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Harmony in Beethoven

David Damschroder’s ongoing reformulation of harmonic theory continues with a dynamic exploration of how Beethoven molded and arranged chords to convey bold conceptions. This book’s introductory chapters are organized in the manner of a nineteenthcentury Harmonielehre, with individual considerations of the tonal system’s key features illustrated by easy-to-comprehend block-chord examples derived from Beethoven’s piano sonatas. In the masterworks section that follows, Damschroder presents detailed analyses of movements from the symphonies, piano and violin sonatas, and string quartets, and compares his outcomes with those of analysts William E. Caplin, Robert Gauldin, Nicholas Marston, William J. Mitchell, Frank Samarotto, and Janet Schmalfeldt. Expanding upon analytical practices from the eighteenth and nineteenth centuries and strongly influenced by Schenkerian principles, this fresh perspective offers a stark contrast to conventional harmonic analysis – both in terms of how Roman numerals are deployed and how musical processes are described in words. david damschroder is Professor of Music Theory at the University of Minnesota. His current research focuses on harmony in tonal music, a project that began with a careful examination of historical analytical practices, the basis for his Thinking about Harmony: Historical Perspectives on Analysis (Cambridge, 2008). The project continues with focused studies on selected repertoires: Harmony in Schubert (Cambridge, 2010), Harmony in Haydn and Mozart (Cambridge, 2012), Harmony in Chopin (Cambridge, 2015), and the present book. He has written textbooks on music fundamentals and ear-training / sight-singing, and his articles and reviews have appeared in numerous journals.

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Harmony in Beethoven david damschroder The University of Minnesota

University Printing House, Cambridge CB2 8BS, United Kingdom Cambridge University Press is part of the University of Cambridge. It furthers the University’s mission by disseminating knowledge in the pursuit of education, learning and research at the highest international levels of excellence. www.cambridge.org Information on this title: www.cambridge.org/9781107134584 © David Damschroder 2016 This publication is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published 2016 Printed in the United Kingdom by TJ International Ltd. Padstow Cornwall A catalogue record for this publication is available from the British Library ISBN 978-1-107-13458-4 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.

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Contents

Preface

[page vii]

part i methodological orientation: harmonielehre (the piano sonatas) [1] 1 2 3 4 5 6 7

IV as intermediary between I and V [3] II as intermediary between I and V [22] A detailed look at the circle of fifths [39] III on the path from I to V [49] The mediant within the orbit of the tonic [64] Notable linear initiatives [74] Parenthetical passages [92] part ii masterpieces

[103]

8 String Quartet in B♭ Major (op. 18, no. 6), La Malinconia in response to William J. Mitchell [105] 9 Piano Sonata in D Minor (op. 31, no. 2, “Tempest”), movement 1 in response to William E. Caplin [120] 10 Violin Sonata in A Minor (op. 47, “Kreutzer”), movement 1 in response to Janet Schmalfeldt [139] 11 Symphony in A Major (op. 92), movement 3 in response to Robert Gauldin [163] 12 Piano Sonata in E Major (op. 109) in response to Nicholas Marston [174] 13 String Quartet in A Minor (op. 132), movement 1 in response to Frank Samarotto [228] Notes [254] List of references to music examples [278] Select bibliography [279] Index of Beethoven’s works [290] Index of names and concepts [291] v

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Preface

Beethoven of course remains a central figure in the musical pantheon – revered both for his substantial and widely performed body of work and for his influence on later musical developments. Anyone intrigued by this book’s title will require no justification for the invitation to join me in a careful study of his harmonic practice. Because the analysis of tonal music is both challenging and beset by controversy, I am committed to focusing on one or two composers at a time in depth – immersing myself in specific preferences and tendencies conveyed in a finite body of work – with the hope that I might achieve more compelling analyses (thus moving the field forward a bit) than would be possible if I were daily engaged with a centuries-wide span of repertoire. Though the intensity of this working method led me to divert to Harmony in Chopin immediately after I had completed Harmony in Haydn and Mozart, that respite from the Viennese tradition (which I explored also in Harmony in Schubert) has made me all the more eager and ready to encounter Beethoven in this way. Each of my analytical volumes is divided into two segments: a methodological orientation, and an exploration of masterpieces. The latter segment is devoted in part to critiques of other analysts’ readings of the same works. By this point, these segments collectively have developed into two distinct and substantial bodies of analytical writing: for the relative newcomer to analysis, the methodological orientations provide a wide-ranging grounding in how tonal analysis might be pursued, while for all who have come to appreciate the insights that can be attained by analyzing complete movements, the sum of my masterpiece essays offers both an extensive survey of compositional practice preceding and during the first half of the nineteenth century and a panoramic view (and assessment) of how, over the past fifty or so years, other analysts have come to terms with this music. The pre-1850 phase of my project on harmony in the long nineteenth century will be completed after one additional volume, Harmony in Mendelssohn and Schumann. Though I regret the resulting neglect of Berlioz, Rossini, and others, given my advancing age it will be time to move on: I intend to pursue an equally

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robust exploration of developments in tonal music after 1850, including volumes on Verdi, Brahms, Liszt and Wagner, Mahler, and Debussy. Concurrently I am at work on a more elementary pedagogical project that begins with Tonal Analysis: A Schenkerian Perspective (to be published by W. W. Norton). That volume should be consulted first if the starting point of the Harmony in . . . books proves to be beyond a reader’s current level. (Though some analysts are making significant contributions to our understanding of this repertoire without overt references to Schenker, the genesis of my analytical practice, which integrates ideas from many historical authors, would be unthinkable without my first having come to terms with the Schenkerian perspective.) That said, for the methodological orientation of Harmony in Beethoven I have elected to work at a pre-Schenkerian level, more basic than in the other volumes of the series. One of the mainstays of musical life in the first half of the nineteenth century was the Harmonielehre, a foundational study of essential harmonic practices, often presented in the context of fabricated block-chord progressions rather than through analyses of musical repertoire. (Many such volumes are assayed in my Thinking About Harmony: Historical Perspectives on Analysis.) Here I offer a belated contribution to that historical body of work with my own perspective on these matters. (Given that the history of music theory has been a focal point throughout my career, it was predictable that I would sooner or later attempt something along the lines of the various books that have been so influential in shaping my perspective on harmony.) Though inevitably much of what I present echoes principles already in print (either from that era or from more recent times), I believe that my formulation is unique and worthy of consideration by anyone for whom harmony is a vital concern. Though I likewise engage with block-chord progressions, each is derived from a specific passage from a Beethoven piano sonata, whose scores should be consulted when studying my commentaries. (I take more liberties in this context than I do in my Schenkerian graphs later in this volume, especially through the insertion of pitches that one might imagine but that do not actually sound in the composition. I also have fabricated rhythmic contexts that suit the block-chord nature of the enterprise without adhering exactly to Beethoven’s compositions.) To enhance readability at this elementary level, I dispense with the standard scholarly procedure of backing up my work with references to a range of published sources. The focus is exclusively the interaction between my readers and me (as was the case between nineteenth-century readers and a Harmonielehre author). I harbor the hope that some future scholars will

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Preface

take the initiative to compare my perspective on Beethoven’s sonatas with passages from the very abundant literature on that topic. My intent is that the perspective enunciated in my Harmonielehre could serve as a replacement for or (more realistically) supplement to what is currently serving as harmony instruction for music of this period at universities or conservatories, following a thorough grounding in music fundamentals (including chord construction) and voice leading (incorporating a detailed study of figured bass). I pursue this method with my sophomore-level students at the University of Minnesota. In a recent end-of-term survey I asked the class whether we instead should have adhered to the conventional harmony instruction presented in our textbook (which they had followed more exactly in earlier semesters of the course sequence, under other instructors). Their response was overwhelmingly against going back to that practice. Though readers who teach undergraduate courses might not yet be ready to follow my lead in this regard, perhaps alerting select students to these other ways of thinking about harmony and encouraging them to explore my Harmonielehre on their own would be in order. (I currently am at work on a complement to the Harmonielehre: a Catechism of Ear-Training that I will offer as the methodological orientation of Harmony in Mendelssohn and Schumann.) For those who lead graduate seminars, by now my body of work is sufficiently conspicuous that your more curious students will find it even if you do not lead them in that direction. In my own teaching I integrate instruction on how to proceed in analysis with detailed critiques of how one ought not to proceed. (With modern technology it is easy to project students’ homework assignments onto a screen, so that the class may compare a range of readings and assess their perspicacity.) In that I find this method very effective for coming to terms with many fine points – both conceptual and notational – in the practice of analysis, I have developed a means of providing a similar experience for the readers of my analytical volumes by selecting masterpiece compositions that have been treated at least once already in the recent analytical literature. A significant part of my essay on each work is a detailed critique of that other analysis, set off from the flow of my own reading through the use of shading. Though this limits the repertoire I may deal with, I have found the benefits to far outweigh that drawback. Because these other analyses are very sophisticated, I of course extend beyond the Harmonielehre level for my analyses in the Masterpieces section of this volume. Though presented in the context of Schenkerian graphs, the Roman numerals in the examples conform to the practice introduced

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in the Harmonielehre section. (That practice also matches the Roman numeral usage in my forthcoming Tonal Analysis: A Schenkerian Perspective.) Given my intense involvement in the analysis of tonal music both as an author and as a teacher, I have given much thought to the process of developing skill as an analyst. Some observations regarding how I undertake this process, intermixed with pointers for aspiring analysts, are provided in a supplementary essay entitled “Developing analytical insight,” available as an online resource at www.cambridge.org/9781107134584. It is no secret that books such as this one generally are read in part or in whole by numerous individuals before publication. I thank first the members of my Beethoven seminar at the University of Minnesota for spending a term working through most of the chapters with me. I also appreciate the encouragement and advice of the reviewers commissioned by Cambridge University Press. I thank the University of Minnesota for supporting my work through an Imagine Fund award, which covered the cost of setting the music examples and provided the resources to acquire books and to visit major research libraries. I am grateful to the New York Public Library, Astor, Lenox and Tilden Foundations, for allowing me to purchase on microfilm and to make references to the Oster Collection: Papers of Heinrich Schenker. As in the earlier volumes of my project, Peter Smucker has provided expert setting of the music examples.

