Harmony in Chopin - David Damschroder

HARMONY IN CHOPIN Chopin’s oeuvre holds a secure place in the repertoire, beloved by audiences, performers, and aesthetes. In Harmony in Chopin, David Damschroder offers a new way to examine and understand Chopin’s compositional style, integrating Schenkerian structural analyses with an innovative perspective on harmony and further developing ideas and methods put forward in his earlier books Thinking About Harmony, Harmony in Schubert, and Harmony in Haydn and Mozart. Reinvigorating and enhancing some of the central components of analytical practice, this study explores notions such as assertion, chordal evolution (surge), collision, dominant emulation, unfurling, and wobble through analyses of all forty-three mazurkas Chopin published during his lifetime. Damschroder also integrates analyses of eight major works by Chopin with detailed commentary on the contrasting perspectives of other prominent Chopin analysts. This provocative and richly detailed book will help transform readers’ own analytical approaches. D AV I D D A M S C H R O D E R 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 and was the basis for his book 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), and the present book. He has written textbooks on music fundamentals and on ear-training and sightsinging and his articles and reviews have appeared in numerous journals. In addition, he is working on a textbook, Tonal Analysis: A Schenkerian Perspective (forthcoming). As a complement to his scholarly work, he occasionally performs on fortepiano and modern piano.

HARMONY IN CHOPIN 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/9781107108578 © David Damschroder 2015 This publication is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published 2015 Printed in the United Kingdom by TJ International Ltd, Padstow Cornwall A catalogue record for this publication is available from the British Library Library of Congress Cataloguing in Publication data Damschroder, David, author. Harmony in Chopin / David Damschroder, the University of Minnesota. pages ; cm Includes bibliographical references and index. ISBN 978-1-107-10857-8 1. Chopin, Frédéric, 1810–1849 – Criticism and interpretation. 2. Harmony. I. Title. ML410.C54D25 2015 786.2092–dc23 2014046686 ISBN 978-1-107-10857-8 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 Part I Methodological orientation: the mazurkas 1 The architecture of a tonic pillar: twenty-seven regular tonic pillars from the mazurkas 2 Between the tonic pillars: tonal trajectories in twenty-seven mazurkas 3 Irregular pillars in the mazurkas: alternatives to the perfect authentic cadence Part II Masterpieces 4 Étude in C Minor(op. 10, no. 12) in response to Graham H. Phipps 5 Nocturne in C Minor (op. 27, no. 1) in response to Felix Salzer 6 Preludes in E Major and E Minor (op. 28, nos. 9 and 4) in response to Fred Lerdahl 7 Prelude in G Minor (op. 28, no. 22) in response to Alison Hood 8 Prelude in C Minor (op. 45) in response to Jean-Jacques Eigeldinger and to Charles J. Smith 9 Ballade in F Minor (op. 52) in response to Edward Laufer 10 Barcarolle in F Major (op. 60) in response to John Rink Notes List of references to music examples Select bibliography Index of Chopin’s works Index of names and concepts

Preface Given my intention to explore harmony from Haydn through Debussy in depth, the decision to devote a volume to Chopin needs no special justification. Despite the narrow range of his compositional activities, Chopin’s oeuvre holds a secure place in the nineteenth-century repertoire, both beloved by audiences and admired by aesthetes. So, having recently published Harmony in Schubert and Harmony in Haydn and Mozart, I take a respite from Vienna (where I assume Beethoven and Brahms will wait patiently), following Chopin westward to Paris. My decades-long fascination with his mazurkas here reaches its culmination in the presentation of probing yet concise analyses of all fortythree mazurkas that Chopin published during his lifetime. (While at work on this project I also performed these compositions in fortepiano recitals and taught them in a graduate seminar.) Readers are invited to join me in exploring these wonderful creations over the course of this volume’s first three chapters. (As was the case in my seminar, a semester’s study of Schenkerian analysis should be regarded as a prerequisite.) The remainder of my offering (chapters 4 through 10) continues a practice I pursued in Schubert and Haydn/Mozart (note my abbreviations for those volumes): a focus on masterpieces by Chopin that have been addressed in print or online by at least one other analyst, so that the reader may juxtapose my interpretations with alternative viewpoints and, with my guidance, explore the differences. Though I provide numerous detailed Schenkerian graphs (crucial for creating hierarchy-sensitive harmonic analyses), the Roman numerals and other symbols below the music notation will be the principal focus of my attention. This study is intended for anyone who both especially enjoys listening to or performing Chopin’s music and concurrently possesses an interest and facility in the analysis of tonal music. Though one might suppose that such attributes would describe all musicians, clearly some are more inclined towards nineteenth-century repertoire and to analytical undertakings than are others. As both teacher and author, I endeavor to offer analyses that are both insightful and vibrantly presented, hoping that any initial resistance might eventually melt. That said, the rigorous pursuit of analysis requires dedication. This is not a book that can be digested quickly. Especially, chapters 1 through 3 should be read at a leisurely pace, ideally with time for repeated listening to each mazurka and (by those who are able) for making each work come alive at the keyboard.

Authors of studies in which harmony is a peripheral concern might reasonably elect to adopt the conventions for harmonic analysis that most readers already know and practice. My study of Chopin, on the other hand, is part of a broader harmony project that eventually will encompass the “long” nineteenth century: this is the fourth of a planned six volumes for the period up to 1850 (including Thinking About Harmony: Historical Perspectives on Analysis [abbreviated as TAH], the two analytical monographs mentioned above, and forthcoming studies on Beethoven and on Mendelssohn and Schumann), to be followed by another six volumes for developments after mid-century (TAH II plus monographs on Verdi, Brahms, Liszt and Wagner, Mahler, and Debussy). Consequently I have taken decisive steps to creatively transform the practice of scale-step (Roman numeral) harmonic analysis, integrating elements from historical harmony treatises, from Schenker’s writings, and from my own thoughts on such matters. Knowing that some readers will be encountering my perspective for the first time in this volume, in the initial chapters I offer especially detailed commentary that should assist in coming to terms with how my system differs from the current conventional practice. Readers already familiar with my analytical work are welcome to pursue the book’s chapters in any order. Concurrent with the creation of Harmony in Chopin I have been developing the textbook Tonal Analysis: A Schenkerian Perspective (to be published by W. W. Norton). Its existence might impact Chopin readers in three ways: anyone whose understanding of basic Schenkerian principles is shaky will have another convenient resource for remedying the situation; I occasionally reference that work in my discussion of specific concepts or to call attention to a particular passage by Chopin that I analyze there; and because of this pedagogical preoccupation my Schenkerian graphs within Chopin have become more disciplined and consistent in their notational deployments. At the heart of my perspective is the notion that imaginative thinking should play a vital role in analysis, since the notes in the score often do not fully convey a work’s structure. Consequently a major impediment to understanding will emerge if a rigid, literalist stance regarding what may come into play prevails when analyzing a composition. This dichotomy vividly struck me as I was viewing a painting depicting Christ in the Garden of Gethsemane, recently attributed to Adriaen Isenbrant, at the art museum in Strasbourg. In a small area above a hedge or wall off to the left, one can make out some illumination. What could it be? Isenbrant has painted it at a slant, as if the source

of the illumination were moving towards the right at a swift pace. Without adding something to what is literally presented in the painting, this passage must remain a mystery. For those who know the story, however, the illumination is central to the painting’s meaning: it comes, of course, from torches (hidden behind the hedge) carried by men, led by Judas, intent upon arresting Christ. Likewise, elements of a musical story may be hinted at though not explicitly stated in a composition. There is much about how music works that will remain a mystery if one is unwilling or unable to imaginatively extend beyond the printed score when analyzing music. By gaining a clear understanding of a composer’s practice when all requisite notes are present one becomes well equipped to make sense of more elusive passages. My close engagement with selected contributions by numerous other analysts gives my harmony project a unique panoramic perspective regarding tonal analysis in the current era. These commentaries (set off by shading in chapters 4 through 10) should not be regarded as neutral reviews such as one might find in a journal, but instead as documentation regarding how other ways of analyzing music appear from my distinctive vantage point. Consequently readers may engage with my perspective through an inviting mix of opportunities to assess my own analyses and to encounter my reactions to various alternative viewpoints (and eventually, in other publications, the reactions of others to my viewpoints). Because so many perspectives will be assessed over the course of my project, I have established some ground rules. First, though some analysts have been very prolific, I will devote only one chapter to each within my set of books about music before 1850. (Where warranted a second turn may be granted during the post-1850 phase of the project.) Second, only analysts whose outcomes significantly contrast mine (even if we share similar methodologies) will be the focus of a chapter. Third, I must hold a neutral relationship with another analyst in order to write candidly about his or her work: friends, mentors, and former students consequently are excluded. As a result, some authors one might expect to find in a monograph on Chopin are not featured in individual chapters. For example, one of the leading Chopin authorities of our time has published admirable analyses of profound insight; and, I occasionally share quarters with him at music theory conferences. Thus for reasons two and three, no chapter herein focuses on his work (though I do quote him on occasion in the endnotes to reinforce my points or to acknowledge alternative interpretations).

I appreciate the feedback on drafts of this work that I have received from various quarters. I also acknowledge the support of an Imagine Fund award from the University of Minnesota. As in the earlier volumes of my project, Peter Smucker has provided expert setting of the music examples. All analyses are based on the scores as printed in the recent National Edition (Cracow). In a few instances other editions and their editorial commentaries are drawn into the discussion. I am grateful to the New York Public Library, Astor, Lenox, and Tilden Foundations, for allowing me to purchase on microfilm and to make reference to the Oster Collection: Papers of Heinrich Schenker.

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 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; one 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:

. (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,

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♭B♭♭-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 unfolded strands: a more prominent outer strand E>D>C, and a subordinate inner strand C>BD>C in C Major – supported by a harmonic progression that proceeds from I through V back to I. Though the ten tonic pillars explored in this section all convey these structural features, they nevertheless offer a considerable variety in terms of how these foundational chords are embellished and connected. Though II or IV often serves as an intermediary between I and V, in some cases Chopin proceeds directly from I to V or pursues a sequential trajectory rather than relying on one of those harmonic resources.

Opus 6/2 The Mazurka in C♯ Minor’s eight-measure introduction projects a B♯C♯ third, covered by G♯. The stemmed notes above the bass in 1.1 reveal the first-species foundation of A1’s linear strands: thirds and

converge upon the cadence’s unison C♯. An element from fourth species –

C♯’s delay in descending to B♯ – is here supported harmonically by II➔, enhancing the foundational I V♯ I progression. (Whereas the full inventory of an evolved harmony’s chromatic elements and added dissonances generally will be displayed beside its Roman numeral below the graph, a shorthand notation such as the solid arrow, which indicates that the harmony has taken on dominant-emulating characteristics, often will appear in the textual commentary. In this case Chopin has replaced C♯ Minor’s diatonic supertonic, D♯F♯-A, with a much more dynamic, dominant-targeting alternative, D♯-F -A♯-C♯. Whereas some analysts would elect to interpret this chord as diatonic in the context of the chord of its resolution –V7 of V♯ – it is interpreted here as a chromatic chord within C♯ Minor, with Roman II indicating that the second scale degree serves as the root.) The melody’s downward shift during V♯, restoring the register of the introduction, adds vitality to the presentation and motivates further registral fluctuation as the mazurka continues. The essence of the tonic pillar’s structure is not compromised by the presentation of its thirdprogression spread over a tenth or by the sounding of inner-strand pitches G♯ and E above the melodic descent’s C♯ goal. (Chopin emphasizes the C♯ by notating G♯ as a grace note and introducing E on beat two.) Because the mazurka continues beyond the tonic pillar, the third-progression (spread over a tenth) is interpreted as motion to the interior of the texture, consequently extending , which serves as the Kopfton (literally “head tone”), the pitch from which the mazurka’s deep structural descent – the ultimate tonic-confirming event – will emanate. Successors to at both the middleground and background levels emerge later (in measures 17 and 42), as we shall see in chapter 2.

Example 1.1 Analysis of Mazurka in C♯ Minor (op. 6/2), mm. 1–16.

Opus 6/5 [a.k.a. opus 7/5] The first-species framework that Chopin deploys during the tonic pillar of his Mazurka in C Major is identical to the one we noted in opus 6/2. Stemmed notes in 1.2 reveal the interaction between E>D>C above and C>BF>E descant in measures 7 and 8 hovers above the principal line, similar to G♯>F♯>E in measures 14 through 16 of opus 6/2 [1.1].2 That contrapuntal structure likewise prevails at the foreground level to project the pillar’s opening tonic harmony. (The Kopfton imagined at the outset is stated during the second local E>D>C descent, which extends from 53 through 63.) The repetition of the pillar, beginning in measure 9, both rescinds the upper-octave hoist of goal C (compare measures 8 and 12) and segues into the B section by destabilizing the goal tonic via a 5–6 shift (G to A in measure 12).3 As numerous later examples will confirm, the tonic’s fifth often will shift to its sixth as a means of segueing between the tonic and the supertonic, which in this case is realized as II➔ (D-F♯-A-C in measure 13, to be discussed in chapter 2).

