scope to include alternative explanations for some of the chordal behavior.

A harmony-intensive perspective Five of the excerpt’s eight measures contain at least one chromatic pitch. Gs in measure 2 and the first half of measure 3 has a destabilizing effect. Though measure 1’s V7 prepares for tonic C-E-G in measure 2, tonic’s G is elided, so that a stable tonic chord is absent at the outset of the progression. Because augmented chords such as C-E-Gs often progress via a descending-fifth root succession, in the manner of a dominant to tonic, some analysts would interpret C-E-Gs as Vs5 in F Major, rather than as Is5 in C Major. The context changes with Gs in the second half of measure 3, where an E7 chord targets A Minor. Consequently the E–F root succession from measure 3 into

225

226

Thinking About Harmony

measure 4 possesses a deceptive flavor, as V7–VI in A Minor.44 A consideration of the local harmonic implications of the first four chords reveals a quick turnover of keys, each of which is inaugurated by a dominant that does not resolve as expected: measure C Major: F Major: A Minor:

1 V7

2

3

4

V7

VI

Vs5

Ds and Fs in measure 6 result in a chord of major quality rooted on B, foreign both to C Major and to the G Major goal of the phrase. E is the most viable tonal center: measure E Major : Minor

3 In7s

4 5 6 nIIn5 ———— Vs5s

Here the antipodal F–B inhabits its most common chromatic context – that from Neapolitan to dominant. As we have seen, the Neapolitan was sometimes regarded as a modified subdominant (A-C-F as displacement of A-C-E). Thus its occurrence after a tonic (E) that takes on the character of the subdominant’s dominant (“V7 of IV”) is not too disconcerting. Of course, in a strictly diatonic perspective, neither the E nor the F chord would fall within either E Major or E Minor. The E chord instead might be regarded as V7 in E’s subdominant key, A, and the F chord as IV in E Minor’s submediant key, C Major. (Compare with 8.6.) Fs in measure 7 occurs in the context of a chromatic retreat: the Ds of measure 6 reverts to Dn in measure 7, and thus a diatonic connection between these two chords is elusive. Instead, dominants in the keys of E and G appear to be juxtaposed. (Compare with 6.12.) Alternatively, from a chromatic perspective the B major chord relates to what follows as a major mediant: measure G Major:

6 IIIs

7 V7

8 I

In all, the seven distinct harmonies of these eight measures might induce analysis within five keys: C Major, E Major , F Major, G Major, and A Minor. It Minor is time now to give the alternative perspective the attention it deserves.

A hierarchical harmonic perspective We saw earlier in this chapter how Rossini refrains from shaping an antecedent phrase within the familiar I–V framework. I–IIIs was proposed

Chromatic chords: major and minor

as a viable analysis for his alternative path. Deformations of conventional structural shapes are of course common in music, their incidence increasing during the nineteenth century. Wagner deforms the beginning, rather than the ending, of his phrase: C, E, and G never sound together. Nevertheless they constitute the governing tonic triad. Gs in measure 2 is a premature chromatic passing note that usurps the time normally allotted for a stable G. The label I – tonic in C Major – fully warrants use at this point (perhaps amended as Is5 to acknowledge the chromatic modification) even if a less conventional, less stable combination of pitches occurs in place of the legitimate tonic. Of course, music requires motion away from tonic. The most apposite succession to initiate the departure is I–IV, with roots related by descending fifth. That succession is often propelled through the insertion of a dissonance. Most often a minor seventh, targeting the subdominant’s third from above, is incorporated [6.20]. Yet the chromatic melody 5–s5–6, attaining the subdominant’s third from below, is also effective. In measure 2 of our excerpt, the initial consonant phase of this latter trajectory is elided, thereby extending the dissonant effect of s5. Regardless of how Wagner complicates matters, the essential harmonic content of measures 2 through 5 is encompassed by the root motion from C (measure 2) to F (measure 4). In a hierarchical comparison of C (measure 2) and E (measure 3), C emerges as the more potent chord. Of course in other contexts E-Gs-B-D will often proceed to A minor, and of course composers sometimes play with listeners’ expectations and pursue paths seldom taken. Yet in the context of these measures, the E7 chord serves as an expansion of the C tonic. The omission of the root, a feature of our very first example [1.1], allows Wagner to mitigate the abundant dissonance of the full chord (C-E-Gs-B-D). Louis and Thuille endorse this view in their analysis of one of their own chord progressions [8.22]. As Wagner well understood, IV often leads to V; the direct succession from IV to V is often expanded into IV–II–V [8.22]; and II, when preceding V, will often adopt the character of V’s dominant (IIs or “V of V”) [6.15a]. For the moment omitting consideration of measure 6, we observe that Wagner’s phrase proceeds from IV (measures 4 and 5) through II7s (measure 7) to V (measure 8). Perhaps not every pitch of the B major chord (measure 6) is harmonically generated. Sechter offers an instructive model [8.23]. Though he labels only the second example, both are intended to represent the root succession G–D in G Major. In each, the pitches at the second measure’s downbeat are not analyzed as an independent harmony. The 63 chord of 8.23a results from

227

228

Thinking About Harmony

8.22 Louis and Thuille: Harmonielehre ([1907], 41913), p. 256. This example’s first three measures and measures 2 through 8 of Wagner’s “Athmest du nicht” share a number of features. In the analysis, note especially the parenthetical I in the second half of measure 1, by which Louis and Thuille assert that the chord they label as III functions as an extension of the opening tonic, on the way to IV. Though the principal analysis is in C Major throughout, the perception of a region in A Minor is acknowledged by a secondary analysis within brackets. That view accords with the “Harmony-Intensive Perspective” for Wagner’s phrase provided above. (See page 226.)

a

b

8.23 Sechter: Die Grundsätze der musikalischen Komposition (1853–54), vol. 1, p. 49 (transposed). The B-D-Fs chord combines elements from the preceding (G-B-D) and following (D-Fs-A-C) harmonies.

7

a merger of elements from the preceding 53 and following 53 chords. Though it contains the same pitches as the mediant in G Major, Sechter does not acknowledge that role. The same outlook pertains to the 53 chord of 8.23b, which results from the merger of elements from the preceding 63 and fol6 lowing 43 chords. In both cases B functions as a suspension (Vorhalt), not as a chordal root. Returning to Wagner’s progression, first consider diatonic passing notes applied to a IV–IIs–V progression [8.24a, b]. (Because Wagner’s progression is not identical to Sechter’s, B is a suspension in 8.23a and a passing note in 8.24b.) Then consider that the bass fourth A–D can be broken up into the succession of a second and a third: A–B–D [8.24c]. (Sechter likewise offers either B or D as bass for his B-D-Fs chord, though when he places B in the bass he resolves it there [8.23a, b].) Then consider a chromatic expansion of the F–E–D descent, with Ds connecting E and D [8.24d].45 No Roman numeral appears below the B chord.46

Chromatic chords: major and minor

a

c

b

d

8.24 Analysis of 8.21, mm. 5–8. (a) A proposal for the skeletal progression of measures 5 through 8. (b) Passing notes fill in the descending spans from F to D (marked by an arrow) and from C to A (marked by a slur). Compare the second and third measures of this example with the second measure of 8.23a. (c) The 63 chord is reconfigured as a 53 chord. Compare with the second measure of 8.23b. (d) A chromatic passing note is inserted between E and D.

Summary The juxtaposition of these two perspectives is not intended as a competition in which one is deemed correct and the other rejected outright. Perhaps both are extreme in the pursuit of their convictions. The best analysis may reside somewhere in the middle. Yet the analysis that emanates from the hierarchical harmonic perspective is the more intriguing, in part because it serves as an antidote to what has been historically a pervasive application of a harmony-intensive methodology to Wagner’s music. The Louis and Thuille team and Sechter supply hints of an incisive, multi-layered manner of perception that should not be overlooked.

The juxtaposition of three root-position triads related by half-step – Db minor, D major, and Eb major – would have appeared odd to most musicians of the mid-nineteenth century. Yet that is what Verdi writes in a dramatic passage from his Luisa Miller. Admittedly exceptional, such an outré

229

230

Thinking About Harmony

event epitomizes the direction music was to head in the decades ahead, a time when the wisdom of past compositional practice was more and more neglected. Or perhaps extended: the parallel progression of thirds and sixths was routine, and we have seen how sequential progressions can mutate into what appears to be the parallel progression of perfect fifths [3.12]. Verdi’s progression possesses no such facile derivation, however. It is a raw and powerful upward thrust motivated by the dramatic moment. Context is a critical factor. As with Wagner’s insertion of a B major chord between F major and D major chords en route to G major, Verdi’s Db and Eb chords can absorb a connecting D major chord because Db and Eb are part of a broader harmonic initiative leading to Ab Major. Yet incomprehension of the motivation for these astonishing chordal progressions was an ever-present danger. Without a justifying context, the juxtaposition of antipodal F major and B major, or of half-step D major and Eb major chords, becomes quirky, a strain on the normative relationships that hold the tonal system together. What may make sense when one chord is subservient to another – when a passing or embellishing chord occurs within a conventional harmonic progression – becomes senseless when, in less skilled hands, all chords are treated as equals. Not only senseless, but also destructive. Weber’s and Weitzmann’s assertion that any chord may lead to any other chord ultimately was a curse upon tonality. The nod from the theoreticians gave composers free rein, and they indeed did succeed eventually in writing music devoid of tonality. Thus as we explore some vivid and daring writing by Verdi, we should focus not so much upon the admittedly unusual juxtaposition of triads related by half-step, but instead upon the fact that the boundary points of the motion, Db and Eb, serve to ground the event. Verdi succeeded in incorporating some novel local motions while leaving the broader tonal initiative intact.

A parallel progression in Verdi’s Luisa Miller Root-position chords in themselves offer no drama. Yet in the hands of a gifted composer, they can be set in contexts that give them an extraordinary power. A progression of three root-position chords related by half-step occurs in an excerpt from Verdi’s Luisa Miller [8.25, measures 68–74]. Miller, an honorable man, wants his daughter Luisa to marry for love. In fact, a recently arrived young man who calls himself “Carlo” has claimed her

Chromatic chords: major and minor

WURM: MILLER: WURM: MILLER: WURM: MILLER: WURM: MILLER: WURM: MILLER:

You feeble old man, your blind affection will cost you quite a lot. What do you mean? The favored fellow is duping you under a false guise. Is this true? You know about it? Hear this! He is haughty Walter’s son! Oh heavens! The son? Of your lord. Adieu. Wait! Did I make myself clear? (he exits) He has torn my heart!

8.25 Verdi: Luisa Miller (1849), Act I, mm. 56–84.

231

232

Thinking About Harmony

8.25 (cont.)

heart. Wurm, the intendant of Count Walter, the new ruler, has other ideas. He wants Luisa for himself and presses Miller to impose his parental will upon her. As our excerpt begins, Wurm advises Miller that it would be a grave error not to do so. He then reveals that the man Luisa loves is in fact Count Walter’s son, Rodolfo. Luisa’s inadvertent transgression of society’s rules horrifies Miller. Verdi must depict a radical transformation in Miller’s emotional state, from devoted and carefree father to a man facing a vexing challenge. Wurm

Chromatic chords: major and minor

8.25 (cont.)

must be menacing. His report of Rodolfo’s identity – injecting a horrendous conflict into what has been a cheerful opera thus far – must be set distinctively. Verdi conveys Miller’s dilemma by contrasting the two keys Db Major (established before our excerpt, when Miller tells Wurm that Luisa is free to pick her own husband) and Ab Major (established just after our excerpt, when Miller elaborates upon why his heart is broken) [8.26]. Eb (Ab’s dominant) occurs between these keys.

233

234

Thinking About Harmony

8.26 Tonal context for 8.25. The principal chords of measures 56 through 84 are displayed between the first and second bar lines. Db Major precedes these measures, while Ab Major follows them.

Measures 56 through 70 Even during the former count’s reign, Wurm had pestered Miller for Luisa’s hand. He becomes impatient listening to Miller again refuse to force Luisa on the matter. At first Miller’s key of Db Major persists, and Verdi’s harmonic support is prosaic. Yet soon Wurm’s intense feelings register more vibrantly through both a quickening of the tempo and a raising of the tonal center to the unexpected region of E Major (measure 61). E Major is the enharmonic equivalent of Fb Major, Db’s lowered mediant.47 Though Db Major and Fb Major are not especially closely related, they do hold a middle rank in charts of key relations such as those of Kirnberger and Jelensperger. (See p. 210 and 8.8, above.) Lobe displays the succession without fanfare [8.27a] (as does Weitzmann [7.25a]) and also presents an appropriate exit strategy [8.27b]. Yet as late as 1890 Jadassohn expresses reservations: “In the chord successions presented . . . the common tone [e.g., Ab/Gs in Verdi’s Db-F-Ab to E-Gs-B succession] appears suitable, as before, as a binding agent; however, many such relationships of chords from distantly related keys remain rather foreign, and the sudden succession of such chords does not always prove suitable for modulation.”48 In this passage from Verdi’s opera Fb Major well prepares what follows, however, since Db Minor (Cs Minor) supplants Db Major in measure 68 [8.27c], in preparation for Wurm’s impending revelation concerning “Carlo.”

Measures 71 through 74 Moving from Db (= Cs; measures 68 through 70) to Eb (measure 73), either as tonic to supertonic (in Db) or as subdominant to dominant (in Ab), was a routine labor for Verdi and other composers of his time, who understood that such successions pose a special danger of parallel fifths, which were generally proscribed [8.28]. Yet Verdi’s progression contains both parallel fifths and parallel octaves. Such breaking of the rules was not, however,

Chromatic chords: major and minor

a

b

c

8.27a, b Lobe: Lehrbuch der musikalischen Komposition, vol. 1 (1850, 21858), pp. 228–229 (transposed). 8.27c Analysis of 8.25, mm. 56–70. Observe that both of Lobe’s successions are present in Verdi’s chord progression of measures 56 through 70.

8.28 Momigny: Exposé succinct du seul systême musical qui soit vraiment fondé et complet [ca. 1809], plate 4, exs. 14, 15. Momigny contrasts the “destroyed unity” of parallel 53 chords with the “conserved unity” of parallel 63 chords.

altogether unheard of.49 Carl Weitzmann includes some of his own “Albumblätter zur Emancipation der Quinten” within his Die neue Harmonielehre im Streit mit der alten (1861) and quotes a famous passage from a Beethoven sonata in support of a more relaxed attitude towards such parallels [8.29]. Lobe likewise quotes the Beethoven example and adds one from Rossini’s Guillaume Tell, explaining: “Traditional theory – the strict style – would no doubt want to clutch its head with its hands for this disregard of its two fundamental prohibitions [against parallel fifths and parallel octaves]. But Aesthetics can triumphantly call attention to its

235

236

Thinking About Harmony

8.29 Beethoven: Sonata in C Major (“Waldstein”), op. 53 (1805), mvmt. 1, mm. 196–197, quoted in Weitzmann’s Harmoniesystem [1860], p. 5.

superiority to Theory, for this passage makes a wonderfully charming impression.”50 Thus inventively, though with precedents, Verdi simply hoists the previous chord up a half step when Wurm reveals Walter as father of Luisa’s suitor (measure 71), at the same time changing its mode to major [8.26]. Likewise when it sinks in to Miller that Carlo is in fact the Count’s son (figlio), another half-step jolt ensues (measure 73). This is not voiceleading in any conventional sense, but tone-painting. It is seismic composition. Without forewarning Miller finds himself elevated a few notches. For a while (measures 75 through 79) he fearfully awaits yet another tremor, which arrives (measure 80) just as he begins to assess the damage to his heart (cor). An astonishing effect, indeed; but not novel even for Verdi: he employs virtually the same material (likewise connecting Db and Eb) near the end of Macbeth (1847), when Macbeth learns to his horror that Birnam Wood is approaching.51 (An apparition had told him, “Macbeth shall never vanquished be until Great Birnam Wood . . . Shall come against him.”) As he calls out hastily for his arms and armor, the conventions of voice-leading go unheeded.

Measures 75 through 84 The final tremor (measure 80) is less destructive. Though Miller’s vocal line ascends yet another half step to Fb, the orchestral bass descends. The resulting diminished seventh chord intensifies the Eb dominant (prolonged since measure 73), affording some continuity after the preceding jolts. Though this dominant will resolve to Ab, that resolution does not occur in measure 83. Sechter provides some intriguing models that resemble Verdi’s strategy [8.30a, b]. Observe how Sechter’s analyses discount the first C. Though a C-Eb-G chord occurs, it is regarded as a passing phenomenon. Expanding upon Sechter’s model [8.30c], a neighboring note (Fb) in the soprano and a passing note (Ab) in the interior do not disturb the fundamental dominant

Chromatic chords: major and minor

a

b

c

8.30a, b Sechter: Die Grundsätze der musikalischen Komposition (1853–54), vol. 1, p. 95 (transposed and converted to major). 8.30c A variant of Sechter’s model, conforming to 8.25. (a) This example demonstrates the prolongation of Eb7 via a voice exchange between the chordal fifth and seventh (“während der Dauer desselben Fundamentes die Sept und Quint vertauscht werden”). Though Sechter regards the sixth (C) above the root (Eb) to be passing (“der durchgehenden Sext”), he nevertheless attempts to establish that the seventh (Db) has both a proper resolution (“eigentlichen . . . Auflösung”) [the C of the second measure] and a passing resolution (“durchgehende Auflösung”) [the C of the first measure]. (b) The principle demonstrated in 8.30a holds even when the passing motion occurs in the bass. (c) This model closely resembles not only those of Sechter, but also one by Vogler [7.15]. In Verdi’s score Eb serves as bass in measure 84: root-position V7 is a more forceful preparation for the ensuing Ab Major region than is V43.

prolongation. Just as Sechter refrains from indicating “C” below C-Eb-G, no “Ab” appears below C-Eb-Ab in the analysis. Ab Major arrives not as a firstinversion chord in mid-progression (measure 83), but only after the rootposition dominant and pausa lunga of measure 84.

237

8

Epilogue

The books may be robust or fragile. Sturdy pages refuse to lie flat: the binding has been little exercised of late. Brittle pages break apart when turned: to dust all shall return. The books assert that the musical experience – the composer’s conception, the performer’s interpretation, the listener’s perception – relies upon skill and insight, learned gradually over time and susceptible to enhancement at any age. Analytical strategies vie for consideration because interpretation and perception encompass more than what the composer’s meager instructions in a score convey. In the preceding pages we have explored many ideas that may enhance one’s relationship with music from the first half of the nineteenth century. Transmission of this music’s essence is more challenging today than in the past because most modern performers and listeners interact with countless styles from many lands and centuries. Schubert knew works of Bach, Mozart, Beethoven, Rossini. But not Josquin, Berlioz, Stravinsky, Carter. So what is the mind’s role in the musical experience? Whose minds from earlier times might one seek to emulate? Is it possible, or desirable, to filter out the many notions lacking relevance to this music that contribute to the outlook of the modern musician? Let us examine Schubert’s “Das Grab” (D. 330) with these questions in mind. Das Grab ist tief und stille, Und schauderhaft sein Rand, Es deckt mit schwarzen Hülle Ein unbekanntes Land.

The tomb is deep and silent, and horrible its edge, Its black exterior conceals an unknown land.

Das Lied der Nachtigallen Tönt nicht in seinem Schoss. Der Freundschaft Rosen fallen, Nur auf des Hügels Moos.

The nightingales’ song does not penetrate its case. Roses of friendship fall, but stop at the mound’s moss.

Verlassne Bräute ringen Umsonst die Hände wund, Der Waise Klagen dringen Nicht in der tiefe Grund.

Forsaken brides wring their hands in vain until raw, The orphan’s laments go unheard in the deep ground below.

Epilogue

Doch sonst an keinem Orte Wohnt die ersehnte Ruh, Nur durch die dunkle Pforte Geht man der Heimat zu.

Yet in no other place does the longed-for rest reside, Only through the dark portal does one reach home.

Das arme Herz, heinieden Von manchem Sturm bewegt, Erlangt den wahren Frieden Nur wo es nicht mehr schlägt.

The poor heart, here below tossed by many a storm, attains true peace only where it beats no more.

(Johann Gaudenz von Salis-Seewis)

The work’s mesmerizing power results in part from the almost archaic plainness of the chordal vocabulary. Dissonances are employed sparsely, and only a few embellishments (double lower neighbors in measures 3 and 7) impede the direct statement of the chordal content. The unhurried progression of fundamentals, considerably slower than the rate at which the individual chords follow one another, results in a ponderous mood well suited to a text that contemplates a tomb. After the initial tonic G chord, measure 1 and most of measure 2 evoke a single fundamental pitch, C, in a manner reminiscent of the opening measures of Beethoven’s String Quartet in C Minor, op. 59, no. 3 [5.14], where fundamental D holds sway. Schubert’s application of the omnibus principle, like Beethoven’s, is deformed: becomes

239

240

Thinking About Harmony

Instead of ascending a third, the bass descends a sixth. Thus Schubert employs bass G in the second chord as a stepping stone to the lower register. (In effect, the chord G-G-Bb-D is an “inversion” of the passing 64 chord D-G-Bb-D. Compare with 5.16.) Four processes unfold concurrently within these measures: conversion from C minor to C major, conversion from root position to first inversion, conversion from a state of consonance (53) to a state of dissonance (65), and transfer of the bass to a lower register. Who would accuse Schubert of playing a mehrdeutig game with us in such a solemn context? The Eb7 chord of measure 2 does not herald the key of Ab Major: as was also the case in the Beethoven quartet, the internal region of a prolongation may include pitch combinations that in other contexts would convey a different intent. Indeed composers sometimes tap such potential ambiguity. But when they do not, an analysis that churns out labels corresponding to the road not taken (as Vogler, for example, generally does) is misleading, and by proffering such an analysis one may stifle further inquiry in quest of a better one. If the performers (here Schubert intends a chorus of male singers) agree upon and endeavor to realize this interpretation of these measures, then the interface between their minds and their sound production should focus upon the endpoints of the prolongation. C is a defining presence for half a measure. Then C is absent. Finally C returns, in an altered context. The upper tenor line (Eb to C) outlines the C minor triad’s lower third, its internal pitches inducing a tension released only when goal pitch C arrives (at which point another tension – Bb – intervenes). The lower bass line (C to En) covers En a more tortuous route, and an additional danger awaits because the G chord of measure 1 may tend to reignite a sense of tonic, as a restoration of the preceding upbeat chord. Instead the line should be projected as extending through the G of measure 1, rather than to it. (Recall Koch’s juxtaposition of C-E-G in diverse roles in 2.11.) The lower tenor line moves from C to Bb. At first Bb resides in a consonant context, but by the middle of measure 2 bass En converts it into a downward-tending dissonance, fulfilled when Bb resolves En to AF at the measure’s end. (Recall the importance of such resolutions to Fétis’s conception of tonalité [7.7].) The upper bass line promotes continuity, with a stable G throughout. If the performers achieve these goals, then the listener indeed may perceive this passage in the way they intend. If the performers fail, or if they have developed no coherent conception for the passage, then the listener is left in the lurch and indeed in default may make a sort of sense of the passage that corresponds to the analysis g:

iv

i

Ab: V7

F: V65.

Epilogue

Three keys within two measures would poorly correlate with the text, which invokes the tomb’s quietude. Instead, a C minor – C major transformation emphasizes the inevitability of the descending-fifths progression in this context. C major, with minor seventh, leads us onward to F. If the F chord that fulfills C’s descending-fifth tendency in measure 2 at first seems fleeting, with patience the listener may perceive its prolongation through measures 3 and 4. (The F–Bb–C–F progression resembles one explored by Sechter [5.9d].) The Bb chord that, at a broader structural level, we expect to succeed F will duly arrive – later. The Bb chord of measure 3 is not that Bb chord; it instead falls within the domain of F. Though the ear often relies on parallelisms when interpreting a musical structure, the upbeat|downbeat relationships at measures 0|1 and 2|3 turn out not to represent similar structural events. Bass G–C and F–Bb function in different tonal planes: G, C, and F are components of the broad chain of descending fifths, whereas this Bb is not. Performers come to understand that, since tonal music employs only twelve pitch classes, inevitably various combinations and successions of pitches take on different meanings in different contexts. In isolation the F and Bb chords at measures 2|3 would likely be understood as V–I in Bb Major. Yet the prevailing context counters that interpretation: the presence of En in measures 2 and 3 suggests that F serves as the local tonal center, and thus F–Bb represents I–IV. The local bass progression F–Bb–C–F is an instance of perhaps the most pervasive of all harmonic motions, one that Halm dissects carefully [6.17]. In this environment the upper tenor line’s D should be presented not as a goal, but as a diversion. D temporarily displaces C, whose priority stems from its role as fifth in the prolonged F chord. Though the Bb in the lower bass line is the lowest pitch in the composition, it is an internal component of a progression that continues onward to F at the downbeat of measure 4, a goal punctuated not only by a comma or a period in the text, but also by the work’s only rest. This F, a reiteration of the one in measure 2, functions at a foundational level. The intervening Bb and C should come across as subservient. Throughout virtually the entire history of harmonic analysis – recall Lampe’s pioneering efforts [1.1] in 1737 – a special relationship has prevailed between the chords G-B-D-F and B-D-F, as well as their equivalents in the other keys. Lampe asserts that the chords are functionally equivalent: one merely abbreviates the other. From fundamental F (measures 2 through 4), we would expect to descend a fifth to Bb. Schubert accomplishes this in the second half of measure 5 using the pitches D-F-Ab. This dissonant chord (like the Bb seventh chord that it represents) heralds the Eb chord that

241

242

Thinking About Harmony

follows in measure 6. A similar third-relationship binds F-A-C (measure 4) and Ab-C-Eb (measure 5). Here three transformations occur simultaneously: a seventh is added to F-A-C

F-A-C-Eb;

the third is lowered, conforming to the key of the goal chord, Eb Major in measure 6

F-Ab-C-Eb;

the root is omitted

and

Ab-C-Eb.

(Recall that Louis and Thuille employ parenthesized Roman numerals in the context of both upper- and lower-third chords in 8.22.) Thus both chords of measure 5 represent other chords: what may seem like (and what Vogler and others would analyze literally as) the fundamental succession Ab–D instead represents the fundamental succession F–Bb. Chromaticism helps propel the performance of this passage. Here the inner line A–Ab–G, like Eb–D–Db–C in measures 1 and 2, gives direction to the connection between the F chord (measure 4) and the Eb chord (measure 6). If the upper tenor Eb that begins measure 5 indeed is derived from an incomplete F7 chord, as proposed, then it should be sung with dissonant conviction, and its resolution on D, accomplished in the second tenor line, should be felt, even as F rises above it. In the lower bass line the goal pitch Eb (measure 6) continues the descending stepwise thrust that proceeds from the first chord. Whereas a normative chain of fifths might transpire as G

C → F

Bb → Eb . . .,

here the Bb (measure 5) is felt but not heard, and bass F extends through to the Eb (with an upper-third detour to Ab and back). The arrows above coincide with dissonances resolving to consonances. 7 C ’s third is modified to achieve a “dominant seventh” character that leads effectively to F, whereas Bb7’s seventh is lowered (and root omitted) in preparation for Eb. The next cycle, A → D, does not so readily accommodate such modification. G Minor’s diatonic A-C-Eb is a diminished triad, doubly deficient in forward thrust compared to A-Cs-En. In addition its A is a diminished, rather than a perfect, fifth from the preceding fundamental, Eb at the downbeat of measure 6. Here Schubert simply sidesteps this problematic chord, instead employing its upper third, C-Eb-G. Without the halfstep resolution of Cs to D (downbeat of measure 7), the pattern of measure 2 (bass En–F) and measures 5|6 (alto D–Eb) is broken. Yet the diatonic fourth scale degree (here C) has its own special aura as precursor of the dominant:

Epilogue

the affiliation of C-Eb-G, C-Eb-A, and C-Eb-G-A is as old as Rameau’s notions of accord de la grande sixte and double emploi (pp. 22–23). Even without root A, G at the end of measure 6 behaves as a chordal seventh, resolving to Fs on the following downbeat. In addition, the C chord is the focus for a diminished seventh chord on Bn (measure 6), in the manner of Weitzmann’s Vorhalte [7.22b]. If Schubert finds Eb–A so awkward as a descending fifth that he replaces A by its upper third, C, then a similar upper third may supplant the Eb: G7 (with a Rameauean substitution of Ab for G, in the manner of 7.2) heralds C. The link in the chain of fifths that might have occurred at the end of measure 6 is the most awkward in the diatonic system. Performers who can imagine what Schubert might have written instead of C-Eb-G are in a position to gauge the emotional temperature of his concluding measures. The dissonant A-C-Eb is shunned, as is the potent chromatic substitution Ab-CEb, the Neapolitan. The sunny A-Cs-En is likewise avoided. Schubert’s C-EbG is decidedly plain in comparison, and in the context of a dominant without seventh (measure 7) and a tonic with raised third (measure 8) it instills a sense of peace and resignation. Yet if the harmonic aspect here is natural and sweet, the melodic aspect is disconcerting. The melody has to a large extent been engaged in a traversal of the path from 5 (measure 0) to 8 (measure 6) and back to 5 (measure 8). Neither the persistent D of the upper tenor line (measures 7 and 8) nor the more melodious A–Bn below it heeds the protocol of closure on 1. Perhaps Schubert here wishes to convey that in the “unknown land” (unbekanntes Land) that, according to the text’s theological underpinnings, one inhabits after death (a land generally regarded as upward, heavenward) a descent to the terrestrial 1 is no longer feasible. Whereas most melodies traverse the span of 31 or 51 (as Schenker observed), Schubert here treads 58. Death is not a termination, but the onset of the infinite. Though our exploration now comes to an end, this termination likewise may mark the onset of ever more dynamic and insightful study for readers who have found value in the agenda we have pursued. The spectacular body of music that has been bequeathed to us will become ever more inspiring and meaningful to all who give it their devoted and careful attention.