Conventions regarding note relations, chords, keys, and Roman numerals Pitch simultaneities (such as C-E-G) are indicated using hyphens (-), while pitch successions (such as C–E–G) are indicated using dashes (–). Direction may be indicated in melodic succession: ascending as CC. A black arrow may be used to indicate a descending-fifth relationship that is or emulates a V(7)–I succession, whereas an outline arrow may be used to indicate a succession from a chord of the augmented-sixth type: for example, C➔F–D➔G➔C; C–A♭–D G➔C. 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. Unless another analyst’s methodology is being discussed, Roman numerals are presented in capital letters regardless of a chord’s quality, modified by one or more accidentals if the chord is altered. Thus C Major: I

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Preface

II V I and not I ii V I; and A Minor: I II V♯ I♯ (closing on a major tonic), not i ii° V I. An accidental to the left of the numeral corresponds to the chord’s root, to the right corresponds to its third. If the chordal fifth, seventh, or ninth is altered, the analytical symbol will incorporate the corresponding Arabic numeral, as in C Minor: II5♯♮ . (Arrow notation – here II➔ – offers an attractive, though less precise, alternative to the complete analytical symbol.) The bullet symbol (•) indicates an absent root. For example, B-D-F in C Major will be analyzed as V7• (or, with less precision, as V➔). Likewise a progression of chordal roots generally is presented in capital letters (C–D–G–C), though on occasions when quality is a factor in the discussion a capital letter may refer to major quality, a small letter to minor quality, and a small letter followed by a degree circle (°) to diminished quality: for example, C–a–F–d–b°–G–e–C. A bracket is used to connect the analytical notation for two musical events that normally would follow one another but that in the context under discussion occur at the same moment: for example, C |F♯ B | E when an F♯-A♯-C♯ chord sounds with, rather than before, root B in a descending circle of fifths. Parentheses around a pitch in an analytical example indicate that it is not actually present in the score, though it is understood. Parentheses around analytical notation may refer to the expansion of a deeper-level harmony (for example, when I is expanded by I IV V I) or to the harmonic assertion of a voice-leading phenomenon (for example, when the 6 phase of a I5–6, as in C-E-G to C-E-A, asserts the harmonic role of VI). Open parentheses designate a voice-leading transition between two harmonies. For example, I ( ) IV indicates that the chords between I and IV (perhaps a circular, parallel, or sequential progression) do not themselves participate in the harmonic progression, but instead serve to connect the harmonies I and IV. When a score’s chordal spellings do not coincide with the structurally appropriate spellings (for example, the substitution of easier-to-read F♯-A-C♯ for cumbersome G♭-Bº-D♭), I generally will use the structurally appropriate spellings in my examples and commentaries, often placing the enharmonic spellings within square brackets to assist readers in locating the pitches in question within the score. I pay very close attention to hierarchies among pitches and chords. To alert readers to various hierarchical relationships I often will underline some pitch names to indicate their hierarchical prominence. For example, CB C above bass C–G–C conveys the relationship between two

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unfolded strands: a more prominent outer strand E>D>C, and a subordinate inner strand C>BA). Yet in this case Beethoven complicates matters a bit through the chromatic lowering of A to A♭. Whereas C>A♮>F♯>D would have projected the V 7♯ harmony that is fully in place at the downbeat of measure 45, apparently Beethoven found the diminished quality of the A-C-E♭ triad ill suited to his vigorous conception, and so he substituted A♭ for A♮ as its bass. During the following beat A♮ is restored (in the right hand). I call such a chromatic

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mutation of a diatonic pitch – a half-step shift followed by a restoration of the diatonic state – a wobbly note (or wobble). (Note that two kinds of A are juxtaposed. This contrasts the notion of chromatic neighboring note, in which G♯ and A would be juxtaposed.) In this context a subsidiary layer of analysis indicating ♭II is not warranted. (Compare with the presentation of IV5–6 in 1.1.) The downbeats of the four consecutive measures convey the essential I–IV–V♯–I progression. What is displayed in 1.6 as a 64 chord embellishing the dominant at 452 appears in 53 position in Beethoven’s score. (Given its context, this G-B♭-D chord should not be interpreted as an asserted tonic.) Block-chord reductions such as 1.6 often will incorporate tacit alterations intended to clarify the basic conception that underlies a passage. (Note also that soprano A at 453 – an important element in the linear melodic trajectory conveyed in the reduction – is not found in the score.) This should not be regarded as the analyst taking on the duty of fixing a composer’s “mistakes,” but instead as the display of a foundational conception that the composer has enlivened by providing an alternative to the most obvious realization.

Op. 10, no. 3/II1–9 Every analysis that one undertakes has as its starting point the accumulated insight attained during all the previous analyses one has completed. The model on display in 1.7, which corresponds to 10.3/II1–9, shares features with other models in this chapter: bass D>C♯>C♮ brings to mind C♯>B♯>B♮ from 1.3, while bass GA corresponds to the same pitches in 1.2 (now with a more highly evolved internal chord). The excerpt’s chief

Example 1.7 Analysis of Piano Sonata in D Major (op. 10, no. 3), mvmt. 2, mm. 1–9.

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IV as intermediary between I and V

novelty lies in how the initial I and interior IV are prolonged. The progression of chords in measures 1 through 4 lies at the borderline between embellishment and local harmonic progression. The pitches C♯, E, G, and B♭ often are used to embellish a D-F-A tonic – something along the lines of the second chord of 1.4 (in G Major), though with a higher concentration of dissonance. However, when such embellishment is distributed over two chords – first with G and B♭ against D, and then with retained G and B♭ along with C♯ and E – the sense of subdominant followed by dominant begins to emerge. In 1.7 that local progression is conveyed via Roman numerals below the principal analysis, which indicates a prolongation of the tonic during this region. The expected resolution to a diatonic, consonant D-F-A tonic is elided in measure 4, making way for the more dynamic I➔ state that propels the progression onward to IV. The reconfiguration of that chord (with bass F♯) at the end of measure 4 allows IV to be introduced in its root position at 51, contrasting the first-inversion presentation in 1.3. (Some analysts might interpret the B♭-D-G chord in the middle of measure 4 in Beethoven’s score as the onset of IV. Reasons to regard it instead as a passing chord within I➔ include the dynamic marking that leads to the root-position G chord and the metrical positioning. Essentially, F♯A passing motions coordinate, with an F♯ substituting for bass A.) The chord of measure 6 might reasonably generate contrasting interpretations among analysts. The reading presented in 1.7 proposes that C♯ is an embellishing pitch, serving as a chromatic lower neighbor to D at the onset of IV’s 6 phase. (That is, G-B♭-D-E, with retained fifth as well as the added sixth, is presented with a C♯ neighbor instead of D.) This embellished IV6 is followed by a more highly evolved state, surging G♯-B♮-D-F (with root E omitted). The five-tiered analytical symbol for this chord in 1.7 generally will be replaced by the symbol II➔ in prose writing. (Note that placing accidentals after Arabic numerals results in a more efficient presentation than the opposite: the symbols 5♭–♮ here convey that B♭ proceeds to B♮, whereas if one instead started with ♭5, one would need to proceed to write ♮5 after the dash, redundantly rewriting the 5.) Though the arrow notation lacks the precision of the numbers and accidentals (since, for example, E-G♯-B-D also would be labeled as II➔), one should assume that prose writing would be accompanied by a music example in which the detailed symbol is present. In measure 8 a conventional 64 embellishment precedes the arrival of the dominant’s fifth and raised third, which, along with dissonant seventh G, lead the phrase onward to a PAC on I.

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Harmony in Beethoven Example 1.8 Analysis of Piano Sonata in A♭ Major (op. 110), mvmt. 1, mm. 5–12.