Example 1.2 Analysis of Mazurka in C Major (op. 6/5), mm. 1–8. My assertion that the introduction conveys a tonic root and Kopfton (displayed within parentheses in 1.2) may be disconcerting. (Such bold assertions are a hallmark of imaginative analytical thinking, which contrasts a literalist perspective.4) Because an E (during 81) precedes the upper-strand D in the repetition beginning at 91, I retrospectively import that context to what precedes 51. In this case the initial tonic is unconventionally presented in position. Interpreting the solo G of measures 1 through 4 as a tonic harmony depends upon a careful assessment of the broader context. A comparison with another mazurka – opus 30/3 – reveals how Chopin will sometimes lead from a lone fifth scale degree into a robust tonic chord during an introduction. In opus 6/5 that evolution is elided. My proposed C and E project what I understand Chopin to have imagined as the opening chordal structure, represented meagerly by pitch G.5

Opus 7/1 The high spirits that Chopin conveys in his Mazurka in B♭ Major result in part from the persistent refusal of the melody to be confined by the line that traverses the pillar’s middleground

structural descent (depicted in 1.3). An upper third

coordinates with each of these elements, and even greater heights are attained as well. For example, the F of 23, already a third above the structural D, is embellished by neighbor G in measure 3, during a

expansion of the tonic. (The is unfurled, with E♭

sounding in the bass. An unfurling is defined as a chordal reconfiguration involving the substitution of a different bass note for the one that characteristically would occur.) This G is embellished by upper-third B♭ before F returns. Also, whereas an E♭ neighbor to Kopfton D sounds as a grace note at 51 before upper third G emerges, the corresponding spot in measure 9, during a varied repetition of the latter part of the phrase, attains greater heights by dispensing with the E♭. The persistent upward striving impacts even the close of the

descent: B♭ sounds an octave higher than expected in measure 8

(though not in measure 12).

Example 1.3 Analysis of Mazurka in B♭ Major (op. 7/1), mm. 1–12. A collision occurs when two successive syntactic entities are juxtaposed during the same moment in time, as in measure 6. Whereas the left hand persists in projecting the initial tonic, the E♮ that joins with B♭ and D in the right hand projects II➔ (here with omitted root: E♮-(G)-B♭-D is interpreted as a dominant-emulating evolution of the diatonic supertonic, C-E♭-G). The collision is conveyed in the harmonic analysis by placing a bracket above Roman numerals I and II. Whereas II➔ in opus 6/2 [1.1] is spelled as D♯F -A♯-C♯, in opus 7/1 the octave of the supertonic root C is displaced by ninth D, resulting in a chord spelled as E♮-(G)-B♭-D. (In the full inventory of chordal elements beside Roman numeral II in the graph, a bullet (•) indicates that the root has been omitted.) Chopin here takes advantage of the fact that B♭ and D are members of both the I and the II➔ harmonies in B♭ Major.

Opus 24/2 The Mazurka in C Major’s introduction provides the venue for the initial sounding of the tonic harmony. By the time A1 commences at 51, the progression has already proceeded to the tonic’s 6-phase chord within a local expansion of I-space [1.4]. Some imaginative thinking is called for in measure 5, since the upper E within an ECC♯, with E reaching over that strand, as shown in 1.9. Though no C♯ sounds in the upper register at measure 1, I imagine the broad chromatic filling-in of a C♯-to-E third (as slurred in 1.9) as a melodic trajectory within the opening thirteen measures. A reciprocal D♯-to-B third is pursued during the remainder of the pillar. Whereas an ascent in thirds connecting I and V, with the outer voices moving in parallel tenths, is a key feature of 1.6, a similar trajectory in the downward direction connects I and IV in 1.9.15 The melody’s subservience to the bass descent in thirds results in an empty space in the upper register during IV. I propose that, as was also the case in measures 5 through 11 of opus 24/3, the melody’s trajectory is more fully worked out in the interior of the texture, here as a connection of Kopfton D♯’s incomplete upper neighbor E through passing note D♯ to the dominant’s fifth, C♯ (at which point the action returns to the upper register). One way to support the E>D♯>C♯ span in a IV–V context is to utilize

IV’s upper-fifth chord as consonant support for IV’s passing seventh, D♯.16 This reading wins out against the hypothesis that the tonic is restored at 183, especially since Chopin’s modified repetition of the concluding measures retains the IV but dispenses with the upper-fifth chord.

Opus 56/2 A Polish folk spirit is especially pervasive in the Mazurka in C Major, with a

drone

sounding throughout the tonic pillar. The four-measure introduction’s G serves as the starting point for an ascending arpeggiation to Kopfton E [1.10]. Though a higher G sounds immediately thereafter, it replicates that in the tenor register, to which the A that follows G at 53 immediately transfers. (That line then continues upwards through B to C.) Consequently the F♯ and D during 61 serve as neighbors to the C and E of 51. (I admit that this reading may seem wayward. Yet compare with Chopin’s variant in measures 53 and 54, where F♯’s role as neighbor between two Es is more overtly stated.) Chromatic F♯ is a wobbly note (or wobble) – a note that temporarily takes on a chromatic inflection that eventually will be revoked – that soon reverts to diatonic F♮. The G initiates an upperoctave replication of the initiating GC descent that it supports taking precedence over the maintenance of E (thereby contrasting the emphasis upon E’s arrival an octave higher in measure 13, confirmed by the reiteration of E in the lower register at 161).

Example 1.10 Analysis of Mazurka in C Major (op. 56/2), mm. 1–28.

Uninterrupted fifth-progressions The four mazurkas in this section project the tonic harmony by means of an uninterrupted fifth-progression descending from the tonic triad’s fifth to its root. Several contrasting means of supporting

and

are deployed, distinguished principally by whether

sounds as a stable element in a tonic context or instead as an unstable element in a dominant context. (One could propose other options not encountered in this section as well.)

Opus 7/4 The determination that , rather than , serves as a composition’s Kopfton can be a difficult call, especially given that another potential reading – the embellishment of Kopfton with an upper third – occurs frequently. How the tonic pillar fits within the mazurka’s broader context sometimes provides useful data. For example, the chord at 363 in the Mazurka in A♭ Major, which I propose would be spelled correctly as G-B♭-D♭-F♭, features the dominant’s minor ninth F♭ [E♮] poised towards resolution to the tonic’s fifth, E♭, for the final statement of the tonic pillar.18 Note also that at 71 (during the initial phrase’s written-out repeat) D♭’s arrival from above is emphasized through the resolution of a suspended E♭ (the grace note). Consequently I propose that the preferred reading should be a fifth-progression from E♭, rather than a third-progression from C with upper neighbor D♭. Though challenging to comprehension, occasionally in music one initiative begins before a prior one concludes: here the bass descent from tonic root A♭ to subdominant third F gets underway before the soprano arpeggiation of the tonic – E♭F D♭>C♭>B♭ fourth transpires during the antecedent phrase, in the consequent phrase that line is more fully realized in the tenor register, though the concluding B♭ is absent and will be imagined during 43. Only the strand that proceeds from G♭ is maintained in register over the course of all four measures; and only that strand attains , by which point it in fact is the highest-sounding strand, which is how it is displayed in 1.15. (An incomplete neighbor occurs between and , as often is the case when IV serves as the intermediary between I and V♮.)

Opus 17/3 The Mazurka in A♭ Major’s sixteen-measure tonic pillar derives its binary shape from the interruption that occurs after the first phrase’s cadential dominant. Chopin’s prolongation of this dominant correlates motivically with the preceding tonic prolongations: whereas C>B♭>A♭ is heard repeatedly during I-space (measures 1 through 6), B♭>A♭>G is projected during V-space (measures 7 and 8) [1.16]. Another set of thirds plays an equally important motivic role: just as E♭ emerges above Kopfton C in measure 2, D♭ follows B♭ and C precedes A♭ during the pillar’s final two measures. (Compare with 1.3.)

Example 1.16 Analysis of Mazurka in A♭ Major (op. 17/3), mm. 0|1–16. Whereas in the context of an interruption the PAC of the second phrase will contrast the dominant close of the first, the two phrases may display other variances as well. Chopin offers a delectable sample in this mazurka. What are we to make of the pitch collection that sounds during 63? From a literalist perspective A♭-C♭-E♭-F might be regarded as a chromatic variant of the tonic’s 6-phase chord, here proceeding directly to the dominant. Yet during the consequent phrase one tiny shift makes a clarifying difference: Chopin lowers E♭ to D♮ (at 143), unleashing the chord’s vibrant II➔ potentiality. In 1.16 that interpretation is parenthetically supplied in the earlier presentation as well. Just as we can discern Michelangelo’s intentions even in his unfinished sculptures, so also a chordal function may be perceived even when

incompletely realized. I have chiseled away at the E♭ to reveal the D♮ that it conceals, using parentheses to acknowledge my participation.28 The phrase’s harmonic “defect,” like its failure to achieve a PAC on , is rectified during the second phrase.

Opus 33/2 [a.k.a. opus 33/3] A composition’s underlying structure and the presentation of that structure by a composer may not exactly match. Consequently pairs of parentheses are encountered frequently in graphs to indicate pitches that the analyst proposes an alert listener will imagine. In Chopin’s Mazurka in C Major, even the Kopfton E (= ) is an imagined note [1.17]. There is evidence of its influence: the E>D suspension/resolution pair in measure 7 depends on the conventional preparation by an E during the preceding I5–6, and the mazurka’s B section twice ascends to the imagined Kopfton’s wobbly displacement, E♭ (measures 20 and 28). The descending parallel sixths in the soprano and alto registers during measures 0 through 6 logically would begin with . Since no such E sounds, I have reconstituted the structure that I propose grounds Chopin’s mazurka. I admire – rather than condemn – Chopin’s free presentation.

Example 1.17 Analysis of Mazurka in C Major (op. 33/2), mm. 0|1–16. The antecedent phrase’s harmonic path conforms precisely to the normative convention for the supertonic’s use: the tonic first shifts to its 6 phase (here surging as VI➔, in measure 6), which leads effectively to the supertonic (also surging: II➔) followed by the dominant. For the consequent phrase, Chopin foregoes the tonic 6-phase chord to facilitate an earlier dominant arrival, leaving time for the tonic in the phrase’s concluding

measure. Not only is the surging VI➔ absent; II’s surge is retracted as well (so that the subtler diatonic II7 serves as herald of the dominant).

Opus 33/3 [a.k.a. opus 33/2] Whereas Kopfton is an imagined pitch in the Mazurka in C Major [1.17], is imagined in my analysis of the Mazurka in D Major [1.18]. Fortunately the redundancy of descent within an interruption structure means that a second opportunity for the sounding of exists. In this case measure 6 achieves what measure 4 neglects. As usual, the altered agenda of the consequent phrase results in revisions of the harmonic progression, geared towards achieving an earlier dominant arrival to make room for the cadential tonic. Here Chopin elects to dispense with his three-measure prolongation of I-space, leaving only the initial one-measure arpeggiation. This drastic cut permits an elective addition preceding the dominant arrival: namely the supertonic, which occupies measure 6.

Example 1.18 Analysis of Mazurka in D Major (op. 33/3), mm. 0|1–8.

Interrupted fifth-progressions Interruption is as useful in developing structures emanating from Kopfton as from Kopfton

. The examples explored in this section demonstrate some strategies for

supporting the descent from that did not emerge among the non-interrupted lines explored above.

Opus 7/2 The tonic pillar’s two phrases in the Mazurka in A Minor offer related yet contrasting harmonizations of the structural line descending from Kopfton . During the antecedent phrase the span from to transpires during an expansion of I-space, followed by II➔, which, with embellishment, serves as the initial support for before the HC dominant arrives [1.19]. During the consequent phrase a shift to I6 coincides with the arrival of . In a minor key I6 is innately suited for a dominant-emulating role, which may be enhanced through the addition of a minor seventh, propelling a surge (as VI➔) towards ♭II. Since Chopin realizes that potentiality here, the two phrases offer a strong contrast at this juncture: supported by II➔ versus ♭ supported by ♭II. (Compare 73 and 141 in 1.19.) Though ♭II is not innately inclined towards V♯, listeners have accustomed themselves to the ♭II–V♯ succession, which composers have promoted as a means of preventing their compositions from leading into the abyss. An extension beyond the diatonic pitch collection is held in check: B♭➔E♭ occurs rarely in A Minor, whereas the antipodal B♭-toE continuation has become the norm. (Here Chopin forgoes presenting ♭II in its first inversion, a common means of softening the effect of the antipodal root connection.) The melody’s B♭ wobble temporarily displaces diatonic B♮, which duly emerges during the dominant that follows – though not in the soprano register, where parentheses denote its imaginative presence within a descending fifth-progression in 1.19.