243

Biographies of music theorists

Johann Georg Albrechtsberger (1736–1809) In addition to his reputation as one of Europe’s leading church musicians and organists, Albrechtsberger’s skill as a teacher made his Vienna address a destination for composers, including Beethoven. During the 1790s he codified his conservative perspective in treatises on counterpoint and thoroughbass, including Kurzgefaßte Methode den Generabaß zu erlernen (Simplified Method for Learning Thoroughbass, Vienna: Artariatca 1791). (Lester (1992) questions whether Albrechtsberger actually wrote the thoroughbass manuals that circulated under his name.) A posthumous compilation by one of his students had a wider impact during the nineteenth century: J. G. Albrechtsberger’s sämmtliche Schriften über Generalbaß, Harmonie-Lehre, und Tonsetzkunst (J. G. Albrechtsberger’s Collected Writings on Thoroughbass, Harmony, and Composition, ed. I. R. von Seyfried, 3 vols., Vienna: Haslinger, [ca. 1825–26], various French and English translations). Its first volume addresses harmony more thoroughly than did any of the earlier works, leading one to wonder whether Seyfried incorporated materials from his lessons with Albrechtsberger or instead supplemented his teacher’s method on his own initiative (with Marpurg’s distillation of Rameau being a likely source). The volume offers a particularly rich treatment of modulation. Jean le Rond d’Alembert (1717–1783) Though not initially inclined towards music, d’Alembert’s prominent position within the Parisian scientific community led him to review one of Rameau’s papers, later published as Démonstration du principe de l’harmonie (Paris: Durand, Pissot, 1750). His enthusiasm for Rameau’s ideas inspired further study and an attempt at integration with his own scientific perspective, resulting in Élémens de musique, théorique et pratique, suivant les principes de M. Rameau (The Elements of Music, Theoretical and Practical, According to the Principles of Rameau, Paris: David l’aîné, Le Breton, Durand, 1752, trans. F. W. Marpurg as Systematische Einleitung in die musicalische Setzkunst, nach den Lehrsätzen des Herrn Rameau, Leipzig:

Biographies of music theorists

Breitkopf, 1757). On the one hand, d’Alembert irons out some of the inconsistencies and excesses of Rameau’s original writings, giving his work great clarity. On the other hand, the transfer of authorship from a master musician to a scientist resulted in some loss of insight. For better or for worse, the Élémens became the primary source for information concerning Rameau’s theories both in France and, via Marpurg’s translation, in Germany. In addition, the “Music” article in the 1784 edition of the Encyclopaedia Britannica incorporates Thomas Blakelock’s partial English translation of d’Alembert’s work. Relations between Rameau and d’Alembert turned sour during the 1750s, when d’Alembert and Diderot were engaged in editing the Encyclopédie, ou dictionnaire raisonné des sciences, des arts et des métiers (1751–65), whose music articles, authored by Jean-Jacques Rousseau, displeased Rameau and led to several published diatribes. This induced d’Alembert to write a long “Discours préliminaire” for the second edition of the Élémens (Lyon: Bruyset, 1762). Johann Anton André (1775–1842) In a life that encompassed composing, teaching, and running the family publishing firm, André is especially noted for his scholarship and editorial work relating to the Mozart-Nachlass, which he acquired from the composer’s widow. Though left unfinished at his death, a grand pedagogical project, Lehrbuch der Tonse[t]zkunst (Textbook on Composition, vol. 1, Offenbach: André, 1832), commences with a volume on harmony. André offers a detailed accounting of the various chords employed in the music of his time. His analytical notation indicates chordal quality and inventories the dissonance content (through the thirteenth) but offers no information concerning each chord’s role within its tonal context. Giorgio Antoniotto (ca. 1692–ca. 1776) Antoniotto, a native of Milan, spent a portion of his adult life in London, where his theoretical ideas found their way into print. L’arte armonica, or, A Treatise on the Composition of Musick (2 vols., London: Johnson, 1760) is rich in examples of chord progressions, all of which utilize root successions of thirds and fifths (or their enharmonic equivalents) only. Sequences, both diatonic and chromatic, are a topic of particular fascination for Antoniotto. Among his models, several that traverse the octave in equal subdivisions are particularly noteworthy: via six major seconds (C A D B E Cs Fs Ds Ab F Bb G C), four minor thirds (C E A Cs Fs Bb Eb G C), or three major thirds

245

246

Biographies of music theorists

(C Eb Ab B E G C). Though figured-bass numbers are employed abundantly, no additional symbols indicate the scale degrees of the chordal roots. Bonifazio Asioli (1769–1832) The appointment of Asioli, a prominent composer in northern Italy during the Napoleonic period, as director and professor of composition at the newly founded Milan Conservatory coincides with the emergence of several pedagogical and theoretical works from his pen. His Trattato d’armonia e d’accompagnamento (Treatise on Harmony and Accompaniment, Milan: Ricordi, [1813]) offers a vigorous accounting of chord progression from a scale-step perspective. Both Arabic numerals and capital letters (T for Tonica, P for Producente [dominant], and S for Sensibile [leading tone]) abound below the bass pitches of his examples. Where warranted (for example, in the chord Ab-Eb-Fs-C in C Major) the raised fourth scale degree is indicated as the root, via the label ×4.a The analyses employ frequent shifts of tonal center, though these shifts are not announced. T may appear below a C major chord in one measure and below A minor and G major chords in succeeding measures (each T preceded by its P or S). T appears below what is now often called the “cadential 64” as well. Thus ×4.a proceeds sometimes to P and sometimes to T. Asioli continued his theoretical writings even after he was dismissed from the Conservatory due to the changed political climate. Carl Philipp Emanuel Bach (1714–1788) In the service of Frederick the Great in Berlin, Bach continued in his great father’s footsteps as a master of keyboard performance and composition. His pedagogical interests, unlike Johann Sebastian’s, extended to include the writing of an extensive and superlative manual for keyboardists, Versuch über die wahre Art das Clavier zu spielen (2 vols., Berlin: Bach, 1753–62, trans. W. J. Mitchell as Essay on the True Art of Playing Keyboard Instruments, New York: Norton, 1949). In addition to exploring all aspects of the keyboardist’s technique, Bach delves into the intricacies of voice-leading and dissonance treatment in a wide variety of chordal contexts, which he organizes according to the figured-bass numbers. He also provides extensive commentary on embellishment and an introduction to improvisation. Harmonic analysis per se is not addressed, though some later authors (notably Schenker) regarded Bach’s Versuch as an ideal preparation for that study. Haydn and Beethoven are among the composers whose training and teaching relied upon Bach’s work.

Biographies of music theorists

F.-B. Henri-Montan Berton (1767–1844) Admired in his day as a composer of operas, Berton served for nearly fifty years on the faculty of the Paris Conservatory, teaching both harmony and composition. His Traité d’harmonie (Treatise on Harmony, Paris: Duhan, [1815]) contains what had by this time become traditional fare regarding harmony, sequences, cadences, counterpoint, and phrase structure. What makes his work unique is its mammoth (three-volume) supplement, a “Dictionnaire des accords” filled with two-chord successions that are either approved of, rejected, or allowed only in certain contexts. The genealogical tree of chords (displayed in a diagram at the outset of the Traité) has three branches. Branch A includes the triad and its inversions, which may incorporate various displacements (of the third by the fourth and of the octave by the ninth). Twelve chords are displayed. Branch B adds a seventh. Eight chords are displayed. Branch C adds both a seventh and a ninth. Again eight chords are displayed. Adding the eleventh and thirteenth chords, in all Berton considers thirty chords. He presents all possible two-chord permutations either with stationary bass or with bass ascending or descending by second, third, or fourth – in all, an astonishing and daunting compilation of over 6,000 successions. Jean Laurent de Béthizy (1702–1781) The French theorist and composer Béthizy, a student of Rameau, propagated his teacher’s method in his Exposition de la théorie et de la pratique de la musique (An Account of the Theory and Practice of Music, Paris: Lambert, 1754). The work covers a wide range of topics, with emphasis on clarity. Rameau’s fundamental bass is displayed in a number of examples, while his principle of supposition is extended to the thirteenth. Béthizy harshly criticized d’Alembert’s account of Rameau’s ideas (Élémens de musique), which preceded the Exposition by two years. Louis-Charles Bordier (1700–1764) The French musician Bordier’s posthumous Traité de composition (Treatise on Composition, Paris: Boüin, [ca. 1770]) is a brief work that relies on Rameau’s writings for its terminology and procedures. It features examples of fundamental bass below some demonstration chord progressions. In addition Bordier offers commentary on figured-bass usage.

247

248

Biographies of music theorists

John Callcott (1766–1821) Callcott’s career as a composer, organist, and author transpired in London. His A Musical Grammar (London: Birchall, 1806) proceeds from music fundamentals through melody to harmony, along the way introducing a wide range of terms, many of which became standard musical terminology in English. It is here, for example, that one first encounters the terms French Sixth (because it is “only found in the Theory of Rameau”) and German Sixth (because Graun used it “with great effect”). (The term Italian Sixth appears in eighteenth-century writings, though with a more inclusive meaning than Callcott gives it.) The text is illustrated through numerous examples from the music literature (Händel, Corelli, Pleyel, etc.), and Callcott frequently cites the opinions of learned authorities. In fact, he provides an impressive list of works consulted. Charles-Simon Catel (1773–1830) Catel began his teaching career in Paris and was among the founding instructors of the Conservatoire National de Musique et de Déclamation in 1795. A committee seeking to bring some order to the teaching of music theory there adopted his Traité d’harmonie (Treatise on Harmony, Paris: Le Roy, An X [1802]). Concise and practical, the work is grounded upon a set of eight “simple chords” (triads through ninth chords), which are subject to modifications such as suspensions to form a wide range of “compound chords.” (The latter category is akin to Kirnberger’s chords with incidental dissonances.) Voice-leading, cadences, and modulation (to all keys) are introduced at a fundamental level. The Traité appeared in German, Italian, and English translations by mid-century, the latter both in London and, under Lowell Mason’s editorship, in Boston. F. T. Alphonso Chaluz de Vernevil (active ca. 1820–1850) See José Joaquín de Virués y Spínola. Alexandre-Étienne Choron (1771–1834) With lively interests in the study of older music and of works by German and Italian theorists, Choron’s writings distinguish themselves from those of other Parisian theorists more firmly entrenched in the avant-garde. The harmony segment in Principes d’accompagnement des écoles d’Italie

Biographies of music theorists

(Principles of Accompaniment According to the Italian Schools, Paris: Imbault, [1804]) seems amateurish, though much improvement can be noted in his second traversal of the topic, in Principes de composition des écoles d’Italie (Principles of Composition According to the Italian Schools, 3 vols., Paris: Le Duc, [1809]). His chord types extend to the thirteenth, and his introduction to modulation includes over one hundred samples called “Tours de clavier.” Choron coined the term tonalité, which was embraced by Fétis, whose historical perspective was strongly influenced by Choron. Raymond Hippolyte Colet (1808/1809–after 1850) A student of Reicha at the Paris Conservatory, Colet later joined that institution’s theory faculty. One product of his pedagogical activities is La panharmonie musicale, ou Cours complet de composition théorique et pratique (Musical Panharmony, or Comprehensive Course on Composition, Both Theoretical and Practical, Paris: Pacini, 1837), a work whose harmonic component is in the tradition of Reicha and Jelensperger. The work also treats contrapuntal techniques and form. William Crotch (1775–1847) The English child prodigy Crotch developed into a respected composer, organist, and lecturer. His Elements of Musical Composition (London: Longman, 1812, 21833) offers a unique analytical methodology based on solfa syllables. Though his commentary on chord succession may be cumbersome (“The triad of Fa may be succeeded by that of Do. The triad of Do may be succeeded by that of Sol . . .”), his pronouncements are sensible, useful to beginners, and amplified by nuanced discussions of style. The analysis of modulation employs “doubtful” chords, which are simultaneously analyzed in two keys. For example, in the progression of the triads C–F–G–C–D–G (all of major quality), the first four represent do fa sol do in C Major, while the last four represent the same progression in G Major. Thus the middle two chords are “doubtful.” An examination of Crotch’s numerous brief analytical examples reveals a progressive stance on passing chords (for example, not every chord in a stepwise progression of 63 chords is given a label), a subdominant perspective on the Neapolitan chord, and a dominant interpretation of the cadential 64 chord. Crotch’s development of analytical procedures here is on a par with Vogler’s in Germany. However, Vogler’s Roman-numeral system (expanded by Weber) became a mainstream methodology while Crotch’s sol-fa syllables never found a wider following.

249

250

Biographies of music theorists

Carl Czerny (1791–1857) As Beethoven’s foremost pupil and Liszt’s principal teacher in Vienna, Czerny’s name would be remembered even without the enduring legacy of his keyboard exercises. His extensive corpus of original compositions has fared less well. Music scholars might find his theoretical magnum opus worthy of resuscitation: his Schule der praktischen Tonsetzkunst (3 vols., Bonn: Simrock, [ca. 1849–50?], trans. J. Bishop as School of Practical Composition, 3 vols., London: Cocks, [ca. 1848?]), an extensive treatise on musical forms, discussed from a theme-oriented perspective and accompanied by abundant examples from the music literature. The range of composers from whose works Czerny draws is impressive, though Mozart and Beethoven predominate. Though harmonic analysis per se is not a topic of the work, Czerny offers some highly intriguing examples in which the embellishment-filled textures of compositions are reduced down to their essential block-chord progressions. These examples provide unique early documentation regarding how elite musicians of the nineteenth century came to terms with the music then being created. Johann Friedrich Daube (ca. 1730–1797) Daube’s treatment of thoroughbass reveals a novel harmonic perspective, perhaps derived indirectly from some of Rameau’s ideas. Even the title of his first work, General-Baß in drey Accorden (Thoroughbass in Three Chords, Leipzig: Andrä, 1756, trans. B. Wallace as “J. F. Daube’s General-Bass in drey Accorden (1756): A Translation and Commentary,” PhD diss., University of North Texas, 1983), provides an indication that a simplified system, based on three chords, is offered. In C Major, these chords are C-E-G, F-A-C-D, and GB-D-F. (Not every pitch need appear in every instance. For example, F-A-C and F-A-D are realizations of the same harmonic function.) After working as a lutenist and composer in several German cities, Daube moved to Vienna, where he prepared a new version of his thoroughbass pedagogy, Der musikalische Dilettant: Eine Abhandlung des Generalbasses (The Musical Dilettante: A Treatise on Thoroughbass, 2 vols., Vienna: Kurtzböck, 1770–71), noteworthy for its use of the Arabic numerals 1, 2, and 3 for his three chords and for demonstrations of their employment in modulatory contexts. Similar numerical analysis appears on a few occasions in his later writings as well: Der musikalische Dilettant: Eine Abhandlung der Komposition (The Musical Dilettante: A Treatise on Composition, Vienna: Edler von Trattner, 1773, trans. S. P. Snook as The Musical Dilettante, Cambridge:

Biographies of music theorists

Cambridge University Press, 1992) and Anleitung zur Erfindung der Melodie (Instruction for the Invention of Melody, 2 vols., Vienna: Christian Gottlob Täubel, 1797 (vol. 1), Vienna: In Commission der Hochenleitterschen Buchhandlung, 1798 (vol. 2)). Alfred Day (1810–1849) In his Treatise on Harmony (London, Cramer & Beale, 1845), Day offers British musicians a derivation of harmonies that shares features with those of Koch and Portmann on the continent from around the turn of the century. Foundational chords extending beyond the boundary of the octave – even as far as the thirteenth – are regarded as the source for a wide range of chordal possibilities. Three such chords ground Day’s system: major chords rooted on tonic, dominant, and supertonic. Other chords are derivative. The subdominant chord is built from the dominant’s seventh, ninth, and eleventh, for example. Day’s treatise contains numerous brief progressions, some highly chromatic. Though he does not indicate the root pitch of each chord, he does usually provide an indication of each chord’s inversion (using alphabet letters: A = root position, B = first inversion, etc.). Macfarren was an early champion of Day’s treatise, and some of its concepts are echoed in works by Ouseley, Stainer, and Prout. Siegfried Dehn (1799–1858) Dehn’s avocational interest in music, pursued in tandem with diplomatic service in Berlin, eventually became the focus of his professional life. His scholarly proclivities were well suited to his roles as librarian of the royal music collection and editor of both print and score publications, including works by J. S. Bach. Esteemed as a teacher, Dehn developed his perspective on harmony in Theoretisch-praktische Harmonielehre (Theoretical and Practical Instruction in Harmony, Berlin: Thome, 1840), a work that establishes a strong historical foundation – Boethius, Franco of Cologne, Lassus, and Palestrina being among the authorities cited. Eventually the work enters distinctly modern territory, with discussions of topics such as the augmented sixth chords, progressions of diminished seventh chords, the deceptive resolution of dissonant chords, and enharmonic reinterpretation. Though Gottfried Weber is an influence, Dehn eschews Weber’s rootoriented practice of Roman-numeral analysis. His numerals instead correspond to bass pitches. Another Berlin theorist, Adolf Bernhard Marx,

251

252

Biographies of music theorists

attempted to expose the “gaping holes” in Dehn’s harmony system in Die alte Musiklehre im Streit mit unserer Zeit (1841). Finlay Dun (1795–1853) Active as a composer and vocal teacher in Edinburgh, Dun stepped onto the music theory stage in exasperation, concerned that Friedrich Schneider’s text on harmony, a work recently translated from German into English, was leading young composers down the wrong path, particularly with regard to modulatory techniques. In “On the Elements of Musical Harmony and Composition” (The Harmonicon, 1829), Dun offers some choice observations: while acknowledging that existing texts “do not bear sufficiently upon the present practice of the art of composition,” he warns that “tables of modulation . . . often put a dangerous weapon in the hand of inexperience,” suggesting that a more gradual shift, in which “intermediate chords” are “dwelt upon,” is necessary in order “to reconcile the ear to the change of key” and thus to “prevent a strangled modulation.” In contrast, Schneider’s examples include modulations that are “uncouth” and “harsh almost to a stunning degree.” Reicha’s Cours de composition musicale [ca. 1816] is cited as an authority on modulatory matters. Johann August Dürrnberger (active 1840s) The Linz organist Dürrnberger counted Bruckner among his pupils. His Elementar-Lehrbuch der Harmonie- und Generalbaß-Lehre (Elementary Textbook of Instruction in Harmony and Thoroughbass, Linz, 1841) offers a particularly vigorous treatment of voice-leading. The Roman numerals in his analyses may correspond to the scale degrees of the chordal roots (in line with the practice of Vogler and Weber), or to the scale degrees of a progression’s bass notes. François Camille Antoine Durutte (1803–1881) The Belgian Count Durutte became music director of the French national guard. His Esthétique musicale: technie, ou lois générales du système harmonique (Musical Aesthetics: Technics, or General Laws of the Harmonic System, Paris: Mallet-Bachelier, 1855) is among the few French treatises of the nineteenth century that perpetuate Jelensperger’s analytical practice of labeling the progression of chordal roots. As does Jelensperger, Durutte uses Arabic numerals for this purpose. He also makes note of chordal sevenths and indicates chordal inversions.

Biographies of music theorists

Philipp J. Engler (b. 1786) Engler was an ecclesiastic and professor of harmony in Bunzlau. His Handbuch der Harmonie (Handbook of Harmony, Berlin: Trautwein, 1825) displays the strong influence of Gottfried Weber’s Versuch einer geordneten Theorie der Tonse[t]zkunst (1817–21). Though in some examples he interprets certain sonorities as a result of passing motion (and thus they lack their own Roman numerals), a vertical orientation is apparent in an example displaying parallel 63 chords, which is accompanied by the analysis I II III IV, etc. François-Joseph Fétis (1784–1871) Fétis, born to a Belgian family of musicians, was drawn to Paris for study at the Conservatory. He later joined the faculty there as a professor of composition, counterpoint, and fugue, a post he held until called back to Belgium in 1833 to head the Brussels Conservatory. His inquisitive mind explored and promoted a wide range of musical repertoires and traditions from diverse eras and cultures, though errors of fact and an exceedingly opinionated outlook mar his scholarly contributions. Fétis founded the Revue musicale and wrote a multi-volume biographical encyclopedia of musicians. His historical bent is apparent in his Esquisse de l’histoire de l’harmonie (Paris: Bourgogne et Martinet, 1840, trans. M. Arlin as Esquisse de l’histoire de l’harmonie: An English-Language Translation of the François-Joseph Fétis History of Harmony, Stuyvesant, N.Y.: Pendragon Press, 1994), which traces the development of harmonic theory up to his own contribution, which he describes as “compete and definitive.” That contribution was soon thereafter made available, as Traité complet de la théorie et de la pratique de l’harmonie (Complete Treatise on the Theory and Practice of Harmony, Paris: Schlesinger, [1844], numerous later edns., trans. P. Landey, Stuyvesant, N.Y.: Pendragon Press, 2007). Fétis carefully examines the attractive tendencies of tonalité (a term that had already been employed by Choron and by Momigny, among others), seeking a metaphysical rather than a physical basis for music. In addition, he proposes an influential classification of musical developments into four phases: the ordre unitonique (music lacking transitions from one key to another, as in Palestrina’s music), the ordre transitonique (in which a composition may modulate from one key to another through strategic use of the dominant seventh chord, as in Monteverdi’s music), the ordre pluritonique (in which enharmonic modulation may occur, as in Mozart’s music), and the ordre omnitonique (in which multiple enharmonic shifts may occur simultaneously, the cutting-edge practice of

253

254

Biographies of music theorists

Fétis’s day, which he suggests might become too sensual through the incitement of nervous emotions). The treatise provides a careful accounting of the various chords employed in music, as well as the means by which these chords may be embellished via notes étrangers such as passing notes, appoggiaturas, and anticipations. It lacks any Roman- or Arabic-numeral analysis of chords progression, by then a common procedure in Germany that had found a foothold in France through Jelensperger’s work. Fétis used his influential position within the press to campaign against progressive music, particularly that of Berlioz and, later, of Wagner. He also hurled vituperative words at authors, including Reicha, whose treatises promoted such composition. Emanuel Aloys Förster (1748–1823) A Saxon by birth, Förster eventually settled in Vienna, where he composed and taught. His Anleitung zum General-bass (Instruction in Thoroughbass, Vienna: Träg, [1805]) contains early Austrian examples of harmonic analysis, with Arabic numerals placed under the score to indicate the scale degrees of the bass pitches. For example, he employs the number 4 for the chord that is now often called the Neapolitan sixth. On occasion he analyzes a chord in two keys concurrently, as when the progression from a C major chord to an F major chord is labeled both as 1 4 (in C Major) and as 5 1 (in F Major). Philipp Joseph Frick (1740–1798) The German organist Frick (or Frike) spent the latter part of his career in London. Among the theoretical works he published there is A Treatise on Thorough Bass (London: Frick, [1786]), wherein he provides guidance on “every chord in harmony worthy the attention of young composers.” Frick meticulously assesses the employment of accidentals, showing how interval qualities are affected by various chromatic modifications and demonstrating correct figured-bass notation for altered chords. Pietro Gianotti (d. 1765) Though we are uncertain of the Italian composer Gianotti’s date of birth, or of when he emigrated to Paris (sometime before 1728), we do know that, in addition to composing and playing double bass in the Opéra orchestra, he studied with Rameau. The discovery by Thomas Christensen of a long-lost

Biographies of music theorists

manuscript treatise by Rameau, “L’art de la basse fondamentale” (ca. 1738– 45), led to a surprising revelation: Gianotti’s Le guide du compositeur (The Guide to Composition, Paris: Durand, 1759) is actually a reworking of Rameau’s treatise, presumably published by Gianotti with Rameau’s approval. The work focuses on the practical aspects of the compositional art, and is noteworthy for its application of Rameau’s theory of fundamental bass as a tool for learning how to compose. August Halm (1869–1929) Halm’s unique perspective on music had a major influence on German music education and thought during the early decades of the twentieth century, extending his influence well beyond the Thuringian region where he taught. Halm absorbed much from nineteenth-century philosophy and music theory (Schopenhauer, Hegel, Hauptmann), from which he developed an aesthetic view that extends from Bach’s melodic–polyphonic fugal culture through Beethoven’s harmonic–formal sonata culture to the synthesis of Bruckner’s symphonies. He was a prolific author and essayist. In his Harmonielehre (Instruction in Harmony, Leipzig: Göschen, 1900, 21925) he focuses especially on the triad as the foundation of the tonal system, and on the cadence as the principal generator of motion: all of music is a vast variation upon the basic form of the cadence, based on the pull of the dominant towards tonic. Gottfried Harbordt (d. 1837) Harbordt, a student of Portmann, produced an interesting treatise that survives in manuscript: “Lehrbuch der Harmonie, Melodie und des doppelten Contrapuncts” (Textbook on Harmony, Melody, and Double Counterpoint, [late eighteenth century], Washington, D.C., Library of Congress Music Division). In that it employs Portmann’s idiosyncratic functional analytical notation, it sheds light on his teacher’s practice. Johann Hasel (active late nineteenth century) Hasel perpetuated the Sechter tradition in Austria late into the nineteenth century with Die Grundsätze des Harmoniesystems (The Foundations of the Harmony System, Vienna: Kratochwill, 1892), an extensive work that progresses from diatonic to chromatic and enharmonic contexts. The frequent insertion of notation for chordal fundamentals in small noteheads at the

255

256

Biographies of music theorists

bottom of the bass-clef staff reveals a clear distinction between individual chords and broader harmonic scale-degrees that may extend through several chords. Moritz Hauptmann (1792–1868) For many years a violinist at the court in Kassel, Hauptmann moved gradually into the domains of composition and music theory, eventually attaining important positions in Leipzig, as Kantor at the Thomasschule, professor of counterpoint at the recently opened Conservatory, and participant in the Bach-Gesellschaft project. His magnum opus, Die Natur der Harmonik und der Metrik (Leipzig: Breitkopf & Härtel, 1853, 21873, trans. W. E. Heathcote as The Nature of Harmony and Metre, London: Sonnenschein, 1888), was a path-breaking work, influencing both the speculations of Riemann and others and the practical works of Jadassohn, his former student. Adapting various strands of German philosophy to musical purposes, Hauptmann went about generating the tonal system – its chords, scales, meters, and so on – from abstract speculation. In various contexts he subjected an initial unity (thesis) to an opposition (antithesis), from which a mediated unity (synthesis) is achieved. For example, subjecting thesis C to antithesis G will result in synthesis E, thus generating the major triad. Die Lehre von der Harmonik (Instruction on Harmony, ed. O. Paul, Leipzig: Breitkopf & Härtel, 1868) attempts a simplification of the system, with examples in music notation (lacking in the original volume). These examples are all brief block-chord abstractions, however. The weak interface between the system and the music of the era, as well as oddities associated with some of the chord derivations (the minor triad being generated from its fifth, for example), make Hauptmann’s contribution appear mainly as instigator of a flowering of thought during the remainder of the century. Johann David Heinichen (1683–1729) The practice of thoroughbass during the peak of the Baroque is well documented in a mammoth work by Heinichen, a composer whose training in Leipzig, extensive sojourn in Venice and Rome, and career in Dresden made him eminently qualified for the task. Der General-Bass in der Composition (Thoroughbass in Composition, Dresden: Heinichen, 1728) masterfully treats the art of figured- and unfigured-bass accompaniment. Of particular interest are his prescriptions regarding keys for modulation. From C Major, for example, G Major, E Minor, and A Minor are suggested as the normative

Biographies of music theorists

choices, while D Minor and F Major are extraordinary. Heinichen positions all twenty-four keys on a circle, with closely related keys appearing in close proximity: G Minor–F Major–D Minor–C Major–A Minor–G Major–E Minor, etc. Heinichen also writes vividly on the novel treatment of dissonance in the stylus theatralis (theatrical style). Ernst Julius Hentschel (1804–1875) Hentschel studied under Logier and Zelter in Berlin and became a music instructor in Weißenfels, near Leipzig. His contributions include the founding of the journal Euterpe in 1841. In his Streitfragen über Musik: Fink und Marx (Disputes about Music: Fink and Marx, Essen: Badeker, 1843), triggered by publications of Marx and Fink concerning Dehn’s Harmonielehre (1840), he paints a vivid picture of the state of harmony instruction in Germany. John Holden (d. ca. 1771) Active in the Scottish musical community, Holden wrote An Essay towards a Rational System of Music (Glasgow: Urie, 1770) with the goal of bringing French innovations to an English-speaking audience, and in fact Rameauean concepts such as supposition and double emploi are introduced. In the work’s first part he offers a wide assortment of practical information on harmony, borrowing Lampe’s analytical notation (K for the Key Note, Arabic numbers for the other scale degrees) to clarify his examples of chord progression, modulation, and chromaticism. The second part focuses on theoretical issues such as proportions and tuning. Here, exasperated with the numerous duties that his Arabic numbers are required to perform, he attains greater clarity by enlisting Roman numerals as labels for the scale degrees. Salomon Jadassohn (1831–1902) Jadassohn held an unusual musical pedigree: conservative theoretical studies under Richter and Hauptmann in Leipzig and progressive piano studies under Liszt in Weimar, where he also came under the spell of Wagner’s music. Added to the mix was a reverence for J. S. Bach. Jadassohn’s creative activity was focused on composition and arranging. He taught composition, theory, and piano for many years at the Leipzig Conservatory. His output during his tenure there included a large number of textbooks

257

258

Biographies of music theorists

and monographs on a range of theoretical topics, including Lehrbuch der Harmonie (Leipzig: Breitkopf & Härtel, 1883; later edns., trans. P. Torek and H. B. Pasmore as Manual of Harmony, Leipzig: Breitkopf & Härtel, 1884) and Die Kunst zu moduliren und zu präludiren (The Art of Modulating and Preluding, Leipzig: Breitkopf & Härtel, 1890). Jadassohn’s analytical practice is modeled on Richter’s. It was stretched to more and more dubious extremes as the music under scrutiny became increasingly chromatic. The quest to place a diatonic Roman-numeral label below as many of a progression’s chords as possible led ultimately to such a wild frenzy of modulating hither and thither – without pivot chords – that any sense of continuity the music may have possessed was lost sight of in the analysis. Daniel Jelensperger (1797–1831) Arriving in Paris from Mulhouse, Jelensperger’s analytical tendencies bear a strong Germanic stamp. His L’harmonie au commencement du dixneuvième siècle et méthode pour l’ étudier (Harmony at the Beginning of the Nineteenth Century, Paris: Zetter, 1830, 2Paris, Krinits, 1833; trans. A. F. Häser as Die Harmonie im Anfange des neunzehnten Jahrhunderts, Leipzig: Breitkopf & Härtel, 1833) advances a highly developed scale-step theory that more closely resembles the practice of Vogler or Weber than any contemporaneous French system. Whereas Vogler’s analytical notation neglects chordal quality and Weber’s dotes on it, Jelensperger pursues a middle path: his Arabic numerals refer to diatonic chords unless a modifying symbol is appended. Thus the numeral 2 in C Major represents a chord of minor quality, built on the second scale degree, and in C Minor represents a chord of diminished quality, but 2) with right parenthesis in either key represents a chord of major quality. His system accommodates chords with a raised or lowered root and acknowledges chordal sevenths and ninths. Jelensperger offers advice concerning chord progressions and choices of keys for modulation. (No progression or modulation is forbidden, but information that he supplies – some of it statistical in nature, derived from close analysis of a large number of musical scores – helps practitioners distinguish the common from the uncommon.) Though his career began auspiciously, encompassing close interactions with Reicha and a teaching appointment at the Paris Conservatory, Jelensperger’s untimely death limited his influence. Scale-step analysis never gained a prominent position in French music pedagogy. Yet thanks to a faithful translation, his ideas migrated to Germany, where Lobe’s works built upon Jelensperger’s foundation.