Op. 110/I5–12 In most respects the strategy that Beethoven deploys to establish the tonic in a late sonata, 110/I5–12, corresponds to what we encountered in an early sonata, as shown in 1.1. Whereas an embellishing chord with the leading tone in the bass there targets a restored tonic in root position in measure 9 (diminished fifth DA ♭ resolving inward), now the embellishing chord resolves with the fourth scale degree in the bass, resulting in a restored tonic in first inversion in measure 8 (augmented fourth DG ♭ resolving outward). (Consult the model provided in 1.8.) And whereas the tonic’s surge results from minor seventh D♭’s emergence at the top of the texture in the early sonata, now the surge-inducing minor seventh (G♭) resides in the bass. Consequently IV is introduced in its 63 position. In comparing the examples, one notes also that in both cases IV is expanded by a 5–6 shift and that the phrase concludes with V (with 64 embellishment) leading to a PAC on I. The shift from IV’s 5 to its 6 phase is more elaborately worked out in the later excerpt. The outer voices during measure 10 demonstrate how a voice exchange may be used to good advantage in a prolongational context: the descending motion from IV’s third F to its root D♭ in the bass is complemented by an ascending D♭-to-F motion in the melody. On its own, that voice leading would merely prolong IV. Beethoven succeeds in concurrently shifting to IV’s 6-phase chord by engaging another strand that moves in parallel sixths with the bass: D♭>C>B♭. The B♭ helps destabilize IV, setting the progression on a path towards the dominant. Here the destabilization is modest. One instead might have chromaticized the voice exchange by substituting D♮ for D♭ in the bass at the end of measure 10. In this instance Beethoven’s restraint is purposeful: soon thereafter (measure 17), B♭, F, and A♭ sound along with D♮ to create a surging supertonic.

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IV as intermediary between I and V

Example 1.9 Analysis of Piano Sonata in C Minor (op. 13), mvmt. 1, mm. 89–100.

Op. 13/I89–100 The expansion of a progression’s initial tonic via a harmonically conceived local progression of chords, introduced in the context of 1.2, flourishes in 13/I89–100 as well. This phrase resides within a tonicization of E♭ Major, the mediant in the movement’s C Minor tonality. Consequently the upper row of harmonic analysis in 1.9 displays merely C Minor: III–––––––––––––––––––––––––––––––

to indicate how this phrase fits within the movement’s broader tonal scheme. Though the deployment of only seven Roman numerals in the context of E♭ Major for the sixteen chords of 1.9 reflects the analytical assumption of affiliations among related chords (so that, for example, F-A♮-C-E♭ in the latter half of measure 95 concludes a harmonic initiative inaugurated by F-A♭-C at the onset of measure 94), even seven harmonies within a phrase often will bond in such a way as to convey a more foundational progression. The analyst should ponder how the chords relate hierarchically. For example, does the I of measure 89 extend through measure 98? Or, does the IV of measure 93 extend through measure 99? Or, does the V of measure 96 extend through measure 100? Those three conceptions cannot all prevail concurrently. In this case Beethoven’s writing clearly projects the first alternative, through the wedge shape of the outer-voice lines moving inexorably outwards – E♭G in the bass over the course of measures 89 through 98 – thereby connecting tonic chords in root position and first inversion. Consequently the second row of Roman numerals displays

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Harmony in Beethoven ♭–––––––––––––––––––––––––––––

I5

for this passage, below which a hierarchically subordinate I–IV–V–I analysis appears. (The 5♭ annotation here merely confirms the diatonic state of the chord’s fifth, which will be raised later as a means of inducing a surge.) A comparison of how IV5–6 is realized in 1.8 and in 1.9 reveals contrasting internal passing chords. Whereas that in the earlier example is diatonic – a neutral outcome of concurrent voice-leading initiatives – in the latter example a chromatic filling-in of the 5–6 second (E♭F>B>E.) These relationships will be explored in detail in later chapters that focus on the mediant. Beethoven’s strategy in 26/III1–30 (to which 3.6 corresponds) extends this progression in a way that instead calls upon the supertonic, thus warranting inclusion within this chapter. In this case the crucial event in Beethoven’s deployment of the circle of fifths is the substitution of a B minor chord in measure 9 for measure 8’s C♭ major chord. (As will be explained presently, the enharmonic shift is merely cosmetic. The major-to-minor shift is the important factor.) By imposing a minor chord at that juncture, Beethoven has facilitated a

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Harmony in Beethoven Example 3.6 Analysis of Piano Sonata in A♭ Major (op. 26), mvmt. 3, mm. 1–30.

further succession of descending perfect fifths (as if starting afresh in B Minor and proceeding through B’s diatonic E and A to D). Yet this persistence of perfect fifths causes the broader progression to veer alarmingly away from the diatonic pitch collection of A♭ Minor. Whether the chord of measure 16 is spelled (when fully constituted by one’s inner ear, using the resolution of measure 8 as a model) as D-F♯-A or, annulling the enharmonic shift that occurred over the bar line between measures 8 and 9, as Eº-G♭-Bº, it is uncommonly remote from the A♭ tonic. In fact, A♭ and D/ Eº form an antipodal relationship – a division of the octave exactly in half (in conflict with the overtone series’ division of the octave unevenly into a perfect fifth plus a perfect fourth). When a circle of fifths proceeds obstinately via perfect fifths for a sufficient period, the bonds of the prevailing major or minor modal configuration begin to weaken, while the modulo 12 system, with its own distinctive properties, begins to take hold. In a context in which the twelve pitch classes are equally weighted (in contrast to the seven favored diatonic pitch classes of a major or minor key), alternative ways of subdividing the octave gain ascendancy. Unthinkable as progressions within modulo 7, +2+2+2+2+2+2 (= +12) or −2−2−2−2−2−2 (= −12) +3+3+3+3 (= +12) or −3−3−3−3 (= −12) +4+4+4 (= +12) or −4−4−4 (= −12) +7+7+7+7+7+7+7+7+7+7+7+7 (= +84 = +7 x 12) or −7−7−7−7−7−7−7−7−7−7−7−7 (= −84 = −7 x 12)

or or or

become viable means of prolonging a chord. Because of the great distance involved, the last of these generally will be deployed using a mix of +7 and

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A detailed look at the circle of fifths

−5 (or −7 and +5) to preserve the normative range. These progressions are least obtrusive in the broader context of a major or minor key when they are pursued for their full course: one may arrive on a harmony within a modulo 7 progression, traverse such a circle within modulo 12, and then (back in modulo 7) proceed to the next harmony. Beethoven’s challenge in 26/III concerns the fact that the circle is incomplete: after six (rather than twelve) −7 links, we would arrive at −42, which is halfway between the −36 and −48 replicates of the octave. (Beethoven presents some of the −7 links as +5 to stay within music’s normative range.) In the score these six links are presented as two groups of three, wherein each −21 is projected as +3: A♭F), A♭’s resolution pitch G is omitted. (In 4.1 a robust chord is supplied to denote the harmony implied by the score’s doubled C in measure 28.) The harmonic trajectory described thus far transpires during a ternaryform minuet’s a1 and b regions (I to III during a1, then onward to V♮ during b). The concluding a2 region must work more efficiently than what has preceded it, for two reasons. First, whereas the span from I to V♮ initially was spread between two regions, now it must be traversed entirely within a2. Second, whereas V♮ was the goal of the two earlier regions, now the progression must move beyond V♮ to a PAC resolution on I. Beethoven responds to this challenge in an unusual way. He begins as if time were available in abundance, treating the tonic to repeated embellishment. Yet that activity persists only through measure 33, where yet another embellishing chord of the tonic sounds. Instead of the expected return to the tonic, however, II➔ surprisingly emerges in measure 34 as an alternative harmonization for soprano A♭. (That sonority relates to the sequential element of measure 27, which targeted the earlier dominant.) Due to this unexpected turn of events, no mediant harmony sounds during a2. Instead,

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III on the path from I to V

the phrase ends on time and in an exemplary fashion in measure 36, followed by four measures of reinforcement.

Op. 31, no. 1/I112–192 The mediant is especially emphasized in the progression from I to V during 31.1/I112–192, which comprises the development section of a movement in sonata form. The model in 4.2 displays only three foundational Roman numerals, notable principally for the chord that emerges to fulfill the mediant function: from the initial tonic in G Major, Beethoven proceeds not to the diatonic mediant B-D-F♯, but instead to ♭III5♮ (B♭-D-F♮), which would be diatonic in G Minor. The minor contagion persists through the onset of the dominant as V♮ (D-F♮-A). The dominant’s major third (F♯) is secured only after a brief tonicization. Minor seventh C and minor ninth E♭ follow, targeting the return of the G Major tonic for the recapitulation. The B♭ mediant gains prominence because it serves as the terminal point of one linear initiative and the initiation point of another. During measure 121 the G tonic chord, already major in quality, incorporates minor seventh F♮, thereby targeting C. Passing note E♭ in measure 120 hints that the C chord will be of minor quality, which in fact is the case. Yet soon this C chord blossoms with a major third and minor seventh, thereby targeting F♮ in measure 130. The same process continues for one more link, reaching B♭ in measure 134. This segment of the circle of fifths is a very common and effective means of connecting the tonic and the mediant in a minor key. Example 4.2 Analysis of Piano Sonata in G Major (op. 31, no. 1), mvmt. 1, mm. 112–192.