Example 1.19 Analysis of Mazurka in A Minor (op. 7/2), mm. 0|1–16.

Opus 17/2 During the Mazurka in E Minor’s tonic pillar, Chopin devotes equal time to the establishment of the initial I-space, with Kopfton , and to the fifth-progression that leads ultimately to a PAC. Both of the pillar’s phrases are twelve measures in length. Over the first six measures a dotted slur in 1.20 connects Kopfton B in its middle and upper registers. Both outer voices pursue arpeggiations of the tonic pitches: EA line of measures 9 through 12, Chopin achieves a PAC in measure 28. The tonic prolongation of measures 17 through 26 is based on a I III♮ V7 I progression, as displayed in 1.26. Note the wobbly E♮ above bass C and the presentation of V7 in its position. The connection between the tonic and the mediant is achieved via a circular progression: A♭ D♭ G C. The first link in that progression is filled in as A♭>F>D♭.40 At this foreground level one belatedly discovers how Chopin incorporates the A♭>F span, introduced during the a1 phrase, into a broader structure. With that succession now condensed into four measures through an elision (A♭>E♭F becomes A♭>E♭D♮ diminished fourth.1 An F, emerging above that D♮ from a strand that transpires in the tenor register, helps to shape the third-progression (beamed in 2.1) that spans the four measures.

Example 2.1 Analysis of Mazurka in E♭ Minor (op. 6/4).

The essence of the mazurka’s form may be represented as | A1 |: B A2 :|, with an immediate, written-out repetition of each component. Though it would be more normative for this form to transpire as |: A1 :|: B A2 :| (a form that often is called rounded binary, though I prefer rounded ternary or simply ternary, due to the three letters required to depict it), here the repetition within A1 created by the interruption, followed by the written-out repetition (measures 5 through 8), followed by a repeat-sign repetition would lead to stagnation. Consequently Chopin elected to omit the conventional repeat sign after measure 8.

Opus 6/5 [a.k.a. opus 7/5] As chapter 2 unfolds we will have opportunities to observe how the non-pillar regions in Chopin’s mazurkas may either prolong the tonic (perhaps with a modal shift) or lead to the mediant, subdominant, dominant, or submediant. The dominant is by far the most common choice. It provides a context for the maintenance of or for an interruption of a descent (from or from ) at , as in the Mazurka in C Major [2.2]. The I-space of its A1 section (analyzed in 1.2) concludes with a brief yet significant sounding of the pitch A (at 123).2 As often is the case, here the 5–6 shift softens the potentially abrupt connection between I5 and II➔, on the path to V.

Example 2.2 Analysis of Mazurka in C Major (op. 6/5). In this mazurka the same thematic content (at two pitch levels) is employed in both the A and B sections. When this happens a background melodic connection between the two may seem doubtful.3 How can the pitches C, E, and G relate linearly with their counterparts a fourth lower? I propose that in this mazurka the tonic’s E and the dominant’s D form a background

connection, even if that interpretation requires

a note that in its tonic context serves as an “upper third” to the Kopfton to perform a deep structural role when transposed into the dominant key. The voice leading works as

follows:

Opus 17/2 The Mazurka in E Minor’s tonic key is established through the fifth-progression that transpires during the A1 tonic pillar [1.20]. The components of the extended B section that follows pursue a range of tonal goals. At first the tonic is prolonged, with a temporary modal shift to E Major in measures 31 and 32 [2.3]. Next E Minor’s mediant G-B-D is tonicized. Chopin extends this mediant through measure 49 using local embellishing chords infused with chromaticism. Finally an unusual realization of IV5–6 leads to the section’s tonal goal, V♯, which falls into place at the last possible moment – at 523, coinciding with the melody’s upbeat B that inaugurates A2. (Compare with 03.) By this point the background descent has reached

, and thus an interruption occurs. This

(which sounds first in the bass and then in the tenor register) is covered by B, the of A2’s initial tonic.

Example 2.3 Analysis of Mazurka in E Minor (op. 17/2). The ascending registral shift of Kopfton B during A1 is rescinded as the lower B is restored during measure 25, at the onset of the B section’s tonic prolongation, which mirrors A1 in traversing a complete fifth-progression, now without interruption. Soon thereafter the mediant emerges, unexpectedly. Whereas the tonic-prolonging phrase proceeds downwards in the bass from E to C via a G➔ embellishing chord (measures 24 through 28), the reprise of this content in measures 32 through 36 proceeds in a contrasting manner, projecting the root progression G–C–D–G as a tonicization of the mediant even though its initial chord is surging towards G’s subdominant C from the outset. Because the new context for measures 33 and 34 motivates a re-orientation of the local chordal hierarchy, the eventually rejected connection between E and C (displayed via

a slur placed within parentheses) and the ultimately triumphant G-to-D tonic-to-dominant motion are juxtaposed in 2.3. The background descent from through

to occurs

during this mediant tonicization. The soprano G (= ) that arrives imaginatively at 373 and literally at 391 does not budge through 491. Neighbors A♭ and A♮ embellish G without weakening its hold. The mediant is maintained throughout, after which the span from measure 49 through measure 52 completes the B section’s structural agenda in an unconventional way – namely, by placing the Urlinie’s descent from to

in the bass and the foundational bass’s ascent

from G through A to B in the soprano. This important activity may take listeners by surprise, since Chopin here converts melodic devices that had played embellishing roles during the mediant prolongation into the instigators of the harmonic motion to

.

This subdominant’s 6-phase chord surges as II➔ in the approach to V♯. Whereas on the one hand Chopin endeavors to make A2 less complex than A1 by rescinding the local interruption, on the other hand he postpones achieving the goal PAC: opportunities for a cadence in measures 64 and 66 are declined, delaying the PAC until measure 68.

Opus 24/3 When a mazurka’s B section leads to the dominant, a background descent from Kopfton or to

often occurs. That option not only provides a high level of contrast, but also

ideally prepares for the tonic’s return during A2 for a post-interruption descent to . Another option occasionally employed by Chopin is to proceed to the mediant, which offers neither the level of contrast nor the tonic-targeting characteristic of the dominant harmony. Because both and are components of the mediant, the Kopfton generally will be prolonged. The Mazurka in A♭ Major’s A1 and A2 sections open with a melodic unfolding of the third from A♭ to C [1.5]. That interval also guides the broad bass trajectory during the B section [2.4]. It appears that Chopin intends to traverse that span via a descending circle of fifths: A♭ D♭ G C. However, in his execution of that agenda the projection of the initial A♭>D♭ fifth as two thirds is abandoned after F is attained at 183. Observe how local upper thirds (reminiscent of the upper thirds that pervade the A1 section) embellish various points along the way. The initial bass A♭ is preceded by downward motion from a C minor chord. Likewise F emerges from upper third A♭. In my view the F minor chord at 192 should initially be perceived as the starting point for another descending third, this time from F to D♭. But Chopin, recognizing that his strategy might become tedious if pursued adamantly, elides this passage. (It appears within square brackets in 2.4.) Instead, a collision occurs: a D♭ indeed does emerge in the bass – sooner than expected and in coordination with an apposite though accelerated soprano A♭>G>F – but concurrently the following chord in the broad circular motion sounds.4 Because this collision does not allow diatonic D♭ to wobble to D♮, the G chord emerges as G⇨.5

Example 2.4 Analysis of Mazurka in A♭ Major (op. 24/3). The goal mediant chord at 201 incorporates a wobble (E♮). Consequently foundational major chords are juxtaposed in the mazurka’s A and B sections, a feature shared with major-key movements that proceed instead from I to V. This chord corresponds to what I call the mediant’s Chromatic Variant ♯1 (CV♯1), with one chromatic pitch.6 Since the preceding passage led the melodic line some distance downwards from Kopfton C (= ), Chopin quickly reconstitutes that register: a melodic C persists from 203 through 242. This C then hooks up with the C of A2, launched by the A♭G>F♯>E from the Mazurka in E Minor’s A1 section

[1.13]

is

complemented

by

an

ascending

sixth-progression

(D♯B♭ fifth, measure 24 is the day of reckoning: will the line achieve its B♭ goal, resulting in a PAC; or will we have to settle for an IAC as the structural close? Whereas earlier the b region (to be explored presently) introduced the second scale degree, now the descent through

to occurs

quickly just as the section (or, during A2, the entire work) comes to a close. The b region that comes between a1 and a2 to shape the mazurka’s A1 section deploys II➔ V to succinctly achieve its dominant goal. Though the that serves as ’s successor in the linear descent is presented forzando in the low and middle registers at 91, its sounding at the top of the texture is delayed until 151 (at the end of a crescendo). The structural content is presented in four measures (9 through 12) followed by a varied repetition, thereby matching the format introduced during the a1 region. Chopin indulges in a flamboyant flourish during that repetition, with a rapid traversal of a circle of fifths supporting a stepwise descent through the dominant’s C>F fifth. The B section is structured as an autonomous trio [3.1b]. The B♭ tonic’s embellishing chord (first heard in measure 2) is here unfurled and asserted as the key of E♭ Major. Though the chordal progressions at various structural levels remain uncommonly simple, the embedding of one interrupted progression within a broader one is sophisticated. Chopin undertakes excursions above the melody’s fundamental structure. The third from C to A♭, filled in chromatically between 343 and 363 and between 431 and 433, is especially intriguing. In fact, given that in both contexts the motion continues downwards (by leap) to F, a reference to measures 15 and 16 may be discerned, despite the contrasting tonal contexts (fifth to root of dominant F in B♭ Major versus ninth to fifth of dominant B♭ in E♭ Major). The that is restored along with the resumption of the B♭ Major tonic for the onset of A2 again serves as the starting point for a descending fifth-progression. Because the A2

section concludes the work, this time that descent corresponds to the Urlinie.

The immediate restoration of I after a I–V tonic pillar

Opus 7/3 In a mazurka whose A1 section closes with a PAC in the tonic key, the B section may initially extend that tonic and then pursue a dominant goal. (As an example, see 2.3.) That strategy may prevail even if A1 ends in a vibrant HC. In 3.2, which displays an analysis of Chopin’s Mazurka in F Minor, observe how the melodic A♭>G that transpires over the course of A1 (with written-out repeat) is followed by the quick reaching-over of B♭, which resolves to a restored Kopfton A♭ early in the B section. Consequently the background tonic extends into measure 28, despite the HC in measures 16 and 24.

Example 3.2 Analysis of Mazurka in F Minor (op. 7/3). The mysterious introduction is grounded on lower-neighbor embellishment of the tonic’s root and third (imagining a G to go along with C and E♮, as occurs literally in measures 77ff.). The potential assertion of the introduction’s C-E♮-(G) as V♮ and F-(A♭)B♮-D♭ as II⇨ will be discussed later, in the context of this material’s recurrence at the juncture of B and A2.3 The initial tonic pillar that follows is simply constructed: the tonic is solidly established by means of upper-neighbor embellishment of its third and fifth in measure 11 (complementing the lower neighbors of the introduction), followed by a progression through II➔ to V♮. The harmonic trajectory that prevails during the B section follows a conventional course, though with one notable omission. Most of the section is devoted to the connection of the F tonic’s 5- and 6-phase chords: F-A♭-C and D♭-F-A♭. One of two intermediary chords often occurs between those points: either C-E♮-G (as

C, an embellishing chord

of the preceding F tonic) or A♭-C-E♭, which likewise possesses a natural dominantemulating tendency (as A♭➔, which embellishes the 6-phase D♭-F-A♭, here abetted by the addition of G♭ at 613). Chopin pursues the latter course, first attaining the A♭ chord via a segment of the descending circle of fifths (measures 26 through 30) and then tonicizing it until it surges towards D♭. The proposal of an omission, mentioned above, stems from the fact that I6 often leads to II, which in turn targets V♮. In a minor key, a very special relationship exists between I6 and II⇨: the former (D♭-F-A♭ in Chopin’s mazurka) may be a subset of the latter (D♭-F-A♭-B♮).4 Yet instead of adding B♮ in the vicinity of measure 73, Chopin allows the three pitches of the unfurled I6 each to descend a half step in turn, in a direct approach to V♮.5 This memorable and unusual voice leading heightens the emotional impact that Chopin seeks to attain also through the pianissimo dynamic indication and the ritenuto, sotto voce, and smorzando markings. Rewarding those listeners who noted the II⇨ omission, the following dominant prolongation (which reprises the mysterious introduction) uses the very notes of II⇨ – D♭-F-A♭-B♮ – in an embellishing context. Though V♮’s arrival concludes the B section’s harmonic progression, the embellishing chords that follow uncannily project the unsounded harmonic predecessor of V♮. The A2 section is constructed as a regular tonic pillar. Though its first phrase again ends on V♮, the phrase that follows is no mere repeat of the preceding one (as are measures 17 through 24). It instead serves as a conventional consequent phrase, concluding in a PAC that supports background . Ultimately the A1 section’s irregular close is of only local significance. The circle of fifths that leads out of I-space soon after the onset of the B section would transpire just the same regardless of what cadence occurs in measure 24.