Biographies of music theorists

Gottfried Keller (d. ca. 1704) A German composer and harpsichordist, Keller migrated to England, where A Compleat Method, for Attaining to Play a Through [sic] Bass (4London: Meares, [ca. 1715–21]) appeared posthumously. This popular work equips initiates with the fundamental principles needed to realize the Arabic numerals of thorough bass at a keyboard. David Kellner (ca. 1670–1748) The German organist and composer Kellner benefited from Heinichen’s massive thoroughbass manual in the creation of his briefer, simpler volume, Treulicher Unterricht im General-Baß (Reliable Instruction in Thoroughbass, Hamburg: Kissner, 1732). Foundational principles of the art are laid out and illustrated, and modulation to closely related keys is addressed. Matthew Peter King (ca. 1773–1823) King was an English composer, particular of songs for theatrical works. When in his twenties he published A General Treatise on Music (London: Golding, 1801), which affirms a Rameauean perspective, in opposition to the new ideas from the pen of Kollmann then entering circulation. He proposes two fundamental “chords of nature”: the fundamental concord (tonic) and the fundamental discord (dominant). All other chords are “chords of art.” Johann Philipp Kirnberger (1721–1783) Though a brief period of study under J. S. Bach in Leipzig inevitably influenced Kirnberger’s musical outlook, the prevailing state of music theory in Germany, which had absorbed more from Rameau than Kirnberger perhaps realized, was also a significant factor. Kirnberger’s harmonic perspective is in some respects an expansion of Rameau’s basse fondamentale. His analyses of excerpts or of complete movements incorporate extra staves below the score for notation of bass and root pitches, as well as figured bass. After extensive service in Poland and Prussia, Kirnberger completed Die Kunst des reinen Satzes in der Musik (2 vols., Berlin: Decker & Hartung, 1771–79, trans. D. Beach and J. Thym as The Art of Strict Musical Composition, New Haven: Yale University Press, 1982). The discussion of chords is simplified through Kirnberger’s division of dissonances into

259

260

Biographies of music theorists

two categories: essential dissonances, permanent members of the chord that resolve only as the chord gives way to its successor, and incidental dissonances that embellish a chord’s consonant members or essential dissonances. The book’s rich agenda includes discussions of melodic embellishment, aesthetic issues, counterpoint, and modulation, a topic that Kirnberger treats thoroughly even if he regards some key relations as too extreme for general use. A synopsis of Kirnberger’s harmonic theory was prepared probably by or in collaboration with his student Johann Abraham Peter Schulz and appeared as Die wahren Grundsätze zum Gebrauch der Harmonie (Berlin and Königsberg: Decker & Hartung, 1773, trans. D. Beach and J. Thym as The True Principles for the Practice of Harmony, Journal of Music Theory 23, 1979, pp. 163–225). A primer of preparatory materials was published as Grundsätze des Generalbasses als erste Linien zur Composition (Principles of Thoroughbass as the Best Preparation for Composition, Berlin: Hummel, [ca. 1781]). Justin Heinrich Knecht (1752–1817) From his base in Biberach (southern Germany), Knecht served as a teacher and church musician and was known more widely as a result of his various pedagogical works and periodical articles. His outlook on harmony stems from his teacher Vogler, whose Roman-numeral analytical notation he employs in Kleines alphabetisches Wörterbuch der vornehmsten und interessantesten Artikel aus der musikalischen Theorie (A Small Alphabetical Dictionary of the Most Important and Most Interesting Music-Theoretical Wares, Ulm: Wohler, 1795). Knecht’s most substantial work on harmony is Elementarwerk der Harmonie, als Einleitung in die Begleitungs- und Tonsetzkunst, wie auch in die Tonwissenschaft (Fundamental Principles of Harmony, as an Initiation into the Arts of Accompanying and Composition, as well as into the Theory of Music, Munich: Falter, 1792–97, 21814), wherein an exceedingly (and in Riemann’s view absurdly) wide range of chords is explored. Heinrich Christoph Koch (1749–1816) Though Koch spent most of his career in the Thuringian town of Rudolstadt, his writings address many of the aesthetic and theoretical concerns of late-eighteenth-century musicians throughout the German lands. His venerable Musikalisches Lexikon (Musical Encyclopedia, 2 vols., Frankfurt am Main: Hermann, 1802) displays a special indebtedness to the

Biographies of music theorists

aesthetic views of Johann Georg Sulzer and the theoretical precepts of Kirnberger. Though harmony is among the topics addressed in his Versuch einer Anleitung zur Composition (3 vols., Leipzig: Böhme, 1782–93, partial trans. N. K. Baker as Introductory Essay on Composition, New Haven: Yale University Press, 1983), that work is most impressive in its treatment of phrase structure. Koch’s later Handbuch bey dem Studium der Harmonie (Handbook for Studying Harmony, Leipzig: Hartknoch, 1811) offers a more sophisticated formulation on harmonic matters, though its perspective remains that of the eighteenth century. One senses Koch’s impatience with his younger contemporaries, whom he accuses of paying insufficient attention to grammatical correctness in their musical works. The Handbuch offers them a convenient refresher course on a wide range of topics, including chord construction and connection, dissonance treatment, sequences, chordal embellishment, cadences, and modulation. Though his treatment of chord progression lacks the insight of some other authors active around this time, his emphasis on the tonic, dominant, and subdominant as a key’s three “essential” chords (the others being “incidental”) reveals a functional outlook. Augustus Frederic Christopher Kollmann (1756–1829) A native of northern Germany, Kollmann moved to London in early adulthood to assume duties as organist of the Royal German Chapel. During his long career there he published some of the most penetrating studies of music then available in English. His program includes both a grammatical and a rhetorical component. His perspective on chords and their embellishment, which falls within the grammatical component, finds its most potent exposition in An Essay on Musical Harmony, According to the Nature of That Science and the Principles of the Greatest Musical Authors (London: Dale, 1796) and its successor, A New Theory of Musical Harmony, according to a Complete and Natural System of that Science (London: Bulmer, 1806, London: Nicol, 21823). The rhetorical component, which addresses issues of form and key relationships, is addressed in An Essay on Practical Musical Composition (London: Kollmann, 1799). Kollmann’s perspective on harmony is derived from that of Kirnberger (with whom he also shares a keen and at that time rare interest in the music of J. S. Bach). Thus he opposes the Rameauean notion of supposition that was championed by Marpurg. Kollmann recommends “the analyzing of all sorts of musical pieces . . . to be able of accounting for every period and note we write ourselves.” One must be careful to avoid regarding a musical entity according to its appearance,

261

262

Biographies of music theorists

for “the more harmony is explained according to those systems, the more perplexing it becomes.” (For example, a perfect fifth might in some contexts not function as a stable entity, but instead as a displacement of a fourth or a sixth.) Kollmann proposes that analysis must penetrate to find a proof of the real nature of each musical event. Franz Joseph Kunkel (1808–1880) As had Finlay Dun a few decades earlier, Kunkel, not otherwise known in the realm of music theory, stepped forward to defend the traditional order against new-fangled theoretical ideas that were being propagated. His Kritische Beleuchtung des C. F. Weitzmann’schen Harmoniesystems, . . . und des Schriftchens: “Die neue Harmonielehre im Streit mit der alten” (Critical Examination of Weitzmann’s System of Harmony and of the pamphlet “The Clash between the Old and New Modes of Harmony Instruction,” Frankfurt am Main: Auffarth, 1863) attempts to sway readers against the “superficial, unclear, contradictory, and destructive” ideas that were emanating from Weitzmann. John Frederick Lampe (ca. 1703–1751) London extended its traditional welcome to foreign musicians when Lampe arrived from Saxony in his early twenties to pursue a career as an opera composer. Another side of his talent emerges in A Plain and Compendious Method of Teaching Thorough Bass (London: Corbett, 1737), the first published work to make extensive use of numbers for chord-bychord harmonic analysis, a practice he might have brought with him from Germany. Lampe employs the Arabic numerals 2 through 7, corresponding to scale degrees, along with the letter K, for Key Note. Either of two bass progressions may be analyzed: the Thorough Bass (the lowest-sounding pitch of each chord) or the Natural Bass (the chordal roots). For example, in the progression labeled I V43 I6 in modern notation, the analysis of the Thorough Bass would be K 2d. 3d., while that of the Natural Bass would be K 5th. K. Rameau’s basse fondamentale and Lampe’s Natural Bass are equivalent concepts, though each analyst has idiosyncratic notions regarding which pitch to regard as the fundamental in certain contexts. Lampe seamlessly moves from one key to another when chromatic pitches appear, even analyzing the boundary chord in both keys. His model strongly influenced the analytical writings of Trydell and Holden in Britain and precedes by four decades Vogler’s first rudimentary Roman-numeral analyses on the

Biographies of music theorists

continent. The Art of Musick (London: Wilcox, 1740) is a work with less explicitly analytical aspirations, though in it Lampe clarifies some aspects of his Method. Honoré François Marie Langlé (1741–1807) Langlé found his way from his native Monaco to Paris via a long stint of study in Naples. Once ensconced in the French capital, he was active as a teacher of singing and as a composer. Upon the founding of the Conservatory, where he taught and served as librarian, he became active as a writer on theoretical subjects, including harmony and fugue. His Traité d’harmonie et de modulation (Treatise on Harmony and Modulation, Paris: Boyer, [ca. 1797]) addresses a wide range of chordal usage from a stacked-thirds perspective. Its examples display a zest for chromatic coloration. In his Traité de la basse sous le chant précédé de toutes les règles de la composition (Treatise on the Harmonization of Melody, Preceded by All the Rules of Composition, Paris: Naderman, [ca. 1798]), Langlé employs diatonic and chromatic scales as the foundation for an extensive demonstration of the art of harmonization. He also presents a variety of innovative sequential progressions. Georg Friedrich Lingke (1697–1777) Lingke was a German musical amateur whose keen interest in theoretical topics led to several publications, including his posthumous Kurze Musiklehre (A Brief Instruction Book on Music, Leipzig: Breitkopf, 1779), which focuses on basic issues of scales, intervals, and triads and seventh chords (and their inversions). Lingke was a system-builder, grounding his theory upon the foundation of scales. Even in his lifetime complaints were lodged regarding the abstraction of his formulations. Johann Christian Lobe (1797–1881) Lobe, a flute virtuoso and composer, resided for many years in Weimar, where he founded an institute for musical instruction. He moved to Leipzig in the late 1840s. While Liszt was stirring up enthusiasm for progressive “Music of the Future,” Lobe’s pedagogical slant remained conservative. (He attempted not to take sides in the fury that was going on around him, regarding Liszt’s innovations as similar in nature to J. S. Bach’s earlier transgression of rules.) His harmonic perspective is closely allied with that of Jelensperger, whose harmony textbook from 1830 was translated by another

263

264

Biographies of music theorists

Weimar resident, Häser, and published in Leipzig in 1833. Thus Arabic, rather than Roman, numerals appear in his harmonic analyses. In the first volume of his Lehrbuch der musikalischen Komposition (Textbook on Musical Composition, 4 vols., Leipzig: Breitkopf & Härtel, 1850–67, 21858; later editions), Lobe addresses harmony first from the perspective of the 1, 4, and 5 chords, only later adding 2, 3, and 6. He systematically displays every possible permutation. Though Lobe considers some chords as passing, in general he tends towards a pervasive use of harmonic labels (for example, 1 2 3 4 5 6 7 1 for an ascending progression of 63 chords). In chromatic contexts, he seeks wherever possible to find a key in which a chord can be interpreted diatonically, even if this means that his analysis represents a progression as moving frequently from one key into another. His later Vereinfachte Harmonielehre (Simplified Instruction in Harmony, Leipzig: Siegel, [1861]) was provoked by Weitzmann’s recent writings dealing with progressive harmonic practices. Lobe’s treatises contain numerous examples from actual music – not just concocted block-chord progressions as in many harmony textbooks – analyzed from his perspective. Anatole Loquin (1834–1903) Active in the musical life of Bordeaux, Loquin wrote a number of innovative works on music theory, including Notions élémentaires d’harmonie moderne (Fundamental Rudiments of Modern Harmony, Bordeaux: Gounouilhou, 1862) and L’harmonie rendue claire et mise à la portée de tous les musiciens (Harmonic Theory Presented Clearly and Set within Reach of All Musicians, Paris: Richault, 1895). In his earlier writings the twelve sons within each octave correspond, according to their spellings, to seventeen degrés (tonic, raised tonic, lowered supertonic, supertonic, raised supertonic, minor mediant, major mediant, etc.) performing seven fonctions (tonic, supertonic, etc.). In 1895 he described the twelve sons as “all equal and like one another,” referencing chords via their son numbers rather than via fonction labels. Exceedingly schematic, with an extensive set of precise labels for vertical chords (numbers) and their interactions (capital letters), Loquin’s analyses are daunting and rigid. Every vertical slice of the composition is given equal treatment, with no accommodation for hierarchical relationships. Rudolf Louis (1870–1914) Despite early leanings towards composition and conducting, Louis’s renown rests on his work as a music critic and author in Munich. In collaboration

Biographies of music theorists

with Ludwig Thuille, a composer and professor of theory and composition, he wrote an innovative and influential Harmonielehre (Instruction in Harmony, Stuttgart: Grüninger, [1907], 41913, trans. R. I. Schwartz, PhD diss., Washington University, 1982). Thorough, engaging, provocative, and pedagogically sophisticated, the work progresses from straightforward diatonic to innovative chromatic and enharmonic procedures. Of special interest are the numerous analyses of excerpts from recent music literature. Though these analyses contain an abundance of Roman numerals and resort to frequent key changes, the authors take a decisive step away from the prevailing one-chord/one-label approach, often urging the listener to hear in terms of broader harmonic motions. George Alexander Macfarren (1813–1887) Macfarren’s fame in Britain resulted from a variety of activities, including composition, conducting, teaching, and writing. In the latter category, he produced both textbooks such as the popular Rudiments of Harmony (London: Cramer, Beale & Chappell, 1860) and compilations of his public presentations, such as Six Lectures on Harmony (London: Longmans, Green, Reader, & Dyer, 1867). His support for Day’s harmonic theory led to his temporary resignation from the faculty of the Royal Academy of Music. Late in his career, in 1885, he edited a second edition of Day’s Treatise on Harmony. Friedrich Wilhelm Marpurg (1718–1795) A prolific author and the translator of d’Alembert’s Élémens de musique, Marpurg was a major force in Berlin’s musical culture and a critical voice to be reckoned with throughout Germany. His devotion to Rameau’s theories sometimes led him to condemn alternative viewpoints, a tendency that erupts most pointedly in disputes with Sorge (concerning a variety of issues including the Rameauean principle of supposition for chord derivation) around 1760 and with Kirnberger (concerning incidental dissonances, fundamental-bass analysis, and chromaticism) in the 1770s. Yet Marpurg, perhaps unwittingly, had strayed from the Frenchman’s tenets himself. Marpurg’s Handbuch bey dem Generalbasse und der Composition (3 vols. plus suppl., Berlin: Schütze, Lange, 1755–60, trans. D. A. Sheldon as Thoroughbass and Composition Handbook, Stuyvesant, N.Y.: Pendragon Press, 1989) explores contemporary compositional practices, with a fresh perspective concerning embellishing pitches. Among the many issues

265

266

Biographies of music theorists

addressed in his Historisch-kritische Beyträge zur Aufnahme der Musik (Historical–Critical Contributions Concerning Music’s Reception, Berlin: Schütze, Lange, 1754–62, 1778) is a detailed listing of the chords used in composing, part of his rebuttal to Sorge. Marpurg devotes due attention to the “classic” chords but also examines “fantastic” chords (e.g., Fs-Ab-C) that are derived from two keys and that occur during some of music’s more colorful moments. Adolf Bernhard Marx (1795–1866) Marx distinguished himself as a professor and composer in Berlin. He wrote numerous books on music–theoretical issues, though harmonic analysis was not an especially prominent facet of his thinking. Innovative ideas on form distinguish Die Lehre von der musikalischen Komposition (4 vols., Leipzig: Breitkopf & Härtel, 1837–47, posthumous edn. by H. Riemann (1887–90), trans. and ed. H. S. Saroni as Theory and Practice of Musical Composition, New York: Huntington, Mason & Law, [ca. 1851]). Concerned that Dehn’s Harmonielehre was leading music pedagogy down the wrong track, Marx published a pamphlet condemning the work: Die alte Musiklehre im Streit mit unserer Zeit (The Clash between the Old Mode of Harmony Instruction and Our Time, Leipzig: Breitkopf & Härtel, 1841). Some of his most perceptive analytical observations appear in Ludwig van Beethoven (2 vols., Berlin: Janke, 1859). Johann Mattheson (1681–1764) Mattheson’s multi-faceted career in Hamburg included activities as a singer, a composer, a diplomat, and a duelist (contra Händel, no less). He was a prolific and astute author on music topics. Several of his treatises, including his celebrated Der vollkommene Capellmeister (1737), were completed after deafness caused him to retire from active musical service. Though the emerging practice of harmonic analysis was not an area in which he made contributions, his Exemplarische Organisten-Probe (A Test of Organists through Examples, Hamburg: Schiller and Kißner, 1719) aptly displays his expertise in the art of thoroughbass, as well as his pedagogical gifts. (The work was revised for republication in 1731, under the title Grosse General-Bass-Schule.) After an extensive introduction, forty-eight test pieces are offered, each accompanied by some expert commentary.

Biographies of music theorists

Jérôme-Joseph de Momigny (1762–1842) Within the domain of music analysis, the Belgian theorist Momigny ranks as a true innovator, a leader in the emerging field of musical hermeneutics. His Cours complet d’harmonie et de composition (A Comprehensive Treatise on Harmony and Composition, 3 vols., Paris: Momigny & Bailleul, 1806), completed after he had established a publishing firm in Paris, includes several extensive analyses that, though lacking the sort of scale-step evaluation then emerging among German and British commentators, nevertheless offer an attentive reading of the musical score, with particular emphasis on phrase structure and cadences. For Momigny, a narrative or poetic interpretation (for example, the evocation of a thunderstorm or of peasants praying) may be the appropriate device for unlocking a composition’s meaning. Momigny’s insights into the structure of scales, chords, and chord progression are most fully developed and best illustrated in La seule vraie théorie de la musique (The Only True Theory of Music, Paris: Momigny, [1821]). Particularly noteworthy is his expansive view of a key, which he understands to include seven diatonic, ten chromatic, and ten enharmonic pitches. (In some keys this will entail the use of triple sharps or triple flats.) His commentary and sample chord progressions vividly document an alternative to the modulation-intensive analyses then in vogue. For example, Momigny opposes the notion that adding Bb to C-E-G (preceding F-A-C) has anything to do with the key of F Major, so long as chords of C Major follow the F chord. In this regard Momigny’s perspective mirrors Kirnberger’s. His audience included readers of Nicolas-Étienne Framery’s Encyclopédie méthodique: Musique (Systematic Encyclopaedia: Music, Paris: Panckoucke & Agasse, 1791–1818), for which he wrote hundreds of articles on musical topics. In addition, he published several pedagogical works, including Exposé succinct du seul systême musical gui soit vraiment fondé et complet (A Concise Exposition of the Only Truly Authentic and Complete Musical System, Paris: Momigny, [ca. 1809]). Frederick Arthur Gore Ouseley (1825–1889) Ouseley, an English church musician and Oxford professor, authored several books on music, including A Treatise on Harmony (Oxford: Clarendon, 1868), which he describes as “a consistent theory, founded in nature, progressively expanded, and involving no purely arbitrary rules.” Most of the harmonic analysis presented therein is accomplished by placing capital letters representing chordal roots below the individual chords of a

267

268

Biographies of music theorists

progression or by placing noteheads representing these roots on a separate staff (in the manner of Rameau’s basse fondamentale). On occasion Ouseley places the words “Tonic” and “Dominant” (or abbreviations “T.” and “D.”) above the staff. The musical style in evidence throughout is distinctly conservative, reflecting Ouseley’s involvement in the English anthem tradition and his preference for Händel and Mozart over contemporary compositional practice. Johann Gottlieb Portmann (1739–1798) Active as a singer and teacher in Darmstadt, Portmann made interesting contributions to both the scale-step and function theories of harmony. His Musikalischer Unterricht (Musical Instruction, Darmstadt and Speyer: Krämer & Boßler, 1785) employs Arabic numerals to indicate the scale degrees of chordal roots, demonstrating an expansion of the scale-step method in Germany just a few years after Vogler’s pioneering Romannumeral efforts. His Leichtes Lehrbuch der Harmonie, Composition und des Generalbaßes (Basic Textbook on Harmony, Composition, and Thoroughbass, Darmstadt: Will, 1789) takes a different approach and includes a distinctive system of analytical notation employing various symbols atop and beside alphabet letters. A limited number of broad chordal formulations (five in all in this treatise, including three distinct dominant-related formulations, six in his next treatise) represent all chordal functions within a key. For example, E-G-B in C Major would fall within the same domain as C-E-G. With fewer different basic chord types, Portmann is able to provide extraordinarily clear guidelines for their succession. Die neuesten und wichtigsten Entdeckungen in der Harmonie, Melodie und dem doppelten Contrapuncte (The Most Recent and Most Important Discoveries on Harmony, Melody, and Double Counterpoint, Darmstadt: [Heyer], 1798) offers further refinements. Portmann’s student Gottfried Harbordt produced a manuscript treatise that makes ample use of Portmann’s functional notation. Ebenezer Prout (1835–1909) In addition to a distinguished career teaching in England and Ireland, Prout produced a popular series of textbooks for the music theory curriculum: instrumentation, counterpoint, fugue, form, and harmony are each addressed. The latter topic found its fullest expression in Harmony: Its Theory and Practice (London: Augener, [1889], 161903) and the accompanying Analytical Key to the Exercises in “Harmony: Its Theory and Practice”

Biographies of music theorists

(London: Augener, [1903]). Though earlier editions had continued in the acoustical speculations introduced into British theorizing by Alfred Day, the 16th edition saw a major overhaul, with a retreat from an explicitly scientific perspective. Prout’s Roman numerals, abundantly supplied in the Analytical Key, follow the German tradition of Richter and Jadassohn, though the positioning of the letter b, c, or d to the right of a numeral to indicate first through third inversion, respectively, is derived from Day. One noteworthy feature is his analysis of chromatic chords in the key of the chord to which they resolve. For example, in the progression C–A6s–G–E6, the first, third, and fourth chords are analyzed in C Major as I V Ib, whereas the second chord is analyzed by means of a parenthetical insert in the key of G Major: (G: vii°b). When not set off thus by parentheses, Prout would supplement the vii°b label with a parenthetical (V7c) to indicate that the leading-tone chord is a dominant seventh with absent root. Jean-Philippe Rameau (1683–1764) Rameau’s musical career ran in two parallel streams: one as France’s leading composer, the other as Europe’s most influential writer on music theory. Prone to revising his formulations based on fresh information or ideas, or in response to criticism, Rameau’s extensive theoretical output is spread over forty years. Highlights include: • Traité de l’harmonie réduite à ses principes naturels (Paris: Ballard, 1722, facs. in The Complete Theoretical Writings of Jean-Philippe Rameau (hereafter CTW), ed. E. Jacobi, American Institute of Musicology, 1967–72, vol. 1, trans. as A Treatise of Musick, Containing the Principles of Composition, London: Walsh, 1752, trans. P. Gossett as Treatise on Harmony, New York: Dover, 1971), which presents Rameau’s initial formulation on chords, their derivation, and their connection. The work established Rameau as a revolutionary musical thinker and inaugurated sweeping changes in how musicians throughout Europe conceived of harmony. • Nouveau système de musique théorique (New System of Music Theory, Paris: Ballard, 1726, facs. in CTW, vol. 2), in which Rameau assesses the implications of the geometric progression (e.g., 1:3:9) and offers materials to supplement or amend his Traité. • “Lettre de M. à M. sur la Musique,” (Letter from One Gentleman to Another concerning Music, Mercure de France (September 1731), pp. 2126–2145, facs. in CTW, vol. 6), an example of Rameau’s polemical writing, in this case incidentally displaying an innovative use of symbols for harmonic analysis.

269

270

Biographies of music theorists

• Génération harmonique, ou traité de musique théorique et pratique (Paris: Prault, 1737, facs. in CTW, vol. 3, trans. D. Hayes as Harmonic Generation, or Treatise on Theoretical and Practical Music, Ann Arbor: UMI Research Press, 1974), a work that, in returning to many of the issues initially discussed in the Traité, displays a more mature appreciation of acoustical phenomena and ratios. • “L’art de la basse fondamentale” (ms., [ca. 1738–45]), a rediscovered practical manual on composition and accompaniment, which served as model for Gianotti’s Le guide du compositeur (1759). • Code de musique pratique (Code of Practical Music, Paris: Imprimerie royale, 1761, facs. in CTW, vol. 4), Rameau’s final treatise, a practical work on composition, wherein some rigidly applied notions from earlier treatises (for example, with regard to suspensions) are tempered. Rameau formulates and addresses the two principal issues of any harmonic speculation: (1) determination of the chordal entities employed in music, the basis for their formation, and the interrelationships among them, and (2) exploration of the rationale for movement from one to another of these entities, distinguishing between normative successions and those accomplished via license. Incorporating recently discovered acoustical information, Rameau asserts that a single pitch (the son fondamental) serves as generator of the major triad (accord parfait). Though the minor triad and dissonant chords do not offer similarly indubitable foundations, Rameau nevertheless manages to assert a fundamental pitch for every chordal entity. Both creative and controversial, his notion of supposition to derive ninth and eleventh chords (or, suspensions of these denominations) engages pitches both above and below the asserted chordal fundamental. For example, in the progression with figured bass G7–C4–3, the pitches at C4 are C-G-F, which Rameau would interpret as a seventh chord rooted on G with “supposed” (sub-positioned) fifth C. In line with other progressive writers, inverted chords are coordinated with foundational chords in the manner still practiced today. Rameau often displays the progression of fundamentals (basse fondamentale) on a separate staff below a music example. This visual field is well suited to revealing the intervallic relationship between successive fundamentals. Rameau favors the succession of a descending fifth, enhanced when a seventh is incorporated within the first chord (as in G7 to C, an example of the cadence parfaite), and the succession of an ascending fifth, enhanced when a sixth is incorporated within the first chord (as in F65 to C, an example of the cadence irregulière or imparfaite). (In Rameau’s usage, the term “cadence” is not restricted to the end of a phrase.) A special case,

Biographies of music theorists

indicative of Rameau’s concern for suitable intervals between adjacent fundamental pitches, occurs in double emploi: the chord F-A-C-D is understood as rooted on F when preceded or followed by a C chord and on D when preceded or followed by a G chord, thus the progression C–F65–G7–C has fundamentals C–F/D–G–C, thereby eliminating analytically what may seem empirically to be a stepwise succession either from C to D or from F to G. Two publications from 1752 expanded the reach of Rameau’s influence: a partial English translation, and a summary of Rameau’s ideas by d’Alembert. The latter was soon translated into German by Marpurg and into English by Blacklock. Antoine-Joseph Reicha (1770–1836) The Bohemian Reicha’s formative years included interactions with Beethoven in Bonn and studies under Albrechtsberger and Salieri in Vienna. He resided in Paris for most of his career, composing (chamber music and opera predominate), writing theory treatises, and, from 1818, teaching counterpoint and fugue at the Conservatory, where he competed with Cherubini and later Fétis for students. Among those who came under Reicha’s direct influence are Berlioz, Liszt, Gounod, and Franck. His Cours de composition musicale, ou traité complet et raisonné d’harmonie pratique (Paris: Gambaro, [ca. 1816], trans. A. Merrick as Course of Musical Composition; or, Complete and Methodical Treatise of Practical Harmony, London: Cocks, [1854]) is grounded upon thirteen basic chord types, employed in a wide range of examples displaying their progression both within a single key and via modulation (both permanent and transient) to another key. He recommends reaching a distant key via a series of less abrupt modulations, though he also explores enharmonic modulation. The Traité de haute composition musicale (Treatise on Advanced Musical Composition, 2 vols., Paris: Zetter, 1824–6) focuses on contrapuntal procedures and musical forms, including the grande coupe binaire (sonata form). Jean-Baptiste Rey (ca. 1760–1822) For many years a cellist in the Paris Opera orchestra and briefly an instructor at the Paris Conservatory, Rey also ventured to publish Exposition élémentaire de l’harmonie (An Elementary Introduction to Harmony, Paris: Naderman, [1807]). The work retains a strong Rameauean orientation in procedure and terminology, in keeping with Rey’s own training from the eighteenth century.

271

272

Biographies of music theorists

Ernst Friedrich Richter (1808–1879) Richter studied music in Leipzig and stayed on to pursue his career there, teaching music theory at the Leipzig Conservatory and serving as cantor at the Thomasschule. His name was spread far beyond these confines due to his series of instruction manuals, including the popular Lehrbuch der Harmonie (Textbook on Harmony, Leipzig: Breitkopf & Härtel, 1853, numerous later editions and translations). Continuing the Roman-numeral scale-step tradition of Vogler and Weber (though without their verve and curiosity), Richter emphasizes part-writing and offers numerous sets of exercises: figured basses to be realized and analyzed, or melodies to be harmonized. The Lehrbuch’s examples and exercises are in a conservative style. The enormous popularity of the work over many decades was irksome to Schenker, who regarded much of its contents as “nonsense.” Hugo Riemann (1849–1919) Riemann held an assortment of teaching positions that eventually led to an appointment in Leipzig, where earlier he had undertaken theoretical studies under Jadassohn. Both in his role as professor and through numerous books on a range of music–theoretical and music–historical topics, Riemann’s influence on musical thought at the turn of the twentieth century was profound. His theoretical formulation is grounded in acoustics, though with the curious assertion of a dual generation: the major triad upwards through overtones (as in C-G-E), the minor triad downwards through undertones (as in C-F-Ab). The ear’s reception and the mind’s cognitive processes also are central concerns in his purview. His harmonic perspective focuses on three chordal functions: tonic, dominant, and subdominant. His analyses provide letter symbols for these functions and for other chords that relate to them. The chords related to C-E-G are its variant (Variante) C-Eb-G, its leading-tone change (Leittonwechsel) E-G-B, and its parallel (Parallele) A-C-E. (Each related triad retains one interval from the original triad.) Among numerous sources for Riemannian analysis are Skizze einer neuen Methode der Harmonielehre (Sketch of a New Method of Instruction in Harmony, Leipzig: Breitkopf & Härtel, 1880) and Systematische Modulationslehre (Systematic Instruction in Modulation; Hamburg: Richter, 1887). Riemann also wrote a monumental history of music theory, Geschichte der Musiktheorie im IX.-XIX. Jahrhundert (The History of Music Theory from the Ninth through the Nineteenth Centuries, Leipzig: Hesse, 1898, parts 1 and 2 trans. R. Haggh

Biographies of music theorists

as History of Music Theory, Lincoln, Nebr.: University of Nebraska Press, 1962, part 3 trans. W. Mickelsen as Hugo Riemann’s Theory of Harmony, Lincoln, Nebr.: University of Nebraska Press, 1977). Joseph Riepel (1709–1782) Austrian by birth, Riepel served as Kapellmeister at the court in Regensburg. During the 1750s and 1760s he published several pedagogical works devoted to contemporary practices of phrase structure and form. These volumes had a decisive impact upon Koch’s later writings. The art of adding a bass to support a melody is a central concern of his posthumous Baßschlüssel (Key to the Bass [Bass Clef], ed. J. K. Schubarth, Regensburg: Montag, 1786). In this work he divides the diatonic chords into two groups: those rooted on the first, fourth, and fifth scale degrees are regarded as foundational, while the others play a subsidiary role. Pierre-Joseph Roussier (ca. 1716–1792) Abbé Roussier is one of the more prolific among the French authors on music theory who worked in Rameau’s wake. His Traité des accords, et de leur succession, selon le système de la basse-fondamentale (Treatise on Chords and on Their Succession, According to the System of the Fundamental Bass, Paris: Bailleux, 1764) is thoroughly Rameauean in perspective, though not without its quibbles and extensions. The coordinating volume of music examples, L’harmonie pratique (Practical Harmony, Paris: Roussier, [1775]), supplies abundant sample chord progressions, often in multiple versions utilizing a variety of inversions, and applies an analytical shorthand for fundamental bass, placing a capital letter for the fundamental underneath a chord in place of pitch notation on a separate staff. Augustin Savard (1814–1881) Savard taught at the Paris Conservatory, and like many of his predecessors and successors he wrote a harmony textbook. His Cours complet d’harmonie théorique et pratique (A Comprehensive Course on Harmony, Theoretical and Practical, Paris: Girod, [1853]) is a work in the tradition of Catel. It contains particularly thoughtful accounts of passing chords and modulation, including enharmonic modulation. Sequences (marches harmoniques) and chromatically altered chords are also featured.

273

274

Biographies of music theorists

Josef Schalk (1857–1900) Schalk, a student of Bruckner, was an instructor of piano at the Vienna Conservatory and an ardent Wagnerian. His article “Das Gesetz der Tonalität” (The Law of Tonality) was serialized in the Bayreuther Blätter from 1888 through 1890. Chromaticism, modulation, and passing chords are among his main concerns. In an unpublished essay on chromaticism (quoted in Wason 1985) he suggests that a contrapuntal voice-leading perspective may answer some questions that harmonic theory is not equipped to resolve on its own. Johann Adolph Scheibe (1708–1776) Scheibe’s progressive aesthetic views caused a stir when, in 1737, he was so bold as to characterize Bach’s music as bombastic and excessively artful in the pages of his journal, Der critische Musikus. Despite the negative stigma that would follow him thereafter, his perceptive commentary on the new stylistic developments that were leading away from the Baroque, particularly his discussion of musical figures derived from rhetoric, is among the most insightful of its time. After a move from Hamburg to Denmark, Scheibe pursued a mammoth project on the theory of music, only the first volume of which was published, as Über die musikalische Composition; Erster Theil: Die Theorie der Melodie und Harmonie (On Musical Composition; Part One: The Theory of Melody and Harmony, Leipzig: Schwickert, 1773). Three hundred pages of erudite commentary on rudimentary concepts such as intervals, chords, chromatic pitches, keys, and passing notes are followed by an appendix of nearly one hundred pages in which Rameau’s contributions, which he knew via Marpurg’s translation of d’Alembert’s Élémens, are critically assessed. Heinrich Schenker (1868–1935) After early studies under Mikuli and Bruckner, Schenker made his initial marks on the Viennese musical scene as a collaborative pianist and critic. The publications that followed document a gradual development and synthesis of a range of original ideas that transformed the analytical enterprise. Highlights include: • “Der Geist der musikalischen Technik” (Musikalisches Wochenblatt 26 (1895), pp. 245–246, 257–259, 273–274, 285–286, 297–298, 309–310, 325–326, trans. W. Pastille as “The Spirit of Musical Technique,” in N. Cook, The Schenker Project, Oxford: Oxford University Press, 2007,

Biographies of music theorists

•

•

•

•

pp. 319–332), in which discussions of melody, counterpoint, and harmony adumbrate Schenker’s later developments. Harmonielehre: Neue musikalische Theorien und Phantasien I (Stuttgart: Cotta, 1906, facs. Vienna: Universal, 1978, abridged trans. E. M. Borgese, ed. O. Jonas as Harmony, Chicago: University of Chicago Press, 1954), an analysis-intensive traversal of topics including tonal systems, a theory of intervals and harmonies, a theory of the motion and succession of scalesteps, and a theory of the progression of keys. Kontrapunkt: Neue musikalische Theorien und Phantasien II (2 vols., Stuttgart and Berlin: Cotta, 1910 (vol. 1 only), Vienna: Universal Edition, 1910–22 (both volumes); trans. J. Rothgeb and J. Thym as Counterpoint, New York: Schirmer Books, 1987, revised trans. Ann Arbor, Mich.: Musicalia, 2001), a masterful reworking of the art of species counterpoint, emphasizing the reasons for the various contrapuntal rules and the relationship of counterpoint to free composition. Das Meisterwerk in der Musik: Ein Jahrbuch (3 vols., Munich: Drei Masken, 1925, 1926, 1930, ed. W. Drabkin, trans. I. Bent et al. as The Masterwork in Music, 3 vols., Cambridge: Cambridge University Press, 1994–7), three volumes of theoretical and analytical essays, in which innovative analyses consisting of score notation plus auxiliary symbols are employed extensively. Der freie Satz: Neue musikalische Theorien und Phantasien III (Vienna: Universal, 1935, 2rev. edn., ed. O. Jonas, Vienna: Universal, 1956, trans. and ed. E. Oster as Free Composition, New York and London: Longman, 1979, reprint trans. Stuyvesant, N.Y.: Pendragon Press, 2001), a detailed formulation of Schenker’s mature thought, concisely presented and extensively demonstrated through analysis.