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Here Beethoven willingly accepts the lowered mediant, at which point a more intense region within the development section commences. The major third formed by the mediant and dominant roots turns out to be an ideal distance to cover using another linear device, the ascending 5–6 sequence (which we encountered in this context in 4.1 as well). In that the 6-phase chords take on surge characteristics, the bass ascends in a chromatic path, as B♭

B♮

C

C♯

D

over the course of measures 134 through 150, as shown in 4.2. By now fully ensconced in the usurping G Minor tonal shift, Beethoven leads from the major B♭ chord through a minor C chord to a minor D chord, whose transformation into G Major’s D-F♯-A dominant transpires over the course of measures 150 through 158. (Note that the F♯ of measure 154 is of only local significance, surging towards IV within a tonicization of D Minor. The definitive displacement of F♮ by F♯ occurs in measure 158.) Once attained, G Major’s major dominant is extended by means of potent embellishing chords that highlight the interval of a diminished third (C♯E♭-G-B♭, not shown in 4.2).

Op. 10, no. 2/I144|145–169 Several interrelated compositional decisions coordinate with the deployment of the mediant as a connector between the tonic and the dominant. In three ways, 10.2/I144|145–169 (to which 4.3 corresponds) utilizes procedures encountered earlier in this chapter.

Example 4.3 Analysis of Piano Sonata in F Major (op. 10, no. 2), mvmt. 1, mm. 144| 145–169.

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III on the path from I to V

First, recall that whereas the diatonic major mediant a minor third above the tonic root is the normative mediant choice in a minor key (as in 4.1), its emergence also in the context of a major key was demonstrated in 4.2. Beethoven again leads to that mediant in 4.3. In this case the switch to a parallel minor context is more overt, with the sounding of the F tonic’s minor third A♭ at the end of measure 152. Second, whereas a circle of fifths (as in 4.2) may serve to connect a major key’s tonic and lowered mediant, in 4.3 that route is truncated: instead of F>B♭>E♭>A♭, now E♭➔ alone directs the progression towards the mediant. 8

Beethoven arrives at E♭➔ in an ingenious way. The 6 chord of measure 153 4

7

might reasonably be understood as intended to resolve into a 5 chord (C➔) 3

that targets the tonic, recalling that of measures 148–151. Yet instead of falling into place as C-E♮-G-B♭, the resolving seventh, fifth, and third instead emerge as the fifth, third, and root of an E♭➔ chord targeting mediant A♭. The succession from F to A♭ is achieved through the transformation of C➔ into E♭➔. Third, though not reinforced by voice leading as regular as that encountered in 4.1 or 4.2, nevertheless the workings of an ascending 5–6 sequence may be discerned in the connection between ♭III5♭ and V. (In 4.3, added bass notes F and B♭ in part fill out Beethoven’s texture.) Whereas surges were noted during the 6-phase chords of this chapter’s first two examples, in 4.3 the 6 phase of B♭ is presented not as surging B♮-D-F-A♭, but instead as supersurging B♮-D♭-F-(A♭) (= G ). We noted an equivalent sonority’s deployment as an embellishing chord after the dominant’s attainment in 31.1/I (measures 158 through 161). Here it plays the more crucial role of directly preceding the dominant arrival, after which a less potent B♮-D-F-G sonority serves as an embellishing chord during measures 162 through 167 (not shown in 4.3). Finally, note that whereas a minor seventh and minor ninth complete the dominant’s fortification in 4.2 before resolution to the recapitulation’s tonic, in the context of 4.3 that fortification (now a minor seventh and a major ninth) is postponed until measure 170, at the onset of the next thematic initiative, during which the F Major tonic is restored.

Op. 14, no. 1/III38|39–83 The movement from which 14.1/III38|39–83 is extracted is a rondo in E Major. (The one-sharp key signature that Beethoven deploys beginning in

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Example 4.4 Analysis of Piano Sonata in E Major (op. 14, no. 1), mvmt. 3, mm. 1–83.

measure 47 is used throughout 4.4, since an E Minor tonicization occurs during the passage under investigation.) After the rondo’s initial refrain (A1), the first episode (B, beginning in measures 14|15) tonicizes E Major’s dominant key, B Major. The re-emergence of the E tonic for the return of the refrain (A2) is easily achieved by adding minor seventh A to the B-D♯F♯ chord (measure 30). Likely choices for the tonal center of the second episode (labeled C in 4.4) would include the parallel minor and the (lowered?) mediant keys. As in 4.3, where Beethoven proceeds from the F Major tonic through a tinge of F Minor (measure 152) to an E♭➔ embellishing chord targeting lowered mediant A♭, in 4.4 we find E Major followed by a tinge of E Minor (measure 39) to D♮➔ targeting lowered mediant G♮. A new thematic initiative coordinates with the emergence of G♮ in measure 47 (the location of Beethoven’s shift from a four- to a one-sharp key signature), and so the passage from 382 through 46 likely will come across to most listeners as a transition. Its wedge-shaped connection between the E and D chords is a variant of the refrain’s opening measures, now redirected towards a new goal. All signs point to Beethoven’s choice of G Major as the key for the C episode. We might expect that Beethoven will traverse a harmonic progression in the tonicized key of G Major over the course of the C episode (just as I5–6 II V7 I in E Major’s dominant key, B Major, defines the B episode). Consequently, at least initially the sequential activity that transpires during measures 47 through 55 will seem to connect I and (diatonic) III in the key of G Major. Indeed, Beethoven is deploying the mediant in two distinct contexts: G Major is the lowered mediant of the rondo’s principal key, E Major; and the tonicization of G Major incorporates an ascent to G’s

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III on the path from I to V

mediant chord, B minor. We note in passing (for a point that will be made later) that the ascending 5–6 sequence, which was deployed in 4.1 through 4.3 to connect the mediant and the dominant, here connects G Major’s tonic and mediant. What Beethoven does next is breathtaking. The V harmony that one would expect to follow G Major’s I and III sounds in an inversion in measures 60 and 61. The chord of measures 62 and 63 is readily accepted, since such a chord often plays a passing role (as an unfurled D64 ) during a dominant prolongation. (Compare with D-G-B in 1.6, measure 45.) Likewise, bass F♯ and soprano A in measures 64 and 65 are the “right” pitches to continue the D dominant’s prolongation. Yet something is wrong: after the passing chord the dominant’s root D mutates to D♯ and seventh C is displaced by B. Looking at 4.4, we note how a prolongational connection between measures 60 and 64, though initially promising, turns out not to be viable. (The line after the V numeral in the G Major row goes awry at that point.) Instead, the B➔ chord of measure 64 reinstates, now surging, the B chord of measure 55. Just as measures 150 through 158 of 4.2 serve to prolong the dominant, in the process converting its quality from minor to major, so also do measures 55 through 64 of 4.4. The remainder of the C episode transpires unexpectedly in the key of E Minor (another of the potential choices for the tonal center mentioned above), inducing a reinterpretation of the preceding events. Whereas at first the B minor chord seemed to function as the mediant within tonicized G Major, as conveyed in the third row of harmonic analysis in 4.4, ultimately that B chord functions as the dominant in E Minor, as conveyed in the second row of analysis. Consequently the ascending 5–6 sequence connects III and V after all (as it does also in 4.1 through 4.3)! The thematic material that deceptively projected a G Major tonic in measures 47ff. migrates to E Minor at measures 66ff. The episode’s fresh start on E in measure 66 approaches the dominant from the subdominant (reached via a descent in thirds from the tonic: E>C>A) rather than from the mediant. Here again Beethoven juxtaposes two contrasting structures (not fully documented in 4.4, though the disposition of the measure numbers provides guidance). At first it appears that within the span of eight measures (66 through 73) a robust progression that engages the minor subdominant, its 6-phase chord, and the dominant will come to rest on the tonic (perhaps still minor, perhaps with a “Picardy third” breakthrough back to major) for a PAC. The dominant’s seventh sounds during the second half of measure 72, so that an DA ♯ augmented fourth yearns for resolution on the tonic’s EGð ♯ Þ . In measure 73 Beethoven

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Harmony in Beethoven

redirects that resolutional energy back to the C chord of measure 70 (internal to the descending-thirds approach to IV) and then slows the progression to the dominant, filling in the AC♯ (measures 83 through 85), after which V➔ and I conclude the tonicizing harmonic progression. (Beethoven’s robust presentation is abridged for the display in 5.3.)