Opus 30/1 Several features of the Mazurka in C Minor [3.3] echo those of the Mazurka in F Minor [3.2]. The A1 sections of both works present a I–V♮ tonic pillar, employing II➔ to lead to V♮. Likewise, a restoration of the tonic function occurs at or near the beginning of both B sections, followed by a segment of the descending circle of fifths that leads to the mediant. In the Mazurka in C Minor that restored tonic (at 163) is surging, already targeting the next chord in the circle of fifths. Both mazurkas tonicize the mediant, and both reach V♮ by the end of the B section. During A2 suitable revisions convert what was an irregular pillar during A1 into a regular one.

Example 3.3 Analysis of Mazurka in C Minor (op. 30/1). The chief difference between the two mazurkas’ structures concerns the manner in which the background V♮ is attained. Whereas the mediant in the Mazurka in F Minor ultimately leads to the diatonic I6, which could have proceeded (but does not) to II before V♮, in the Mazurka in C Minor the mediant is followed by a chromatic variant of I6 at 283. This chord in fact does lead through II➔ to V♮.6 Yet Chopin’s conception is even richer. As the two tiers of measure numbers in 3.2 and 3.3 suggest, both mazurkas make extensive use of repetition. For a few measures of the Mazurka in C Minor, Chopin eschews that practice and composes distinctive content, so that the connection between the mediant and dominant in measures 22 through 24 (not graphed) does not match that which occurs between measures 28 and 30. (Note also that the mediant is expanded – measures 20 through 22 – during the former phrase, while the dominant is extended – measures 30 through 36 – during the latter.) The former leads from III through IV to V♮. (The stepwise connection between III and IV is facilitated by the shift to III’s 6-phase chord at 232.)

Because of the persistent repetition during the A1 and B sections, the two dominant arrivals should be understood as equivalent. Chopin achieves his goal; then he backtracks and presents another pathway to the same goal. To enhance clarity the graph integrates those trajectories as much as possible, favoring the latter when they diverge. One way or another, the irregular tonic pillar of A1 must be transformed into a regular one during A2. The latter’s opening phrase reprises the full content of A1’s I–V♮ progression. What follows starting at 451 – which one might even resist calling a phrase – attains tonic closure in an unusual way. Instead of proceeding through the dominant to the expected PAC, it merely prolongs its initiating tonic. Consequently the local E♭>D>C descent of measures 46 through 48 serves as a motion to background , the endpoint of descending lines from at three distinct structural levels, as indicated by the multiple beams in 3.3.

Op. 30/4 The chords of the Mazurka in C♯ Minor’s introduction precede not only the tonic harmony that opens the A1 section, but also, through their recurrence at the end of the B section, the initial tonic of A2 as well. Their structural implications will be discussed below in terms of the latter context, which the introduction replicates only in part. Once the tonic harmony and Kopfton E emerge in measure 5, a broad tonic expansion ensues. F♯’s roles as both neighboring note to E and passing note to upper-third G♯ are on display in 3.4. The ♮II harmony serves as the principal connector between I and V♯ during the expansion of . Though the arrival of the pillar’s cadential dominant is placed at measure 31 in 3.4, Chopin’s writing in measures 28 through 31 teases listeners: should the passage be interpreted as repetitions of V➔ I followed by V♯, or instead as repetitions of V (with the chords unfurled)?

Example 3.4 Analysis of Mazurka in C♯ Minor (op. 30/4). As in the other mazurkas explored in this segment of the chapter, the tonic harmony and the Kopfton are restored early in the B section. Initially the C♯ minor chord is fortified through motion to its upper fifth, G♯ (measures 39ff.). The broad melodic descent E>D♯>C♯ over measures 34 through 65 shifts from representing the third to root of the C♯ tonic chord to the seventh to fifth of an F♯ chord. Whereas Chopin utilizes the descending circle of fifths in the B sections displayed in 3.2 and 3.3 to connect the tonic and the mediant, here the circle extends only to its third chord: C♯ F♯ B. This B chord is tonicized

between measures 66 and 95 (parts of which are displayed in 3.4). Chopin’s tonal plan involves a conversion from subtonic B to dominant G♯.7 The harmonic analysis in 3.4 displays the B chord as a not yet fully formed dominant: the pitch B is the wobbly third of the G♯ major dominant, with the arrival of root G♯ delayed until measure 99. The B-D♯F♯ tonicization is an upper-third substitution for the rightful G♯-B♯-D♯ dominant tonicization. Chopin negotiates the transition between B and G♯ by juxtaposing embellishing chords targeting each: F♯➔ in measures 94 through 96 and D♯➔ in measures 97 and 98. By the time the G♯ chord arrives, it is too late for further tonicization. Its minor seventh F♯ is already in place, and so instead of content extending its role as I in tonicized G♯, it asserts its background role as

, announcing the restoration of the C♯ tonic for

the A2 section. As mentioned above, the D♯➔ and G♯➔ chords were first encountered within the mazurka’s introduction. The A2 section offers an intriguing reprise of the dominant–subtonic relationship. Certainly a PAC must be attained at the close of A2. The dominant at measure 128 is where the precedent harmonic trajectory of A1 concludes. How will Chopin achieve a tonic cadence? His extraordinary response involves a plan to proceed from the already attained dominant to its subtonic upper-third chord and then back again. Both of those moves are accomplished through an inspired yet unconventional construction. Whereas the subtonic–dominant connection within the B section was negotiated via a shift of embellishing chords, in these final measures Chopin instead deploys a linear progression to connect the G♯ and B chords themselves: a wondrous application of the descending circle of fifths, filled with altered pitches, added dissonances, and enharmonic spellings, which transpires as m.

128

G♯

129

C♯

F♯

130

B

E

131

A

D♮

132

G♮

C♮

In this interpretation, a collision at beat 3 of measure 132 involves two adjacent chords within the circle – F♮ (which in a familiar evolved state would be correctly spelled as AC♭-E♭-G♭) and B (spelled as B-D♯-F♯-A) – that are enharmonic equivalents of one another. The passage in fact comes across as a parallel progression of major-minor seventh

chords – as a temporary transfer from diatonic modulo 7 tonal space into the modulo 12 realm, where spans such as this G♯>B may be traversed by unconventional means, in this case through a descent in half steps: 8 (7) 6 5 4 3 2 1 0 11 (with C = 0).8 The dominant restoration is likewise inventive. Whereas B♯-D♯-F♯-A would be a suitable successor of the subtonic chord, projecting a conventional intensification of the dominant function, in this case leading tone B♯ is displaced by an anticipation of its resolution: C♯-D♯-F♯-A is prolonged during measures 133 through 138.9 At the cadence F♯ resolves to E and A resolves to G♯ above tonic root C♯. The soprano tonic , anticipated during the dominant harmony, sounds only in the bass at the cadence. Consequently the C♯ that concludes the background

melodic descent is displayed within parentheses in 3.4.

Without opus 42A A prominent feature of the irregular tonic pillar that serves as A1 for the Mazurka in A Minor is its array of

descents [3.5a]. Most are local manifestations, within their

own four-measure phrases. Some are preceded by their upper thirds. (The descending third E>D♯>D♮>C beginning in measure 9 inverts the ascending sixth EA) in A Major transpires over the course of eight measures [3.7]. During a repetition of this passage beginning in measure 58, Chopin creatively modifies the harmonization so that a fully chromatic filling-in of a descending seventh connects the tonic root A at 581 and the supertonic root B at 631. The chromatic line takes on the character of a stupefying feat, enhancing the mazurka’s robust character.

The restoration of the tonic in measure 69 coincides with the onset of a fresh BE♭ seconds are filled in, but also the upper line’s concluding C>B♭ and the FG thirds and B♭G♯EC♯ supporting a descending sixth-progression from Kopfton E, in this case the G♯ chord is internal to a1 and thus resolves to tonic C♯ before the A chord emerges in measure 17. During the II➔ that follows after the sequence, the melody gradually builds back upwards to the D♯ (measure 27) that succeeds Kopfton E at the middleground level and connects with the D♯ of V♯ (measure 32). As indicated above, a2’s tonal plan demotes the impact of the tonic restoration, instead favoring dominant prolongation. Consequently the b region’s

ultimately is left

dangling at the end of the a2 region. Chopin’s re-engagement with the thematic content of a1 here involves contraction: the essence of measures 0|1 through 9 is stated in measures 32|33 through 37 and is then repeated even more succinctly. The region closes with a fourmeasure melodic arpeggiation of the pitches of V♯, segueing into the B section, which begins in measure 45. Though the V♯ that concludes the A1 section – unexpectedly lacking a tonic resolution – is a middleground event and the V♯ that ends the B section (measures 89–92) is a background event, the uncommon dominant density at this juncture makes a conventional I-to-V♯ trajectory ill suited for B. Chopin therefore has elected instead to tonicize a chromatic variant of the dominant’s upper-third chord. Because dissonant B♯D♯-F♯ cannot be tonicized, Chopin allows B♯ to wobble to B♮. That lowering, introduced in measure 45, is not rescinded until measure 89. Because B Major is in a sense the “wrong” key, the trajectory that Chopin sets in motion for its tonicization – a local ternary form divided by an interruption after the

that arrives at measure 70 [3.9a] – is not

fully realized (and thus resonates with the unresolved ternary interruption during A1). In this case the y region is extensively developed, with a surging I leading through IV5–6 to V, while the x2 region that follows proceeds only through its initial pre-surge I phase.

One foreground detail (not graphed) plays an important role in the realization of Chopin’s tonal plan for the B section: namely, the incorporation of the B tonic’s 6-phase chord as a substitute for the dominant during the repeat of x1 (measures 53 through 60). The basic idea, which extends into the onset of the y region, is I8–7♮, the conversion of the stable B-major tonic into a surging chord targeting IV. That tonic is expanded via a local B>F♯C♯, covered by F♯>E. Concurrent with the background close on , this E opens the tonal space that will be traversed – as a reprise of the E>D♯>C♯ descent – during the coda.13) The magnificent coda deploys the lowered supertonic (measures 165 and 171) as the principal intermediary between the tonic and the dominant [3.9b]. Though usually that chord’s wobble (here D♮) would be rectified by the dominant’s D♯, in this case a supertonic evolution during measure 173 results in a D♯-rooted version of II occurring prior to the onset of V.14 (I have displayed the chord as F -A-C♯-(E) in 3.9b, though D♯ might be imagined instead of E: both convey the function II⇨.) Chopin’s means of connecting the tonic and the lowered supertonic incorporates an obstinate circular progression that I propose resides outside of conventional modulo 7 tonal space. Instead, once it gets on track modulo 12 chromatic tonal space subdivides into four equal segments. Using the numbers from 0 through 11 (with C = 0), the progression proceeds as m.

157

158

159

160

161

162

163

164 170

165

166

167

168

169

melody:

1

1

3

4

6

7

9

10

0

1

3

bass:

1

6➔

11

9➔

2

0➔

5

3➔

8

6➔

11

The conversion of this lucid and elegant circular progression into modulo 7 music notation inevitably results in some enharmonic inelegance, requiring a mix of minor third and augmented second intervals. (Though Chopin chose to notate the bass as BA♯>G♯>F♯.