Schenker disdained recent German developments concerning harmony (both the Richter/Jadassohn pedagogical initiatives and the Hauptmann/ Riemann speculative initiatives). His analyses in Harmonielehre are closely allied with the earlier Viennese practice of Sechter (upon which Bruckner’s teaching had been grounded). His capital Roman numerals are often adorned by accidentals (sometimes along with small Arabic numerals that indicate which chord members are altered) to indicate chromatic modifications, a practice closely allied with Vogler’s of over a century earlier, though Schenker’s expanded conception of scale degrees (Stufen) results in a less dense application of these numerals than Vogler or others had advocated. Schenker’s later practice of harmonic analysis moves decisively beyond any nineteenth-century formulation in its application in tandem

275

276

Biographies of music theorists

with voice-leading and formal considerations (often in the context of his characteristic analyses using music notation), in its hierarchical complexity, and in the interpretation of a composition’s various tonal centers as regions within the overall tonic key. Gustav Schilling (ca. 1803–1880) The prolific author Schilling, who was born near Hanover and was employed at the Stuttgart court, wrote his Polyphonomos, oder die Kunst . . . sich eine vollständige Kenntniß der musikalischen Harmonie zu erwerben (Polyphonomos, or the Art . . . of Attaining a Complete Knowledge of Musical Harmony, Stuttgart: Weise & Stoppaní, 1839) several decades before fleeing Germany in debt. (He eventually reached Nebraska.) In one of the work’s examples, a conventional descending-fifths sequence is enhanced by subsidiary chordal content. Schilling’s analysis does not lose sight of the deeper hierarchical layer of the basic sequence. Friedrich Schneider (1786–1853) Schneider was a prominent member of the musical communities of Leipzig and Dessau and traveled widely beyond that region as a director of music festivals. His Elementarbuch der Harmonie und Tonse[t]zkunst (Leipzig: Peters, [1820], trans. Engelbach as Elements of Musical Harmony and Composition, London: Chappell, 1828) continues in the tradition of Vogler and Weber, making use of Weber’s system of capital and small-capital Roman numerals for harmonic analysis. After it had hit British shores in translation, Finlay Dun condemned its “uncouth” and “harsh” modulations. Arnold Schoenberg (1874–1951) Throughout his life – in Vienna and in Berlin, and later in California – Schoenberg taught music theory both to prepare students for the study of composition and to earn an income. His idiosyncratic Harmonielehre (Vienna: Universal, 1911, 31922, trans. R. Carter as Theory of Harmony, Berkeley: University of California Press, 1978) extends the Austrian tradition of Sechter and Bruckner, with relevance principally to the style of music Schoenberg himself was then composing. He dispenses with distinctions between harmonic and non-harmonic elements, so that all simultaneously sounding pitches attain harmonic status. The most analytically sophisticated of the works derived from his teaching in California

Biographies of music theorists

is Structural Functions of Harmony (ed. H. Searle, New York: Norton, 1954), in which he establishes a means for relating the keys that may appear within a composition (for example, Mm for the “mediant major’s mediant minor”: Gs Minor in C Major) and then develops a system of Roman-numeral analysis, often with individual chords analyzed simultaneously in more than one key. His strategies for accommodating nondiatonic elements, including substitutes, transformations, and vagrant or roving harmonies, are of special interest. Christoph Gottlieb Schröter (1699–1782) In his Deutliche Anweisung zum General-Baß (Clear Instructions on Thoroughbass, Halberstadt: Groß, 1772), Schröter, a Thuringian organist and composer, addresses forty-seven combinations of numbers that may occur above a bass note in traditional figured-bass notation, from the foun8 6 9 7 dational 53 and 53 to rarities such as 65 and 64. Yet, coming as it does in the same decade as Vogler’s pioneering analytical writings, the work holds special interest for its reliance upon numbers in less traditional contexts. On occasion Schröter employs Arabic numerals to indicate the scale degrees of melodic pitches. In referring to chords rather than pitches, Roman numerals are called into service. Interestingly, Schröter’s numerals indicate the scale degrees of the bass pitches – not the roots. What Vogler might label as I with figure 6 is labeled “auf III” (“on [scale degree] three”), along with 63 above the bass, by Schröter. In yet another numeral construct, I represents the tonic chord (e.g., C-E-G), II the chord of its upper fifth (G-B-D), and III the chord of its lower fifth (F-A-C). (The ranking stems from a comparison of the ratios 2:3:4, which divides the octave at the fifth, and 3:4:6, which divides the octave at the fourth. Daube had recently proposed a similar scheme, but his “2” is F-A-C and his “3” is G-B-D.) Schröter’s fascination with numbers extends into the domain of temperament as well. Johann Abraham Peter Schulz (1747–1800) Schulz held music posts in several cities of northern Europe, most notably Berlin and Copenhagen. His principal connection with music analysis stems from his years of study under Kirnberger and resultant collaboration with him on Die wahren Grundsätze zum Gebrauch der Harmonie (Berlin and Königsberg: Decker & Hartung, 1773, trans. D. Beach and J. Thym as The True Principles for the Practice of Harmony, Journal of Music Theory 23, 1979, pp. 163–225). Though Kirnberger is named as the work’s author, several

277

278

Biographies of music theorists

discrepancies with other writings by Kirnberger regarding fundamental bass and suspensions suggest that Schulz may have included some of his own Rameau-inspired ideas. Schulz’s presentation on passing chords is vivid and progressive. The treatise includes demonstration analyses of fugues from Bach’s Well-Tempered Clavier. Simon Sechter (1788–1867) An influential teacher in Vienna for over half a century, Sechter expands upon Rameau’s fundamental-bass theory in Die Grundsätze der musikalischen Komposition (3 vols., Leipzig: Breitkopf & Härtel, 1853–54, vol. 1 trans. C. C. Müller as The Correct Order of Fundamental Harmonies, New York: Pond, 1871, partial trans. J. Chenevert as “Simon Sechter’s The Principles of Musical Composition,” PhD diss. The University of Wisconsin, 1989). Whereas Rameau displays a progression’s fundamental notes on a separate staff below the bass, Sechter instead uses capital letters. Capital Roman numerals indicate the scale degrees of chordal roots in some examples. The same progression may be analyzed in several keys simultaneously, a practice that in chromatic contexts may facilitate a chord’s derivation from pitches of two or more keys. For example, the augmented sixth chord Ab-C-Eb-Fs is a hybrid chord (Zwitterakkord) rooted on D, merging elements from V in G Minor and II (with ninth) in C Minor. Sechter’s endorsement of root motion by fifth or third only and his concerns regarding the appropriate preparation and resolution of dissonance inform his detailed discussion of harmonic progression. Some successions are banned, others are understood as contractions – for example, I–II stands for I–VI–II, in which VI is an intermediate chord (Zwischenkakkord) that descends by fifth to reach II. Sechter’s treatment of embellishment is notably hierarchical for the time. Numerous examples document his conviction that a progression of several chords may fall within the domain of a single fundamental. Thus, in contrast to most contemporaneous German harmony manuals, numerous chords within Sechter’s examples appear without an analytical label (capital letter or Roman numeral). Sechter is well known for his pronouncement that a diatonic progression must ground any chromatic progression. Though he provides insightful examples and commentary to display how sophisticated structures emerge out of simple diatonic foundations, these examples do not extend into tonal territories just then being explored by some of the more innovative composers of the time. Perhaps the Grundsätze’s date of publication is misleading. Certainly its contents stem from a teaching practice that began early in the century. Thus Sechter’s

Biographies of music theorists

analytical precepts probably correspond more closely to the music of Schubert (who took a counterpoint lesson from Sechter) than to that of the mature Wagner. Yet several later authors who do address the late-tonal repertoire (for example, Louis and Thuille in Munich and Schoenberg in Vienna) clearly borrow much from Sechter. Ignaz Ritter von Seyfried (1776–1841) Seyfried, a very successful Viennese composer and conductor, entered into the realm of pedagogy to compile a synthesis of his teacher Albrechtsberger’s musical writings, as J. G. Albrechtsberger’s sämmtliche Schriften über Generalbaß, Harmonie-Lehre, und Tonsetzkunst [ca. 1825–26] (see Albrechtsberger entry, p. 244, above). In that Albrechtsberger had never published a manual on harmony, Seyfried crafted the necessary materials. It remains uncertain whether this portion of the work bears a direct relation to Albrechtsberger’s teaching or whether, instead, Seyfried formulated it independently. Its precepts bear a distinctively Rameauean stamp. Peter Singer (1810–1882) Singer, who spent most of his adult life at Salzburg’s Franciscan monastery, was a composer and organist whose theoretical bent led him to write Metaphysische Blicke in die Tonwelt (Metaphysical Glimpses into the World of Tones, München: In Commission der Literatur-artist. Anstalt, 1847), a work that treats harmony from the perspective of three basic chords, continuing a trend that had begun in the German lands with Daube nearly a century earlier. Georg Andreas Sorge (1703–1778) Sorge makes sophisticated use of numbers – be they logarithms, ratios, or measurements – in pursuit of his musical interests: organ construction, tuning and temperament (equal temperament is promoted), and composition. Court organist in the Thuringian town of Lobenstein, Sorge produced an impressive array of books and pamphlets, of which the most substantial is his Vorgemach der musicalishen Composition (Preparatory Studies in Musical Composition, 3 vols., Lobenstein: Sorge, [1745–47], trans. A. D. Reilly as “Georg Andreas Sorge’s Vorgemach,” PhD diss., Northwestern University, 1980). Among its contents are advice on chord progression, a ranking of closely related keys for modulation, examples of passing chords,

279

280

Biographies of music theorists

and an early use of numerical chord labels. Sorge attracted wide attention by criticizing the irascible Marpurg on a variety of issues in his Compendium harmonicum (The Harmonic Compendium, Lobenstein: Sorge, 1760, trans. J. M. Martin as “The Compendium harmonicum (1760) of Georg Andreas Sorge,” PhD diss., The Catholic University of America, 1981). Whereas Marpurg derives ninth, eleventh, and thirteenth chords by descending a third, fifth, or seventh, respectively, below a seventh chord’s root (expanding upon Rameau’s supposition strategy), Sorge instead ascends from the root, stacking thirds in accordance with numerical ratios. He accepts the ninth chord as a foundational entity, while the eleventh and thirteenth generally behave as chordal embellishments. Sorge addresses that art of improvisation in his Anleitung zur Fantasie (Primer on Improvisation, Lobenstern: Sorge, [1761]). John Stainer (1840–1901) In addition to careers as organist at St. Paul’s Cathedral, London, and professor at Oxford, Stainer contributed A Theory of Harmony (London: Rivingtons, 1871, editions from 1884 onward under the title A Treatise on Harmony) to the growing mix of materials for musical instruction in Victorian England. A protégé of Ouseley, Stainer promoted an intensely vertical, “stacked-thirds” approach to harmony, wherein the complete thirteenth chord was regarded as a “scale drawn out in thirds.” Two such chords, built upon the tonic and dominant roots, provide the foundation for his entire system. August Swoboda (1787–1856) The Bohemian Swoboda pursued his musical career in Vienna, where he championed and developed the ideas of his teacher, Vogler. His Harmonielehre (Instruction in Harmony, Vienna: Haykul, 1828) includes a broad-ranging consideration of modulatory techniques, emphasizing connections between distantly related keys. He also champions innovative deployments of diminished seventh and augmented sixth chords. For example, he shows how to lead from a single diminished seventh chord into any of the twenty-four keys. Ludwig Thuille (1861–1907) See Rudolf Louis.

Biographies of music theorists

Otto Tiersch (1838–1892) Tiersch taught music theory at the Stern Conservatory in Berlin and was active as an author of both textbooks and articles. His Elementarbuch der musikalischen Harmonie- und Modulationslehre (Primer on Musical Harmony and Modulation, Berlin: Oppenheim, 1874, 21888) contains sample analyses that show how a confluence of passing notes may create a colorful pitch combination that does not warrant interpretation as a harmony. John Trydell (c. 1715–1776) The Irish rector Trydell produced a concise manual of fundamental principles for musicians, Two Essays on the Theory and Practice of Music (Dublin: Grierson, 1766). The essays address theoretical and practical issues in a sophisticated, quasi-scientific manner. Block-chord harmonic progressions are analyzed using a variety of symbols: the letter K for the chord rooted on the “Key” (tonic), the numbers 2 through 7 for chords rooted on the remaining scale degrees, and the flat symbol in the context of b6 and b7 in minor keys. The system closely follows Lampe’s work of several decades earlier. Because Arabic numerals are used as well to indicate the interval each pitch forms with the bass, the examples may have seemed daunting to readers unaccustomed to such a profusion of information. The work was reprinted as the “Music” article in the first edition of the Encyclopaedia Britannica (Edinburgh, 1771). Daniel Gottlob Türk (1750–1813) For most of his adult life Türk was the leading musician in Halle, where he taught, performed, and composed. Several of his treatises address issues relating to the keyboard, including performance and temperament. His Kurze Anweisung zum Generalbaßspielen (Brief Instruction in Thoroughbass Playing, Halle and Leipzig: Türk, 1791) offers a summation of figured-bass practice, then in decline. The careful presentation, which incorporates ideas derived from Kirnberger and other theorists, made it a work of great utility for Türk’s contemporaries, and it remains so for modern musicians who seek to acquire a command of eighteenth-century musical practices.

281

282

Biographies of music theorists

Heinrich Josef Vincent (1819–1901) The forward-looking Viennese writer Vincent, whose pen name is a simplification of his actual name, Winzenhörlein, used figures of geometry as a stimulus for harmonic thinking in Die Einheit in der Tonwelt (Unity in the World of Tones, Leipzig: Matthes, 1862). Circles with clocklike divisions into twelve (representing the twelve chromatic pitches) intersect enclosed triangles and quadrilaterals that provide visual images of the basic triads and seventh chords of the tonal system. Kein Generalbass mehr! (No More Thoroughbass!, Vienna: Klemm, 1860) exposes the inadequacies of the older system in coping with modern chromatic harmony. José Joaquín de Virués y Spínola (1770–1840) The musical ideas of the Spanish general Virués y Spínola were assembled after his death by F. T. Alphonso Chaluz de Vernevil in An Original and Condensed Grammar of Harmony, Counterpoint, and Musical Composition (London: Longman, 1850). This work develops a function theory based, like Daube’s a century earlier, on three principal chords: the Cadence (C, the tonic chord), the Precadence (P, the dominant chord), and the Transcadence (T, chords that come after tonic or before dominant). Georg Joseph Vogler (1749–1814) Vogler’s musical career took him far beyond his native Germany. In his formative years he visited Italy, where Francesco Antonio Vallotti had a strong influence, and for decades thereafter his contributions to cultural life were felt in a number of musical centers and courts, including Paris, London, and locales in eastern Europe and Scandinavia. Though he was esteemed as a keyboardist, organ designer, and composer, his most lasting impact has been in the area of harmonic theory and analysis. Beginning in the 1770s, in conjunction with his teaching in Mannheim, he published volumes promoting an analytical perspective in which each chord of a block-chord progression is annotated with indication of its root (presented in staff notation), figured-bass numbers, and a capital Roman numeral corresponding to the root’s scale degree within the prevailing key. Though this practice was extended and popularized by his pupil Gottfried Weber, Vogler’s mature analyses from the first decade of the nineteenth century confirm that it was he, and not Weber, who made the most significant contributions to its development.

Biographies of music theorists

Vogler’s early writings include Tonwissenschaft und Tonse[t]zkunst (Musical Science and Composition, Mannheim: Kuhrfürstliche Hofbuchdruckerei, 1776), a compilation known as Vogler’s Tonschule, consisting of Kuhrpfälzische Tonschule and Gründe der kuhrpfälzischen Tonschule in Beispielen (The Palatine Music School and Foundations of the Palatine Music School in Examples, Offenbach: André, [1778]), and a periodical, Betrachtungen der Mannheimer Tonschule (Deliberations of the Mannheim Music School, Mannheim, 1778–81). Already at this stage, Vogler was exploring the outer reaches of harmonic practice, such as modulation via enharmonic respelling of diminished seventh chords and innovative chord progressions that proceed systematically through the keys until the starting point is reached again. (Progressions of this sort are notated on music systems shaped into full-page circles.) Vogler’s Handbuch zur Harmonielehre und für den Generalbaß (Manual of Instruction in Harmony and Thoroughbass, Prague: Barth, 1802) is an assured and Roman-numeral-saturated work, in which chromatic events are acknowledged by the analytical notation. (For example, Fs-A-C in C Major is now labeled as IVs, rather than as IV.) An entire chapter is devoted to the concept of Mehrdeutigkeit (the multiple meanings of a chord, with or without enharmonic respelling), an indispensable tool for modulating from one key to another. Among Vogler’s later works demonstrating analysis of complete compositions is his Zwei und dreisig Präludien (Thirty-Two Preludes, Munich: Falter, 1806). Johann Gottfried Walther (1684–1748) The German organist and theorist Walther is known principally for his erudite and wide-ranging Musicalisches Lexicon (Musical Dictionary, Leipzig: Deer, 1732), an extensive work incorporating both musical terms and biographies of musicians. Walther’s sizeable personal music library was the source for much of the knowledge represented in the Lexicon. Friedrich Dionys Weber (1776–1842) Friedrich Dionys Weber, a pupil of Vogler, was a founder of and instructor at the Prague Conservatory. His Theoretisch-praktisches Lehrbuch der Harmonie und des Generalbasses (Theoretical and Practical Textbook on Harmony and Thoroughbass, Prague: Berra, 1830–41) offers instruction spanning the gamut from triads through thirteenth chords. Of particular interest are examples displaying unusual contexts for dissonance. Weber

283

284

Biographies of music theorists

explains how through elision a normally required resolution pitch may be omitted. He displays the more complete versions of such progressions in separate music examples for side-by-side comparison. Gottfried Weber (1779–1839) Scale-step analysis using Roman numerals, practiced at a sophisticated level by Vogler, was fully embraced by Gottfried Weber, who concurrently pursued a legal career and musical activities in Mainz and Darmstadt. The most extensive explication of this methodology during the early nineteenth century is Weber’s Versuch einer geordneten Theorie der Tonse[t]zkunst (Mainz: Schott, 1817–21, 3rd edn., Mainz: Schott’s Söhne, 1830–32, trans. by J. F. Warner as Theory of Musical Composition, Boston: Wilkins & Carter, 1842–46, augmented by John Bishop, London: Cocks, 1851). Weber packs more data into his symbols than does Vogler: each chord’s quality is indicated by the size of the numeral (capital versus small capital for major or minor, respectively, or a degree circle to the left of a small-capital numeral for diminished quality), and the presence of a chordal seventh is indicated by an Arabic 7 appearing alongside the numeral (slashed if the seventh is of major quality). In addition, Weber is more tolerant of passing phenomena than was Vogler. Not all vertical entities are given separate labels (though he, like Vogler, asserts that what is now often called the “cadential 64” should be labeled “I” and that those who disagree are indulging in an “unnecessarily ingenious fiction”). Weber also is less rigid in assigning chordal roots: for example, to Vogler B-D-F or B-D-F-Ab would inevitably be assigned root B. Weber might assign G instead. Both authors are fascinated by multiple meaning (Mehrdeutigkeit), including that which incorporates enharmonic reinterpretation. And both focus principally on connections of adjacent chords, rather than on broader harmonic trajectories. In fact, Weber asserts that there are in all 6,888 two-chord progressions, any of which may be utilized. His ingenious chart of key relationships places relative keys, parallel keys, and keys related by fifth in the closest alliance. Carl Friedrich Weitzmann (1808–1880) Weitzmann’s writings on harmony are among the most innovative and insightful contributions to the field from the middle of the nineteenth century. His bond with Liszt made him something of a “house theorist” for the progressive movement in Germany (literally so, since he gave lessons to Liszt’s daughter and Wagner’s future wife, Cosima). His systematic investi-

Biographies of music theorists

gation of the chords most susceptible to enharmonic reinterpretation led to the publication of Die übermäßige Dreiklang (The Augmented Triad, Berlin: Trautwein, 1853) and Der verminderte Septimen-Akkord (The Diminished Seventh-Chord, Berlin: Peters, 1854). Though he acknowledges conventional resolutions of chordal dissonance, his exploration of a wide range of “common-tone” resolutions (e.g., B-Es-Gs-CS to B-Fs-Ds) is more revelatory. He shows how one diminished seventh chord may proceed to closure in any of the twenty-four keys. (Swoboda had developed ideas along these lines as well.) Yet Auflösung – resolution into a consonant chord – is not the only option. A new dissonant chord may appear where the resolution is expected, creating a Trugfortschreitung (deceptive succession, a term also employed by Dehn). Spurred by a competition sponsored by the Neue Zeitschrift für Musik, Weitzmann composed a summation of his ideas, later expanded for publication as Harmoniesystem (System of Harmony, Leipzig: Kahnt, [1860]) and defended in Die neue Harmonielehre im Streit mit der alten (The Clash between the Old and New Modes of Harmony Instruction, Leipzig: Kahnt, [1861]). His views on chordal succession are liberating: he follows Gottfried Weber in suggesting that any chord may lead to any other. He especially favors the close relation between adjacent chords achieved when only one pitch moves (e.g., C-E-G to C-E-A or to B-E-G). Andreas Werckmeister (1645–1706) The Thuringian organist Werckmeister was a prolific author of music treatises, which appeared at frequent intervals from 1681 until his death. These works encompass a wide range of topics pertinent to Lutheran musicians of the Baroque, with emphasis on organ construction, tuning and temperament, and thoroughbass. His fascination with mathematics is blended with a vigorous and imaginative theological perspective. Ernst Wilhelm Wolf (1735–1792) Wolf ’s career as a composer blossomed in Weimar, where he performed duties as court concertmaster and organist. Though influenced by contemporary composers such as C. P. E. Bach, he also esteemed J. S. Bach and Händel. His Musikalischer Unterricht (Musical Instruction, Dresden: Hilscher, 1788) addresses a wide range of musical topics, including harmonic and contrapuntal practices. Especially noteworthy is an ambitious analysis (called an Erklärung, or explanation) of a passage from one of Händel’s oratorios. His prose commentary focuses on naming the keys through which the

285

286

Biographies of music theorists

eleven-measure excerpt modulates, identifying the dominant chords, and making note of the cadences. Gioseffo Zarlino (1517–1590) The celebrated Venetian church musician Zarlino was the voice of authority to musical authors of the eighteenth century, especially to Rameau. In Le istitutioni harmoniche (The Harmonic Institution, Venice: 1558), Zarlino undertakes a synthesis of speculation and practice that, in an updated context, was mirrored by Rameau in his Traité de l’harmonie (1772). Both authors base their speculations upon numerical ratios tested on a monochord. Zarlino accepts the first six integers (his senario) as the source for consonant intervals – both the perfect consonances of antiquity and the imperfect consonances that had been absorbed into the practice of his time. His pronouncements on chordal formations had a profound impact upon later generations, and his formulation of contrapuntal rules served as a guide for composition in the prima prattica. Carl Friedrich Zelter (1758–1832) Active in Berlin as a choral conductor and lieder composer, Zelter was an avid correspondent with Goethe regarding musical matters and played an important role in reforming music instruction in the German lands. He had studied under Kirnberger, and he taught a number of younger composers, including Mendelssohn and Meyerbeer.

Notes and references

The reader wishing to follow up a citation of a primary source, such as Kirnberger’s Die Kunst des reinen Satzes in der Musik (1771–79), will find it under Kirnberger in the Biographies of music theorists (starting on p. 244), including details of any English translation (here, Beach and Thym). Citations of selected secondary sources, such as Lester’s Compositional Theory in the Eighteenth Century (1992), may be found in the Select bibliography (starting on p. 322).

1 Chord identification 1 Kirnberger, Die Kunst des reinen Satzes in der Musik (1771–79), vol. 1, p. 27 [Beach and Thym, p. 41]. This view was widely shared. 2 Joel Lester assesses both the theoretical recognition of chordal inversion and its spontaneous application by Iberian guitar and theorbo players in the late sixteenth and seventeenth centuries. See his Compositional Theory in the Eighteenth Century (1992), pp. 96–100. 3 “Since the tonic note, its mediant, and its dominant can each bear a chord made up of the same sounds, we should bear in mind that whenever the natural progression of the bass leads to the principal one of these notes, which is the tonic, either of the two others may be substituted for it.” Rameau, Traité de la harmonie (1722), p. 225 [Gossett, p. 245]. 4 An example of Rameau’s notational practice appears in 1.18. Note especially the captions “4me. Notte” and “Notte tonique.” On rare occasions Rameau labels bass pitches using thin abbreviations of his terms for the scale degrees, as shown in 7.3a. 5 Lampe, who advertised himself as a “sometime student of Helmstad in Saxony,” perhaps carried this practice with him on his migration to London. For facsimile pages, selective transcription, and commentary on these rudimentary analyses, see Lester, Compositional Theory in the Eighteenth Century (1992), pp. 82–87; Alfred Dürr, “Ein Dokument aus dem Unterricht Bachs?,” Musiktheorie 1/2 (1986), pp. 163–170; and Heinrich Deppert, “Anmerkungen zu Alfred Dürr,” Musiktheorie 2/1 (1987), pp. 107–108. 6 A partial English translation of Rameau’s Traité de l’harmonie (1722) appeared in London in 1752, suggesting that the goings-on across the channel were being followed with interest in England before that date. In fact, Lampe quotes – in the original French – passages from the Traité in his second book, The Art of Musick (1740), pp. 46 and 47.

288

Notes and references to pages 4–10

7 “die Gleichgültigkeit gegenüber der Differenz zwischen dem 53- und dem 63-Klang mit gleichem Baßton. Der Akkordzusammenhang beruht auf dem realen Baß, nicht auf der abstrakten ‘Basse fondamentale’.” Dahlhaus, Üntersuchungen über die Entstehung der harmonischen Tonalität (1968), p. 134. 8 Holden, An Essay towards a Rational System of Music (1770), p. 131. 9 Sorge, Vorgemach der musicalischen Composition [1745–47], p. 115; Compendium harmonicum (1760), p. 9. 10 Vogler, Tonwissenschaft und Tonse[t]zkunst (1776), p. 50. Those lacking prior exposure to German musical terminology should note that “B” stands for Bb and “H” for Bn. (The famous melody B–A–C–H is Bb–A–C–Bn.) 11 Vogler, Tonwissenschaft, p. 82. Observe that Vogler displays none of Lampe’s or Sorge’s timidity concerning chords containing a diminished fifth above their root. Whereas Lampe labels B-D-F in C Major as “5.th” [1.1] and Sorge avoids diminished triads in his table, Vogler labels B-D-F-Ab as VII. 12 Portmann, Musikalischer Unterricht (1785), examples supplement, p. 12, fig. 9. 13 “Die in jedem Fache der Sextquinten- Terzquarten- und Secundenaccorde beygefügte Zahl zeigt die Stufe der Tonleiter an, auf welcher der Stammaccord derselben seinen Sitz hat.” Koch, Versuch einer Anleitung zur Composition (1782–93), vol. 1, pp. 97–99. 14 Though Richter and Lobe represent the main branches of notation for harmonic analysis at mid-century, there were interesting variants throughout Europe. François Camille Antoine Durutte, whose Esthétique musicale: technie, ou lois générales du système harmonique appeared in Paris in 1855, merges three Arabic numerals as an analytical symbol. For example, 723 corresponds to a seventh chord rooted on the second scale degree, in third inversion (e.g., C-D-F-A in C Major). Heinrich Josef Vincent, whose Kein Generalbass mehr! appeared in Vienna in 1860, uses capital Roman numerals followed by a variety of squiggly lines indicating triadic quality, be it hart (C-E-G), weich (D-F-A), klein (B-D-F), hartklein (C-E-Fs), übermässig (C-E-Gs), or weichübermässig (C-Eb-Ab). 15 “Wir wenden uns nun zu den Accorden selbst, die man bey Erlernung des Generalbaßes, in einer jeden Tonart, zu wissen nöthig hat, solche sind: der vollkommene und herrschende Accord; dieser hebt ein Stück an, und endigt auch dasselbe. Seine beyden untergebenen Accorde, die im Laufe der Melodie vorkommen, nämlich der zweyte und dritte Accord. Ihre Harmonie ist ganz vom herrschenden Accorde unterschieden. Wir werden sie in der Folge erklären.” Daube, Der musikalishe Dilettant: Eine Abhandlung des Generalbasses (1770–71), p. 49. 16 Rameau’s foundational Clermont notes, which precede his epochal Traité de l’harmonie (1722), formulate only three basic chords: the accord parfait, accord de grande-sixte, and accord de 7e de dominante. These notes, now lost, are described by Thomas Christensen in Rameau and Musical Thought in the Enlightenment (1993), pp. 23–26. 17 Rameau, Nouveau système de musique théorique (1726), p. 24. Whereas for Daube tonic is the foundation of the system, with the ascending numbers 1

Notes and references to pages 10–11

through 3 corresponding to the order in which the chords would most typically occur in a composition, Rameau’s “triple progression” is symmetrical: for example, in the geometric ratio 1:3:9 tonic G (3) is flanked by C (1) and D (9). The subdominant thus grounds his system. It is awkward for Rameau that tonic is a derived chord, yet the subdominant cannot otherwise relate to the other chords in whole-number ratios. Thomas Christensen assesses how the subdominant gradually attained status – at the expense of the Renaissance-favored mediant – in Rameau and Musical Thought in the Enlightenment (1993), pp. 179–185. 18 Schröter, Deutliche Anweisung zum General-Baß (1772), p. 30. He explains: “Secondly one will recall from the preceding that the Fifth is always preferable to the Fourth; thus one will agree that G Major is the first and F Major the second relation to C Major, and consequently the following hierarchy prevails among these three: [Example].” [“Zweytens errinere man sich aus dem vorigen, daß die Quinte in allen Vorfällen den Vorzug vor der Quarte habe; so wird man überzeuget, daß G dur der erste, und F dur der zweyte Verwandte vom C dur sey, mithin unter diesen dreyen folgende Rangordnung entsteht: [Example].”] Sorge presents a similar ranking in his Anleitung zur Fantasie [1767], p. 27: C-E-G is the “Grund- oder Endigungs-Accord” (foundational or closing chord), G-B-D is the “herrschende Accord” (dominating chord), and F-A-C is the “NebenAccord” (auxiliary chord). A trace of this perspective recurs well into the following century in Peter Singer’s Metaphysische Blicke in die Tonwelt (1847), where a chart shows the major triad and, in its train (im Gefolge), “der I. Hilfsharmonie auf der Oberdominante” and “der II. Hilfsharmonie auf der Unterdominante” (after p. 64). 19 “Zu noch leichterer Erlernung des Generalbaßes in der Tonart C dur haben wir hier die Baßstimme durch unten angehenkte Bögen so bezeichnet, daß ein jeder gleich sieht, wie viele Baßnoten zu einem Accord angeschlagen werden, und welcher von den drey Accorden es ist. Hat nun ein Liebhaber die drey Accorde recht gefaßt, so kann er etlichemale die Accorde, wie sie da stehen, nehmen: dann darf er nur auf die, in dem Bogen stehende, Ziffer sehen, und nach dieser denjenigen Accord anspielen, welchen sie vorstellt, ohne sich an die in Noten ausgedrückte Accorde zu kehren. Nimmt er auch die drey Accorde in einer andern Stelle oder Umwendung, als sie hier im Sopran vorgestellt sind; so hat es nichts zu bedeuten, es bleibt doch allezeit ein- und der nämliche Accord. Es ist ohnehin gar nicht gemeinet, daß ein Liebhaber die Accorde jederzeit so nehmen solle, wie sie hier stehen: denn diese haben keine andere Bestimmung, als dadurch zu zeigen: wenn, und wo zu einer Baßstimme ein Accord kann angegeben werden, welches vor einen Angehenden keine geringe Erleichterung ist.” Daube, Der musikalishe Dilettant: Eine Abhandlung des Generalbasses (1770–71), p. 90. 20 Koch, Versuch einer Anleitung zur Composition (1782–93), vol. 1, p. 53. Similarly Joseph Riepel, in his Baßschlüssel (1786), p. 6, segregates the Grundbaßnoten (the foundational bass notes on the first, fourth, and fifth scale degrees) from