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Op. 49, no. 1/I0|1–63 The chords of 5.4a chart the essential harmonic trajectory of the minor-key exposition and development from 49.1/I0|1–63. The exposition’s TR deploys a circle of fifths to connect P’s tonic G and S’s tonicized mediant B♭. In contrast to the major-key situation on display in 5.3, here only perfect fifths are deployed in the circle: G>C>F>B♭. Observe how the C minor chord is first expanded via a voice exchange (EC ♭
CE ♭ during measures 12 through 14) before a surge emerges, propelling C➔ towards a medial caesura (MC) on F. Once B♭ Major is attained (with the help of a surge-inducing E♭ at the onset of S, so that the consonant F chord of the MC is transformed into F➔), a harmonic progression in the key of B♭ Major (through measure 29) supports a melody that gradually descends by step from F to B♭. (The soprano F displayed in 5.4a sounds during measures 17 and 19 but is not reiterated during measure 21, where bass A♭ induces a surge targeting IV.) In this case Beethoven treats the B♭ mediant as a surrogate for the G Minor tonic. A bold reading of this excerpt’s harmonic structure is proposed in 5.4a: that its three principal chords are the initial I (measure 1), IV (measure 50), and V♯ (measure 54). From chapter 1 we know that such a progression often will engage a surge in leading from I to IV and a 5–6 shift in leading from IV to V♯. Here Beethoven deploys the surge not within the initial tonic chord itself, but instead in the context of its upper-third chord, B♭ major. As the development opens, the B♭ chord is first extended via a passing 64 chord (unfurled into 63 position) in measure 36. When the B♭ chord re-emerges in measure 37, it possesses a minor seventh. Already major in quality, this added dissonance serves to generate a surge, which leads the progression to an E♭ major chord in measure 38. After a brief tonicization (not shown in 5.4a), a descending third to C minor transpires during measures 48 through 50. This descent reverses the ascending-third motion that occurred during the exposition. Consequently the broad succession from I to IV is achieved by first proceeding from I to its upper-third chord (III), then allowing that III to surge, targeting VI, and finally descending a third from VI to IV, thereby instilling the sense that VI has served as IV’s upper-third chord. (Note the deployment of a bullet beside both the I and IV numerals in 5.4a to indicate an omitted root.) This IV undergoes a 5–6 shift prior to the arrival of the development’s goal V♯. To understand how Beethoven accomplishes this, let’s assess the situation in several steps. First, for comparison look at measures 12 through 14, where a C minor chord (serving as an internal link within a

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Example 5.4 Analysis of Piano Sonata in G Minor (op. 49, no. 1), mvmt. 1 (a) Mm. 0|1–63; (b) Mm. 50–53. (a)

(b)

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circle of fifths) is prolonged by means of a voice exchange, as noted earlier. The melody’s E♭>D>C third works in coordination with the bass’s CC, and C>G. Though this places the uncommon option of a chord in second inversion at the endpoint of the tonic expanse, the restoration of the tonic root C during measure 13 grounds the continuation through D to G, resulting in the impeccable harmonic progression I5–6♮ II➔ V. (The A♮ of measure 13 facilitates the emergence of a supertonic with diatonic root D; a diatonic C-E♭-A♭ 6-phase chord would have offered a strong incentive to proceed instead to ♭II.) Our excerpt is the minuet of a minuet and trio movement, a ternary form. The letters a1, b, and a2 in 6.1 convey a (rounded) ternary subdivision within the minuet as well, in this case with a lack of tonal contrast in the b region, which concludes on C Minor’s tonic chord in measure 24. Though closing a middle region on the tonic is unusual, opening one with a restoration of the tonic is a straightforward and conventional option. In this case Beethoven achieves that restoration without deploying C Minor’s leading tone (B♮). Instead the dominant’s diatonic minor third, B♭, is retained as the restored tonic’s seventh, a factor in the tonic’s evolution into I➔, targeting IV. The middle region concludes with V➔ (IV’s successor) followed by I in the context of an IAC. Now graced by suspensions (A♭ in measures 28–29 and G in measures 32–33), the structure that inaugurates a2 (beginning in measure 25) clearly replicates that of a1. Yet listeners ought not to become overconfident in predicting how Beethoven will proceed. Whereas the G-C-E♭ chord of measure 12 reinstates the initial tonic, a new context for that chord during measures 34 through 37 places it interior to IV5–6, as shown in 6.1. (Before the 64 chord, diatonic A♭ and F serve as members of the IV harmony; after it, chromatic F♯ and A♮ serve as members of IV’s evolved 6-phase chord, surging as II➔.) Thus the hypothesis of a subdominant function, which

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listeners might have formed in the context of measures 10 and 11 only to go unfulfilled, is belatedly realized during a2. The dominant function is delayed until another 64 chord emerges, in measure 38. The a2 region concludes with a quick fulfillment of II➔’s push towards that dominant followed by a PAC on the tonic.

Op. 2, no. 2/I46–92 An ascending 5–6 sequence often is energized by surges. The first example of this technique that we explored – 1.4 – deploys this sort of sequence to connect I and IV in G Major. Note that all of its 5-phase chords are diatonic: major or minor in accordance with G Major’s key signature. The 6-phase chords, on the other hand, all incorporate whatever accidental(s) are required to induce a dynamic push towards their 5-phase successors. The sequential trajectory in 2.2/I46–92 (displayed in 6.2) features a construction that may be interpreted as a “stretched” version of a 5–6 shift, incorporating an extra half-step rise. Whereas E-G-B (measure 58), which temporarily imposes a minor modal quality on the E tonicization at the onset of the exposition’s S region, might conventionally be followed by E♯-G♯-C♯ targeting F♯, here instead F♯-A-D (incorporating dissonant C♮ to generate some extra propulsion) targets G♮. This is like climbing the steps while on an escalator: two means of locomotion work concurrently to bring about a swifter passage through space. The particulars of Beethoven’s voice leading involve an enharmonic shift. Whereas the chord of measure 60, spelled as F♯-A-C♮-D♯, could have served as an embellishing chord Example 6.2 Analysis of Piano Sonata in A Major (op. 2, no. 2), mvmt. 1, mm. 46–92.

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resolving back to the E chord (perhaps in its first inversion), the lowering of D♯ to D♮ in measure 61 signals that the D♯ in fact has behaved as E♭: F♯-A-C♮-E♭ serving as D➔. (The juxtaposed arrows between the letters E and G♮ in 6.2 are intended to convey this shift from the chord’s potential role as an embellishment of E into a connector between E and G♮.) Because two rising mechanisms coordinate, what normally would be the third 5-phase chord within a diatonic ascending 5–6 sequence in E Minor has already arrived in measure 62. (Given the “stretched” trajectory, E Minor’s diatonic F♯-A-C, which inconveniently is of diminished quality, is sidestepped altogether.) Recall that in the diatonic model of an ascending 5–6 sequence the disposition of the third through fifth 5-phase chords does not match that of the first through third: the minor scale ascends whole-half followed by whole-whole. Beethoven pays no heed to that fact. He instead uses G as the starting point for exactly the same sort of ascending motion as he just deployed to ascend from E to G, thereby passing through an inverted F♮➔ chord to attain B♭. (Compare with 3.6, measures 1–16.) Fortunately B♭ remains internal to the sequential initiative: one is not called upon to make sense of it within the broader tonal context, where it bears an antipodal relationship to the tonicized E. There is some compensation in the next cycle, where Beethoven does modify the pattern, thereby ascending a major third from B♭ to D, the diatonic seventh scale degree in E Minor. This is an astonishing moment. Whereas the concentration of dissonance in the chords of measures 60 and 64 is lessened through the lowering of one of the four pitches by a half step, in the equivalent chord of measure 68 the same lessening of dissonance is achieved instead by the raising of the other three pitches by a half step, thereby converting what would have been an A♭➔ D♭ motion (woefully remote from E Minor) into A➔ D. From D onwards the ascending motions correspond to those of a conventional ascending 5–6 sequence (now oriented toward the E Major goal of measure 84, thus passing through a major 5-phase chord on E and a minor 5-phase chord on F♯). Beethoven intervenes at the very end of the sequential initiative. Whereas after F♯ the chord spelled as F♯-A-C♮-D♯ would perpetuate the sequential pattern by being enharmonically reinterpreted as F♯-A-C♮-E♭, with the E♭ descending a half step to D (thus D➔ targeting E Minor’s mediant G, replicating measures 60 through 62), in this case Beethoven actually allows D♯ to function as a leading tone, propelling a resolution to an inverted E Major tonic chord, rather than to a lowered mediant chord. Once this outcome is achieved, listeners may come to interpret the entirety as a broad ED>C during II is a means of prolonging the ♭ E , which is understood to resolve to D with the arrival of the dominant in measure 37 despite Beethoven’s presentation of that chord with only root G in four octaves. (In 6.4 the chord is filled out, thereby revealing how root D’s seventh C and ninth E♭ resolve downwards by step in one’s imagination if not in actual sound.)

Op. 57/I36–108 In 6.4, the alternation between chords of minor and major quality (interlocking in such a way that adjacent chords share two pitch classes) results in a path whose first four chords do not quite fill an octave (C to D♭). In 57/I36–108, to which 6.5 corresponds, various modal shifts inserted within a similar descending series of chords results in the achievement of a fulloctave (A♭ to A♭) traversal. As is inevitable when using notation designed for modulo 7 composition in the context of modulo 12 initiatives that return to the starting point, some enharmonic respelling is required, a chore that Beethoven completes near the outset, at measure 66. If he had

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Example 6.5 Analysis of Piano Sonata in F Minor (op. 57), mvmt. 1, mm. 36–108.

followed the pattern of 6.4 during 6.5, the following progression of chords would have resulted: E♭ C A♭

M

C A♭ F

m

A♭ F D♭ M

F D♭ B♭ m

(Because the starting chord is of major quality, the goal is a whole step shy of the octave. The same procedure starting on a minor chord, as in 6.4, misses the octave by only a half step.) To stretch the progression in a way that achieves the full octave, Beethoven adds an internal operation – converting a major chord into a minor chord – three times so that, instead of just one descent of four half steps (F>D♭ in the model above), all three descents traverse four half steps, as follows: E♭ C A♭

M

E♭ C♭ A♭

m

D♯ B♮ G♯

enh.