Idiosyncratic tonic pillar contexts

Opus 33/4 The opening tonic pillar in Chopin’s Mazurka in B Minor (measures 0|1 through 24, followed by a written-out repeat) is classified as irregular because it cadences on the dominant. This is a conventional sort of irregularity, like several we encountered earlier in this chapter. Chopin makes a predictable adjustment during the pillar’s final presentation, where the second phrase concludes with a PAC (measure 200).24 Such a construction justifies the mazurka’s placement within this chapter, though not within this section, which is devoted to idiosyncratic pillars. That categorization results from Chopin’s extraordinary continuation after the HC of measure 24: the a1 pillar is repeated, but with a remarkable, strange, and unexpected turn of events at its cadence. The lowered supertonic (“Neapolitan”) chord arises naturally in a minor key: a diatonic presentation of I5–6 (here B-D-F♯ to B-D-G) produces a chord that (especially when enhanced by the addition of the pitch F♮ to B-(D)-G, as at 171) inherently leads towards ♮II. In accordance with an unwritten covenant among composers pertaining to the use of the lowered supertonic, the key’s foundational BG♭>F♮, with G♭ serving as a chromatic passing note. Whereas II➔ generally proceeds to V (as in measures 5 and 6), the lowered supertonic’s inherent dominant-emulating tendency generally will not be tapped by composers, since ♮II➔ leads into the abyss: it points towards the tonic’s antipode, in this case F♮. Consequently the meek F♮ at the end of measure 48, which in

fact introduces that antipode, is an astonishing event. It causes the b region, which commences in measure 49, to open in the highly unusual key of ♭I. Ultimately the mazurka’s tonal course will be corrected: by the end of the b region the conventional F♯ dominant is attained. Yet a half-step depression within tonal space prevails from 483 through measure 63. How is this accomplished? Whereas F♯ is expected in measure 48, F♮ occurs instead (as explained above); and whereas F♮ is expected after what should initially be interpreted as a C chord in measure 63, that chord is enharmonically transformed into an F♯ chord. Observe in 3.14 how ♮II in B Minor is reinterpreted as II in B♭ Major, leading to V in that key. Given that build-up, it is not surprising that the b region robustly asserts a B♭ Major tonic. In fact, a standard progression prevails in that key through measure 63: I is followed by IV, and IV undergoes a 5–6 shift in which the 6-phase E♭-G-C sounds in its evolved state E♮-G♭-B♭-D♭ (= II⇨). Without the visual clues that Chopin provides in the score, listeners should reasonably expect this chord to resolve to V in B♭ Major. Yet Chopin (as also most readers of this book) certainly had learned that this particular variant of II (often referred to as the “German” augmented sixth) may be enharmonically transformed into a dominant seventh. It so happens that this C⇨ chord’s enharmonic equivalent is the very F♯➔ chord that would lead the progression back to B Minor. Under normal circumstances the mazurka might continue with a2 (concluding the A1 section) followed by B, after which a concluding A2 would offer the final PAC. Yet in this case there are two contrasting a1 models from which the content of a2 might be derived: either the conventional irregular version of measure 0|1 through 24, which ends on V♯, or instead the key-shifting irregular version of measures 25 through 48, with its half-step depression. By choosing the latter for a2, Chopin arrives at a tonal juncture (at the end of measure 88) not well suited to precede a normative B section (which in this case will begin in the initial tonic’s parallel key, B Major). Rather than grapple with that juxtaposition, Chopin takes the unusual step of inserting a full statement of the b region, thereby putting his tonal house in order before the onset of the B section. Though b content is employed, Chopin achieves the same tonal goal as if a2 had instead proceeded as in the initial a1 model. This is the only instance of a direct succession from a b region to a B section within Chopin’s published mazurkas: the b designation in 3.14 truly deserves the exclamation point that annotates it.

The B section opens in measure 105 with two eight-measure phrases, each proceeding from the tonic to the dominant in the key of B Major. Both phrases are shaped by the traversal of a descending fourth from Kopfton F♯, thereby matching the contour of the original a1, though with alternative harmonic routes between the initial I and goal V. The next sixteen measures repeat these phrases with modest adjustments and one significant change: the second phrase concludes without achieving its dominant goal. The dominant instead serves as the initial chord of the following phrase, where it supports background , which is followed by ♯ at the tonic resolution. After several repetitions, the passage breaks off at background , supported by V♯, in measure 151. A written-out cadenza that expands the dominant (and recalls content from the preceding measures) transpires during the next seventeen measures. As mentioned above, the original tonic pillar is constructed in such a way that a PAC may be attained with minimal modification. Yet Chopin’s tonal plot thickened during the initial a1’s repetition: due to the extraordinary C♮G♭>F♮ again lead away from the B Minor dominant? No! Aroused afresh, Chopin instead uses C♮, the other of the two pitches he has been dangling before the listener, as the initiation point for a similar descent in half steps: C♮>B>A♯ introduces the B Minor dominant’s leading tone. The measure (200).

and I that conclude the mazurka sound within a single

Opus 56/3 Chopin’s Mazurka in C Minor contains one of the most astonishing constructions in his entire oeuvre. To understand it, imagine a keyboard mechanism placed on rollers, so that it may move freely to the left or right, consequently hitting different piano strings and thereby facilitating transpositions. Whereas normally such a mechanism would be in the locked position, imagine a pianist performing a mazurka with it accidentally unlocked while several earthquake tremors occur, moving the keyboard a total of seven times to the right, each resulting in either a half-step or a whole-step shift. Despite these seismic shifts, the performer maintains the integrity of the tonal plan according to what the fingers are doing instead of according to the sounds that the strings are emitting.25 It so happens that these seven seismic shifts add up to twelve half steps, so that, despite the extraordinary sonic output, the mazurka ends in the key in which it began. The mazurka’s basic tonal plan incorporates an irregular tonic pillar – I II V♮ – during its A1 section and prolongational I II V I progressions in the dominant key during both the A1 and B sections. The chordal roots are displayed in the context of C Minor at the top of 3.15a, with much of the content in that line shaded to indicate where seismic shifts ensue, resulting in alternative sonic output, as displayed below the shaded regions. The A1 section opens with a progression that broadly extends from I to V♮, incorporating an evolved tonic 6-phase chord and a minor supertonic [3.15b]. Chopin proceeds with a written-out repeat, during which a seismic shift raises supertonic D to E♭ in measure 49. Whereas the minor D chord might have undergone chordal evolution so as to result in a D➔ surge directed towards dominant G, now instead E♭➔ targets “dominant” A♭, which arrives in measure 52. Another seismic shift affects a repetition of that passage: F➔ B♭ occurs in measures 53 through 56. This B♭ chord represents C Minor’s dominant even if by now the seismic activity has moved it three half steps higher. The tonic pillar concludes with a prolongation of this “dominant,” engaging a fifth-progression in the melody during measures 56 through 72 (with the normative D>G dominant span raised to F>B♭). Though at first the chord introduced in measure 57 may seem to be yet another II➔ (a third seismic shift: E♭➔, F➔, F♯➔), the progression ultimately incorporates that chord within the B♭ “dominant” prolongation. Consequently the chord spelled by Chopin as if its root were F♯ functions as a C-rooted chord (initially II⇨ in tonicized B♭ Major, shifting to II➔ during measure 68), as clarified by the modified spelling in 3.15b.

Example 3.15 Mazurka in C Minor (op. 56/3) (a) Tonal content of mm. 2–136; (b) Analysis of mm. 0|1–136; (c) Analysis of mm. 137–220. Onset measure

Seismic shift (in half steps)

2

C Minor:

Foundational progression

C

D

(= G Major:

G

––––––––––––

–––––––––

G

A

G )

D

49

+1

E♭

A♭

53

+2

F

B♭

134

+2

D

G

135

+2

E

A

135

+2

F♯

B

136

+2

G♯

C♯

136

+1 ____ +12 = octave!

C

G

The key of B♭ Major prevails during most of the B section (from measure 73 until the renewed seismic activity beginning in measure 134). That choice conveniently allows the composition to retain the pitch D as : though normally D would be the fifth of dominant G Minor, here it instead serves as the third of the seismically achieved “dominant” B♭ Major. The ternary B section opens with an x1 region (measures 73 through 88) that pursues the tonicizing I II V I harmonic progression that will be subjected to numerous seismic shifts during the x2 region. (Note how the B♭ tonic extends through the end of measure 77, where elements of its embellishing chord – F and C – and its surging third and minor seventh – D and A♭ – collide.) The B section continues with a y region that, after adopting the hue of B♭ Minor, leads conventionally via II➔ to the dominant in measure 105 (extended through measure 120). Though a middleground interruption of the melody on

typically would be

resolved by during the x2 region, the intended DC>B♭ melody that is initiated in measure 121 is jolted by repeated seismic shifts that move the goal B♭ up a major sixth to G (in the bass at 1363). Examining the phrase that begins with melodic pitch D at 1291, note how upper-neighbor E♭ is supported by II at 1341. This C-G-E♭ chord might evolve to surging B♭-E♮-D♭ (= II➔) before dominant A♮-F-C (whose C would be

within the

local melodic descent) arrives. Yet at that very moment a new wave of seismic shifts begins, so that B♭-E♮-D♭ is jolted upwards to C-F♯-E♭ (thereby being distinguished from the preceding diatonic II only by the half-step descent of G to F♯). The dominant’s thus is represented by D – rather than by C – at the end of measure 134. Each of three repetitions of II➔ V coordinates with another whole-step seismic shift, so that V within

the dominant prolongation, represented by an F chord during most of the B section, is raised not only to root G, but also to A♮, B♮, and C♯. Whereas the G♯-B♮-D-F chord at 1362 might initially be interpreted as yet another whole-step shift (as C -E♯-G♯-B♮, functioning as II➔ in G♯), the bass instead descends as G♯[A♭]>G, and therefore the goal I of the dominant-tonicizing progression is achieved. Whereas the “dominant” C♯ chord of 1361 normally would resolve to F♯, one final seismic shift – this time the shift of a half step – leads to goal G, completing the trajectory presented in 3.15a. The tonic pillar of A1 is doubly irregular: not only does it conclude on V♮, but that V♮ has shifted seismically upwards a minor third. During A2 we expect that such irregularities will be foresworn and that the tonic pillar will conclude regularly – with a PAC on tonic C (to which Chopin applies a Picardy third, E♮, in measure 189). The decisive swerve away from the precedent of A1 occurs at measure 173. The ensuing progression begins as if Chopin intends to pursue a conventional harmonic course: I IV5–6♭

in measures 171

through 176. Yet the chord with bass B♮ in measure 176 eventually evolves into the chord with bass C♭ in measure 180. From that point, the bass moves chromatically downwards to F (at 1871). As 3.15c shows, an idiosyncratic descending circle of fifths that connects IV’s 5-phase F-A♭-C and chromatic 6-phase F-A♭-D♭ chords propels this line.26 This extended IV yields to

in measure 188, followed by goal I♮ in measure 189.

The coda, which commences in measure 189, contains a double CC bass arpeggiation, supporting

and

. Each half is repeated, as

is conveyed by the measure numbers annotating 3.15c. Chopin’s treatment of ♭ is of special interest. When D♭ occurs below

, it at first reverts to D♮ (at 1963) before V♮’s

resolution. Yet during the repetition of that segment the wobbly note does not yield to the diatonic pitch: D♭ holds out at 2043. However, during the span from wobble yields to D♮ in both traversals, at 2083 and at 2123.

to the D♭

Opus 59/1 The Mazurka in A Minor is constructed in the most extended of Chopin’s mazurka forms, with four tonic pillars in all: A1 and A2 sections (both with a ternary division into a1, b, and a2 regions) surrounding an internal B section (where the parallel key – A Major – prevails). Chopin defies his own conventions by presenting the third of the tonic pillars (at the onset of A2) not in A Minor, but instead in G♯ Minor. As we shall see, he begins preparations for this unusual event as early as A1’s b region. The mazurka’s inaugurating tonic pillar opens with a three-measure prolongation of the tonic’s E-G♯-B-D embellishing chord. (A local embellishment in measure 1, before E sounds at the bottom of the texture, should not be confused with the arrival of tonic A.) This chord will be asserted as a relatively deep structural V♯ at the onset of a2 (measures 25–27), following a b region that proceeds only as far as an evolved IV6. (See 3.16a.) The juxtaposition of surging B➔, E➔, and A➔ chords during measures 9 and 10 and the weak metrical placement of the A➔ chord might call into question the deep structural role assigned to that A chord in 3.16a. Yet an elision occurs: instead of a conventional expansion of the broader I-space (via a local supertonic and dominant) followed by a transformation of the goal I to surge towards IV, the tonic reinstatement at 103 is already surging. Perhaps compensating for this fleeting A-chord restoration, an expanded version of the progression during the b region extends the equivalent tonic harmony for five measures (17 through 21) before proceeding to IV♯.

Example 3.16 Mazurka in A Minor (op. 59/1) (a) Analysis of mm. 1–36; (b) Analysis of mm. 37–130.

The Kopfton E is the first pitch heard in the mazurka. Extended via upper-third G (in conjunction with the local shift to tonic A Minor’s upper-third chord – C-E-G – in measures 5 through 8), a middleground descent – E>D>C – over the course of the pillar likewise incorporates an upper-third embellishment of D (F>D in measure 11) before goal C, presented as an anticipation at the end of measure 11, sounds. The descent only as far as during the initial tonic pillars (a1 and a2) will affect how Chopin proceeds during the B section (measures 37 through 50) and will be rectified during A2’s a2 region, to be explored below.