289

290

Notes and references to pages 12–14

21 22

23

24

25

26

27 28

the others, which he names in three ways: Nebentöne (subsidiary notes), Ausfüllungstöne (filler notes), and, promoting their status “in recognition of their good service,” Mittelbaßnoten (intermediate bass notes). Weber, Versuch einer geordneten Theorie der Tonse[t]zkunst [1817–21], vol. 1, pp. 219, 222 [Warner, p. 259]. “Sie sind nur deßwegen erfunden worden, um der Harmonie manche unvermuthete Wendung, und überhaupt mehr Abwechslung zu verschaffen.” Swoboda, Harmonielehre (1828), p. 76. “Dieser Accord wird nur gebraucht, um nicht immer die Tonica und Dominante hören zu müssen, und heißt darum Mittel- oder Wechselharmonie, weil er eine Abwechslung der Klanghören erzeugt.” Swoboda, Harmonielehre (1828), p. 64. In his “Tabelle III” (after p. 88), he shows progressions that incorporate both I– IV–V and V–IV–I. (The Roman numerals, which display a retained allegiance to the Stufentheorie perspective, are his.) The preeminence of tonic and dominant is affirmed by Matthew Peter King, an English composer of theater music, in A General Treatise on Music (1801), p. 21: “The whole system of harmony is founded on two chords; on the fundamental concord, and a fundamental discord: and from these two chords or roots, arise all others. In a word; the two fundamental chords, are the chords of nature, and those derived from them the chords of art.” Portmann, Die neuesten und wichtigsten Entdeckungen in der Harmonie, Melodie und dem doppelten Contrapuncte (1798), pp. 27–33. An earlier formulation, in his Leichtes Lehrbuch der Harmonie, Composition und des Generalbaßes (1789), contains five rather than six Grundharmonien: the Quartenharmonie is lacking. As mentioned above (pp. 6–7), his first work on harmony, Musikalischer Unterricht (1785), pursues an altogether different agenda. It is a Stufentheorie whose Arabic-numeral symbols correspond to the chordal roots. The interpretation of B-D-F as representative of G-B-D-F was Lampe’s principal point in 1.1, above. Interpreting D-F-A as a derivative of G-B-D-F-A may not be palatable to musicians accustomed to the notion of a supertonic chord that precedes the dominant, though Portmann is not alone in making this claim. (See 1.16.) Gottfried Harbordt, a student of Portmann, completed a fascinating and extensive manuscript treatise in which Portmann’s analytical system is employed. This work, “Lehrbuch der Harmonie, Melodie und des doppelten Contrapuncts,” is housed at the Library of Congress in Washington, D.C. Virués y Spínola and Chaluz de Vernevil, An Original and Condensed Grammar of Harmony, Counterpoint, and Musical Composition (1850), p. 73. Readers interested in exploring Riemann’s perspective will find Carl Dahlhaus’s “The Theory of Harmonic Tonality” in his Studies on the Origin of Harmonic Tonality (trans. Gjerdingen, 1990, pp. 7–65) a useful starting point. For provocative recent resuscitations of function theory, see Daniel Harrison, Harmonic Function in Chromatic Music (1994); and Eytan Agmon, “Functional

Notes and references to pages 17–22

29 30

31

32

33 34

Harmony Revisited: A Prototype-Theoretic Approach,” Music Theory Spectrum 17/2 (1995), pp. 196–214. Harrison calls Riemann “the celebrated inventor of the theory of harmonic function,” though acknowledging that he “so confused its explanation that the idea virtually self-deconstructs, leaving conflicting motivations – some noble, some mean – strewn across his field of discourse, leaving it to others to pick up whatever pieces they find useful” (p. 253). Weber: Versuch einer geordneten Theorie der Tonse[t]zkunst (1817–21, 3 1830–32), vol. 1, pp. 276–277 [Warner, p. 228]. Lampe, A Plain and Compendious Method of Teaching Thorough Bass (1737), p. 23. This perspective correlates with Sorge’s chart of chords (presented on p. 5, above) published in the following decade. Koch describes the fifth scale degree as the leading tone triad’s true (eigentlich) root in his Versuch einer Anleitung zur Composition (1782–93), vol. 1, pp. 73–74; Weber explains that “a principal four-fold chord with the fundamental tone omitted appears exactly like a diminished three-fold chord” in his Versuch einer geordneten Theorie der Tonse[t]zkunst (1817–21), vol. 1, p. 159 [Warner, p. 193]; at the end of the nineteenth century Ebenezer Prout calls the leading-tone chord a dominant “derivative” (see p. 312, n. 42, below). Rameau, Traité de l’harmonie (1722), p. 43 [Gossett, p. 50]. As with so much else in his theoretical output, Rameau’s ideas concerning the diminished seventh chord shifted over time. In his Génération harmonique (1737), chapter 14, Rameau builds the diminished seventh chord by combining elements from the dominant and subdominant chords. Concerning essential and incidental dissonances, see p. 37. Likewise the origin of the minor triad was a perennial problem from an acoustical perspective. Yet theorists could not dismiss minor quality so readily as some did diminished quality. The conundrum led to one of the most egregious wrong turns in the history of tonal theory: Riemann’s undertone series. Whereas the major triad is derived upwards from its root ( G E ) Riemann derived the minor C triad by proceeding downwards F )! C Ab

35 “entweder ein verkürzter Septimenaccord der Dominante einer Durtonart, davon der Grundton weggelassen ist, oder ein verkürzter Nonenaccord der Dominante einer Molltonart, wovon zwei Intervalle weggelassen sind.” Portmann, Leichtes Lehrbuch der Harmonie (1789), p. 26. In this treatise Portmann pursues a Stufentheorie perspective, not the Funktionstheorie perspective that, as we have seen, he would later adopt. Yet his treatment of the diminished triad under discussion would not change in his functional outlook: it would be regarded as a representative of the minor key’s Dominantenharmonie, E-Gs-B-D-F-A-C. 36 Christensen, in Rameau and Musical Thought in the Enlightenment (1993), p. 124, explains: “The argument is not . . . simply that the octave is the ‘boundary’ of all intervals. While Rameau indeed made this point, the real issue for him

291

292

Notes and references to pages 22–30

37 38

39

40

41 42 43 44 45

46 47

48 49 50

was that dissonance should be reduced to a single source if at all possible, and the seventh seemed to serve as that source.” Rameau, Traité de l’harmonie (1722), pp. 73–74 [Gossett, p. 88]. André, Lehrbuch der Tonse[t]zkunst (1832), vol. 1, pp. xiii–xvi. Though his symbols were not widely adopted, his penchant for presenting a wide range of chordal possibilities is shared by numerous authors. “[Macfarren’s] explanation was that Mendelssohn was so opposed to theorizing about the beautiful art which he so enriched by his productions, not that he rejected Dr. Day’s theories in themselves.” See Henry Charles Banister, George Alexander Macfarren: His Life, Works, and Influence (London: George Bell & Sons, 1892), pp. 117–118. Stainer’s most extensive discussion of this passage, in which he evaluates several hypothetical alternative contexts for the 6s chord, occurs in A Treatise on 5 Harmony, a revision of his A Theory of Harmony (1871). In the undated eighth edition (1884 or later), the relevant page numbers are 79–82. A Treatise of Musick, Containing the Principles of Composition (1752), p. 107; Rameau, Traité de l’harmonie (1722), p. 290 [Gossett, p. 308]. Macfarren, Rudiments of Harmony (1860), p. 37. We have encountered these chords before, as Portmann’s Hauptprimenharmonie and Dominantenharmonie. See p. 13, above. Stainer, A Treatise on Harmony [1871, 8A Treatise on Harmony, 1884 or later], pp. 16–17. Ibid., p. 100. “Other degrees do, in a modified form, bear upon them certain chords, but the number of chords thus to be formed is limited by the fact that any attempt to construct a series of chords on the same principle pursued when forming them upon the tonic or dominant will be found to result in the production of chords having definite tonic or dominant relations, and which have already been explained in their proper place” (p. 97). This perspective does not prevent Stainer from later naming six “common chords” within a key: tonic, dominant, subdominant and their relative minors (p. 110). Ibid., p. 46, transposing the sample D-F-A-C chord to Fs-A-Cs-E. Ibid., pp. 48–49. Macfarren takes a more relaxed view concerning this seventh in his Six Lectures on Harmony (1867), pp. 160–161: “There being then no sounded note with which the 7th forms a dissonance, in the absence of both the root and the 3rd of the chord, the 7th has no longer any of its septimal characteristics, but is . . . free in its progression.” Macfarren, Six Lectures on Harmony (1867), p. 161. Kirnberger, Die Kunst des reinen Satzes in der Musik (1771–79): vol. 1, table II (between pp. 32 and 33) [Beach and Thym, pp. 49–50]. Kirnberger, Die Kunst des reinen Satzes in der Musik (1771–79), vol. 1, p. 114 (n.) [Beach and Thym, p. 131 (n.)].

Notes and references to pages 31–34

2 Chordal Embellishment 1 Among the low-integer ratios from the root, 1:2 and 1:4 produce octave replicates, while 1:3 generates a compound perfect fifth (origin of the major triad’s fifth) and 1:5 generates a compound major third (origin of the major triad’s third). Of course, the interface between acoustics and composition falls apart when considering the minor triad. That issue remained one of the central problems of harmonic speculation from Rameau through Riemann. Today most musicians who think about such things regard minor as a product of human intervention upon the major triad, not as directly derived from the acoustical properties of the pitches involved. Rameau had proposed a dual generation merging the root’s perfect fifth and the third’s major third (C-G + Eb-G), while Riemann built the chord as a major third and perfect fifth downwards from the fifth (G-Eb-C). 2 Lobe, whom we encountered briefly in chapter 1 [1.15], offers an especially thorough and notation-intensive perspective on embellishment. We will explore his terms and symbols in detail later in this chapter. (See pp. 40–42, below.) 3 Of course, thoroughbass practice antedates the widespread awareness of chordal roots and the tracking of their progression (which emerged in the early eighteenth century). The problem became acute only as root began to displace bass as a central concern of theoretical discourse. 4 Scott Burnham offers a sympathetic assessment of Rameau’s fundamental-bass perspective on suspensions in his “Musical and Intellectual Values: Interpreting the History of Tonal Theory,” Current Musicology 53 (1993), pp. 76–88. 5 The example would possess a fundamental bass with no ascending seconds if all the fourths and ninths were treated as suspensions. An alternative fundamentalbass line might read as G | D B | E | B | . . . 6 “La note de suspension n’est que de goût, elle n’a point de basse fond et si on luy en donne une ce n’est seulement que pour la prouver la satisfaction de voir qu’elle tire le plus souvent son origine de la supposition. Mais comme cela n’est d’aucunne utilité dans la pratique il vaut mieux en reconnoissant la note de suspension la compter pour rien et luy donner pour basse fond celle de consonance qu’elle suspend et qui la suit immédiatement.” Rameau, “L’art de la basse fondamentale,” folio 86r, quoted by Thomas Christensen in Rameau and Musical Thought in the Enlightenment (1993), p. 126, fn. 73; see also pp. 309–12. 7 See Lauren M. Longo, “Pietro Gianotti’s Le guide du compositeur, A Reworking of Rameau’s ‘L’art de la basse fondamentale’: An Annotated Translation and Critical Edition of Part I” (PhD diss., City University of New York, 1997). 8 Rameau, Traité de l’harmonie (1722), p. 214 [Gossett, p. 234]. 9 “Il y a deux manieres de pratiquer les accords de neuviéme & de onziéme, sçavoir, la supposition & la suspension.” Béthizy, Exposition de la théorie et de la pratique de la musique suivant les nouvelles découvertes (1754), p. 187.

293

294

Notes and references to pages 37–46

10 In his Vorgemach der musicalischen Composition [1745–47], p. 335, Sorge employs the same terminology, though with a different meaning. For Sorge seconds (ninths) and sevenths above the bass are essential dissonances, while consonances that form a second or seventh with an upper pitch, such as the D— CB fourth C in C–B or the fifth C in DF DG, are incidental dissonances. G— 11 Kirnberger, Die Kunst des reinen Satzes in der Musik (1771–79), vol. 1, p. 33 [Beach and Thym, p. 46]. 12 Ibid., insert between pp. 32 and 33 of vol. 1 [Beach and Thym, p. 51]; Kirnberger/[Schulz], Die wahren Grundsätze (1773), p. 46 [Beach and Thym, p. 202]. 13 Kirnberger, Die Kunst des reinen Satzes in der Musik (1771–79), vol. 1, p. 66 [Beach and Thym, p. 85]. For commentary on Kirnberger’s derivation of the diminished seventh chord, see 1.14a. 14 “Die Vorschläge sind eine der nöthigsten Manieren. Sie verbessern so wohl die Melodie als auch die Harmonie. . . . Im andern Falle verändern sie die Harmonie, welche ohne diese Vorschläge zu simple würde gewesen seyn.” Bach, Versuch über die wahre Art das Clavier zu spielen (1753–62), vol. 1, p. 63. 15 Kirnberger, Die Kunst des reinen Satzes in der Musik (1771–79), vol. 1, p. 86 [Beach and Thym, p. 104]. 16 Ibid., vol. 1, p. 191 [Beach and Thym, p. 207]. 17 Koch presents Kirnberger’s conception of dissonance in the article “Accord” (Chord) in his massive Musikalisches Lexikon (1802), columns 97–126. In his figure 15 (column 103), both the 6 and the 4 of a suspension 64 chord are classified as incidental dissonances (Kirnberger’s zufällige Dissonanzen), which Koch in his Handbuch calls Hauptdissonanzen. 18 Here Koch concurs with Sorge, who asserts that “a dissonant chord as little becomes consonant through inversion as can a consonant chord become dissonant through inversion.” [“Ein dissonirender Satz wird durch die Versetzung so wenig consonirend, als ein consonirender Satz durch die Versetzung dissonirend werden kan.”] See Vorgemach der musicalischen Composition [1745– 47], p. 113. 19 Stainer, A Treatise on Harmony [1871, 8A Treatise on Harmony, 1884 or later], p. 89. 20 Beethoven slurs all three of the excerpt’s F–E melodic steps and marks F with a rinf [orzando] in the first two instances. Stainer either was unaware of these markings or elected to omit them. Certainly they support the interpretation of F as a neighboring embellishment (appoggiatura). Also note that, just as a 64 chord occurs interior to the voice exchange (FAb⫻Ab in measure 3 of 2.7 (discussed F E E above), similar 64 chords occur in the voice exchanges (Cs ⫻Cs ⫻Cs ) in 2.12. In the E . former case, Lobe’s analysis is an unwavering Es: 5 (dominant seventh in Eb Major); in the latter case, it likely would be d: 5° (dominant ninth in D Minor, with absent root). 21 Chordal hierarchy is the topic of chapter 5.

Notes and references to pages 48–50

22 The stepwise descent of a seventh (Db to Eb) does not establish a harmonic relationship between the Db (II) and Eb (V) chords. That view is espoused by Gary E. Wittlich in his “Compositional Premises in Schubert’s Opus 94, Number 6,” In Theory Only 5/8 (1981), pp. 31–43. Instead Db is a neighbor to tonic’s third, C, as the bracket connecting bass pitches Ab and C in 2.15a suggests. 23 An interesting question concerns the hierarchical relation between the two chords in measure 6: does bass G connect Ab and F, or does bass F connect G and Eb? In support of the first view, consider the other associations that Schubert has set up within the phrase: measure 1 leads into measure 2, as does measure 3 into 4 and measure 7 into 8. At a swifter pace, the first chord of measure 5 leads into the second, and the first chord of measure 6 into the second. If IIn were in root position, then the two chords of measure 6 might have appeared as a conven8–7 tional 6–5 (all over bass Bb), in which the dependency of the first chord upon the 4–3n second would be less ambiguous. (For example, see the third measure of 6.21a, though note that Schenker analyzes IIn–V as V–I in the dominant key.) 24 William Kinderman provides further evidence that “the influence of Beethoven’s sonatas tends to surface in Schubert’s works in the corresponding keys.” See his “Schubert’s Piano Music: Probing the Human Condition” in The Cambridge Companion to Schubert, ed. Christopher H. Gibbs (Cambridge: Cambridge University Press, 1997), p. 157. See also Edward T. Cone, “Schubert’s Beethoven,” The Musical Quarterly 56/4 (1970), pp. 779–793. 25 “Als nämlich Schubert das Liedchen ‘Die Forelle’ komponiert hatte, brachte er es am selben Tage zu uns ins Konvikt zum Probieren, und es wurde mit dem lebhaftesten Vergnügen mehrmals wiederholt; plötzlich rief Holzapfel: ‘Himmel, Schubert, das hast du aus dem ‘Coriolan’. ” “In der Ouvertüre jener Oper ist nämlich eine Stelle, die mit der Klavierbegleitung in der ‘Forelle’ Ähnlichkeit hat; sogleich fand dieses auch Schubert und wollte das Lied wieder vernichten, was wir aber nicht zuließen und so jenes herrliche Lied vom Untergang retteten.” Johann Leopold Ebner, reporting from Innsbruck on May 3, 1858. Quoted in Schubert: Die Erinnerungen seiner Freunde, ed. Otto Erich Deutsch (Leipzig: Breitkopf & Härtel, 1957), p. 55. 26 Newbould makes this comment in reference to a Mozart/Schubert connection. See his Schubert: The Music and the Man (Berkeley and Los Angeles: University of California Press, 1997), p. 85. 27 The Sardanapalus legend also inspired a play by Byron (1821) and a painting by Delacroix (Salon of 1827–28). 28 “son harmonie, formée d’agrégations souvent monstrueusés de notes, était néanmoins plate et monotone . . . dans ce long morceau . . . il n’y a que des monstruosites d’harmonie, sans charme, sans effets qui réveillent.” Fétis’s review appeared in Revue musicale 9/5 (February 1, 1835), pp. 33–35. A translation of the entire review by Edward T. Cone appears in his Berlioz “Fantastic Symphony”: An Authoritative Score, Historical Background, Analysis, Views and Comments (New York: W. W. Norton, 1971), pp. 215–220. For an overview of Fétis’s

295

296

Notes and references to pages 50–57

29

30

31

32

activities as reviewer and editor, see Katharine Ellis, Music Criticism in Nineteenth-Century France: “La Revue et Gazette musicale de Paris,” 1834–80 (Cambridge: Cambridge University Press, 1995), chapter 11, pp. 219–234. Schumann’s review appeared in Neue Zeitschrift für Music 3/1, 9–13 (July–August 1835), pp. 1–2, 33–35, 37–38, 41–44, 45–48, 49–51. This excerpt appears on p. 41. Complete English translations of the review appear in Cone, Berlioz “Fantastic Symphony” (1971), pp. 222–248, and in Ian Bent, Music Analysis in the Nineteenth Century (Cambridge: Cambridge University Press, 1994), vol. 2, pp. 166–194. Both Cone and Bent provide additional commentary, and Cone offers a substantial analysis. The passage quoted reads as follows: “Ist mir jemals etwas unbegreiflich vorgekommen, so ist es das summarische Urtheil des Herrn Fétis in den Worten: je vis, qu’il manquait d’idées melodiques et harmoniques. Möchte er, wie er auch gethan, Berlioz alles absprechen, als da ist: Phantasie, Erfindung, Originalität, – aber Melodieen- und HarmonieenReichthum? da läßt sich nicht darauf antworten. Es fällt mir gar nicht ein, gegen jene übrigens glänzend und geistreich geschriebene Recension zu polemisieren, da ich in ihr nicht etwa Persönlichkeit oder Ungerechtigkeit, sondern geradezu Blindheit, völligen Mangel eines Organs für diese Art von Musik erblicke.” The manuscript version of measures 82 through 86 is published in Cone, Berlioz “Fantastic Symphony” (1971), p. 256. A dominant does harmonize this segment of the melody later in the movement (measures 253–254), in the tonicized key of G Major. Cone regards measure 84 as a 64 preparation for dominant, scantily represented by its seventh F in measure 85. This reading of what he calls “the deliberate ambiguity of the harmony” is feasible, but I think it sanitizes Berlioz more than the passage deserves. See Cone, Berlioz “Fantastic Symphony” (1971), pp. 254–256. I regard the return of tonic to be intentionally premature, enhancing the musical depiction of our protagonist’s emotional state. The melody had been employed previously in Berlioz’s cantata Herminie, which took Second Prize in the 1828 Prix de Rome competition. Based on Tasso, it is a tale of unhappy love. The text reads, in part: “But I adore you, alas! irrevocably, hopelessly.” The Herminie harmonization made its way into the Fantastique manuscript, but Berlioz then tinkered with it. (Alas! Berlioz’s irrevocable and hopeless love for Smithson did eventually subside. They separated in 1844, and Berlioz married his mistress soon after Smithson died in 1854.) Reicha, Cours de composition musicale [1816], p. 44. Similar progressions had previously been printed in treatises by Kirnberger and Catel [3.11b]. Fétis offers a vivid and very negative assessment of Reicha’s theory in the concluding book of his Traité complet de la théorie et de la pratique de l’harmonie (1844). A brief excerpt: “These observations suffice to demonstrate that, no less erroneous than the systems already analyzed, that of Reicha does not have even the merit of logical conception, for it rests on a defective foundation. Such then is this system that has been so much in fashion among some artists in Paris, because the

Notes and references to pages 58–60

professor who conceived it would neglect these faults in the explanations and practical applications which he would present to his students. Let me repeat, this system is the least rational conception of the theory that it would be possible to imagine, and the most deplorable return to the gross empiricism of the outmoded methods from the beginning of the eighteenth century.” [“Ces observations suffisent pour démontrer que, non moins erroné que les systèmes précédemment analysés, celui de Reicha n’a pas même leur mérite de conception logique, reposant sur une base vicieuse. Tel est donc ce système qui a eu beaucoup de vogue parmi quelques artistes de Paris, parce que le professeur dont il est l’ouvrage faisait oublier ses défauts dans les explications et dans les applications pratiques qu’il donnait à ses élèves. Je le répète, ce système est une conception de la théorie la moins rationnelle qu’il fùt possible d’imaginer, et le retour le plus déplorable vers l’empirisme grossier des anciennes méthodes du commencement du dix-huitième siècle” (p. 242).]

3 Parallel and sequential progressions 1 Portmann, Musikalischer Unterricht (1785), example supplement, p. 9, fig. 7. This perspective prevails in his function-theory notation as well. (See 3.1f, an analysis by Portmann’s student Harbordt.) 2 “Daß aber die Griechen keine andre Harmonie sollen gehabt haben, als nur den Einklang, die 8, 4 und 5, ist kaum zu glauben, da doch die Terzengänge im Singen so natürlich und leicht sind, daß man öfters Leute singen hört, die nicht das geringste in der Musik gelernet haben, und dennoch terzenweis zu singen wissen.” Daube, Der musikalishe Dilettant: Eine Abhandlung des Generalbasses (1770–71), pp. 19–20. Schenker quotes Albrechtsberger’s pronouncement that more than three consecutive thirds or sixths in similar motion in simple counterpoint would resemble a street song (Schenker, Kontrapunkt (1910–22), book 1, p. 220). In an earlier article he writes: “If the intervals of the fifth and the fourth predominate in the early practice of two- or three-voice singing, this happened, I am convinced, not because the theory deems these intervals to be consonant, but rather because it was possible for everyone to sing the melody as they knew it, even if some sang higher or lower than others. Is it not both touching and natural that initially no one resolved merely to provide musical support for the other singers, that it would not have occurred to anyone to give up the melody that was, so to speak, an item of personal property?” [“Wenn man beim ersten Anbruche der Zwei- und Dreistimmigkeit in Quint- und Quartintervallen sang, so geschah dies, wie ich überzeugt bin, nicht etwa darum, weil die Intervalle nach der Theorie consonirten, sondern weil es so Jedermann möglich war, die Melodie zu singen, wie er sie kannte, trotzdem er sie aus einem anderen Tone sang. Ist das nich rührend und natürlich zugleich, dass sich am Anfange Niemand gerne entschliessen wollte, dem Anderen (Mitsingenden) in Tönen blos zu dienen, es Niemandem zunächst einfallen wollte, auf die Melodie, die

297

298

Notes and references to pages 60–85

3

4

5

6 7 8

9 10

11

gleichsam sein persönliches Gut war, zu verzichten?”] See Schenker, “Der Geist der musikalischen Technik,” Musikalisches Wochenblatt 26/20 (1895), p. 258. “A quels intervalles deux Mélodies peuvent elles marcher ensemble?” Momigny, La seule vraie théorie de la musique [1821], p. 25. In La panharmonie musicale (1837), p. 19, Raymond Hippolyte Colet confirms the superiority of thirds in such contexts: “It is evident then that two parts proceeding in [parallel] thirds will yield an effect that is full of charm and melodiousness.” [“Il est évident alors que deux parties marchant par 3ces produiront un effet plein de charme et de mélodie.”] Of course, every 63 chord contains a fourth between its third and sixth, and thus Keller’s progression displays parallel fourths as well as parallel thirds and sixths. However, in thoroughbass practice the third and sixth are directly derived, whereas the fourth is incidental. Rameau touches upon this issue in his commentary to 3.3a. Chapter 4 addresses harmonic progressions of a more conventional sort. Introducing parallel and sequential progressions first is intended to provide readers with the background to weigh the convictions articulated in that chapter in a more circumspect and critical manner. Lester, Compositional Theory in the Eighteenth Century (1992), p. 119. Weber, Versuch einer geordneten Theorie der Tonse[t]zkunst (1817–21, 31830–32), vol. 3, p. 125 [Warner, p. 624]. Vogler emphasizes the necessity of temperament by presenting the music notation for chord chains on circular systems. For example, one progression has a C major chord at 12 o’clock, F major at 1 o’clock, Bb major at 2 o’clock, Eb major at 3 o’clock, and onward through Ab, Db, Gb, B (enharmonic for Cb), E, A, D, G, and finally back to the same C chord at 12 o’clock. See his Gründe der kuhrpfälzischen Tonschule in Beispielen [1778], table XXX, fig. 1 [reproduced in Wason, Viennese Harmonic Theory (1985), p. 17]. Rameau, Traité de l’harmonie (1722), p. 286 [Gossett, pp. 304–305]. An augmented sixth chord is often analyzed as a modified supertonic. (See 1.4, 1.6, 7.3, 7.4, 7.18a, and 7.18c.) The topic is addressed in chapter 7, where derivations both from II and from V are explored. For an extensive discussion of how Schubert employs this sequence type, see my article “Schubert, Chromaticism, and the Ascending 5–6 Sequence” (Journal of Music Theory, forthcoming).

4 Harmonic progression 1 “Nach und nach lernt man alsdenn verstehen, daß alle Musik nichts anders als eine künstliche Abwechselung des harmonischen Dreyklangs sey; und alles was darinnen vorgehet sein Haupt-Absehen auf die abwechselnde Harmonie desselben gerichtet habe.” Sorge, Vorgemach der musicalischen Composition [1745–47], p. 422.

Notes and references to pages 85–86

2 Daube, like Sorge, places harmony at the core of a composition’s creation: “Harmony, the synthesis of individual voices, is comprised of the progression of consonant and dissonant chords. Thoroughbass is comprised of unadorned chords. Knowledge of chords leads to their interchange and breaking apart, the origin of preludes. Making preludes points the way to the invention of melodies. All sorts of vocal music derive from melodies . . . It is absolutely essential to know all this for vocal composition, and in other branches of composition even more must be mastered.” [“Die Harmonie oder Zusammensetzung unterschiedener Stimmen bestehet in nacheinander folgenden Con- und Dissonanzen Accorden. Der Generalbaß bestehet in bloßen Accorden. Die Kenntniß der Accorde führet zur Abwechselung und Zergliederung derselben. Aus dieser entspringen Präludien. Das präludiren ist der Wegweiser zur Erfindung der Melodien. Melodien werden alle Gattungen von Gesängen gennenet . . . Allhier sind sie zu wissen nöthig, in der Composition aber unentbehrlich, wovon im andern Theile von der Composition noch mehrers soll gewiesen werden” (Daube, General-Baß in drey Accorden (1756), p. 13).] 3 “Voici la vraie Théorie de la Musique, la seule toujours d’accord avec cet instinct naturel et presque divin qui conduit le génie en l’absence des lois écrites.” Momigny, La seule vraie théorie de la musique [1821], p. i. 4 “presque toujours faible ou fausse.” Ibid. Of course, since Momigny was writing a work entitled The Only True Theory of Music, his own rules would be exempt from such criticism. 5 “Lag ein Mechanisches, weil von der lebendigen Stimmführung Abgewandtes schon im Grundgedanken Rameaus, so zeugte das erste Mechanische nun Mechanisches um Mechanisches auch in der Folge . . . Statt eines musikalischorganischen Zusammenhanges gab es nur mechanische Folgen: Motive kamen und gingen, . . . Klänge kamen und gingen, ohne durch Auskomponierung beglaubigt zu sein, – wahrlich, das schlechteste Kochbuch bürgt für mehr Zusammenhang in seinen Rezepten, als die auf Rameaus Grundlage fußenden Kompositionslehren in ihren Rezepten.” Schenker, “Rameau oder Beethoven? Erstarrung oder geistiges Leben in der Musik?,” Das Meisterwerk in der Musik (1925–30): vol. 3, pp. 17–18. 6 In his Streitfragen über Musik (1843), Ernst Julius Hentschel files the following report: “Among one hundred music instructors there is barely one who troubles his pupils with instruction in harmony. Most of them even rejoice in having nothing to do with it and willingly remain on the path on which . . . nature points them. Nowadays especially, though with longstanding precedent, it is routine that far too little is done to foster the necessary understanding of the ways of chords, even in Germany. One is so preoccupied with practical exercises and technique-building that one generally is hardly in a suitable state to think about it. It has gotten to the point that the vast majority of instructors have to be coaxed before they agree to offer instruction on the subject of harmony even to a music student already skilled as a performer and melodist.” [“Unter hundert

299

300

Notes and references to pages 86–92

7

8

9 10

11 12

13

14

Musiklehrern ist kaum ein einziger, der seine Zöglinge mit Harmonielehre behelligt; die meisten sind sogar froh, daß sie nichts damit zu thun haben und bleiben mit Vergnügen auf dem Pfade, den, nach dem Ausdrucke des Hr. Verf., die Natur wie mit Fingern antippt. Viel eher geschieht auch in unserm Vaterlande, hauptsächlich jetzt und seit lange, für nothwendige Einsicht in das Wesen der Accorde gar zu wenig; man ist mit praktischer Uebung und Fertigkeitskünsten so stark beschäftigt, daß man in der Regel kaum daran zu denken im Stande ist. Es ist so weit gekommen, daß sich die allermeisten Lehrer sogar oft lange genug erst bitten lassen, bevor sie sich dazu entschließen, irgend einem in Praktischen und Melodischen bereits geübten Jünger der Tonkunst Unterricht im Fache der Harmonie zu ertheilen” (pp. 42–43).] “die analytische Interpretationsgeschichte musikalischer Werke, nicht unähnlich der praktischen, ein niemals abgeschlossener Prozeß ist, in dem der jeweils aktuelle Stand des Komponierens zur Entdeckung kompositionstechnischer Tatsachen inspiriert, die dadurch, daß kein Zeitgenosse des Komponisten sie wahrnahm, nicht aufhören, Tatsachen zu sein.” Dahlhaus, Neues Handbuch der Musikwissenschaft, vol. 6: Die Musik des 19. Jahrhunderts (Wiesbaden: Akademische Verlagsgesellschaft Athenaian, 1980), p. 215. Weber, Versuch einer geordneten Theorie der Tonse[t]zkunst (1817–21, 31830–32), vol. 2, p. 212 [Warner, p. 429]. Though neglecting Weber’s early formulation, Daniel Harrison traces the notion that “any chord can follow another chord” from Weitzmann through Liszt to Reger. See his Harmonic Function in Chromatic Music (1994), pp. 1–2. Weber, Versuch einer geordneten Theorie der Tonse[t]zkunst (1817–21, 31830–32), vol. 2, p. 201 [Warner, p. 419]. This undertaking is accomplished in separate volumes under the title “Dictionnaire des accords in trois volumes,” a compilation of almost 900 pages of two-chord successions. Crotch, Elements of Musical Composition (1812), p. 23. “Pour les autres successions audessus du centre, la réalisation est assez arbitraire, mais pour celles au-dessous, elles sont très délicates et demandent presque toutes, et principalement celles du second ordre, que leur deuxième accord soit dans le premier renvensement.” Jelensperger, L’harmonie au commencement du dix-neuvième siècle (1830, 21833), p. 31 [Häser, p. 23]. Measuring intervals between successive roots had been practiced for a century before Jelensperger. (See Rameau, Traité de l’harmonie (1722), pp. 185–196 [Gossett, pp. 206–217].) Rameau makes statements such as “[The fundamental bass] should proceed by consonant intervals, which are the third, the fourth, the fifth, and the sixth . . . The smaller ones should always be preferred to the larger; i.e., rather than having the bass ascend or descend a sixth, we should have it descend or ascend a third.” Portmann, Die neuesten und wichtigsten Entdeckungen in der Harmonie (1798), pp. 107–111. An earlier formulation, made at a time when Portmann acknowl-

Notes and references to pages 95–101

15 16

17 18 19

20 21 22 23 24 25 26

27

28 29 30 31 32

edged only five Grundharmonien (lacking the Quartenharmonie), appears in his Leichtes Lehrbuch der Harmonie (1789), pp. 41–48. In both works he also addresses successions involving a shift from one key to another. Rameau, Traité de l’harmonie (1722), 3rd page of the Préface [Gossett, p. xxxv]. For example, the German author Christoph Gottlieb Schröter, in his Deutliche Anweisung zum General-Baß (1772), p. 3, appends the following question to his discussion of overtones (Mitklänge): “Who does not recognize in this connection the finger of the all-knowing and infinitely good creator of nature, through which the substance of music has been presented to us clearly on the resounding string, for intensification and emulation in singing?” [“Wer erkennet hierbey nicht den Finger des allweisen und allgütigen Urhebers der Natur, womit uns der Stoff zur Musik auf besaiteten Werkzeugen, zur Verstärkung und Nachahmung des Singens, deutlich angewiesen wird?”] Rameau, Traité de l’harmonie (1722), pp. 190–191 [Gossett, pp. 210–211]. Rameau, Traité de l’harmonie (1722), pp. 207, 269, 291 [Gossett, pp. 227, 288, 309]. Context affects interpretation. If F-A-C-D proceeds to C-E-G, then F is the fundamental while D is the dissonance. If, in contrast, F-A-C-D proceeds to G-B-D-F, then D is the fundamental while C is the dissonance. See p. 23, above. Lampe: A Plain and Compendious Method of Teaching Thorough Bass (1737), pp. 20–22. Lampe: The Art of Musick (1740), plate 3 (following p. 54), ex. 5. Lampe: A Plain and Compendious Method of Teaching Thorough Bass (1737), p. 24. Ibid., plates 11 and 12 (adjacent to p. 26). Ibid., p. 32. Kirnberger, Die Kunst des reinen Satzes in der Musik (1771–79), vol. 1, p. 92 [Beach and Thym, p. 110]. Vogler, Handbuch zur Harmonielehre (1802), pp. 45–46. Vogler is careful to point out that I–V may be perceived as IV–I in the dominant key; and that IV–I may be perceived as I–V in the subdominant key. Sechter’s tuning, anachronistic for the mid-nineteenth century, includes several pure fifths and thirds. D is the second pure fifth above C. A is a pure third above an F tuned a pure fifth below C. In this context a D–A fifth will be audibly flat, motivating Sechter to impose the requirement of downward resolution upon the A. Rameau, Traité de l’harmonie (1722), pp. 50–51 [Gossett, p. 60]. See p. 88, above. Rameau, Traité de l’harmonie (1722), p. 50 [Gossett, p. 60]. Ibid., p. 49 [Gossett, p. 59]. Ibid., pp. 62–63 [Gossett, pp. 71–73]. In this case Rameau achieves a descending-fifth root succession by interpreting G-B-D-F to A-C-E as G7 to C6 (wherein the seventh and the sixth dissonate within their chords). On other occasions he posits A as the second chord’s fundamental.