B♮ G♯ E♮

B♮ G♮ E♮

M

m

G♮ E♮ C

G♮ E♭ C

M

m

E♭ C A♭ M

(Note that in the third major-to-minor conversion, the major triad is elided.) The principal chords on display in 6.5 fulfill the initiatives outlined in the grid above. The second major-to-minor shift is accomplished in the context of a tonicization of E Major (4 M in modulo 12), which abruptly is terminated

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Notable linear initiatives

by the onset of an E minor chord over the bar line between measures 78 and 79. Additionally, embellishing chords are inserted at the junctures between E and C (4 and 0) and between C and A♭ (0 and 8). The chord of measures 89 and 90 is curious. Though ultimately A♮ functions as a Bº upper neighbor to the A♭ root, at the onset it may seem that a tonicization of A♭ is being initiated via a I6 (= VI➔) chord targeting A♭’s supertonic, which never emerges. Because this operation is being conducted within a modulo 12 context, the internal E major, E minor, and C minor chords play no role in the movement’s F Minor key or mediant tonicization. Traditional harmonic procedures lead from the exposition’s opening tonic region (not shown in 6.5) to the mediant. Even before the end of the exposition, the modulo 12 initiative begins its work, with the C>C♭ shift of the mediant’s third. This process proceeds along its course through measure 87, at which point A♭’s role in the broader modulo 7 tonal context is reasserted. The minor seventh that emerges in measure 105 activates III’s surge potential, targeting VI, which will arrive in measure 109. The development’s V♮ goal is reached in measure 122.

Op. 90/I79–108 The extraordinary content of 90/I79–108 (for which 6.6 serves as a model) initiates a development section, following an exposition that has led from an E Minor tonic to a tonicization of its dominant. The exposition’s final B minor chord appears at the left edge of 6.6. Given that the next tonal goal is C major (measure 110), the excerpt engages in a broad connection between the B minor dominant’s 5- and 6-phase chords (the latter surging towards C): B-D-F♯ to B-D-F♮-G. Example 6.6 Analysis of Piano Sonata in E Minor (op. 90), mvmt. 1, mm. 79–108.

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A connection between B and G chords could be accomplished efficiently by means of a descending circle of fifths: B–E–A–D–G. This at first appears to be what Beethoven intends to do. Note how the F♯-A-B chord at the end of measure 84 leaves an open slot for the imaginative raising of the chordal third to D♯. (Since likely not all listeners would make that shift, the D♯ notehead has been placed within parentheses in 6.6.) As expected, this B➔ resolves to an E minor chord in measure 86. The next few measures are astonishing. The G♯-B-D-F♮ chord of measure 87 may be interpreted as an evolved state of the preceding E minor chord, now surging toward A. In fact, an A minor chord tantalizingly sounds during measures 88 and 89. Yet the sonority of measure 87 recurs in measure 90 (in a different inversion and in an enharmonic spelling). At this point listeners should ponder: did the earlier diminished seventh chord resolve, or did it not? Given what follows, it seems that it did not. Retrospectively the A minor chord may be interpreted as a passing chord between the two diminished seventh chords. (Or, one might hear an E➔ A resolution followed by E➔’s reinstatement for an alternative continuation that results in A’s abandonment within the broader trajectory.) This unexpected turn of events gives Beethoven a fresh opportunity. As is well known, the diminished seventh sonority is susceptible to several enharmonic interpretations. With the unexpected emergence of B♭ at 911, the chordal spelling D-F♮-A♭-C♭ comes into focus. Two successive positions within an idiosyncratic descending circle of fifths – E and B♭ – are represented by the same sonority! (Consequently a collision bracket appears among the letter names and arrows below the bass in 6.6.) The revised course of the circle of fifths thus becomes B–E–B♭–E♭–A–D–G. The E♭ chord emerges at measure 92. By imposing two extra chords within the circle, Beethoven accommodates both perfect and diminished fifths between adjacent roots. Yet after E♭ the circle begins to morph into a descent in thirds. A circle-of-fifths continuation could be achieved as B♭ G E♭

E♭ C A

A F♯ D

D B G

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Making the progression more gradual, Beethoven elects to fill in two of these fifths and fortifies some of the chords with their sevenths, as B♭ G

B♭ G♭

E♭

E♭

G♭ E♭ C

(G♭) (E♭) C

A

E♭ C A F♯

C A F♯

D

F♮ D B

G Once achieved, G➔ is prolonged for several measures, first with a gradually descending melody and eventually with a concurrent reciprocal ascending bass, all filled in by passing chords and passing notes.

Op. 10, no. 3/II65–76 Some passages in Beethoven’s piano sonatas mystify, with two (or more) possible interpretations of how their chords interact vying for ascendancy. Such a strategy both displays the composer’s skill and generates a distinctive emotional impact. At some point along such a trajectory, Beethoven must commit to one or another of the viable courses. That does not mean that the other interpretation(s) were bogus – merely that their full realization did not materialize. The progression of the first three chords in 10.3/II65–76 (to which 6.7 corresponds) may be interpreted as an instance of a very common musical device: a tonic chord (D-F-A) shifting to its 6 phase (D-F-B♭, here unfurled into 53 position), then proceeding to a form of the supertonic. In a minor key the inconvenient dissonant relationship (here B♭B♭ is realized by means of a surrogate relationship a third lower: C>G. Beethoven proceeds first from E♭ down a third to its unfurled diatonic 6-phase chord (E♭-G-B♭ to C-E♭-G), attains the dominant of C Minor rather than that of E♭ Major (as shown in a separate row of

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Example 6.8 Analysis of Piano Sonata in E♭ Major (op. 81a), mvmt. 1, mm. 1–21.

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Notable linear initiatives

analysis in 6.8), and finally restores the E♭ tonal center by ascending a third (G-B♭-D to B♭-D-F, to which minor seventh A♭ is added). Contrasting the elaborate procedure that transpires during the broad descending fifth’s first third, the second third – C♭ to A♭ – is traversed swiftly via a segment of the descending circle of fifths, as shown in 6.8. Though the internal B♭ chord “should” be spelled B♭-D♭-F, Beethoven fills in the E♭>D♭ major second with D♮. By the time D♭ arrives, further chordal evolution (diminished fifth F♭, minor seventh A♭) has occurred, leading to the circle’s E♭ chord, followed by goal A♭. After this attainment of IV♭, a brief passing chord at the end of measure 11 connects to the dominant, which is extended via an DF
DF voice exchange (stated twice during measures 12 through 14). As mentioned above, the tonic resolution is accompanied by – rather than followed by – its surge-inducing minor seventh D♭ during 142. Because that D♭ sounds in the bass, the IV targeted by I➔ emerges in its 63 position. (Given the prominence of chords from E♭ Minor up to now, Beethoven persists in pondering which mode should prevail: the IV of E♭ Minor sounds first, but in a reiteration of the surge resolution E♭ Major’s C-E♭-A♭ emerges.) The 63 configuration is especially well suited for use within parallel progressions, since the threat of parallel fifths is minimized. In this case Beethoven deploys such a progression to serve as a downward connection between IV and V7. (As the progression reaches its goal in measure 19, the 63 position is fortified by the addition of a 4, the dominant’s root: F-A♭-B♭-D in place of F-A♭-D. This results in the dominant’s attainment at the parallel progression’s fifth rather than seventh chord.) Whereas the model of 6.8 shows the essence of the parallel progression, Beethoven’s realization is chromaticized, resulting in the curious situation in which the members of the parallel progression’s first two internal chords do not all sound at once. For example, in connecting C-E♭-A♭ and B♭-D-G, Beethoven fills in the major second C>B♭ using a passing note that he spells as B♮. Since the E♭>D connection above is only a half step, D emerges against that passing B♮. By the time chord member B♭ sounds in the bass, Beethoven has already started filling in the D>C major second above using D♭. Soon after the dominant shifts to its root position (during measure 20), the resolution to I occurs and the exposition gets under way.

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Parenthetical passages

Some events in music do not fit neatly within the flow of harmonies displayed via Roman numerals in a music analysis. Sometimes the best way to make sense of a passage is to display it within parentheses – isolated from its surroundings, which generally will form a coherent structure. Given Beethoven’s resourcefulness, it would be difficult to list all the contexts that might induce an analyst to place some of a movement’s chords within parentheses. In this chapter’s sampling we explore several representative cases, from which readers may expand as warranted during their study of other compositions.