The b region draws upon a1’s establishment of the A Minor tonic and of Kopfton to launch its tonal trajectory, which is similar to that which inaugurates a1: the II➔ of measure 13 replicates much of what occurred in measure 9, leading to V♯ in measure 14 (as in measure 10). What follows is unusual, an instance of a seismic shift. Instead of proceeding directly to I➔, Chopin repeats the II➔ V♯ succession in a transposition down a half step (measures 15 and 16), consequently achieving tonic A not via its normative E dominant predecessor, but instead via E♭ – its antipode! This half-step depression is displayed within a box in 3.16a. While the ear may succeed in making the broad connection between roots E (measure 14) and A (measure 17), the passage sets the stage for a more remarkable deviation that will occur later, at the onset of A2. Though a b region often will conclude on V♯, here the dominant function is already built into the initial measures of the tonic pillar, as mentioned above. Consequently the prolonged I➔ of measures 17 through 21 proceeds only to IV♯ and its evolved 6-phase chord (D♯-F♯-A-C) before the pillar theme enters in the left hand at 251. The a2 tonic pillar’s progression is similar to that of a1, with the structural melody again descending E>D>C. The goal C is transferred down an octave and wobbles to C♯ for the onset of the B section (in A Major) in measure 37. Indeed the fact that the linear progressions descend only a third from during the initial two tonic pillars results in some unfinished business that Chopin addresses at the onset of the B section, where the major-hued C♯ yields to B and then A in measures 37 through 42 [3.16b]. Only upon that line’s completion is Kopfton E freshly stated, with a full descent of the E>A fifth transpiring during measures 42 through 50. The E>D>C♯ component of that fifth is complemented by ascending motion in the bass, in an A5–6 B5–6 C5♯ sequential trajectory. A C♯➔ chord is, of course, a common predecessor of the tonic’s 6-phase chord. The next round of tonic prolongation (measures 49 through 82) is extraordinary. Note the extended prolongation of the E minor chord first sounded in measure 56. Chopin explores several possible continuations before proceeding through F♯➔ to B➔ in measures 71 and 72 (the version displayed in 3.16b). That B chord “should” lead to dominant E. (Compare with the B chord of measure 13.) Yet at that point an extended half-step depression (another seismic shift) begins. Now with augmented fifth, B-D♯-F

leads not as expected to E-G♯-B (to inaugurate the third statement of the tonic pillar, as in measures 25 and 26), but instead to D♯-F -A♯, which shares two common tones with the preceding II➔. This D♯ “dominant” sets A2 in motion, resolving to “tonic” G♯ in measure 82. The entire a1 region maintains this half-step depression. Fortunately Chopin has already devised a means of re-establishing the rightful tonal center. The depressed chords of measures 15 and 16 (displayed within a box in 3.16a) are the same as the last two depressed chords displayed within a box in 3.16b. Chopin simply persists along the course of a1 and b until those chords emerge (stating them twice so as to maintain the dimensions of the b region from A1), and then does exactly what he did during the earlier b region to emerge out of the depression. (Compare measures 16–17 and 94–95.) The remainder of b and the onset of a1 correspond to their counterparts within A1. Whereas both the a1 and a2 tonic pillars within A1 traverse the linear progression of a third descending from Kopfton , during the final pillar (the a2 of A2), a revision of the harmonization in measure 114 prevents the occurrence of an unsuitable IAC. (See 3.16b.) The pitch C (background ) is supported by an embellishing chord (D♯-F♯-A-C, which later evolves into D♯-F♮-A-C) that comes between presentations of the dominant supporting (at 1133) and (at measures 123 through 129). The PAC in the work’s final measure coordinates with the descent from B to A (= ) in conjunction with the tonic’s arrival. Despite the irregularities of cadence and tonal center that have characterized the earlier statements, a regular tonic pillar – in A Minor throughout and with a full descent from to – finally prevails.

Part II ◈

Masterpieces

4

Étude in C Minor (op. 10, no. 12) ◈ in response to Graham H. Phipps Graham H. Phipps, drawing upon precepts of the eminent Austrian theorists Simon Sechter and Arnold Schoenberg, offers a robust study of Chopin’s Étude in C Minor in an article from 1983.1 That composition was selected with good reason: Phipps was keen to explore Schenker’s extensive and detailed graphs of the work and to reveal ways in which his own Sechterian/Schoenbergian perspective offers contrasting and, in his view, superior insights, just as my taking up the work again now offers an opportunity to assess Phipps’s perspective. I, too, am uncomfortable with aspects of Schenker’s reading, but so as not to complicate the presentation or distract from my focus on Phipps’s analysis, my comments relating to Schenker’s graphs will be relegated to the notes, for the most part. Phipps contends that Schenker’s theory is “restrictive in a manner which prevents him from perceiving significant musical relationships” (p. 544) and that it is at fault by (as Schoenberg contends) “ignoring the musical facts” (p. 545). He does not attempt to build upon Schenker’s insights, as I do.

The introduction and the A1 section, part 1

The introduction and the A1 section, part 1 (measures 1–18) Charged with preparing the C Minor tonic arrival at 91, the introduction projects two variants of the tonic’s most characteristic embellishing chord: G-B♮-D-F and its more potent variant, B♮-D-F-A♭. Whereas the A♭>G appoggiatura of 11 is reiterated con forza at the top of the texture during 51 (embellishing the pitch G, which will emerge as the work’s Kopfton), that motive is raised a step – to B♭>A♭ – during 73 to assert the chordal ninth, which reverts to G during 83 as a G>E♭>C arpeggiation of the tonic triad commences. (Make special note at this point that I underline the pitch names G and A♭. My contention that the work’s Kopfton is G – rather than E♭ – likely will be controversial, and so my attentiveness to how G is deployed throughout will warrant the reader’s attentive consideration.) Through this means the A1 theme’s GG neighboring-note motive is adumbrated during the introduction. (See 4.1.) That tonic arpeggiation also provides the unfolded E♭>C resolution of the introduction’s pervasive

diminished fifth. (Thus

advocates of Kopfton may also find supportive evidence in Chopin’s introduction.) This third (ascending from C to E♭ and filled in by passing note D) likewise is incorporated within the A1 theme.

Example 4.1 Analysis of Étude in C Minor (op. 10/12), mm. 1–18.

The descending triadic arpeggiation leading into 91 is complemented by the A1 theme’s ascending arpeggiation during measures 10 and 11: CA♭ during 73. Phipps does not make that association. Instead he proposes that this B♭ serves as a chord member: the dominant root in a potential shift of the tonal center to E♭ Major (p. 554 and ex. 2, systems 2 and 3). Whereas I perceive an unwavering presence of B♮ (against which B♭ clashes) from its sounding during 73 to its sounding during 82, Phipps places the B♭ on a higher plane, with a B♭>A♭>F>D arpeggiation of V7 in E♭ Major potentially resolving to its tonic during 81. That interpretation requires some curious hierarchical shifts: in a context in which the first and third sixteenth notes of a beat embellish the second and fourth, exceptionally the B♭ during 73 and the E♭ during 81 must counter that trend.3 Phipps proposes that the introduction serves as the Schoenbergian Grundgestalt for the Étude. If that is the case, then it seems to me he has overlooked an important feature of its shape: the neighboring motion from G to A♭, then back to G (as displayed in 4.1), conveying an intensification and then retreat prior to the tonic resolution. That process is then mapped onto the tonic, with the A♭ at 121 embellishing Kopfton G. It is heartening to know that Phipps (in alignment with Sechter’s view) concurs with my reading of the F♯-A♮-C-E♭ chord’s root as D (measure 14), though my II➔ label (or II with numbers, accidentals, and a bullet symbol, as in 4.1) conveys something slightly different from his “dominant of G” terminology (p. 556). Phipps suggests that the emergence of this chord will come as a surprise: focusing on the right-hand A♮-C-E♭, he proposes that root F♮ is “expected” in the left hand. I hold a more neutral perspective on what might happen after a phrase’s initial tonic, regarding II (in which A♮, C, and E♭ serve as the fifth, seventh, and ninth) and IV (in which those pitches serve as the third, fifth, and seventh) as equally viable successors. In this case Chopin employs F♯-A-C-E♭, initiating an exploration of the chord’s mehrdeutig character.4 Here it leads to G, whereas, reinterpreted as A-C-E♭-G♭ (which Chopin presents in its F-A-C-E♭ variant), it

leads to B♭ in measures 24 and 25, and, reinterpreted as C-E♭-G♭-B , to D♭ in measures 64 and 65. Phipps and I propose opposing hierarchies for the chords of measure 15. Whereas he regards the first-inversion G major chord at 151 as the onset of a “four-measure resolution” – extending through measure 18 – of the F♯-A-C-E♭ “dominant” (p. 556), I instead regard all that has transpired within the phrase thus far as contributing to the establishment of the phrase’s initial I-space, culminating in a potent I➔ at 153–4. (Phipps and I agree that this chord functions as a tonic, as a comparison of his ex. 6 and my 4.1 confirms.5 We disagree regarding its hierarchical depth.) Consequently the IV at measure 16, which supports the the melodic path between and

on

, resides deeper within the structure in my

reading than in Phipps’s. A consistent descending half-step motive transpires within many of the phrase’s measures: from the melody’s signature A♭>G in measure 12 to the bass’s B♮>B♭ and A♮>A♭ (measures 15 and 16) to the melody’s E♮>E♭ and E♭>D (measures 17 and 18). Though Phipps’s ex. 6 displays most of these seconds, for the most part he does not propose any hierarchical relationships among them. Had he done so, the contradiction between the B♮>B♭ pitch hierarchy and the V (I) analytical hierarchy in measure 15 would have stood out glaringly.

The A1 section, part 2 (measures 19–48)

The A1 section, part 2 (measures 19–48) After a two-measure allowance for the C Minor tonic chord to settle in (measures 9 and 10), the A1 section proceeds with eight measures – 10|11 through 18 – during which Chopin traverses a conventional I-to-V♮ harmonic progression, supporting the descending melodic fourth from Kopfton G to D. That content is reprised in a more definitive and much expanded statement during measures 21 through 41, which are organized as 8 + 8 + 5 measures. (The five-measure unit dovetails with a reprise of the introduction material. The tonic re-emerges in measure 49 to inaugurate A2.) Whereas in the first phrase the bass trajectory from C through B♭ and A♭ to G coordinates with the harmonic progression I ➔ IV V♮, for the expanded version Chopin instead pursues a circular progression that incorporates C, B♭, and A♭ as roots (C F B♭ E♭ A♭ … ), thereby providing an alternative means of support for the stepwise descent from Kopfton G. The circle’s component chords are delineated in 4.2, in which two alternative conclusions for the passage are juxtaposed. (These measures are displayed in graph notation in 4.3, which will be introduced during our consideration of the A2 section but which may be consulted now.) Chopin in fact jumps off the circle’s tracks in an unexpected development over the course of measures 33 through 35. How does he initiate the circular progression, and why does he elect to abandon it?

Example 4.2 Analysis of Étude in C Minor (op. 10/12), mm. 21–41.

Example 4.3 Analysis of Étude in C Minor (op. 10/12). The two parts of A1 begin along the same course: measures 10|11 through 13 map onto measures 20|21 through 23. Even the melody’s A♮ at 241 stems from the earlier passage. Yet the upward drive initiated by that pitch now persists for three measures, in coordination with a crescendo and even a stretto. Though numerous combinations of pitches sound during these measures, I propose that they are guided by an evolutionary process that may be expressed in symbols as C ➔ ⇨: that is, in targeting the circle’s second chord (F during measure 27), the C minor tonic chord first becomes dominantemulating (C-E♮-G-B♭ during 261–2) and then takes on an augmented-sixth character (E♮G♭-B♭-(D♭) during 264). The augmented sixth (which most often occurs in the context of a supertonic), in coordination with the embellishment of the following major F chord, gives a strong sense of a B♭ Major tonicization (II⇨ V I) to the passage from 264 through 281, though from a broader perspective this trajectory remains bounded by C Minor’s C tonic and potential G dominant. With that internal B♭ Major tonicization in mind, the A♮ of measure 24 serves as a diatonic component of a sequential connection between the C supertonic’s root position and surging first inversion: m.