301

302

Notes and references to pages 101–112

33 See pp. 23 and 38, above. 34 Kollmann, A New Theory of Musical Harmony (21823), p. 39. 35 F. D. Weber, Theoretisch-Praktisches Lehrbuch der Harmonie (1830–41), vol. 1, p. 195, ex. 23. 36 “Bekanntlich muss, wenn nach dem Dreiklang der 4ten jener der 5ten oder der Septaccord der 5ten Stufe folgen soll, dazwischen der Dreiklang oder Septaccord der 2ten Stufe wirklich genommen oder hinein gedacht (und demnach gehandelt) werden, wodurch folgende Fundamentalfolgen entstehen: 7

I IV II V I

oder

I IV II V I

7

oder

7

I IV II V I.”

Sechter, Die Grundsätze der musikalischen Komposition (1853–54), vol. 1, p. 102. 37 Hauptmann, Die Natur der Harmonik und der Metrik (1853, 21873), p. 61 [Heathcote, p. 46]. 38 Lampe, A Plain and Compendious Method of Teaching Thorough Bass (1737), pp. 26–27. Schröter likewise recommends the use of contrary motion for both 4–5 and 5–4 root successions in his Deutliche Anweisung zum General-Baß (1772), p. 47. The issue at hand is, of course, parallel fifths and octaves. 39 Ibid., plate 5 (adjacent to p. 25), exs. XII and XIII. 40 Sorge, Vorgemach der musicalischen Composition [1745–47], p. 422: “durch steigende oder fallende Secunden, deren aber nicht mehr als zwey hinter einander statt haben, und zwar von der Quarta Modi in Quintam, und von dieser in Sextam, als im C dur F G A, und so auch absteigend A G F; und im A moll D s E F, aber nicht absteigend.” In his Leichtes Lehrbuch der Harmonie (1789, plate 33, ex. 66), Portmann goes so far as to demonstrate an ascending progression of six stepwise roots (C–D–E–F–G–A), but classifies its descending counterpart (A–G–F–E–D–C) as übel (wrong). Even consecutive major chords (dominants) can occur in ascending progression: C major–D major–E major–F major (plate 34, ex. 71); but again not a descent, such as C major–B major–A major–G major. Riepel, in his Baßschlüssel (1786, pp. 18–19), justifies his prohibition of descending major triads (such as G major followed by F major) by invoking the time-honored “Mi-contra-fa” rule, which is triggered when the first triad’s third and the second triad’s root (e.g., B contra F) create an offensive cross-relation (ein unartiger Querstand). (F major followed by G major also creates an augmented fourth, but that interval can be absorbed within the G chord, as G7.) 41 The controversial issue of labeling a chord such as Fs7–as VI7s, as V7s of II, or as B Minor: V7s–will be addressed in chapter 6, on modulation. 42 Some readers may assert that there is a B chord after the F#7 chord of measures 19 and 20. Yet as 4.10 suggests for the equivalent situation at measure 13, the accented, appoggiatura-laden moment at the downbeat of measure 21 can be (and I suggest should be) regarded as an embellishment of a D7 chord. 43 I explore this topic in detail in my forthcoming article, “Schenker, Schubert, and the Subtonic Chord.”

Notes and references to pages 113–119

5 Chordal hierarchy 1 “Daß eine Dissonanz in eine Wechselnote eigentlich resolviren könne, ist falsch. Wohl aber kann es uneigentlich geschehen. Denn wer kennet die Harmonie, und siehet nicht, daß in dem Exempel [5.1a] die Auflösung der Septime durch Verwechselung der Harmonie figürlich aufgehalten wird, und solche mit nichten auf das mit einem Zeichen bemerkte Achttheil, sondern auf die lezte halbe Note [e] erst geschicht?” Marpurg, Handbuch bey dem Generalbasse und der Composition (1757), vol. 2, p. 85, transposed from C7–F to G7–C. 2 These statements, which express Koch’s view, likely would have been rejected by Schenker and thus will seem antiquated to some modern readers. In his analysis of a very similar passage, Schenker applies the label “IV (Kons Dg) V” – subdominant leading to dominant – to chords corresponding to Koch’s chords with bass A, C, and G. The intervening C chord provides consonant (kons[onant]) support for passing note (D[urch]g[ang]) E. See Schenker, Der freie Satz (1935, 2 1956), Anhang, p. 24, ex. 561c [Oster, Supplement, ex. 561c]. This interpretation of the C chord as the subdominant’s upper fifth is not necessarily a notion that emerged only in the twentieth century, as we shall see in the “Hierarchy in fifthrelated chords” section of this chapter. 3 “Wenn die verminderte Quinte in der gebundenen Schreibart . . . an und für sich selbst als die Dissonanz des verminderten Dreyklanges förmlich aufgeführet wird, muß sie jederzeit vorbereitet und aufgelöset werden. In diesem Falle geschiehet die Auflösung am gewöhnlichsten in die Terz, wenn dabey der Baß eine Stufe steigt, wie bey [5.1b]. Sie verträgt aber auch folgende ungewöhnlichere Auflösungen, und zwar, 1) in die Sexte, wenn der Baß eine Terz abwärts tritt, wie bey [5.1c] . . . ” Koch, Handbuch bey dem Studium der Harmonie (1811), cols. 236–237. 4 “Es giebt in der Harmonie durchgehende Accorde, die sich auf keine Grundharmonie gründen; sie sind wie die durchgehenden Töne in der Melodie anzusehen, und entstehen aus diesen, wenn verschiedene Stimmen sich durchgehend bewegen . . . Daher sind durchgehende Accorde Zwischenaccorde, bey denen eine oder mehrere Stimmen durch eine stufenweise mehrentheils consonirende Fortschreitung von dem vorhergehenden zu dem folgenden Grundaccord übergehen. Sie stehen allezeit zwischen zweyen Grundaccorden, die entweder dieselben sind, oder doch sehr natürlich auf einander folgen . . . Man erkennt sie ferner an dem Unnatürlichen ihrer harmonischen Fortschreitung, indem entweder irgend eine Dissonanz ohne Resolution bleibt, oder, wenn sie auch den Anschein eines regelmäßig behandelten Grundaccordes haben, dennoch dieser Grundaccord die natürliche Fortschreitung der Grundharmonie hemmen würde.” Kirnberger/[Schulz]: Die wahren Grundsätze zum Gebrauch der Harmonie (1773), pp. 34–35. 5 “Die als Durchgang bezeichneten Töne können auch als Akkord genommen werden.” Lobe, Lehrbuch der musikalischen Komposition, vol. 1 (1850, 21858), p. 163.

303

304

Notes and references to pages 119–131

6 Jelensperger, L’harmonie au commencement du dix-neuvième siècle (1830, 21833), p. 62 [Häser, p. 61]. 7 Though Schulz claims that passing chords “can occur only on weak beats,” Kirnberger suggests that this rule should apply only in the strict style. He presents a six-measure example that contains passing chords (marked by asterisks) on two of its downbeats. See Kirnberger/[Schulz]: Die wahren Grundsätze zum Gebrauch der Harmonie (1773), pp. 34–35 [Beach and Thym, p. 192]; Kirnberger: Die Kunst des reinen Satzes in der Musik (1771–79), vol. 1, p. 86 [Beach and Thym, p. 104]. See also a model by Sechter [4.10a]. 8 “Sa résolution peut avoir lieu par prolongation de son, lorsqu’elle a été préparée par la même note.” Durutte, Esthétique musical (1855), p. 146. Durutte’s description corresponds to Jelensperger’s “resolution of the second order.” 9 The Eb that joins F-A-C in Beethoven’s measure 7 adds an additional layer of complexity to the situation. Such added minor sevenths are assessed in chapter 6, on diatonic modulation. See especially the discussion of 6.18 through 6.21. 10 On the one hand, many nineteenth-century analysts regard the E-Gs-Bn, E-GsBb, Gs-Bn-D-F, Gs-Bb-D, and Gs-Bb-D-F simultaneities that occur in measures 2 and 3 as offspring of a common root, E. Thus a superficial analysis might allege that Clementi is merely juxtaposing closely related alternatives, all targeting goal A. On the other hand, the voice exchanges powerfully enhance D and F, making E unwelcome as a sounding chord member in their vicinity (even if E is the generator of seventh D and ninth F), thereby discouraging the interpretation of EGs-Bb (measure 2, beat 2) and E-Gs-Bn (measure 3, beat 2) as harmonic. Bass Bn, coming from Bb, may induce the expectation that the phrase will continue with C6–5 to F, a hypothesis that must be abandoned once Bb returns in the bass. 4–3 11 “Die eigenthümliche Erscheinung des Quartsextakkords in dem Beispiel . . . ist nur durch die im Charakter der Durchgangsnoten erfolgte stufenweise Fortschreitung aller Stimmen zu ihrem nächsten Ziele (dem Akkord der Thesis im folgenden Takte) zu erklären.” Richter, Lehrbuch der Harmonie (1853, 211897), p. 131. 12 Lobe, Vereinfachte Harmonielehre [1861], p. 144. 13 Swoboda explores the use of “leading dominants” within a progression of chords whose bass pitches descend in thirds (C–A–F–D–B6–G6–E6–C) in his Harmonielehre (1828), pp. 156–157. For example, between the first two chords (C-G-C-E and A-A-C-E) he inserts B-Gs-D-E. Without explanation his basic progression is subtly altered from his original model (53 chords descending C–A– F–D–B–G–E–C). The sudden switch to 63 chords beginning with B6 (B-D-G) is certainly in order to avoid the diminished 53 chord (B-D-F), an unsuitable goal for a leading dominant. 14 “Die andere Art Vorspiele wird verfertiget, wann man sich einige Melodiearten erfindet und sie mit dem jedesmal vorliegenden Choral also verbindet, daß man zwischen dessen häuffig auf einander folgende Primenaccorde, ihre Dominantenaccorde einschiebt, oder auch auf den Dreiklang einer harten Tonart mit seiner Dominante, den Dreiklang der ähnlichen weichen mit seiner

Notes and references to pages 132–134

15 16

17

18

Dominante folgen läst – oder anstatt des Dreiklanges seinen Sextenaccord erwählt. Man sehe f. 24, eine Strophe des Chorals ‘Sünder willst du sicher seyn’ und f. 25, wo zwischen die auf einander folgenden Primenaccorde ihre Dominanten eingeschoben sind.” Portmann, Musikalischer Unterricht (1785), p. 23. The analysis is found on pp. 300 through 304. In that both Vogler and Gottfried Weber analyze music giving diligent attention to potential harmonic meanings that are not fulfilled by the compositional context, either could have been selected for comparison with Dehn. The choice of Vogler emphasizes Dehn’s application of an eighteenth-century perspective. A more immediate model – Weber’s 1831–32 analysis of the opening measures from Mozart’s “Dissonance” String Quartet (K. 465) – is well documented elsewhere: see Ian Bent’s translation and commentary in his Music Analysis in the Nineteenth Century, Volume One: Fugue, Form and Style (1994, pp. 157–183) and Jairo Moreno’s “Subjectivity, Interpretation, and Irony in Gottfried Weber’s Analysis of Mozart’s ‘Dissonance’ String Quartet” in Music Theory Spectrum 25/1 (2003), pp. 99–120. Kevin Korsyn presents a fascinating juxtaposition of Weberian analysis and David Lewin’s formal model of perception in Decentering Music: A Critique of Contemporary Musical Research (Oxford, Oxford University Press, 2003), pp. 166–175. “D mit der Unterhaltungssiebenten ist der fünfte Ton vom G. Dis mit der verminderten ist der siebente vom weichen E. E mit der kleinen Vierten und kleinen Sechsten ist eine Umwendung, worin die Fünfte vom weichen A zum Grunde leigt. F mit der Unterhaltungssiebenten, als der fünfte Ton vom B.” Vogler’s Tonschule, Tonwissenschaft und Tonse[t]zkunst: Kuhrpfälzische Tonschule [1778], pp. 180–181. Vogler introduces Roman numerals for harmonic analysis in this work, especially in the accompanying volume of music examples (Gründe der Kuhrpfälzischen Tonschule in Beispielen). (See 1.4.) While the text generally employs “fifth” (Fünfte) or “fifth tone” (fünfte Ton) when referring to a dominant chord, some of his music examples (though not our 5.15) employ “V.” The numeral “VII” appears both in the text and in his examples. “Die Einleitung beginnt mit dem verminderten Septimenakkord von G moll; durch stufenweise Fortschreitung des Basses fis nach f findet eine Trugfortschreitung statt in den Dominantenakkord von B dur oder B moll, Takt 3 und 4; anstatt der regelmässigen Auflösung dieses Akkords folgt wieder eine Trugfortschreitung in den Quartsextenakkord von A moll, Takt 5; Takt 6 der Dominantenakkord von G dur oder G moll und auf dem letzten Viertel desselben Taktes die dritte Umkehrung dieses Akkords, auf der Quarte der Tonart.” Dehn, Theoretisch-praktische Harmonielehre (1840), p. 301. Dehn pursues his analysis with words rather than Roman numerals. His use of numerals elsewhere in the treatise is bass- rather than root-oriented. For example, he would have labeled the dominant chord at the end of measure 6 (in “third inversion, on the fourth degree of the key”) as IV, in reference to the bass, rather than as V, in

305

306

Notes and references to pages 134–142

19

20

21

22

23

reference to the root. (See table IX, inserted between pp. 128 and 129 of the Harmonielehre. See also 1.2c, above.) “irrt und tastet wie in tiefem Dunkel haltlos die Harmonie umher . . .” Marx, Ludwig van Beethoven (1859), vol. 2, pp. 52–53. Beethoven’s Introduction has generated a number of colorful prose descriptions. Gerald Abraham invokes the image of “mysterious chords . . . melting into each other almost imperceptibly” and goes so far as to call the passage “an atonal fog.” See his Beethoven’s SecondPeriod Quartets, London: Oxford University Press, 1942, pp. 41, 45. Robert Wason shows how the omnibus idea develops out of progressions by Vogler, such as that in 5.15. See his Viennese Harmonic Theory (1985), pp. 16–19. Paula J. Telesco explores eighteenth-century compositional usage of omnibus-like material in “Enharmonicism and the Omnibus Progression in Classical-Era Music,” Music Theory Spectrum 20/2 (1998), pp. 242–279. See also Victor Fell Yellin’s The Omnibus Idea (Warren, Mich.: Harmonie Park Press, 1998). The score from which both Dehn and Marx worked retains C for the secondviolin part in measure 9, thus impeding their comprehension of the passage. In fact, Dehn again invokes the notion of Trugfortschreiting to account for the chord of measures 8 and 9, which too greatly contrasts the G chord he expects as resolution of the preceding D7 chord. The diminished seventh’s mehrdeutig capacity is again at play. In the context of the preceding Eb major chord, the diminished seventh of measure 13 would be spelled D-F-Ab-Cb; in the context of the following C minor chord, it is spelled Bn-D-F-Ab. An examination of analytical strategies regarding augmented sixth chords appears in Chapter 7. Nineteenth-century authors present examples in which each chord member serves in turn as bass, validating Beethoven’s choice of D in place of the more conventional Ab.

6 Modulation to closely related keys 1 “Unter dem Worte Modulation versteht man überhaupt das Aufeinanderfolgen verschiedener Harmonieen. Insbesondere aber begreift man gegenwärtig unter Modulation die Kunst, von einen Harmonie in eine andere, welche durch ein oder mehr Versetzungszeichen von den erstern verschieden ist, fließend, ungezwungen, zuweilen überraschend und oft auch unerwartet überzugehen.” Swoboda, Harmonielehre (1828), p. 89. Christoph von Blumröder provides a detailed account of the term’s history in the entry “Modulatio/Modulation,” Handwörterbuch der musikalischen Terminologie (ed. Hans Heinrich Eggebrecht, 1972– ). In German the term Ausweichung appears often as well. 2 Rameau, Traité de l’harmonie (1722), pp. 208–209 [Gossett, pp. 228–229]. 3 Daube claimed minimal acquaintance with Rameau’s theory in a letter to Marpurg, published in Marpurg’s Historisch-kritische Beyträge zur Aufnahme der

Notes and references to pages 143–147

4 5

6

7 8 9

10 11 12

Musik (1754–78), vol. 3, pp. 69–70. Lester speculates that Rameau’s ideas “had already entered common musical discourse” by this time and that Daube was unaware of their source. See his Compositional Theory in the Eighteenth Century (1992), p. 202. See also p. 10, above. Koch, Versuch einer Anleitung zur Composition (1782–93), vol. 1, pp. 291–296; vol. 2, pp. 188–192. See David Ferris, “C. P. E. Bach and the Art of Strange Modulation,” Music Theory Spectrum 22/1 (2000), pp. 70–71. Rameau had developed a hierarchical perspective on modulation through his teaching of composition in the 1730s and 1740s. Unfortunately the most careful explanation of his ideas was recorded in an unpublished and long-neglected treatise that he gave to d’Alembert, among whose papers it has resided ever since. Thomas Christensen’s assessment, in “Rameau’s ‘L’Art de la Basse Fondamentale’, ” (1987), pp. 18–41, enumerates Rameau’s three “varieties” of tonic: (1) the “tonique principale” or “veritable tonique” (the tonic of the composition as a whole), a concept presented in his Code de musique pratique (1760), p. 162, under the name “ton regnant”; (2) “sensée tonique” (a temporary tonic confirmed by its leading tone); and (3) “toniques étrangères ou passagères” (tonics not confirmed by their leading tones). Crotch, in Elements of Musical Composition (1812), pp. 85–88, classifies modulation to these keys as “natural modulation,” in contrast to “unnatural modulation” into “such keys as have more than one flat or sharp, more or less, than the original key.” Such modulations may be “gradual” (connection via one or more chords interpretable in both keys) or “sudden.” Early in the eighteenth century, even the keys that Koch and Crotch favor had been divided into “ordinary” (ordentlich) modulations, as in C Major to G Major, E Minor, and A Minor, and “extraordinary” (außerordentlich) modulations, as in C Major to D Minor and F Major. See Heinichen, Der General-Bass in der Composition (1728), pp. 761–762. Wolf, Musikalischer Unterricht (1788), p. 37. “Ich muß hierbey anmerken, daß durchgehende Kadenzen mit vermiedenen einerley Zwek haben.” Wolf, Musikalischer Unterricht (1788), p. 52. “Ces modulations passagères sont si brèves que l’oreille ne perd pas l’ impression du Ton d’Ut, et elles ont encore l’avantage de rendre piquante une phrase chantante qui, sans elles, serait souvent commune.” Reicha, Cours de composition musicale [ca. 1816], p. 62. Weber, Versuch einer geordneten Theorie der Tonse[t]zkunst (1817–21), vol. 2, p. 99 [Warner, p. 330]. Weber, Versuch einer geordneten Theorie der Tonse[t]zkunst (1817–21, 31830–32), vol. 2, p. 143 [Warner, p. 360]. Like Koch and Reicha, Weber adopts terminology to differentiate between a permanent key shift – “perfect” (vollkommen) or “entire” (überwiegend) modulation – and a transient move to another key – “imperfect” (unvollkommen) or “half ” (halb) modulation. Weber, Versuch einer geordneten Theorie der

307

308

Notes and references to pages 147–150

13

14

15

16

17

18

19

Tonse[t]zkunst (1817–21, 31830–32), vol. 2, p. 99 [Warner, p. 329]. In “The Concept of Ausweichung in Music Theory, ca. 1770–1832” (2003), Janna Saslaw takes me to task for criticizing Weber’s modulation-intensive analytical practice. My point is that whether his modulations are perfect or imperfect, too many chords do not register within the broader tonal framework of the composition. Thus in my view Lampe’s analytical practice of 1737 is superior in this regard to Weber’s of nearly a century later: for example, the B chord of measure 3 in 6.1 is not only the focus of what Weber would call an imperfect modulation to the key of B Minor, but also, as Lampe reveals, a representative of the fifth scale degree in the key of E Minor. For example, a Schenkerian analyst might contend that the first nine chords represent an expansion of the structure 5I V4 7 I3. I prefer to regard 6.7 not as Weber’s assertion that nineteenth-century musicians were not capable of or interested in hearing the passage in that manner, but instead as evidence that his analytical system lacked a sufficiently sophisticated mechanism for dealing with tonal hierarchies that occur even in his own concocted examples. Lobe’s prescription (Lehrbuch der musikalischen Komposition, 1850, 4th edn. of vol. 1, p. 249) is characteristic: “So long as the progression consists of diatonic harmonies, the sense of the prevailing key is retained. But as soon as a chromatic chord appears, one is led into another key.” [“So lange leitereigene Harmonien auf einander folgen, bleibt das Gefühl in der angeschlagenen Tonart; sobald ein fremder Akkord auftritt, wird man in eine andere geführt.”] It was common to regard the leading tone as the seventh scale degree in minor keys, rather than as a borrowing from the parallel major. In that perspective, the diminished seventh chord on the leading tone is fully diatonic in minor. Jadassohn’s system is not equipped to correlate vii°7 in C Minor and V in C Major, between which a subsidiary connecting chord flows. The second through fourth chords of 6.8 interrelate in a way that is more complicated than but nevertheless similar to the way the second through fourth chords of 5.1c relate, from a passing-chord perspective. Weber, Versuch einer geordneten Theorie der Tonse[t]zkunst (1817–21, 31830–32), vol. 2, pp. 162–163 [Warner, pp. 372–373]. As discussed in chapter 3, above, alternative linear interpretations of such progressions coexisted with Weber’s harmonic non-interpretation. This is the same set of keys that Koch targets. (See p. 145, above.) To demonstrate keys related to a minor tonic, Holden analyzes a progression in D Minor by Pasquali (his example LVI on plate VIII, facing p. 94 of An Essay). The letter k (for “occasional key”) appears below the following chords, each preceded or followed by its major dominant: F Major, G Minor, G Major, A Minor, A Major, and Bb Major. Holden, An Essay towards a Rational System of Music (1770), p. 87. Fn may occur as a chord member when C is k (as in measure 1 of 6.9) but not as a k itself.

Notes and references to pages 150–151

20 Kirnberger, Die Kunst des reinen Satzes in der Musik (1771–79), vol. 1, p. 104 [Beach and Thym, p. 122]. 21 Kirnberger, Die Kunst des reinen Satzes in der Musik (1771–9), vol. 1, pp. 110–111 (n.) [Beach and Thym, p. 128–129 (n.)]. 22 Vogler, Handbuch zur Harmonielehre (1802), table II, figs. 13–15. The analytical symbols employed in Portmann’s Leichtes Lehrbuch der Harmonie, Composition und des Generalbaßes (1789), wherein Fs-A-C-E in C Major is labeled 4+, may have inspired Vogler’s sharps. 23 “Der Schlußfall vom fünften zum ersten, und der vom ersten zum fünften sind auch in der weichen Leiter . . . anwendbar, so bald die kleine Dritte des fünften Tones erhöhet, die Harmonie dadurch entscheidend und . . . schlußfallmäßig wird.” Vogler, Handbuch zur Harmonielehre (1802), p. 46. 24 The subdominant resists convincing acoustical derivation. In Rameau’s 1:3:9 proportion [1.8] the number 1 corresponds – curiously – to the subdominant, rather than to tonic, putting into question the primacy of the latter since it appears to be a derived entity. Vogler capitalizes upon the subdominant’s tenuous acoustical position to justify the use of the raised fourth scale degree. Working upwards from C, the tenth partial is an E and the twelfth partial is a G. The eleventh partial is between F and Fs, closer to the latter. (Just as 2:3:4 corresponds to the filling-in of an ascending octave with the larger interval positioned lower – C–G–C – likewise 10:11:12 corresponds to the filling-in of a minor third with the larger interval positioned lower. Since the minor third equals three halfsteps, the internal pitch is somewhere between 112 and 2 half-steps higher than E, audibly a pitch “in the crack” between F and Fs.) 25 “Wie sich der siebente Ton in harter Leiter und der siebente erhöhte Ton in weicher Leiter zum ersten oder achten verhält, so verhält sich der vierte erhöhte zum fünften. Daß man mit dem fünften Ton einen, wo nicht völligen, doch einsweiligen Schluß bewirken könne, ist . . . erwiesen und durch die Beispiele . . . bestättigt worden. Wenn man aber den vierten Ton in der harmonischen Fortschreitung, das 1/11 . . . untersucht, so ist es zur F-Leiter mehr h als b, zur C-Leiter mehr fis als f; folglich darf der vierte Ton, auch außer der Analogie mit dem siebenten, erhöhet werden.” Vogler, Handbuch zur Harmonielehre (1802), p. 47. 26 “Der Schlußfall vom zweiten in den fünften Ton findet nur in weicher Tonart statt . . .; da hingegen in der harten Tonart, sobald man dem zweiten Tone seine grose Dritte beilegen wollte, er nicht mehr der zweite sondern ganz bestimmt der fünfte von einem andern Tone wäre, z. B.: a f D II von C

a fis D V von G.” Vogler, Handbuch zur Harmonielehre (1802), p. 48.

27 Vogler, Handbuch zur Harmonielehre (1802), pp. 48–50. By placing two rows of analysis (“II von A” and “V—E”) below the note names H-dis-f, Vogler appears

309

310

Notes and references to pages 152–153

28 29

30 31

to be suggesting that a dominant may be altered so as to contain, in its second inversion, an augmented sixth. (This would require the lowering of the second scale degree from Fs to Fn.) Yet the music example to which Vogler directs his readers shows only one analysis: II. Momigny, La seule vraie théorie de la musique [1821], p. 10. “Ce fa# est en ut et non en sol, comme on le croit généralement.” Momigny, La seule vraie théorie de la musique [1821], p. 51. Several decades later, Franz Joseph Kunkel expressed strong opposition to such expansion: “That such a theory leads into the abyss is clearly apparent. According to such principles, then indeed it would even have been unnecessary to deal with the various key systems and to deduce again quite so many different seven-note scales from them. It would have been much more straightforward, novel and indeed even ingenious to remove all restraints and make available once and for all the twelve-note chromatic scale, or even the enharmonic scale with seventeen notes, or perhaps ultimately the entire brigade of . . . thirty-five notes [Cbb, Cb, C, Cs, CS, Dbb, Db, . . .] to create a veritable universal scale of tones as the basis for diatonic chords and ‘powerfully protruding’ melodic and harmonic pitch structures!!” [“Das eine solche Theorie in’s Bodenlose führte, ist leicht ersichtlich. Nach solchen Principien wäre es aber dann auch unnöthig gewesen, sich mit den verschiedenen Tonartensystemen zu befassen und daraus wieder eben so viele verschiedene siebentönige Tonleitern zu deduciren; viel einfacher, neu und gewiß auch genial wäre es, ein für allemal die zwölftönige chromatische Tonreihe, oder auch die enharmonische mit ihren 17 Noten, oder gar endlich das ganze Regiment der oben für’s ‘Tonsystem’ aufgestellten Fünfunddreißig, so eine wahrhaftige Universaltonleiter, als Grundlage leitereigener Accorde und ‘mächtig hervortretender,’ melodischer und harmonischer Tongebilde ganz uneingeschränkt zur Verfügung zu stellen!!”] See his Kritische Beleuchtung des C. F. Weitzmann’schen Harmoniesystems (Frankfurt am Main: Auffarth, 1863), p. 14. Momigny, La seule vraie théorie de la musique [1821], p. 75. “Quand la distinction entre la demi-modulation et la modulation entière est douteuse, il est indifférent d’indiquer une autre tonique, ou d’écrire avec des parenthèses; dans tous les cas, on choisit la manière qui parait être le plus simple.” Jelensperger, L’harmonie au commencement du dix-neuvième siècle (1830, 21833), p. 49 [Häser, pp. 44–45]. In a curious about-face, Jelensperger goes on to suggest that his parenthesis notation is merely an abbreviation of his modulation-intensive version. For example, though he applies only the symbols 1 la

7)

3)

2

2)

5

to the music notation of 1.7, his textual commentary states that the “true succession of chords” (la véritable succession des accords) is actually 1 la

5 Do

1

2 la

5 mi

5 la.