Op. 7/IV142|143–166

92

The fourth and final statement of a rondo movement’s refrain is presented in 7/IV142|143–166. For the most part this refrain is in the tonic key, E♭ Major, as were its three predecessors. For the time being omitting consideration of what tonal implications the passage inside parentheses (measures 155 through 160) might have, note how 7.1 projects a local ternary form in which two outer regions (a1 and a2, both of which progress to a PAC in E♭ Major) are juxtaposed with an interior region (b, which prolongs E♭ Major’s B♭ dominant). In the second of the earlier refrains, the a2 region is omitted. In that case (at measures 62 through 64) Beethoven leads chromatically from the b region’s dominant root to the submediant root, which is tonicized during the episode of measures 64 through 88. That transition thereby introduces listeners to a consequential and boldly stated B♭E) in the tenor register makes important use of the pitch G. The transition between the dominant (as represented by its upper-third chord during measures 13 through 15) and the tonic (inverted and in an evolved state later in measure 15) maintains G as a common tone. A breathtaking compositional construction is revealed in Model 5. First, note that the last two chords of Model 2 correspond to the first and sixth chords of Model 5. Between those points Beethoven deploys the latter sonority initially within a local tonicization of G Major (the first asterisked chord in Model 5). Thus when G-B♭-E-C♯ sounds during 152 (the second asterisked chord in Model 5, which transpires after a modal shift to G Minor), listeners might initially correlate it with the earlier usage. Yet this time (the third sounding of the sonority) the bonds of the G Major/Minor tonicization are broken: the chord behaves as I➔ in A Minor rather than as II➔ in G Minor. The long-drawn-out E>C♯ melodic third of measures 5 through 15 (slurred in Models 1 and 2 and in 10.2) is then matched by a quick DD>C♯ third-progression during measures 2 through 4. The similar melody of the next five measures sounds in an altered chordal context, which in my view causes a shift in its hierarchical organization. Let’s first affirm the continuity that does exist. The four pitches F♯

E

D

C♯

during measures 1 through 4 correspond to the pitches F♮

E

D

C♮

during measures 5 through 9, wherein a second F♮ at the violin’s re-entry point during measure 8 reaches over the piano’s D so that the C♮ goal (projected by the violin) is surmounted by an E during measure 9. From this perspective Schmalfeldt’s reading of measure 7 is problematic. During 62–3 the pitches E, D, G♯, and E represent the structure’s four principal strands. The low E proceeds to F♮, the D to C♮ (misprinted as C♯ in Schmalfeldt’s example), and the G♯ to A. What follows soprano E? It seems to me there are only two viable options. E could persist as an imagined pitch into measure 7, functioning as a suspension; or, the melody’s AE slur and beamed E. Though it is awkwardly positioned, I understand the line underneath measure 4 in ex. 4.2 to convey an extension of the I Roman numeral of measure 4 into measure 5. Consequently Schmalfeldt’s analysis of measures 5 through 9 deploys eight Roman numerals in all.3 Whereas my commentary above conveys my reasons for rejecting the V7 and VI numerals, the [V65 ]➔ that follows seems to me no more than an evolved

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state of the earlier D minor chord. (That is, only one root – D – prevails between 52 and 73, during which two stages of evolution – the addition of the chordal seventh and the raising of the chordal third – transpire.) Perhaps the most problematic aspect of the interpretation is the abrupt shift into a new key (the mediant, III) in the middle of the trajectory: I through VI are harmonies of A (Minor?),4 while the succeeding V and I are harmonies of C Major. Though I eschew Roman numerals during the interior of circular progressions (see 10.4, Model 3), if I were to use them I would maintain one key throughout, so that either A Minor: C Major:

I VI

IV II

VII V

III I

or

might be displayed for this passage. Beginning with I and IV from one key and then shifting to V and I from the other obscures what to me is the central feature of the passage, its unimpeded (and surge-enhanced) progression of descending fifths. Schmalfeldt asks us to process F-A(C)-D to F♯-A-C-D (in my system a straightforward and predictable surge) as a conversion from the 6 phase of VI in A Minor to an applied dominant of the dominant in C Major. Another abrupt key shift ensues in Schmalfeldt’s analysis soon thereafter, during the ascending 5–6 sequence of measures 11 through 13. Whereas two tenths are highlighted in her ex. 4.2 (GE ♯ and AF ♮ ), I suggest that both of those lines continue upwards another step, to GB ♮ (with the B taken by the violin only, in conjunction with a shift to the register of the piano). Those melodic thirds seem to me indivisible, a linear connection between E-G♯-B-D and upper-third chord G♮-B-D. Yet Schmalfeldt juxtaposes Roman numerals from A Minor and C Major. Whereas again I would eschew the use of Roman numerals in this linear context, in my view either A Minor: C Major:

V III

VI IV

VII V

or

would be superior to the juxtaposition of A Minor’s V and VI and C Major’s V, as appears in Schmalfeldt’s analysis. Furthermore, Schmalfeldt’s weighting of the hierarchy in favor of the G chord (note the HC indication) contrasts my maintenance of E as the principal root during the region, with the expectation (soon fulfilled) that root E’s normative successor, A, will emerge (as represented by C♯-E-G-B♭ during 152), even if that E is temporarily represented by a chromatic variant of its upper-third chord.5

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Violin Sonata in A Minor (op. 47, “Kreutzer”)

Whereas I acknowledge that my interpretation of G-B♭-C♯-E during 152 as a surging restoration of the A tonic chord (see 10.2) may be controversial, I can point to Beethoven’s emphasis of A➔D by means of repetition (eight times in all, with variants in both inversion and surge intensity) through measure 18. Schmalfeldt analyzes only the third of those eight projections of that succession, leaving its initial presentation unmarked. Thus the relationship between the G minor chord at 151 and the D minor chord at 161 comes across as [iv]➔ iv, with the interior [V]➔ emerging only later. Though I do not endorse Schmalfeldt’s placing of [iv] and [V] within the tonal plane of D Minor (iv), the more serious flaw, in my view, is the positing of a direct succession between the G and D chords, without an intervening A (at first represented by C♯-E-G-B♭, but soon thereafter by A-C♯-E-G). Though root A sounds only briefly at the end of measure 15, it is the culmination of an A prolongation (eventually elevated to a surge state) that began in measure 5. The opening violin solo is so distinctive and so boldly projected that, knowing Beethoven, listeners will expect it to have a pronounced impact on later developments within the movement. Already in measures 5 through 7 the notion takes on new implications as bass D’s prolongation overwhelms the potential shift to E, thus creating a problem awaiting remedy over the course of P. I contend that the E➔A succession corresponding to measures 2 through 4 transpires at measures 20 and 21. Schmalfeldt does not.6 Because her exx. 4.3 and 4.4 commence at the upbeat to measure 19, an important element of the subdominant is chopped off – namely, the violin D of 153. The DC♯ during measures 3 and 4 would have been welcome in measures 42 through 45 (ex. 4.4), through a slurring or even a beaming of E>D>C>B>A. (Schmalfeldt does indicate PAC below the goal A.) The opening violin solo ultimately is transformed in four ways over the course of P: the mode, the tempo, the meter, and the extent of the descending trajectory from the Kopfton.

The exposition’s transition, secondary-theme zone, and closing zone (TR, S, C, measures 45 through 193) What goes on in a composer’s mind of course remains largely a mystery. Even someone interviewing Beethoven during his lifetime might not have received very precise answers, either because the composer had not

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Violin Sonata in A Minor (op. 47, “Kreutzer”)

Example 10.5 Alternative theme for Violin Sonata in A Minor (op. 47), mvmt. 1, based on content from mm. 5–192.

formulated a conscious awareness of various processes that had become instinctive or because the analytical terminology of that time was not adequate to convey his thoughts. Through analysis we attempt to reconstruct some of the relationships that one might propose were factors in the compositional process – factors that the composer might not have consciously pondered but that nevertheless may have had an impact. Two features of this exposition’s S and one feature of its C are so distinctive that the relationship to earlier material probably is not coincidental. I refer to the emphasis consecutively on B and then E (both starting points for descending linear progressions) during S (displayed in 10.7, which will be explored below) and to the return of the tonic (with soprano D>C) at the close of C (likewise displayed in 10.7).8 Observe how BD>C♯, supported by V8–7 I, is exactly what listeners already have heard in the solo violin theme, measures 2 through 4. With some truncation of the dominant prolongation and a chordal evolution of measure 1’s supertonic to more strongly target the dominant, an alternative minor-key opening theme might appear as in 10.5. The annotating measure numbers assert that this theme defines the exposition’s structure.9 Whereas earlier I proposed that the remainder of P is closely allied to measures 1 through 4, I now make a bolder assertion: that the exposition from measure 5 onwards replicates the structure announced in measures 1 through 4. The A>F♯ third of measure 1 (and incorporated within 10.5) expands to become A>G>F♯ during measures 66 through 73. (See 10.6.) In both contexts F♯ serves as a neighbor to Kopfton E, which, as mentioned earlier, is at times either covered or replaced by A. That descending third transpires in conjunction with a circular progression of ascending fifths: A is supported by root A, G by root E, and F♯ by root B. Both internal ascending fifths proceed within local tonicization contexts: A to E as I ➔ IV5–6 (= II➔) V in A Minor, and E to B as I IV5–6 (= II➔) V♯ in E Minor. More broadly, though, the B➔ goal corresponds to II➔ in A Minor, a common choice for TR’s medial caesura. Though the F♯ neighbor of measure 73 will be understood to resolve to E at the onset of S, the in-register E corresponding to the model of 10.5 does not occur until measure 148.

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Example 10.6 Analysis of Violin Sonata in A Minor (op. 47), mvmt. 1, mm. 5–118.