(=

23

24

x

25

C5–

–6

(D5–)

–6

26 E♭5

E♮6

C ———————————————————)

This sequence is somewhat rambunctious, in that the D5 component is elided. The addition of the pitch F to C6 fosters the direct link to D6, as F➔B♭.6 Drawing upon the momentum

generated thus far, Chopin extends further during measure 26, from C to E♮ in the top voice and from E♮ to G♭ in the bass. Root C finally yields to root F at 271. Chopin begins a shift from notation in flats to notation in sharps during measure 28. The curiously juxtaposed G♯ and B♭ during 284 should be regarded as components of a B♭7 chord, targeting the circle’s next component, E♭ [D♯].7 Chopin complicates matters by employing an unfurled embellishment to precede that E♭ arrival (measures 29 and 30), as displayed in 4.2.8 Consequently the B♭ chord’s dissonant A♭ [G♯] at 284 is suspended for a full measure before resolution to G♭ [F♯] at 301. Though the similarity in how the F chord in measure 27 and the E♭ chord in measures 29 and 30 are embellished might have created a parallelism within the circle, the E♭ chord’s minor quality prevents it from imparting a dominant function. (Thus a potential tonicization of A♭ Major following that of B♭ Major is declined.) Yet the minor quality of the E♭ [D♯] chord followed (after some linear connection) by an A♭ [G♯] chord of dominant character (measure 33) constitutes the onset of an alternative and quite striking tonicization: that of the lowered supertonic (Neapolitan) key, D♭ Major. The continuation marked as “Alternative 1” in 4.2 realizes that potentiality and proceeds onward to the G goal. However, Chopin abruptly changes course after the A♭ [G♯] chord. If left unattended, a descending circle of (perfect) fifths does not chart a course from the tonic to the dominant. Instead, C would lead through F, B♭, E♭, A♭, and D♭ to G♭, the tonic’s antipode. Composers are left with two options (unless they are willing to take the long route – reaching G [A ] at the circle’s twelfth chord): either they can modify one of the perfect fifths by a half step (generally at F–B♮, at A♭–D, or at D♭–G); or they can abandon the circular progression before the dominant arrives. The two alternatives displayed in 4.2 reveal how these options might be realized. In the first, the melodic descent overshoots the mark, requiring a corrective shift from D♭ to diatonic D♮ in coordination with a D♭–G diminished fifth in the bass. This is a common occurrence in music, one that Chopin in fact will call upon later in the Étude (as the measure numbers 72 and 75 in 4.2 indicate). Yet he here elects instead to pursue the second of the two options, deploying two seismic shifts to hoist the A♭➔ [G♯➔] chord targeting D♭ upwards first to B♭➔ (measure 34) and then to C➔ (measure 35).9 Perhaps a factor in Chopin’s choice was the desire to realign this part of A1 harmonically with the I ➔ IV V♮ trajectory of the section’s first part, despite the altered relationship with the melody’s descent from Kopfton

G to D. Or perhaps he wanted to reserve the Neapolitan chord, which will be featured during A2 (measure 72).10 In any event, the section’s melodic goal , supported by V♮, is achieved at 411.11 Though both Phipps and I are drawn to the F➔ B♭ succession of measures 27 and 28, we contextualize it in contrasting ways. Whereas he singles out the F chord of measure 24 as “the means for movement to the B♭-major cadence” (p. 558), therefore apparently proposing a four-measure extension of F➔ (though no further details are provided), I instead interpret that initial F➔ within the expansion of an evolving C chord, with the C-to-F succession occurring over the bar line between measures 26 and 27. (Though he acknowledges a cadence in measure 28, Phipps calls the F-B♭-D chord at 271–3 a “tonic harmony in B♭ major” (p. 558), further distinguishing his interpretation of the broad C–F–B♭ circular trajectory from mine.) Equally problematic, in my view, is his assertion that this B♭ Major cadence marks a sectional close (p. 558), thereby relegating measures 29 through 40 to the status of a “retransition” (p. 564). I instead regard root B♭ as internal to a dynamic circular trajectory whose continuation to E♭ is already under way by the end of measure 28, with the arrival of B♭’s minor seventh, A♭ [G♯]. (Phipps’s detailed harmonic reduction of measures 28 through 36 – his ex. 10 – omits that A♭.) Phipps’s ex. 10 (p. 560) is rich in information. I commend his interpretation of the hierarchical relationship between the chords of measures 29 and 30, and of measures 31 and 32. (He displays IV I successions in E♭ Minor and in C♯ Minor. Schenker, on the other hand, binds the A♭ chords of measures 29 and 33, thereby reversing the hierarchy that both Phipps and I propose.12) Though I go one step

further, interpreting Phipps’s G♯-to-D♯ motion as E♭[D♯]

, and though I

do not regard this brief flourish on E♭ as a tonicization, I acknowledge that, within the context of his perspective, the analysis is exemplary. That said, the interpretation of measure 29’s content as IV (in E♭ Minor) causes syntactic difficulties, since the preceding B♭ dominant chord would be

leading to an A♭ chord. This infelicitous succession is spirited away through Phipps’s insertion of a “silent interdominant” (p. 559), which he labels as I within parentheses in his ex. 10 (between the V and IV numerals). Though I am a vigorous advocate of imaginative analysis in general, in this context – in which the B♭ dominant’s seventh, A♭ [G♯], arrives at 284 and is then retained within the following measure – the tactic’s viability becomes doubtful. (As mentioned above, Phipps avoids that issue by omitting the A♭ from his example.) I propose instead a broader, hierarchically differentiated trajectory: from B♭ (the first chord in Phipps’s example) to E♭ [D♯] (the third chord) and then onward to A♭ [G♯] (the sixth chord). Chopin’s writing in measures 33 through 37 has elicited quite different responses from Schenker, from Phipps, and from me. Schenker inserts a parenthetical D♭ chord to resolve the surging A♭➔, and a parenthetical E♭ chord to resolve B♭➔.13 Phipps, on the other hand, inserts a parenthetical F chord (presumably surging) between A♭ and B♭ and a parenthetical G chord between B♭ and C in his ex. 10 to justify Chopin’s “deceptive resolutions of dominant harmony” (p. 559). I propose a more radical interpretation, in which only the third of these chords actually resolves: the tendency inherent in the surging A♭➔ chord is simply raised two notches, first to B♭➔ and then to C➔, in the double application of a seismic shift (a strategy introduced on page 133, above). By this means the progress of the broad progression (C to A♭➔) in measures 21 through 33 is retracted through the reinstatement of the tonic chord (now surging), so that IV becomes the principal intermediary between the perimeter I and V♮ harmonies, as it was also in measures 9 through 18.

The A2 section and coda (measures 49–84)

The A2 section and coda (measures 49–84) The recurrence of the A1 section’s opening part at the onset of A2 helps to define the form as binary. (See 4.3.) Indeed, Chopin might have proceeded in a parallel construction until the vicinity of the A2 cadence, where a PAC would replace A1’s HC. He instead chose to compose fresh material that in several ways expands upon constructions already set forth. The chord of measure 14 proves to be a source from which diverse continuations flow. It was of course no secret during Chopin’s formative years that diminished seventh chords are susceptible to multiple enharmonic interpretations. In its spelling as F♯-A-C-E♭ in measure 14, it serves as II➔, leading to V♮ in a local tonic-prolonging progression (displayed in 4.1). In its spelling as A-C-E♭-G♭, it would lead to a B♭ chord. Resolving the chord’s ninth G♭ (an incidental dissonance) to F, that is what Chopin accomplishes in measures 24 and 25, as explained above. At the outset of A2 the II➔ function of measure 14 is reprised in measure 54. That leaves one remaining opportunity for a novel resolution, which Chopin fulfills with aplomb. Though the chord of measure 64 is spelled like that in measure 54, it targets ♭II, and thus its “correct” spelling would be C-E♭-G♭-B (as shown in 4.3). The downward-resolving B displaces the chordal root A♭. Yet the D♭-F-A♭ resolution that might have occurred as early as 651 is postponed through a embellishment.14 At this point Chopin taps another of the structural notions he has been pursuing: the avoidance of a functional ♭II harmony. The embellishment of ♭II never achieves its expected resolution. Recall that the seismic shifts during measures 33 through 35 resulted in the juxtaposition of three chords with the same resolutional tendency in an ascending trajectory. Only the third of those chords resolves. Now three chords with the same resolutional tendency are juxtaposed in a descending trajectory, at the downbeats of measures 65, 67, and 69.15 Only the third of these chords resolves to the expected : E♭ descends to D at 701, whereas G descends to F at the end of measure 70. At this point yet another factor comes into play: having descended a third from the potential ♭II resolution to subtonic VII, Chopin now engages (as a collision, before the

has fallen into place) a subtonic-to-dominant shift. (Compare with the third model in FC, fig. 111a.) The remainder of the progression proceeds from this dominant in a conventional trajectory, one that includes (finally!) an uncontested ♭II.16 The cadential tonic at 771 is of major quality. It is followed by a coda that twice traverses the melodic third CC♯ descent to the tonic root in the bass normalizes the melody’s eccentric E>D♮>C♯; (2) the melody’s G♯>F♯>E third echoes the E>D♮>C♯ third and establishes a precedent for the prominent G♯>F♯>E span between 112 and 131; and (3) the mediant’s later emergence in measure 48 is adumbrated. The tonic pillar’s evocative calmness is enhanced by the cessation of melodic and harmonic activity in measure 10 (the final measure of the A1 section’s a1 half). Having just heard a V⇨ I succession in measures 5 and 6, listeners will understand that a tonic resolution has been deferred. The contorted dominant that lingers through measure 10 creates a singular antecedent effect. Closure is attained only with a2’s PAC in measure 18, concluding the initial presentation of A1.

Example 5.1 Analysis of Nocturne in C♯ Minor (op. 27/1), mm. 1–28. The a2 half of A1 (measures 11 through 18) is built from two phrases that relate to one another as a local antecedent–consequent pair, as graphed in 5.1. (That is, a local interruption occurs in measure 14, within the second half of the period delineated by the more basic interruption in measure 10. The dominant of 143–4 is interpreted as possessing an imagined diatonic D♯.) Note especially Chopin’s persistence in employing the F♯>D♮ third first stated in measures 4 and 5. The cadence in measure 18 completes the tonic pillar’s agenda. A written-out repeat of A1 (with variants) commences in measure 19. The listener’s sense of the nocturne’s formal shape will shift during the repeat. Whereas initially it appears that the nocturne opens with a regular tonic pillar of binary construction (in which Kopfton is introduced and then extended via a descending thirdprogression to the tonic root), the non-completion of its repetition – with the onset of the contrasting B section beginning at measure 29 – leads to the revised designation of the tonic pillar as irregular – that is, without closure on the tonic (likewise the case in many of the mazurkas that we explored in chapter 3). The agenda of measures 19 through 28 (including a two-measure extension at the end), which repeat a1, is not further pursued until measures 84 through 94 (including a two-measure preface and a one-measure internal expansion), which constitute the A2 section. In the meantime, the initial tonic and Kopfton are restored near the onset of the B section, whose exuberance starkly contrasts the languid repose of the outer A sections.

For me the A1 section’s mesmerizing effect stems in large part from the persistent traversal of descending third-progressions from Kopfton E. Comparison with Chopin’s Mazurka in A Minor (op. 7/2), measures 33 through 40, is instructive. Observe how an upward detour from the tonicized A Major tonic’s third C♯ to incomplete neighbor D precedes a descending motion through B to A four times within eight measures (graphed once in 2.15).5 The arpeggiation B>G♯>E transpires during the succession from

to

, during which the preceding

D neighbor is transferred to the tenor register for downward resolution in conjunction with the arrival of I. In the Nocturne in C♯ Minor, a similar upward detour from Kopfton E to incomplete neighbor F♯ (via chromatic passing note E♯ during the tonic’s surge, since the mode is minor) is followed by a D♮>B♯ arpeggiation during the succession from IV6♮ to a dominant configured as V⇨ rather than as V➔. Though the neighbor F♯ does not sound before the resolution during measures 5–6 or at the dominant of measures 9–10, it follows the mazurka’s precedent through transfer to the tenor register for the resolutions of measures 13–14 and 17–18. Salzer does not display a descent from the Kopfton during the first two of these four statements. Instead he focuses on an ascending third from E through F♯ to G♯. In his analysis of the third statement (see his fig. 5), an E>D♮>C♯ descent (against which F♯ resolves to E in the tenor register) coordinates with an EA>G third-progression. (This A undergoes a downward migration so that the third-progression’s G ends up sounding at the bottom of the texture, while the tonic root E, expected in the bass, sounds at the top of the texture. See the arrows in 6.6.)

Example 6.6 Analysis of Prelude in E Minor (op. 28/4), mm. 12|13–25.