Notes and references to pages 154–161

32

33 34

35

36

37

38 39 40 41

Perhaps he was attempting to forge a compromise position between Weber’s and Momigny’s perspectives. But his suggestion that the non-modulatory method merely abbreviates the modulatory method is in fact traitorous to Momigny. “Neuere Theoretiker wollen Akkorde wie die bei a. x und b. x in [6.13a] nicht als wirkliche ausweichende, sondern als leitereigene, alterirte Akkorde gelten lassen. Warum? Weil das Gefühl der herrschenden Tonart durch solche eingeschobene Akkorde nicht verdrängt werde . . . [The chord] erscheint hier gleichsam nur ein wenig verkleidet . . .” Lobe, Lehrbuch der musikalischen Komposition, vol. 1 (1850, 21858), pp. 242–243. The augmented sixth chord, often labeled as “2” or “II” during the nineteenth century, is explored in chapter 7. “Ueberhaupt sind die Begriffe von chromatischer Fortschreitung und wirklichem Tonwechsel (Modulation) so durcheinander geworfen worden, dass sie nur sehr schwer zu entwirren sind. Vor allem ist das Gebiet einer Tonart im weiteren Sinne zu fassen als bisher. Man wird dann nicht nöthig haben fortwährend Uebergänge zu konstatiren, wo nur chromatisch alterirte akkorde auftreten, und wird die eigentliche Modulation für jene Stellen aufsparen, wo sich eine zweite Tonart wirklich selbständig für eine oder mehre Perioden oder Abschnitte geltend macht.” Schalk, “Das Gesetz der Tonalität,” Bayreuther Blätter 11 (1888), p. 195. Vogler, Handbuch zur Harmonielehre (1802), table VII, fig. 2. The chapter titled “Mehrdeutigkeit” appears on pp. 101–110. Vogler’s fascination with multiple meaning is evident throughout his writings. For example, in his early article “Summe der Harmonik” he labels B-D-F-A not only as VII in C Major and as II in A Minor, but also as IV in F Major. (Betrachtungen, vol. 3 (1780), table 2, ex. 6.) Weber, Versuch einer geordneten Theorie der Tonse[t]zkunst (1817–21, 31830–32), vol. 2, pp. 152–154 [Warner, pp. 365–368]. Janna Karen Saslaw explores Weber’s perspective on multiple meaning in “Gottfried Weber and the Concept of Mehrdeutigkeit” (1992). In his Harmonielehre (1906), Schenker, a fervent adversary of the frequentmodulation stance, presents a “complete major–minor system” in which a major triad resides on every pitch within the octave except the raised fourth. (See especially the chart on p. 395, unfortunately absent from the English translation. dur Note that D moll was inadvertently omitted from the chart.) His presentation is assessed (and the chart reproduced) by Matthew Brown in “The Diatonic and the Chromatic in Schenker’s Theory of Harmonic Relations,” Journal of Music Theory 30/1 (1986), pp. 2–11. Not everyone viewed this situation in a favorable light, of course, as Kunkel’s denunciation, quoted in n. 29, above, demonstrates. Halm, Harmonielehre (1900, 21925), p. 15. “Die Tonika ist der König der Tonart.” Ibid., p. 104. Prout’s “transitional dominants” are akin to Swoboda’s “leading dominants” (führende Dominante), discussed in chapter 5.

311

312

Notes and references to pages 161–168

42 In Prout’s system the leading-tone chord is regarded as a dominant “derivative.” The symbol V7 often appears within parentheses below the symbol vii°, though not in this example. Prout explains: “When derivatives are used as transitional dominants, their harmonic origin is not given, in order not to complicate the analysis too much. The student can easily find it for himself ” (Analytical Key [1903], p. 49). A similar pairing of V7 and vii° (and also of V97 and vii°7) is found in P. J. Engler’s Handbuch der Harmonie (1825). See especially Engler’s examples 53, 55, and 58 (pp. 33–35). See also 1.1. 43 Emulating Schenker’s mature practice, I reject the potential tonic implications of the Bb major chord on beat 3 of measure 6 and thereby assert greater continuity between the two phrases than Prout himself might have acknowledged. In a Schenkerian perspective, soprano D at this point would be understood as a passing note between Eb and C. It is made consonant through the insertion of a 5 chord on Bb, the subdominant’s upper fifth. Compare with Schenker, Der freie 3 Satz (1935, 21956), Anhang, p. 24, ex. 561c [Oster, Supplement, ex. 561c]. See also chapter 5, n. 2 (p. 303). 44 Callcott, A Musical Grammar (1806), p. 221. The “Leading Tone to the Tonic” – i.e. An to Bb – likely would have been regarded as occurring in measure 6 by Callcott’s contemporaries. However, as mentioned in n. 43, at least one analyst active around the time Prout’s analysis was published – Heinrich Schenker – would have regarded the decisive return to tonic as occurring in measure 8, not measure 6. 45 Prout, Analytical Key [1903], p. iii.

7 Chromatic chords: diminished/augmented 1 Holden, An Essay towards a Rational System of Music (1770), p. 100. 2 Ibid. 3 Holden’s work was published in Glasgow, and a later edition appeared around the end of the century in Calcutta! Daniel Harrison cites John Callcott’s A Musical Grammar (London, 1806) as the first treatise to use all three national nicknames. See his “Supplement to the Theory of Augmented-Sixth Chords” (1995), p. 181. That terminology was not adopted universally. For example, John Stainer blandly numbers the chords 1, 2, and 3: “At * Ex. 3 is chord No. 3” (A Theory of Harmony (1871), undated 8th edn., p. 104). 4 See Code de musique pratique (1760), plate 4 (ex. L2), plate 15 (ex. K8), and plate 18 (ex. N[1]). In contrast to this perspective Rameau suggested to d’Alembert that augmented sixth chords are beyond the authority of the fundamental bass. A polemic ensued. See Jonathan W. Bernard, “The Principle and the Elements: Rameau’s Controversy with d’Alembert” (1980), p. 53. 5 Marpurg, Historisch-kritische Beyträge, 5/2 (1761), pp. 162, 167–168. For the same reason Sechter employs the term “hybrid-chord” (Zwitteraccord) in Die Grundsätze der musikalischen Komposition (1853–54). See 7.5.

Notes and references to pages 169–179

6 Sorge, Vorgemach der musicalischen Composition [1745–47], p. 21; part 3, table XIV, figs. 6–9. 7 Chords of this disposition appear in 3.12. 8 Choron, Principes de composition des écoles d’Italie [1809], vol. 1, p. 16. A similar chart from Reicha’s Cours de composition musicale [ca. 1816], p. 8, appears in Christensen, The Cambridge History of Western Music Theory (2002), p. 586. Renate Groth compares charts by Reicha, Colet, Elwart, Barbereau, and Durutte in Die französische Kompositionslehre des 19. Jahrhunderts (1983), p. 43. For a German exemplum, see Swoboda, Harmonielehre (1828), pp. 151–153. 9 “Will man nun vom weichen C, welches 3 b hat, ins harte A mit 3 s oder auch ins weiche A, wobei doch das gis, als die grose Dritte des fünften Tones unentbehrlich ist: so darf nur der siebente Ton des weichen C, sich in den siebenten Ton des weichen A verwandeln. VII vom C VII vom A und dann kann

10

11

12 13 14

15

16

H h h

d d d

f f E

as Gis gis der beiden Tonarten

gemeine Schlußfall ins A treten.” Vogler, Tonwissenschaft und Tonse[t]zkunst (1776), pp. 82–83. “La clavier n’ayant que douze touches par octave, il n’y a, physiquement, que trois accords de septième diminuée différens, chacun de ces accords prenant quatre touches, et trois fois quatre faisant douze.” Momigny, La seule vraie théorie [1821], p. 98. Fétis, Traité complet de la théorie et de la pratique de la harmonie [1844], p. 55. The substitution principle enunciated by Fétis in his Traité is closely related to that of Rameau and Holden, discussed above. Fétis’s restriction of resolution to a root-position dominant chord echoes Holden’s restriction in the context of augmented sixth chords in 7.1, measure 3. Even the resolution in Progression 4 is a bit strained, in that the diminished fifth F would more conventionally lead to ECs, rather than to GA. B Using a greater variety of resolution strategies than does Fétis, Swoboda shows resolutions from a single diminished seventh chord to all twenty-four major and minor keys. For example, Gs-B-D-F may resolve conventionally to A-C(s)-E; or with a common tone to Ab-C(b)-Eb; or via Gs-Bs-Ds-Fs to Cs-E(s)-Gs; or via G-B-D-F to C-E(b)-G. Utilizing these resolution strategies for the various enharmonic respellings of Gs-B-D-F, all the other keys are covered. See his Harmonielehre (1828), tab. V (between pp. 102 and 103). The manuscript of a “Prélude omnitonique” by Liszt surfaced in London in 1904, but its current whereabouts is unknown. See E. Perényi, Liszt: The Artist As Romantic Hero (Boston: Little, Brown, 1974), p. 321. During Act One Ds is a member of the tonic chord from the outset, sustaining an Eb from the chord that precedes the Largo. The conventional B minor/D major connection of the Overture thus mutates into B major/D major during Act One.

313

314

Notes and references to pages 179–185

17 In the connection between D major and D minor, Weber employs a deformed omnibus reminiscent of the one we encountered in Beethoven’s String Quartet Eb –E –F –Fs in C Major [5.17a, b]. Its normative state proceeds D– whereas Weber’s Fs– F– E– Eb–D D– Ds– E–F score reads Fs– F– E– D. Beethoven modifies its first chord, whereas Weber modifies its last chord. Both Beethoven and Weber omit the next-to-last chord. Weber incorporates the seventh C only in its second and third chords. 18 With this third diminished seventh chord, all twelve pitch classes have now been employed in a diminished seventh context. 19 “Um entferntere Ausweichungen zu bestimmen, muß man Vortheile suchen, welche die verminderten Siebente . . . leisten. denn wie

Gis h d f kann dem Gehöre vorkommen ab H d f gis h d Eis as ces D f Sie sind die nämliche Griffe auf der Orgel, und doch könnte Gis der siebente Ton vom weichen A sein H C Eis Fis D Es” Vogler, Tonwissenschaft und Tonse[t]zkunst (1776), p. 81. 20 Marx uses the same verb to characterize a progression from Beethoven String Quartet in C Major, discussed in Chapter 5. (See p. 134, above.) 21 Edward Aldwell and Carl Schachter adopt this viewpoint in their analysis of Schubert’s “Der Wegweiser” (Winterreise, no. 20), measures 55 through 67. See their Harmony & Voice Leading (32003), pp. 579–581. The song was written about four years after Euryanthe. Schubert was on close terms with Weber during the Vienna premiere of the opera. Elmar Seidel correlates this passage from “Der Wegweiser” and a diminished seventh prolonging progression dubbed the Teufelsmühle (Devil’s Mill) that Förster introduces in his Anleitung zum GeneralBass [1805]. See Seidel’s “Über den Zusammenhang zwischen der sogennanten Teufelsmühle und dem 2. Modus mit begrenzter Transponierbarkeit in Liszts Harmonik” in Liszt-Studien 2: Kongreßbericht Eisenstadt 1978 (Munich: Katzbichler, 1981), pp. 173, 182. 22 In some other examples Vogler pursues a chord-to-chord assessment. See, for example, Handbuch zur Harmonielehre (1802), table V, fig. 1m. 23 The term “Italian sixth” was current in the eighteenth century: we observed Holden using it earlier in this chapter. In his Musical Grammar (1806), Callcott coins the label “French” assuming that configuration’s invention by Rameau, while “German” acknowledges effective use of that version by Graun. 24 Marx critiques the term “übermässige Sext-Akkord” in Die alte Musiklehre im Streit mit unserer Zeit (1841), p. 126 (fn.). The chapter of Dehn’s Harmonielehre (1840) that he condemns is titled “Ueber die Behandlung der drei übermässigen

Notes and references to pages 185–191

25

26

27 28

29 30

31 32

33 34

Sextenakkorde” (pp. 216–222). Hermann S. Saroni, whose English translation of a part of Marx’s Die Lehre von der musikalischen Komposition appeared in New York as Theory and Practice of Musical Composition around 1851, renders “übermässig” as “superfluous,” a term that fortunately did not persist for long in American music pedagogy. Marx, Lehre von der musikalischen Komposition (1837–47) [Saroni, p. 261]. Hardly new: Marpurg labels the chord “verminderte verminderte” nearly a century earlier. (See p. 168, above.) In his Exposition élémentaire de l’harmonie [1807], Rey discusses the same chord under the caption “Emploi de l’Accord de Quinte et Tierce diminuées” (p. 49). “Aber dieser Name ist nicht blos überflüssig, er ist auch unsystematisch, irreleitend und unzulänglich.” Riemann added this language to Marx’s Lehre von der musikalischen Komposition when preparing a posthumous edition (1887, vol. 1, p. 320). Weber, Versuch einer geordneten Theorie der Tonse[t]zkunst (1817–21, 31830–32), vol. 1, table 8 (opposite p. 255), ex. 123 [Warner, p. 210]. The dominant chord is a phenomenon of scale degree 5 (e.g., G-B-D-F in C Major) that composers replicate on the second scale degree (among others) to create what is now often called an“applied” or“secondary” dominant (e.g., D-Fs-A-C). Marx’s lowering of the chordal fifth (G-B-Db-F) can be extended to this applied chord, resulting in D-Fs-Ab-C, our “French” augmented sixth. Weber’s principal derivation, in contrast, raises the supertonic’s third: D-F-Ab-C in C Minor becomes DFs-Ab-C. A careful reading of Weber’s Versuch (particularly Sections 94 and 202 of the 3rd edn.) reveals that he permits alternative derivations: B-Ds-F-A could result either from elevating the third of B-D-F-A (supertonic when A is tonic) or from depressing the fifth of B-Ds-Fs-A (dominant when E is tonic). In Singer’s Metaphysische Blicke in die Tonwelt (1847), cited in chapter 1, n. 18, either Hilfsharmonie may be modified to create an augmented sixth chord: for example, Db-F-G-B may be derived either from G-B-D-F, the “I. Hilfsharmonie” in C Major or C Minor, or from Bb-D(b)-F-G, the “II. Hilfsharmonie” in F Major or F Minor. Saroni’s nineteenth-century English terms are employed here. Marx, Lehre von der musikalischen Komposition (1837–47) [Saroni, pp. 258, 261]. The modified dominant of measure 204 occurs during the coda. It is preceded by conventional dominants in measures 188 (the structural close) and 196 and followed by conventional dominants in measures 208, 212, 214, and 216. I plead guilty as well: Listen and Sing (New York: Schirmer, 1995), pp. 623–624. The notes in the first half of measure 90 do not form a Vorhalt because the Eb to which Fb resolves is present in the chord. Rejected as a chord component, Fb instead performs a melodic role, connecting F and Eb. We encountered the term Trugfortschreitung in Siegfried Dehn’s analysis of Beethoven. See p. 134, above. During the first statement of this material (measure 63) Eb, G, Bb, and Db do share a moment of time: half a beat.

315

316

Notes and references to pages 191–204

35 Weitzmann, Der verminderte Septimen-Akkord (1854), p. 24. 36 A detailed consideration of the Neapolitan chord appears in chapter 8. 37 “Einem consonirenden Accorde kann jeder andere consonirende Accord folgen.” Weitzmann, Harmoniesystem [1860], p. 19 (emphasis in the original). 38 Another funereal piece, the Marcia funèbre sulla morte d’un eroe from Beethoven’s Sonata in Ab Major (op. 26), proceeds, like Funérailles, from Ab through Cb (Bn) to Ebb (Dn). I discuss this work and its impact on Liszt in “Liszt’s Composition Lessons from Beethoven (Florence, 1838–39): ‘Il penseroso’,” Journal of the American Liszt Society 28 (1990), pp. 3–19. Weitzmann offers brief comments on the march in Die neue Harmonielehre im Streit mit der alten (1861), his response to critics of his Harmoniesystem. He asserts that without the notion of enharmonic equivalence one would have to regard the movement as beginning in Ab Minor but ending in Bbbb Minor (pp. 27–28). 39 n. 14 of this chapter describes several other novel treatments of the chord.

8 Chromatic chords: major and minor 1 Rosen, The Romantic Generation (1995), pp. 535–536. 2 An early formulation of the concept of accented passing notes appears in Marpurg’s Handbuch bey dem Generalbasse und der Composition (1755–58), vol. 2, pp. 83–86. Marpurg’s term for this phenomenon is Wechselgang. 3 Sechter’s diatonic progression likely derives from the opening measures of an example in Rameau’s Traite de l’harmonie (1722), p. 195 [Gossett, p. 216], discussed by Cecil Powell Grant in “The Real Relationship between Kirnberger’s and Rameau’s Concept of the Fundamental Bass,” Journal of Music Theory 21/2 (1977), pp. 324–338. 4 In his discussion of these progressions in Viennese Harmonic Theory from Albrechtsberger to Schenker and Schoenberg (1985, pp. 56–57), Robert Wason calls F-Ab-Db the Neapolitan. Sechter, in contrast, speaks of the pitch Db being held up (aufhalten) and in need of resolution (Auflösung). A subdominant is understood to have occurred even if by the time its C arrives, its F and Ab have departed. Compare with 8.2. 5 In the succession from the seventh to the eighth chord of 6.1 Lampe averts similar commotion – A-C-E to As-Cs-Fs – by employing A-Cs-E rather than E Minor’s diatonic A-C-E. 6 Mattheson, Exemplarische Organisten-Probe (1719), part 1, pp. 19–20. See also the article “Modus Musicus” in Walther’s Musicalisches Lexicon (1732), p. 415 and table XVIII, fig. 1, and Riepel’s Baßschlüssel (1786), p. 62. Walther’s categorization of diatonic and chromatic pitches in both major and minor keys differs somewhat from Mattheson’s. It is reprinted in Lester, Compositional Theory in the Eighteenth Century (1992), p. 86. Philipp Joseph Frick employs the symbols 2n, 2b, and 2bb (the accidental varying according to the key) for the lowered

Notes and references to pages 204–208

7 8 9

10 11 12

13 14

15 16 17

18

19

20

second scale degree in minor keys in A Treatise on Thorough Bass ([1786], pp. 12–15). In major keys the pitch between 1 and 2 is labeled 1n, 1, or 1. Daube, Der musikalische Dilettant: Eine Abhandlung des Generalbasses (1770– 71), p. 138. Rameau, Code de musique pratique (1760), plate 27. “Quoique le réb ait ici son octacorde comme s’il était tonique du Ton de réb majeur, il n’est malgré cela que la seconde chromatique par bémol du ton d’Ut, vu que l’établissement de ce ton d’ut le précède et s’assujetit tout le reste. Il en est de même de l’octacorde uts si la sols fas mi rés uts qui n’est pas en ut dièse mineur, mais en ut naturel majeur, par les mêmes raisons. Prendre chaque octacorde de cet exemple pour une Gamme et un Ton différens, c’est la méprise de ceux qui n’entendent rien au genre chromatique.” Momigny, La seule vraie théorie de la musique [1821], p. 79. Weitzmann, Harmoniesystem [1860], p. 47, ex. 4. “la Sixte Mineure sur la quatrieme note du ton.” Langlé, Traité de la basse [ca. 1798], p. 226. Crotch, Elements of Musical Composition (1812), p. 72. In a footnote Crotch claims that the names for the augmented sixths and the Neapolitan sixth “are denominated after the nations which invented them” (p. 71). Lobe, Vereinfachte Harmonielehre [1861], p. 159. In his Lehrbuch der musikalischen Komposition (1850, 21858, vol. 1, p. 241), Lobe amplifies Vogler’s perspective by listing several choices for a harmonic interpretation of the Neapolitan, as follows: B: 1; F: 4; d: 6; Es: 5; es: 5. He concurs with Vogler that F: 4 is the best choice. Vogler, Zwei und dreisig Präludien (1806), p. 10. Weber, Versuch einer geordneten Theorie der Tonse[t]zkunst (1817–21, 31830–32), vol. 2, p. 213 [Warner, p. 430]. Vogler’s discussion of antipodes appears in Zwei und dreisig Präludien (1806), pp. 38–41. An assessment of antipodal relationships in music appears later in this chapter, in the context of an excerpt from Wagner’s Lohengrin. “La Fondamentale de l’accord de quinte mineure qui est le second degré de la gamme en mode mineur, ne peut être haussée, parce qu’une telle modification introduirait un son étranger à la tonalité; mais elle peut être abaissée, et il en résulte une harmonie fort belle et très-usitée.” Durutte, Esthétique musicale (1855), pp. 108, 117. “C’est, à proprement parler, un accord de quinte diminuée sur la sus-tonique, état deux, dont on a baissé la sus-tonique d’un demi-ton.” Loquin, Notions élémentaires d’harmonie moderne (1862), p. 35. “Mit anderen Worten: b-d-f ist nicht b-d-f, sondern h-d-f!” Lobe, Vereinfachte Harmonielehre [1861], p. 158. Lobe rejects “a: 2” as analysis for either Bb-D-F or B-Ds-Fs in A Minor. The former is instead “F: 4”; the latter is instead “E: 5” [6.13]. Further discussion on this issue appears in his Lehrbuch der musikalischen Composition, vol. 1 (1850, 21858), pp. 242–244, where he presents a narrow

317

318

Notes and references to pages 208–211

21 22

23

24 25 26

27

definition of an altered chord: “The distinguishing characteristic of an altered chord is that it cannot be built exclusively from the diatonic pitches of any one key, but must include a chromatically raised or lowered pitch. In other words, an altered chord has its rightful place within a given key, though one of its pitches is borrowed from another.” [“Das unterscheidende Merkmal eines alterirten Akkordes ist, dass er in keiner Tonart aus durchaus leitereigenen Intervallen zu bilden ist, sondern eines derselben chromatisch erhöht oder erniedrigt werden muss. Mit anderen Worten: Ein alterirter Akkord hat zwar seinen bestimmten Sitz in einer bestimmten Tonart, aber ein Intervall davon ist einer anderen entlehnt.”] Macfarren, Six Lectures on Harmony (1867), pp. 106–107. Stainer, A Theory of Harmony (1871, 8n.d.), pp. 119–120. The likely source for Stainer’s dual-root derivation is Frederick Arthur Gore Ouseley’s A Treatise on Harmony (1868), p. 163. In his earlier Notions élémentaires d’harmonie moderne (1862), p. 4, Loquin had juxtaposed lists of Sept fonctions (Tonique, Sus-tonique, Médiante, etc.), Douze sons (one for each of the twelve positions within the octave), and Dix-sept degrés (seven diatonic pitches plus five pairs of dually-named pitches – e.g., raised tonic and lowered supertonic). Sorge, Vorgemach der musicalischen Composition [1745–47], p. 50. Kirnberger, Die Kunst des reinen Satzes in der Musik (1771–79), vol. 1, p. 105 [Beach and Thym, p. 123]. Kirnberger’s ranking of the goal keys for direct modulation displays a subtlety not found in earlier models such as that in David Kellner’s Treulicher Unterricht im General-Baß (1732, p. 52), where all the keys that require the addition of a sharp for the leading tone (d, e, G, and a) appear on the left side of a chart, followed by the key that requires the addition of a flat for the fourth scale degree (F). Johann David Heinichen’s two-tiered classification in Der General-Bass in der Composition (1728) is consistent with Kirnberger’s, though without his level of variegation. (See p. 307, n. 6, above.) On the other hand, Kirnberger’s ranking of closely related keys exactly matches that in Sorge’s Vorgemach der musicalischen Composition [1745–47], p. 53. Sorge rejects Heinichen’s use of the term “extraordinary” (außerordentlich) for F and d. In his view that term should be reserved for keys such as c, g, Eb, Bb, f, and Ab. For comparison, Kellner’s ordering (Treulicher Unterricht, p. 53) begins with keys that require the addition of a sharp for the leading tone (A Minor to d, e, and G), followed by the key that requires the addition of a flat for the fourth scale degree (F), followed by the key that requires no alteration (C). Heinichen sanctions ordinary modulations from A Minor to C Major and E Minor and extraordinary modulations from A Minor to D Minor and F Major. His classification of the connection between A Minor and G Major is ambiguous: his textual commentary places it in the second category, but both the chart that corresponds to that passage and a later “Musical Circle” place A Minor and G Major in close alliance, thereby contrasting Kirnberger’s view (Der General-Bass in der

Notes and references to pages 211–215

28 29

30 31 32

33

34 35 36

Composition, 1728, pp. 761–762, 837). Sorge’s ordering is apparently nothing more than a descent of the scale: G, F, e, d, C. (See Vorgemach der musicalischen Composition [1745–47], p. 55.) Kirnberger, Die Kunst des reinen Satzes in der Musik (1771–79), vol. 1, pp. 106, 121–133 [Beach and Thym, pp. 124, 138–150]. Kirnberger, Die Kunst des reinen Satzes in der Musik (1771–79), vol. 1, p. 122 [Beach and Thym, p. 139]. In Heinichen’s widely circulated circle of 1728, the keys are arranged as follows (converting German H to B and B to Bb): C–a–G–e– D–b–A–fs–E–cs–B–gs–Fs–ds–Cs–bb–Gs–f–Ds–c–Bb–g–F–d–C (Der GeneralBass in der Composition, 1728, p. 837). Sorge revises some of the spellings – for example, Ab (As) in place of Gs (Gis) – and offers an alternative arrangement (a– C–G–e–b–D–. . .) in his Vorgemach der musicalischen Composition [1745–47], part 1, table XXVI. Daube, General-Baß in drey Accorden (1756), pp. 110–181. Momigny, Le seule vraie théorie de la musique [1821], p. 96. Dun, “On the Elements of Musical Harmony and Composition” (The Harmonicon, 1829, p. 212). Dun’s title refers to Frederick Schneider’s Elementarbuch der Harmonie und Tonse[t]zkunst, recently published in English translation, which the article attacks. Borrowing from Reicha (Cours de composition musicale [ca. 1816], p. 53), Dun adopts the term “strangled modulation” (modulation étranglée) for “abrupt and unpleasing” writing in which “the requisite number of intermediate chords is not introduced . . . and further, [in which] these chords are not dwelt upon sufficiently, so as to reconcile the ear to the change of key” (p. 213). On the other hand, Franz Joseph Kunkel, in reviewing Weitzmann’s Harmoniesystem [1860], emphasizes what Weitzmann calls the “mystical connection” (mystischen Zusammenhang) of distantly related keys such as C Major to Fs Major (Kritische Beleuchtung des . . . Weitzmann’schen Harmoniesystems, 1863, p. 19). As we have seen (pp. 153–154, above), this perspective was championed by Lobe. He argues against the non-modulatory stance as follows (Lehrbuch der musikalischen Komposition, vol. 1, 21858, p. 244): “In order to remain consistent, one would have to say that every foreign chord that appears between two chords within a key is no foreign chord, but an altered chord within the key, regardless of what other keys it in fact may be found in.” [“Um konsequent zu bleiben, müsste man sagen: jeder fremde Akkord, der zwischen zwei leitereigenen erscheint, ist kein fremder, sondern ein leitereigener, aber alterirter, er mag in so viel anderen Tonleitern wirklich vorhanden sein als er kann.”] See pp. 151–152, above. See 8.8, where the keys are ranked in the context of C Major. Choron, Principes de composition des écoles d’Italie [1809], vol. 1, p. 42. “This succession fundamentally has little more reason to exist than in the case of a chord on a major key’s first scale degree ascending to a seventh chord on its third scale degree, as a means of leading to the relative minor key.” [“Cette succession n’a

319

320

Notes and references to pages 217–234

37

38 39 40

41

42 43

44

45

46 47

guères lieu fondamentalement que lorsque la première d’un ton majeur monte à la troisième portant Accord de septième, pour passer au mode mineur relatif.”] Alternatively, the D minor chord could be regarded as a neighboring chord to the A major chord, similar to the relationship explored by Jelensperger in 5.4 but with A-D-F transformed from 64 into 53 position. The introduction that precedes the period under consideration opens with a I6 chord in which A is featured prominently. See p. 211, above. “ ‘Ah, was sind das für kühne Modulationen! So was könnte unsereinem im Traume nicht einfallen!’. ” Anselm Hüttenbrenner reporting to Franz Liszt from Vienna, 1854. Quoted in Schubert: Die Erinnerungen seiner Freunde, ed. Otto Erich Deutsch (Leipzig: Breitkopf & Härtel, 1957), p. 207. In David Lewin’s analysis, measure 11’s bass Gs is interpreted as a neighbor between the surrounding Ass, putting the cadential 64’s arrival at measure 9. (This concurs with Schenker’s reading in Der freie Satz.) See Lewin’s “Auf dem Flusse” in Nineteenth Century Music 6 (1982): 47–59; reprinted in Walter Frisch’s Schubert: Critical and Analytical Studies (Lincoln, Nebr.: University of Nebraska Press, 1986, pp. 126–152). Seyfried’s potent contemporary model suggests a different reading [8.19], as does consideration of the motivic connection between G–A–B and B–As–Gs, mentioned above. Gs–As–B (or Gs–A–As–B) figures prominently in the E-Major section of the song (see the bass in measures 23–24, 27–30, 31–32, 35–38), while B–A–G occurs several times after the return to E Minor (see the bass in measures 52–53, 66–67, and 68–69). Allowing enharmonic reinterpretation, equivalent relationships occur between F and Cb in Eb Minor and Gb Major, or between Es and B in Ds Minor and Fs Major. Allowing enharmonic reinterpretation, equivalent relationships occur between Cb and F in Bb Major and Bb Minor, or between Bn and Es in As Major and As Minor. In an intensely harmonic view the vocal C at beat 3 of measure 3 would be regarded as a chordal thirteenth, giving way to the chordal fifth at beat 4. From a voice-leading perspective C functions as a suspension. Likewise the pitches at the downbeat of measure 4 might be regarded as an inversion of a Gs-B-D-F diminished seventh chord (still targeting A), or as suspended components of the E7 chord clashing against the root F of the E chord’s successor. In Wagner’s composition the E of this descent occurs only in the vocal melody. The orchestra presents E–Ds–D more emphatically in the following phrase (measures 11 and 12). The empty-parentheses notation in 8.24c and 8.24d is borrowed from Schenker. Though the presentation of Fb as E avoids the obvious nuisance of writing and reading music in a key with eight flats, Verdi may have smiled at the parallel with the opera’s plot: Wurm is about to tell Miller that “Carlo” is actually Rodolfo, courting Luisa under a false guise (sotto mendace aspetto). The same situation prevails between “E” and Fb!

Notes and references to pages 234–236

48 “In den unter Beisp. 10 folgenden Akkordverbindungen wird sich der gemeinschaftliche Ton wohl eher als Bindemittel geeignet zeigen; immerhin aber behalten auch manche dieser Verbindungen von Akkorden, welche entfernten Tonarten angehören, etwas Befremdliches, und die plötzliche Aufeinanderfolge solcher Akkorde zeigt sich nicht immer zur Modulation geeignet.” Jadassohn, Die Kunst zu moduliren und zu präludiren (1890), p. 6. 49 Nineteenth-century compilations of parallel perfect intervals from the music literature can be found in Wilhelm Tappert’s Das Verbot der Quinten-Parallelen (Leipzig: Heinrich Matthes, 1869) and Johannes Brahms’s Oktaven und Quinten, ed. Schenker (Vienna: Universal Edition, 1933). In his Kritische Beleuchtung des C. F. Weitzmann’schen Harmoniesystems (Frankfurt am Main: Auffarth, 1863, p. 11), Franz Joseph Kunkel likens an occasional parallel fifth to “an otherwise successful poem with here and there clumsy lines or false rhyme” [“ein sonst gelungenes Gedicht mit hier und da hinkenden Versen oder falschem Reim”]. 50 “Die alte Theorie, der strenge Styl möchte wohl über diese Nichtachtung ihrer beiden Grundverbote die Hände über dem Kopfe zusammenschlagen, die Aesthetik aber kann triumphirend auf ihre Uebermacht über die Theorie hinweisen, denn auch diese Stelle macht einen wundersam reizenden Eindruck.” Lobe, Vereinfachte Harmonielehre [1861], pp. 175–176. 51 In the chapter on Italian opera in The Age of Beethoven: 1790–1830 (The New Oxford History of Music, vol. 8, ed. Gerald Abraham), Winton Dean relates that “Bellini had used the semitone shift in plunging from the chord of B flat into B major during Imogene’s Act I cavatina [Il pirata (1827)]. Though not unprecedented (it occurs in Spontini and for comic effect in Cimarosa and Mayr), it is not characteristic of Rossini, but was to become a favourite pattern for a strong dramatic gesture throughout Italian romantic opera” (pp. 440–441).