The surging supertonic occupies nearly twenty measures, aided by a local tonicizing progression (I➔ IV♮ V➔ I in B Major during measures 75–77 and 79–81).10 The injection of its minor seventh during measure 90 leads directly to the arrival of dominant E in measure 91, the onset of S. As also was the case with the juxtaposition of A Major and A Minor tonics during P, now E Major and E Minor vie for hegemony during the dominant tonicization. Whereas it appears at first that the same major-to-minor shift occurs (with E Minor prevailing during most of S), the re-emergence of G♯ at the end of C (measure 190) would support the view that G♮, implanted in measure 107, is a long-extended wobbly note. After all, an E major dominant is prolonged in the initial theme (measures 2 and 3) prior to the resolution to the tonic. In keeping with that earlier context and acknowledging the ultimate restoration of G♯, the foundational model of 10.5 does not display a G♮ within its dominant prolongation. Without taking into account the motivic relationship with the B ^4> ^3> ^2 descent within TR, already at the onset of S the descending fifth-progression from B (displayed in 10.7, measures 118 through 144) should seem distinctly provisional. The higher E that emerges at measure 148 both fulfills the expectation generated by TR’s neighbor F♯

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Example 10.7 Analysis of Violin Sonata in A Minor (op. 47), mvmt. 1, mm. 5–192.

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(itself derived from measure 1’s F♯) and completes a broad restatement of measure 2’s B ^ region will pick up that thread with 2. Yet normally a2 would close in a PAC, thereby requiring significant modifications from the a1 presentation. Though Beethoven does pursue a different course during a2 (involving a reduction in content), he nevertheless does not bring the descending linear progression from 5^ down to the tonic root F. (See 11.2, noting how the D neighbor that transpired in the upper register starting in measure 37, shown in 11.1, now resides in the bass of measures 114 and 116. The harmonic progression lacks the tonic 6-phase chord between I and II➔ and thus also the A➔ embellishing chord that was so memorably projected during a1.) The descent from B♭ to A (^4>^3) sounds five times in all during

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Symphony in A Major (op. 92)

measures 125 through 136, with goal A emphasized in multiple registers during measures 136|137 through 148. (During a1 this material emphasized C♯, wafting between Kopfton C and its neighbor D; at the end of a2 it emphasizes A, the point to which the broad descent has arrived over the course of A1.) This non-closure will have implications for how the latter part of the movement transpires. (For now the “missing” material is displayed within parentheses at the right edge of 11.2, with the letter x twice among the measure numbers indicating that these chords do not sound at this point.) Though Gauldin’s reading of the scherzo coordinates closely with Schenker’s published and unpublished analyses (as noted above and in endnote 7), on one important point his interpretation contrasts both Schenker’s and mine. Though measure numbers are in short supply, I think that the F-F-A chord three-fourths of the way through the first staff of Gauldin’s fig. 5 corresponds to the tonic expanse at the onset of a2 (measures 88|89 through 98).9 If that in fact is what he intended, then he reads the IV at the onset of what I regard as the b region as proceeding directly back to I, in what appears to be a plagal motion. I instead regard the harmonic trajectory from I through III♯ to IV (with which I have some reservations, as noted above) to be proceeding inexorably to V, which duly arrives during measure 85. Gauldin’s commentary reinforces his IV-to-I reading with the following words: “ . . . the return of the theme in the subdominant(!) of B♭ major. Beethoven sets matters right by its immediate restatement in the tonic of F” (p. 93, italics added). The B♭ chord’s impact ends around measure 84 (with the emergence of the subdominant’s 6-phase G), while the F chord is reintroduced at 883. Instead of a direct connection, as he proposes, another harmony intervenes – one that I regard as among the most foundational of the entire scherzo (as indicated by root C’s presentation via one of the five bass stems connected to a broad beam in 11.2). The disparity between Gauldin’s and my interpretations of the B♮ during measures 114 and 116 is not critical. Given his interpretation of the Kopfton as ^3, B♮ may serve as a passing note to upper-third C; ^ B♮ will serve as a lower neighbor to that C, whereas given my Kopfton 5, substituting for the upper neighbor D of a1, which Beethoven here deploys in the bass.

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The B1 section and retransition (measures 149–236) A structural “problem” with which Beethoven challenges listeners is his failure to achieve a PAC during A1. The ^5>4>^3 descent shown in 11.2, measures 89 through 128, leaves the pitch A available as a focal point for the trio, thereby revealing its mehrdeutig versatility: not only as the tonic (^ 1) of the symphony as a whole, but also as 3^ of the scherzo’s F Major key and as ^5 of the trio’s D Major key.10 At a foundational level, this A is maintained throughout the trio (as a member of both the D tonic and A dominant harmonies) and is then re-integrated into the scherzo with the violin A of measure 237.11 Yet the situation is even more intriguing. The closure of A1 will be a moment when the composer (and by extension the work’s informed listeners) must come to terms with the fact that there is some unfinished business: the desirability (sooner or later) for a ^3>^2>^1 descent to complete the structure erected over the course of the scherzo. It turns out that this overriding concern dominates the trio, where – even though the key has shifted – a ^ 3>^ 2>^ 1 descent is traversed. Though additional content is displayed as well, a large part of 11.3 is devoted to the B1 section and to the retransition that follows. A very straightforward ternary form transpires: the projection of D Major’s ^3 (F♯), prolonged via a descending local third-progression, during the x1 region; descent to ^2 (E), supported by V, during the y region; and a postinterruption descent to ^1 (D) during the x2 region. The dashes connecting beam segments in the graph are intended to convey the fact that the F♯>E>D linear progression serves as a lower-third substitute for the A>G>F third that would complete the line inaugurated in measure 90, while bass DD likewise represents the FF that might have supported that descent. The retransition, which reinstates F♯ at its onset, juxtaposes surging embellishing chords of D and of F. During measures 233 and 234 we might expect an imminent restoration of the D tonic (as will occur in measure 327). But the modifications to that embellishing chord through the lowering of C♯ to C♮ and the shift from A to B♭ serve to reposition the resolutional goal, back to F for the onset of A2.

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Example 11.3 Analysis of Symphony in A Major (op. 92), mvmt. 3.

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Though we subscribe to somewhat different notational conventions for the display of interruption (a controversial and irresolvable matter12), Gauldin’s and my conceptions for the trio concur. Gauldin’s treatment of the retransition might warrant a bit more explanation along with a graph displaying greater detail: his slur connecting bass D>C♯>C♮ does not convey C♯’s initial upward resolutional urge, which must be offset in order to bring the tonal center back to F. I also miss the pitch E, which creates an augmented fourth against B♭ in measures 235 and 236. Because E leads to F, the first violin G leads to A (not F), justifying my A dyad at the left edge of 11.1 (as opposed to F followed by A, a crucial F component of Schenker’s reading of measures 1 through 10 as an initial ascent from F through G to Kopfton A).

The movement as a whole The unusual second pass through the trio (beginning in measure 409) stems from the lack of PAC closure during A2. Since Beethoven did not take decisive steps to rectify the cadential concern, the movement by now appears to be proceeding through an infinite loop, back and forth between F Major and D Major. At first, modifications to the scherzo’s a2 region might have seemed the most likely way to resolve the issues regarding the construction of a1 (which, because it descends only to ^3, may not merely be repeated for a2 as a means of bringing the scherzo – and by extension the movement – to a close). Yet the exact repetition of the scherzo (minus the repeat signs) causes that structural aberration within a2 to become even more entrenched. Fortunately Beethoven had an alternative venue at his disposal for resolving the dilemma: the coda. Though in most cases a coda begins after a decisive tonic PAC, in the context of this specific movement those final measures accommodate the traversal of that necessary content (displayed as missing at the right edge of 11.2 and as principal elements of the structure, using open noteheads, at the right edge of 11.3). Even so, the G (= ^ 2) does not actually sound at the top of the texture during measure 652. But that lacuna falls well within the conventions for imaginative thinking in musical perception: the leading tone (here E) often sounds where ^ 2 “belongs.” Beethoven proceeds to this close via a feint: for a few measures beginning at 645 it appears that yet another traversal through the trio may be in store

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Symphony in A Major (op. 92)

(that is, that the infinite loop has not yet been exited). In this case, however, the broad 5–6–5 motion that helps define the trio (as noted just below the system in 11.3) quickly reverts from 6 back to 5, coordinating with the assertion of dominant root C at 6511 (preceded by passing notes B♭ and B♮, which fill in an CA third). That moment comes across as a cadential 64 chord, as a result of which F descends to E (sounding in the soprano of measure 652) and A descends to G (most clearly perceptible in the second violin line, with an AG♯>E) as an arpeggiation in the soprano melody. In contrast,

Example 12.1 Analysis of Piano Sonata in E Major (op. 109), mvmt. 1, mm. 0|1–4 (a) Graph of the theme; (b) Non-alignment of tonic-chord pitches within the theme’s opening tonic expanse. (a)

(b)

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the phrase’s dominant harmony sounds only briefly, and so a complementary ascending arpeggiation (such as D♯F♯ over the bar line between measures 7 and 8 (thereby giving F♯ hierarchical precedence over G♯). Successive measures from 6 through what we might assume would occur in measure 9 project the following roots: B E F♯ (B). In this context the E chord is internal to a tonicizing B(B) bass arpeggiation and thus warrants interpretation as IV in B Major.11 From his ex. 3.26 and from comments in the second complete paragraph on p. 52, one may discern that Marston instead regards that E chord as a continuation of the initial tonic: I in E rather than IV in B. In my view, G♯ cannot be “reached” in measure 7 if it serves as a neighbor to the F♯ within a melodic BB) and then upwards (B