321

Select bibliography of secondary literature

Agmon, E., “Functional Harmony Revisited: A Prototype-Theoretic Approach,” Music Theory Spectrum 17 (1995), pp. 196–214 Aldwell, E. and Schachter, C., Harmony and Voice Leading, 3rd edn., Belmont, Cal.: Schirmer/Thomson Learning, 2003 Baker, N. K., “ ‘Der Urstoff der Musik’: Implications for Harmony and Melody in the Theory of Heinrich Koch,” Music Analysis 7 (1988), pp. 3–30 “An ars poetica for Music: Reicha’s System of Syntax and Structure,” in Musical Humanism and Its Legacy: Essays in Honor of Claude V. Palisca, eds. N. K. Baker and B. R. Hanning, Stuyvesant, N.Y.: Pendragon Press, 1992, pp. 419–449 Bass, R., “From Gretchen to Tristan: The Changing Role of Harmonic Sequences in the Nineteenth Century,” 19th-Century Music 19 (1995–96), pp. 263–285 Beach, D., “The Harmonic Theories of Johann Philipp Kirnberger: Their Origins and Influences,” PhD diss., Yale University, 1974 “The Origins of Harmonic Analysis,” Journal of Music Theory 18 (1974), pp. 274–306 “The Influence of Harmonic Thinking on the Teaching of Simple Counterpoint in the Latter Half of the Eighteenth Century,” in Eighteenth-Century Music in Theory and Practice: Essays in Honor of Alfred Mann, ed. M. Parker, Stuyvesant, N.Y.: Pendragon Press, 1994, pp. 159–185 Bent, I., “Analytical Thinking in the First Half of the Nineteenth Century,” in Oxford International Symposium (1977: Christ Church College): Modern Musical Scholarship, ed. E. Olleson, Stocksfield and Boston: Oriel Press, 1980, pp. 151–166 “The ‘Compositional Process’ in Music Theory 1713–1850,” Music Analysis 3 (1984), pp. 29–55 “History of Music Theory: Margin or Center?,” Theoria: Historical Aspects of Music Theory 6 (1992), pp. 1–21 Music Analysis in the Nineteenth Century, 2 vols., Cambridge: Cambridge University Press, 1994 Music Theory in the Age of Romanticism, Cambridge: Cambridge University Press, 1996 Bent, I. and Pople, A., “Analysis,” in The New Grove Dictionary of Music and Musicians, 2nd edn., London: Macmillan, 2001 Bernard, J., “The Principle and the Elements: Rameau’s Controversy with d’Alembert,” Journal of Music Theory 24 (1980), pp. 37–62

Select bibliography of secondary literature

“The Marpurg–Sorge Controversy,”Music Theory Spectrum 11 (1989), pp. 164–186 Brown, M., “The Diatonic and the Chromatic in Schenker’s Theory of Harmonic Relations,” Journal of Music Theory 30 (1986), pp. 1–34 Burnham, S., “Method and Motivation in Riemann’s History of Harmonic Theory,” Music Theory Spectrum 14 (1992), pp. 1–14 “Musical and Intellectual Values: Interpreting the History of Tonal Theory,” Current Musicology 53 (1993), pp. 76–88 Caldwell, G., “Harmonic Tonality in the Theories of Jérôme-Joseph Momigny,” PhD diss., The Ohio State University, 1993 Caplin, W., “Harmony and Meter in the Theories of Simon Sechter,” Music Theory Spectrum 2 (1980), pp. 74–89 Chevaillier, L., “Les théories harmoniques,” in Encyclopédie de la musique et Dictionnaire du Conservatoire, eds. A. Lavignac and L. de la Laurencie, Paris: Delagrave, 1925, part 2, pp. 519–590 Christensen, T., “Rameau’s ‘L’Art de la Basse Fondamentale’, ” Music Theory Spectrum 9 (1987), pp. 18–41 “Nichelmann Contra C. Ph. E. Bach: Harmonic Theory and Musical Politics at the Court of Frederick the Great,” in Carl Philipp Emanuel Bach und die europäische Musikkultur des mittleren 18. Jahrhunderts, ed. H. Marx, Göttingen: Vandenhoeck & Ruprecht, 1990, pp. 189–220 “The Règle de l’Octave in Thorough-Bass Theory and Practice,” Acta musicologica 64 (1992), pp. 91–117 “The Spanish Baroque Guitar and Seventeenth-Century Triadic Theory,” Journal of Music Theory 36 (1992), pp. 1–42 “Music Theory and Its Histories,” in Music Theory and the Exploration of the Past, eds. C. Hatch and D. Bernstein, Chicago: University of Chicago Press, 1993, pp. 9–39 Rameau and Musical Thought in the Enlightenment. Cambridge: Cambridge University Press, 1993 “The Music Theory of Georg Friedrich Lingke,” Indiana Theory Review 16 (1995), pp. 35–59 The Cambridge History of Western Music Theory, Cambridge: Cambridge University Press, 2002 Cohn, R., Dahlhaus, C., Hyer, B. et al., “Harmony,” in The New Grove Dictionary of Music and Musicians, 2nd edn., London: Macmillan, 2001 Dahlhaus, C., Üntersuchungen über die Entstehung der harmonischen Tonalität, Kassel: Bärenreiter, 1968, trans. R. Gjerdingen as Studies on the Origin of Harmonic Tonality, Princeton: Princeton University Press, 1990 Die Musik des 19. Jahrhunderts, Wiesbaden: Athenaion, 1980, trans. J. B. Robinson as Nineteenth-Century Music, Berkeley and Los Angeles, Calif.: University of California Press, 1989 Die Musiktheorie im 18. und 19. Jahrhundert. Erster Teil: Grundzüge einer Systematik; Zweiter Teil: Deutschland (ed. Ruth E. Müller), Geschichte der

323

324

Select bibliography of secondary literature

Musiktheorie, ed. Frieder Zaminer, vols. 10–11, Darmstadt: Wissenschaftliche Buchgesellschaft, 1984–89 Dale, C., Music Analysis in Britain in the Nineteenth and Early Twentieth Centuries, Burlington, Vt.: Ashgate, 2002 Damschroder, D. and Williams, D. R., Music Theory from Zarlino to Schenker, Stuyvesant, N.Y.: Pendragon Press, 1990 Dill, C., “Rameau’s Imaginary Monsters: Knowledge, Theory, and Chromaticism in Hippolyte et Aricie,” Journal of the American Musicological Society 55 (2002), pp. 433–476 Dunsby, J. and Whittall, A., Music Analysis in Theory and Practice, London: Faber, 1988 Eggebrecht, H. H., ed., Handwörterbuch der musikalischen Terminologie, Stuttgart: Steiner, 1972– Eicke, K.-E., Der Streit zwischen Adolph Bernhard Marx und Gottfried Wilhelm Fink um die Kompositionslehre, Regensburg: Bosse, 1966 Ferris, D., “C. P. E. Bach and the Art of Strange Modulation,” Music Theory Spectrum 22 (2000), pp. 60–88 George, D., “The Traité d’harmonie of Charles-Simon Catel,” PhD diss., North Texas State University, 1982 Gessele, C., “The Institutionalization of Music Theory in France: 1764–1802,” PhD diss., Princeton University, 1989 “The Conservatoire de Musique and National Music Education in France,” in Music and the French Revolution, ed. Malcolm Boyd, Cambridge: Cambridge University Press, 1992, pp. 191–210 “Base d’harmonie: A Scene from Eighteenth-Century French Music Theory,” Journal of the Royal Musical Association 119 (1994), pp. 60–90 “Fundamental Bass Theory Meets Practice: Evidence from a Composition Contest,” The Journal of Musicology 12 (1994), pp. 19–50 Gosman, A., “Rameau and Zarlino: Polemics in the Traité de l’harmonie,” Music Theory Spectrum 22 (2000), pp. 44–59 Grant, C. P., “The Real Relationship between Kirnberger’s and Rameau’s Concept of the Fundamental Bass,” Journal of Music Theory 21 (1997), pp. 324–338 Grave, F., “Abbé Vogler’s Theory of Reduction,” Current Musicology 29 (1980), pp. 41–69 Grave, F. and Grave, M., In Praise of Harmony: The Teachings of Abbé Georg Joseph Vogler, Lincoln, Nebr.: University of Nebraska Press, 1987 Groth, R., Die französische Kompositionslehre des 19. Jahrhunderts, Wiesbaden: Steiner, 1983 Gruber, G., ed., Zur Geschichte der musikalischen Analyse: Bericht über die Tagung München 1993, Laaber: Laaber-Verlag, 1996 Harrison, D., Harmonic Function in Chromatic Music: A Renewed Dualist Theory and an Account of Its Precedents, Chicago: University of Chicago Press, 1994 “Supplement to the Theory of Augmented-Sixth Chords,” Music Theory Spectrum 17 (1995), pp. 170–195

Select bibliography of secondary literature

Hyer, B., “ ‘Sighing Branches’: Prosopopoeia in Rameau’s Pigmalion,” Music Analysis 13 (1994), pp. 7–50 “Before Rameau and After,” Music Analysis 15 (1996), pp. 75–100 “Tonality,” in The New Grove Dictionary of Music and Musicians, 2nd edn., London: Macmillan, 2001 Jung, H., “ ‘Der pedantische geniale Abt Vogler’: Musiktheorie und Werkanalyse in der zweiten Häfte des 18. Jahrhunderts,” Musiktheorie 3 (1988), pp. 99–115 Keiler, A., “Music as Metalanguage: Rameau’s Fundamental Bass,” in Music Theory: Special Topics, ed. R. Browne, New York: Academic Press, 1981, pp. 83–100 Konecne, J., “Harmonic Reduction Techniques in Music Analysis, c. 1770–1917,” PhD diss., The University of Iowa, 1984 Korsyn, K., Decentering Music: A Critique of Contemporary Musical Research, Oxford: Oxford: University Press, 2003 Kopp, D., Chromatic Transformations in Nineteenth-Century Music, Cambridge: Cambridge University Press, 2002 Kramer, R.,“The New Modulation of the 1770s: C. P. E. Bach in Theory, Criticism, and Practice,” Journal of the American Musicological Society 38 (1985), pp. 551–592 Lambert, J. P., “Eighteenth-Century Harmonic Theory in Concept and Practice: Kollmann’s Analysis of J. S. Bach’s Chromatic Fantasy,” In Theory Only 8/3 (1984), pp. 11–29 Lester, J., Between Modes and Keys: German Theory 1592–1802, Stuyvesant, N.Y.: Pendragon Press, 1989 Compositional Theory in the Eighteenth Century, Cambridge, Mass.: Harvard University Press, 1992 Mickelsen, W., Hugo Riemann’s Theory of Harmony: A Study, Lincoln, Nebr.: University of Nebraska Press, 1977 Moraitis, A., Zur Theorie der Musikalischen Analyse, Frankfurt am Main: P. Lang, 1994 Moreno [Rojas], J., “Theoretical Reception of the Sequence and its Conceptual Implications.” PhD diss., Yale University, 1996 “Subjectivity, Interpretation, and Irony in Gottfried Weber’s Analysis of Mozart’s ‘Dissonance’ Quartet,” Music Theory Spectrum 25 (2003), pp. 99–120 Morgan, R., “Schenker and the Theoretical Tradition: The Concept of Musical Reduction,” College Music Symposium 18 (1978), pp. 72–96 Morrow, M., German Music Criticism in the Late Eighteenth Century: Aesthetic Issues in Instrumental Music, Cambridge: Cambridge University Press, 1997 Nelson, R., “Theories of Harmonic Modulation in Selected German Treatises of the Eighteenth Century,” PhD diss., The University of Rochester, 1984 Niecks, F., “The Foundations of Harmony,” Sammelbände der Internationalen Musikgesellschaft 4 (1903), pp. 577–588 Peters, P., “French Harmonic Theory in the Conservatoire Tradition: Fétis, Reber, Durand, and Gevaert,” PhD diss., The University of Rochester, Eastman School of Music, 1990

325

326

Select bibliography of secondary literature

Pischner, H., Die Harmonielehre Jean-Philippe Rameaus: Ein Beitrag zur Geschichte des musikalischen Denkens, Leipzig: Breitkopf & Härtel, 1963 Ratner, L. G., Classic Music: Expression, Form, and Style, New York: Schirmer Books, 1980 Romantic Music: Sound and Syntax, New York: Schirmer Books, 1992 Reilly, A., “Modulation and Key Relationships in Eighteenth-Century German Theory,” In Theory Only 8/4–5 (1985), pp. 45–56 Rosen, C., The Romantic Generation, Cambridge, Mass.: Harvard University Press, 1995 Roth, L., “Kirnberger’s Concept of Reductive Analysis,” In Theory Only 9/8 (1987), pp. 21–29 Rudd, R., “Karl Friedrich Weitzmann’s Harmonic Theory in Perspective,” PhD diss., Columbia University, 1992 Rummenhöller, P., Musiktheoretisches Denken im 19. Jahrhundert, Regensburg: Bosse, 1967 “Harmonielehre,” in Die Musik in Geschichte und Gegenwart, ed. Ludwig Finscher, Kassel: Bärenreiter, 1996 Saslaw, J., “Gottfried Weber’s Cognitive Theory of Harmonic Progression,” Studies in Music from the University of Western Ontario 13 (1991), pp. 121–144 “Gottfried Weber and the Concept of Mehrdeutigkeit,” PhD diss., Columbia University, 1992 “The Concept of Ausweichung in Music Theory, ca. 1770–1832,” Current Musicology 75 (2003), pp. 145–163 Seidel, W. and Cooper, B., Entstehung nationaler Traditionen: Frankreich, England, Geschichte der Musiktheorie, ed. Frieder Zaminer, vol. 9, Darmstadt: Wissenschaftliche Buchgesellschaft, 1986 Shamgar, B., “Romantic Harmony through the Eyes of Contemporary Observers,” Journal of Musicology 7 (1989), pp. 518–539 Sheldon, D., “The Ninth Chord in German Theory,” Journal of Music Theory 26 (1982), pp. 61–100 Shirlaw, M., The Theory of Harmony: An Inquiry into the Natural Principles of Harmony, with an Examination of the Chief Systems of Harmony from Rameau to the Present Day, London: Novello, 1917, reprint edn., New York: Da Capo, 1969 Simms, B., “Choron, Fétis, and the Theory of Tonality,” Journal of Music Theory 19 (1975), pp. 112–139 Telesco, P., “Enharmonicism and the Omnibus Progression in Classical-Era Music,” Music Theory Spectrum 20 (1998), pp. 242–279 “Forward-Looking Retrospection: Enharmonicism in the Classical Era,” The Journal of Musicology 19 (2002), pp. 332–373 Thomson, U., Voraussetzungen und Artungen der österreichischen Generalbasslehre zwischen Albrechtsberger und Sechter, Tutzing: Schneider, 1978 Todd, R. L., “The ‘Unwelcome Guest’ Regaled: Franz Liszt and the Augmented Triad,” 19th-Century Music 12 (1988), 93–115

Select bibliography of secondary literature

Veit, J., “Versuch einer vereinfachten Darstellung des Voglerschen ‘HarmonieSystems’, ” Musiktheorie 6 (1991), pp. 129–149 “Gottfried Webers Theorie der Tonsetzkunst und Voglers Harmonie-System,” in Studien zu Gottfried Webers Wirken und zu seiner Musikanschauung, ed. C. Heyter-Rauland, Mainz: Schott, 1993, pp. 69–84 Verba, E. C., “The Development of Rameau’s Thoughts on Modulation and Chromatics,” Journal of the American Musicological Society 26 (1973), pp. 69–91 Music and the French Enlightenment: Reconstruction of a Dialogue, 1750–1764, New York: Oxford University Press, 1993 Vogel, M., ed. Beiträge zur Musiktheorie des 19. Jahrhunderts, Regensburg: Bosse, 1966 Wagner, M., Die Harmonielehren der ersten Hälfte des 19. Jahrhunderts, Regensburg: Bosse, 1974 Wason, R., “Schenker’s Notion of Scale-Step in Historical Perspective: Non-Essential Harmonies in Viennese Fundamental Bass Theory,” Journal of Music Theory 27 (1983), pp. 49–73 Viennese Harmonic Theory from Albrechtsberger to Schenker and Schoenberg, Ann Arbor, Mich.: UMI Research Press, 1985 “Progressive Harmonic Theory in the Mid-Nineteenth Century,” Journal of Musicological Research 8 (1988), pp. 55–90 Werts, D., “The Musical Circle of Johannes Mattheson,” Theoria: Historical Aspects of Music Theory 1 (1985), pp. 97–131 Wirth, F., Untersuchungen zur Entstehung der deutschen praktischen Harmonielehre, Bamberg: Rudolf Rodenbusch, 1966 Yellin, V., The Omnibus Idea, Warren, Mich.: Harmonie Park Press, 1998 Zeleny, W., Die historischen Grundlagen des Theoriesystems von Simon Sechter, Tutzing: Schneider, 1979

327

Index

Abraham, G., 306 accord de la grande sixte, 10, 22–23, 167, 243, 288 Albrechtsberger, J. G., 58–60, 220, 244, 271, 279, 297 Aldwell, E., 314 d’Alembert, J., 36, 244–245, 247, 265, 271, 274, 307, 312 André, J. A., 22–23, 245, 292 anticipation, 32, 40 antipode, 207, 224, 317 Antoniotto, G., 68, 245–246 Arabic-numeral analysis, 3, 4, 5, 7, 20 Asioli, B., 99, 246 augmented sixth chords, 6, 8, 14, 24, 93, 137, 166–171, 185–190, 203, 298, 306, 310, 312, 314, 314–315, 315, 317 Bach, C. P. E., 200, 246 Bach, J. S., 2 Banister, H. C., 292 basse fondamentale, 2, 4, 21–23, 101, 168, 270 Beethoven, L. v. Coriolan Overture (op. 62), 49 Fidelio (op. 72), 78–79 Piano Sonata in A Major (op. 26), 316 Piano Sonata in C Major (op. 2, no. 3), 64 Piano Sonata in C Major (Waldstein, op. 53), 235–236 Piano Sonata in C Minor (op. 10, no. 1), 40–41, 194 Piano Sonata in C Minor (Pathétique, op. 13), 36, 46–49 Piano Sonata in D Major (op. 10, no. 3), 45, 294 Piano Sonata in F Major (op. 10, no. 2) , 121–122 String Quartet in A Major (op. 18, no. 5), 115–119 String Quartet in C Major (op. 59, no. 3), 132–138, 177, 197, 239, 306, 314 Symphony No. 5 in C Minor (op. 67), 35–36 Symphony No. 6 in F Major (Pastorale, op. 68), 55

Berlioz, H. Symphonie fantastique, 49–57, 296 Berton, H.-M., 66–69, 74, 76, 87, 205, 247 Béthizy, J. L. de, 22, 34, 68, 247 Blumröder, C. v., 306 Bordier, L.-C., 3, 247 Brahms, J., 321 Variations on a Theme by Händel (op. 24), 163 Burnham, S., 293 cadence, 6 complétive ou confirmative (confirmative), 94, 98 double, 98, 206 half, 146, 187 irréguliere (irregular, imperfect), 22–23, 95, 98, 270 parfaite (perfect, final), 68, 95, 98, 98, 270 Phrygian, 146–147 plagal, 146–147 rompuë (broken, deceptive), 62, 101, 226 Callcott, J., 162, 248, 312, 314 Catel, C.-S., 69–71, 171, 199, 248, 273, 296 Chaluz de Vernevil, F. T. A., 13–15, 16, 27, 282 Chopin, F. Étude in E Minor (op. 25, no. 5), 40–42 Mazurka in A Minor (op. 7, no. 2), 157–160 Mazurka in C Minor (op. 56, no. 3), 187–189 Mazurka in Cs Minor (op. 30, no. 4), 70–75 Prelude in Db Major (op. 28, no. 15), 164–165 chord or triad augmented, 8, 191, 225, 227 cadential 64, 14, 31, 42–45, 94, 187, 188, 206, 284, 294, 296 diminished, 17–20, 26, 288, 291 diminished diminished, 168, 315 inversion, 1, 3, 287 major diminished, 168 manca, 169 minor, 291, 293 ninth, 54, 72–73, 102

Index

passing, 113–122, 124–125, 304 perfect, 1, 12, 141, 270, 288 pivot, 143, 156, 161 root (fundamental), 17–24, 293 Zwitteraccord, 171, 312 see also augmented sixth chords, diminished seventh chords, Phrygian II chord chordæ elegantiores, 204 chord of the added sixth see accord de la grande sixte Choron, A.-É., 170–171, 215, 248–249, 253 Christensen, T., 289, 291–292, 307 chromaticism, 4, 6–7, 81, 112, 139–156, 166–172, 187–190, 213, 242, 310, 316 Clementi, M. Piano Sonata in D Minor (op. 43, no. 3), 124, 304 Colet, R. H., 249, 298, 313 Cone, E. T., 295–296 Crotch, W., 7, 62–65, 88, 100, 156–157, 206, 249, 307, 317 Czerny, C., 123–126, 250 Dahlhaus, C., 2–4, 86 Daube, J. F., 9–11, 16, 60, 142–144, 204, 211, 250–251, 279, 282, 299, 306–307 Day, A., 24, 162–63, 199, 251, 265, 269, 292 Dean, W., 321 Dehn, S., 2–3, 132–138, 185, 251–252, 257, 266, 285, 305–306, 306, 314–315, 315 diminished seventh chords, 6, 12, 18–20, 71–73, 124, 126, 132–134, 136, 137, 148–149, 166–184, 190, 190–197, 203, 206, 291, 306, 308, 312, 313, 314 dissonance essential and incidental, 19, 32, 37–39, 43–45, 102, 259–260, 294 unauthentic, 39, 102 dominant, leading, 130, 137, 162, 165, 172, 227, 304, 315 double emploi, 23, 26, 38, 160, 243, 271, 301 Dun, F., 212–213, 252, 262, 276, 319 Dürrnberger, J. A., 2–4, 252 Durutte, F. C. A., 120–121, 168, 207–208, 252, 288, 313 Ebner, J. L., 48–49 Engler, P. J., 187–188, 253, 312 enharmonicism, 68, 76, 81, 172–184, 191, 196, 205, 310, 316, 320 Fétis, F.-J., 49–57, 172–176, 180–181, 190, 196, 240, 249, 253–254, 271, 295–296, 296–297, 313

figured bass see thoroughbass Förster, E. A., 2–3, 206, 254, 314 Frick, P. J., 254, 316–317 function theory see Funktionstheorie Funktionstheorie, 9–16, 90–93 Gianotti, P., 34–35, 39, 254–255 Grant, C. P., 316 Groth, R., 313 Grundharmonie; Stammakkord, 3, 12–14, 16–17, 21, 27–28, 42, 43–45, 90–93, 98, 169 Halm, A., 21–22, 158–160, 241, 255 Händel, G. F., 220 Alexander’s Feast, 145–147 Harbordt, G., 59–60, 62, 255, 268, 290 Harrison, D., 291, 300, 312 Hasel, J., 183, 197, 255–256 Hauptmann, M., 103–4, 256, 257–258, 275 Heinichen, J. D., 256–257, 259, 307, 318, 319 Hentschel, E. J., 257, 299–300 Holden, J., 4, 149–150, 153, 166–167, 171, 257, 262, 308, 312, 313 Hüttenbrenner, A., 220 intervalles attractifs, 50–52, 55 Jadassohn, S., 8, 104, 147–148, 162–63, 199, 234, 256, 257–258, 275, 308 Jelensperger, D., 7–9, 88–92, 100, 119, 120, 121, 126–128, 152–153, 207, 211–212, 213–218, 249, 252, 254, 258, 263, 304, 310–311, 320 Keller, G., 60–61, 259, 298 Kellner, D., 259, 318 Kinderman, W., 295 King, M. P., 259, 290 Kirnberger, J. P., 1, 18–19, 29–30, 32, 45–46, 66–68, 72, 97–98, 102, 105, 114–115, 117, 150, 210–212, 248, 259–260, 260–261, 261, 265, 267, 277–278, 281, 278, 294, 296, 304, 318, 319 Knecht, J. H., 6, 110–111, 188–190, 260 Koch, H. C., 7, 11, 43–46, 94, 106–112, 113–114, 143–145, 240, 251, 260–261, 273, 291, 294, 307, 308 Kollmann, A. F. C., 102–103, 259, 261–262 Korsyn, K., 305 Kunkel, F. J., 262, 310, 319, 321

329

330

Index

Lampe, J. F., 1–2, 4, 16–17, 20, 26, 80, 96–97, 104–105, 139–141, 143, 149–150, 156, 204, 241, 257, 262–263, 287, 288, 290, 291, 308, 316 Langlé, H. F. M., 69–71, 75–79, 80–83, 205, 263 Lester, J., 287, 306–307, 316 Lewin, D., 305, 320 Lingke, G. F., 68, 263 Liszt, F. Années de Pèlerinage, Deuxième Année, 70–75 Funérailles, 190–197, 316 “Prélude omnitonique,” 313 Réminiscences de Don Juan, 198–200 Lobe, J. C., 7, 20,40–42, 45–46, 115–118, 121–122, 123–126, 153–155, 162–63, 177, 191, 194, 206, 208, 215–217, 219, 234–236, 258, 263–264, 293, 294, 308, 317, 317–318, 319 Loquin, A., 208–209, 264, 318 Louis, R., 67–70, 115–116, 123, 162–163, 228–229, 242, 264–265 Macfarren, G. A., 24–29, 72, 208, 251, 265, 292 Marpurg, F. W., 22, 36, 68, 113–114, 117, 168–169, 244, 244–245, 261, 265–266, 271, 274, 280, 306–307, 316 Martini, G. B., 16 Marx, A. B., 134, 185–190, 251–252, 257, 266, 314, 314–315, 315 Mattheson, J., 204, 266, 316 Mehrdeutigkeit, 17, 119, 136, 143, 155–161, 162–64, 240, 306, 311 Mendelssohn, F., 292 Song without Words in D Major (op. 102, no. 2), 17–18 Wedding March from A Midsummer Night’s Dream, 24–30 modulation, 139–165, 207, 209–213, 213–219, 220–223, 225–226, 307, 308, 318, 319 Momigny, J.-J. de, 12, 16, 60, 72, 85–86, 94, 98–99, 151–152, 156, 205, 211–213, 214, 219, 234–235, 253, 267, 311 Mozart, W. A. Don Giovanni (K. 527), 118, 198–200 String Quartet in C Major (K. 465), 54 Mozartean fifths, 186 multiple meaning see Mehrdeutigkeit natural bass see basse fondamentale Neapolitan sixth see Phrygian II chord neighboring note, 32, 40–42, 46, 119–121 Newbould, B., 49

omnibus, 134–136, 239, 306, 314 ordre omnitonic, 176, 313 pluritonic, 174 transitonic, 174 unitonic, 174 Ouseley, F. A. G., 251, 267–268, 280, 318 Paesiello, G. Cavatina, “Nel cor più non mi sento,” 15 parallel fifths and octaves, 60, 81, 124, 186, 234–235, 302, 321 passing note, 32, 40–42, 46, 113–122, 316 pedal point, 55, 56, 199 Phrygian II chord (Neapolitan sixth), 193–196, 198–209, 224, 316, 317 Portmann, J. G., 6–7, 12–14, 16, 20–22, 28, 31, 58, 59, 90–93, 94, 98, 130–131, 251, 255, 268, 290, 291, 292, 297, 300–301, 302, 309 progression geometric, 10 harmonic, 85–112 parallel, 58–65, 75, 298 sequential, 65–84, 105, 191–197, 205–206, 298 triple, 288–289, 309 Prout, E., 160–165, 251, 268–269, 291, 312 Rameau, J.-P., 1, 9, 10, 16, 22–23, 26, 31–36, 39, 42, 46, 61–62, 67, 68, 85, 94–96, 101–105, 115, 139–143, 166–168, 195, 204, 243, 244, 244–245, 247, 247, 250, 254–255, 257, 259, 259–260, 261, 262, 265, 268, 269–271, 271, 273, 274, 278, 278, 287, 288, 288–289, 291, 291–292, 293, 298, 300, 301, 306–307, 307, 309, 312, 313, 314, 316 Reicha, A.-J., 56–57, 62–65, 77–78, 115–117, 119, 120–121, 145–147, 152, 249, 252, 254, 258, 271, 296–297, 313, 319 Rey, J.-B., 21–22, 271, 315 Richter, E. F., 7–8, 123–126, 257–258, 272, 275 Riemann, H., 14–16, 90, 256, 260, 266, 272–273, 275, 290–291, 291, 293, 315 Riepel, J., 273, 289–290, 302, 316 Roman-numeral analysis, 1, 3–4, 6, 7 Rosen, C., 198–200 Rossini, G. Guillaume Tell, 213–219, 235 Soirées musicales, 54 Roussier, P.-J., 3, 273

Index

sacré quaternaire, 98 Saroni, H. S., 315 Saslaw, J., 308 Savard, A., 115–116, 157, 273 scale-step theory see Stufentheorie Schachter, C., 314 Schalk, J., 155, 274 Scheibe, J. A., 128–130, 274 Schenker, H., 46, 73, 85–86, 105, 123, 162, 164–165, 217, 243, 246, 272, 274–276, 295, 297–298, 303, 308, 311, 312, 320 Schilling, G., 128–129, 276 Schneider, F., 20, 252, 276, 319 Schoenberg, A., 164–165, 276–277, 279 Schröter, C. G., 2–3, 10, 277, 289, 301, 302 Schubert, F. “Auf dem Flusse” (Winterreise), 219–223, 320 “Die Forelle,” 48–49 “Das Grab,” 238–243 “Aus Heliopolis II,” 79–84 Moment musical in Ab Major (op. 94, no. 6), 46–49, 295 Quintet in A Major (“Trout,” op. 114), 106–112 “Der Wegweiser” (Winterreise), 314 Schumann, R. Neue Zeitschrift für Musik, p. 50 Piano Sonata in Fs Major (op. 11), 67–70 Schulz, J. A. P., 38–39, 46, 114–115, 117, 119, 122, 277–278, 304 Sechter, S., 57, 62, 65–67, 98, 99–100, 103, 106–108, 115–117, 126–128, 130, 134–135, 171, 200–203, 228–229, 236–237, 241, 255, 275, 276, 278–279, 301, 312, 316 Seidel, E., 314 Seyfried, I. R. v., 220–223, 244, 279, 320 Singer, P., 279, 289, 315 Sorge, G. A., 5, 85, 105, 115–117, 210, 265–266, 279–280, 288, 291, 294, 318, 319 Stainer, J., 25–29, 45, 208, 251, 280, 292, 294, 312, 318 Stammakkord see Grundharmonie Stufentheorie, 2, 8–9, 93–94 substitution, 166–167, 198 supposition, 22, 270 suspension, 18–19, 31–36, 39, 40–42, 48, 56, 293, 320 see also Vorhalt Swoboda, A., 12, 130, 137, 140, 280, 290, 304, 313 Tappert, W., 186, 321 Telesco, P. J., 306

temperament, 66, 298, 301 Teufelsmühle (Devil’s Mill), 314 thoroughbass, 1, 4, 6, 168, 293, 298 Thuille, L., 67–70, 115–116, 123, 162–163, 228–229, 242, 265 Tiersch, O., 125–126, 130, 281 tour de l’harmonie, 75–79 triad see chord Trugfortschreitung, 134, 191, 306, 315 Trydell, J., 4–5, 262, 281 Türk, D. G., 217, 281 Vallotti, F. A., 282 Verdi, G. Luisa Miller, 229–237, 320 Macbeth, 236 Il Trovatore, 209 Vincent, H. J., 282, 288 Virués y Spínola, J. J. de, 13–15, 16, 27, 282 Vogler, G. J., 5–6, 16–17, 19, 62–65, 105, 132–134, 150–152, 156–158, 169–170, 171, 173, 180, 182–184, 200, 206–207, 237, 240, 249, 252, 258, 260, 262–263, 268, 272, 275, 276, 277, 280, 282–283, 284, 288, 298, 301, 305, 309, 309–310, 311, 314, 317 voice exchange, 117, 123–124, 294 Vorhalt, 191–196, 200, 228, 243, 315 see also suspension Wagner, R. Lohengrin, 223–229 Walther, J. G., 283, 316 Wason, R., 306, 316 Weber, C. M. v. Euryanthe, 177–184, 197, 313, 314 Weber, F. D., 103, 115–118, 283–284 Weber, G., 7–8, 11–12, 16, 17, 58–59, 62–65, 66–68, 70, 74, 77–79, 87, 94, 130, 147–149, 153, 156, 161, 171, 181–183, 187, 190, 194, 207, 211, 249, 251, 252, 253, 258, 272, 276, 282, 284, 285, 291, 305, 307–308, 308, 311, 315 Weitzmann, C. F., 190–197, 206, 234–236, 243, 262, 264, 284–285, 316, 319, 321 Werckmeister, A., 210, 285 Wittlich, G. E., 295 Wolf, E. W., 145–147, 285–286 Zarlino, G., 22, 101, 286 Zelter, C. F., 29, 257, 286 Zweideutigkeit, 151, 156, 278

331