Even without the fanfare of a surge comparable to that which transpired during 82, IV emerges as the principal connector between I and V♯ during A2. (Note how closely the melody that IV supports during 181 relates to that of 92.) The IV chord’s 6-phase F♯ (at the fourth eighth note of measure 18) serves as the starting point for a descending third to the leading tone (F♯>E>D♯) whose E gets “stuck” for two measures, making the arrival of D♯ at 202 all the more gratifying. (Compare with the repeated sounding of resolution pitch D♯ in the corresponding passage of A1 – measures 10 through 12.) Coordinating with that interior strand, the structural A (= ) thrice descends to F♯ (= ), again as in the earlier passage. In this case the truant never sounds (in contrast to A1, where a belated G is heard at 121), and thus the structural G (= ) is displayed within parentheses in 6.6. In both phrases the extension of the initial I-space coordinates with the filling-in of the tonic triad’s upper third (B>G♯ during measures 1 through 8 and B>G during measures 13 through 17). Consequently the filling-in of the dominant triad’s upper third (F♯>D♯ during measures 18–20 through 24) is especially appealing.32 Yet Chopin goes further. The initial phase of the dominant prolongation in measures 18 through 20 (like that in measures 10 through 12) engages, in the bass, the same BB neighboring motion that embellishes the melody in the phrases’ opening measures. Thus C’s recurrence in the bass at 211, supporting the passing note E within the dominant’s F♯>D♯ third, invokes several layers of association. One of tonal music’s more poignant embellishing chords, built from four pitches each a half step distant from one of the major dominant triad’s members, emerges over the course of measure 21: C-E-G-A♯[B♭]. Though the

augmented sixth

typically would resolve outwards to a octave, Chopin luxuriates in the chord, pursuing in two voices the same sort of descending chromatic motion as was utilized in three or four voices during both phrases’ opening measures: C>B>A♯ coordinating with A♯>A♮>G♯>G. (Brackets in 6.6 mark the locations of the two intervals that are filled in.) Consequently the augmented-sixth interval sounds as a diminished third ( Chopin as

, spelled by

, at the bottom of the texture at 231), resolving to a unison B in coordination

with the dominant root’s restoration at 241. E’s descent to D♯ completes the dominant’s prolongation, which is followed by the cadential tonic at the final downbeat. At the outset I suggested that “Chopin has reconstructed the [second] phrase’s interior to a greater extent than would have been necessary.” In assessing how Lerdahl interprets the second phrase in his fig. 3.19, it appears to me that he has reconstructed the second phrase’s interior to an even greater extent than has Chopin. Comparing my 6.5 and 6.6, note that the two phrases are of approximately the same length – twelve and thirteen measures. The dominant arrives in the tenth measure of the first phrase, whereas in the second it arrives somewhat abruptly in the sixth measure, after a curtailed subdominant. Chopin has emphasized the revving up – the presentation of the initial I-space – in the first phrase, while focusing more on the leave-taking – the expansion of the cadential dominant – in the second. Yet in both cases the harmonic progression proceeds from I through IV to V♯. Even with Chopin’s alterations in pacing, one can perceive a strong correlation between IV in measure 9 and in the first half of measure 18, and between V♯ in measures 10 through 12 and in the second half of measure 18 through measure 20. Granted, the bass B at 171 is a conspicuous note: low, loud, and metrically strong. Yet I propose that Chopin has applied those markers to convert a chord that earlier (measure 6) played no harmonic role into a functional dominant within a middleground progression that expands the phrase’s initial Ispace, before the continuation to IV and then V♯. Lerdahl instead hears the onset of the dominant function at 171 as extending for eight full measures, though indeed he proposes that not all of the dominant’s pitches are in place until the second half of measure 20. (Note the B–F♯ diagonal line spanning those measures in his PR c– d.) Consequently the seeming correlation between his regional prolongational analysis in fig. 3.21b, which displays the noteheads E, A, B, and E, and my I IV V♯ I harmonic analysis in 6.6 is incidental: his A and B correspond to measures 14 and 16, respectively, whereas my IV and V♯ both reside in measure 18. In addition, though I concur with his placement of the first phrase’s soprano pitch G at the downbeat of measure 12 in PR c–d, placing the second phrase’s G in measure 17, thereby neglecting the A of the thrice-stated A>F♯ third (corresponding to an A that was significant to the analysis in the first phrase),

seems inconsistent. In my imaginative approach to analysis, A>F♯ may stand for A>G>F♯ whether (measure 12) or not (measure 20) a G actually sounds within the composition at that point. In his reading a sounding G in the “wrong” location trumps the parallelism between the two phrases (based on the similarity of context). Finally, two small points: (1) both phrases begin with an upbeat BD fourth that transpires at the top of the texture. That chromatic line causes the subdominant that comes between I and V♯ to be presented as a major chord (with E♮ rather than diatonic E♭ at 62 and 72). A concurrent interior line also takes on a maximally chromatic aspect: D♭ occurs during 61, resulting in a potent I⇨ surge towards IV♮. Though IV8–7 might have directed the Urlinie downwards from C to B♭, so that A (the antecedent phrase’s goal ) could arrive in conjunction with the onset of V♯, in this case C extends into the dominant’s domain, with the descent through B♭ to A occurring during 82. In the context of a small-scale A1 A2 binary form, the antecedent phrase’s descent from to

is interpreted as a background line, interrupted before the

final . Consequently 7.1 displays four open noteheads with upward stems connected to a beam. (Note the upward transfer of Kopfton D just after it is established. The lower register will be reinstated later.)

Example 7.1 Analysis of Prelude in G Minor (op. 28/22), mm. 0|1–8. The instability of the pitch B♭ at 82 (in a dominant context) is an important factor in deciding how to interpret the pitches that precede measure 1. Rather than displaying A as a passing note between tonic pitches B♭ and G, 7.1 proposes (through what it includes and what it omits) that the listener (aided by the discerning performer’s shaping of the line) instead should interpret the initial B♭ as an appoggiatura embellishment of A, followed by G>F♯ (below E♭>D).4 The resulting F♯-A-C-D chord, which targets the initial tonic, is prolonged until 42, in the process evolving into the more dissonant state F♯-A-C-E♭. I applaud a perception displayed within Hood’s Graph 2G: a stepwise descent at the top of the lower staff during measures 5 through 8 (D>C>B♭>A). Though I would advise beginning the slur that binds these notes with the prior D of measure 4 (thereby capturing the not-yet-evolved tonic support that inaugurates the I-to-V♯ progression), this line – in the register that both Hood and I acknowledge to be the melody’s principal domain – should be a primary focus of the listener’s attention. Its halting on A (one step shy of the key’s tonic pitch) is a prime motivating factor for the impending onset of what one initially should expect will be a normative eight-measure consequent phrase, the second half of a parallel period. What Hood makes of her perception cannot be discerned from her graphs 2G and 2H, for two reasons: (1) though 2H contains abundant Roman numerals over most of its substantial length, this passage curiously appears without a harmonic analysis; and (2) though slurs within 2G bind elements within the passage together,

there is no visual indication of how these measures connect to what precedes and follows them. Both quandaries are clarified by looking elsewhere – at graph 1E or 1F for a sense of the local harmonic progression, and at graph 1D for Hood’s interpretation of A as neighbor to the tonic third. Hood and I are at opposite poles regarding both the extent and structural depth of the phrase’s goal dominant chord. For me, it arrives at 81 and functions as the prelude’s background V♯, supporting the Urlinie’s pre-interruption

(as

shown in 7.1); for her, its emergence occurs instead at 52, and its foreground role apparently allows a Roman numeral (V in her style of analysis) to be omitted, even in a graph (1G or 2H) in which dozens of other numerals are included. To clarify my reading of Chopin’s harmonic conception, for a moment assume that measure 5 does not exist. The preceding chord (B♭-D-G) and the following chord (B♮-D♭-F-A♭) are, in my view, the same harmony, first in its diatonic state and then in a highly evolved state. Such an evolution of the tonic generally comes about as the succession to IV (here represented by IV♮ during 62) draws near. Though in this case that evolution is extreme – I⇨ rather than I➔ – the transfer of root from G to C at 62 nevertheless shines through. Now reinstating measure 5, we come to understand that the tonic is prolonged via a conventional local progression (not fully displayed in 7.1) whose concluding tonic happens to be highly evolved: I II⇨ V♯ I⇨. The fifth-relationship between II and V♯ transpires with exactly the same ⇨ evolution as that between the terminal I and the IV♮ that follows.5 Taking into account this more developed harmonic conception, the fact that the phrase fills eight measures within an opus that includes several preludes of around sixteen measures in length, and a realization that the next phrase (to be discussed in detail below) begins exactly as would a consequent phrase within a parallel period, I propose that the dominant arrival in measure 8 and the to which the melody descends conform to the normative closure of A1 within an A1 A2 binary form. If the music that one is analyzing seems ambiguous, it is important to compare the passage in question with other passage(s) within the same movement that the composer may have fleshed out more fully.6 In this case the logical

comparison is between measures 0 (for which supportive harmony is absent) and 8. Hood’s and my graphs both convey that the G and B♭ in the middle of measure 8 do not correspond to a tonic resolution of the preceding dominant. (Though Hood displays the G as a passing note between F♯ and A in her graph 2G and I display it as a neighboring note between two F♯s in 7.1, neither conception projects G as an asserted tonic root.) Hood reverses that hierarchy in her reading of measure 0, where A appears as a passing note within a slurred B♭>G third. (“The first appearance of this figure unmistakably outlines tonic harmony” (paragraph 17, emphasis added).) She indeed replicates this tonic in measures 8|9, starting with upbeat bass G.7 Though I am strongly supportive of imaginative thinking as a component of analysis, my internal ear prolongs the right-hand notes E♭, A, C, and E♭ through the rests of measures 8 and 9, with (importantly) the conclusion of a chromatic descending fourth that began with the high G of measures (4)|5 achieved with the arrival of D at 92. Bass G at 91 connects the A and F♯ of that prolonged chord. For me, an imagined tonic chord (unmistakably!) does not emerge above that G. Transferring this reading of measures 8–9 to measures 0–1, B♭, G, and E♭ would be interpreted as appoggiaturas to members of the opening F♯-A-C-D sonority. I likewise suggest that no tonic chord occurs in measure 2, where E♭ sounds throughout and where I imagine C continuing after its eighth-note sounding as well. The chord is G-B♭-C-E♭, rather than the tonic Hood proposes. As 7.1 shows, the chord of measure 2 may be interpreted as a connector between two different inversions of the embellishing chord that precedes the initial tonic. (In the context of the consequent phrase that begins in measures 8|9, this embellishing chord takes on the role of extending the dominant harmony of measure 8.) Chopin later provides strong support for this reading. Near the end of the prelude the G-B♭-CE♭ chord is repeated during each measure from 36 through 38. Then, magnificently, in measure 39 it evolves further, with a chromatic shift from C to C♯ coinciding with the concurrent sounding of all four pitch classes in one of the prelude’s boldest chords. This embellishment of the dominant possesses a ⇨ quality. Recall my assertion that the chord at 61 serves as I⇨. Comparing those two chords, one notes their obvious dissimilarity. Consequently, I cannot endorse the notion that a tonic chord occurs in measure 2. The tonic’s first sounding occurs

in measure 4, supporting Kopfton in the melody. A conventional descent from to ensues, in coordination with a harmonic progression from I through IV♮ to V♯.

The A2 section that Chopin might have composed

The A2 section that Chopin might have composed (measures 8|9–(16)) Not all of a work’s notes are of equal importance. I propose that the doubled A♭ at the end of measure 15 is an extraordinary note with far-reaching consequences. That measure’s slur connecting the bass melody’s E♭, C, and A♮ (also incorporating passing note B♭) and the right-hand chord that sounds immediately thereafter – which listeners as yet have no reason to regard as anything other than F♯-C-E♭ – bring to mind the content of 81: a dominant harmony (successor of the subdominant), which in the consequent phrase is positioned a tad earlier to make room for the tonic during the phrase’s final measure (which we suspect will be measure 16, thereby complementing the eight-measure antecedent). This is a conventional compositional strategy that Chopin ultimately does not realize. A hypothetical conclusion to A2 that fulfills the promise of what precedes the fateful A♭ (resulting in a prelude of sixteen measures) is displayed in 7.2. Postponing a consideration of that A♭’s consequences until the next section of this chapter, let’s explore (with the help of 7.3) the normative eight-measure version of A2 that Chopin might have composed.

Example 7.2 Alternative version of Prelude in G Minor (op. 28/22), measures 15 and 16.

Example 7.3 Analysis of Prelude in G Minor (op. 28/22), mm. 8|9–16 (incorporating 7.2). The chief difference between the two phrases (prior to the cadence) concerns how the tonic, once attained, is prolonged. (Compare measures 4–6 and 12–14.) Both versions are highly chromatic, yet they pursue different strategies, resulting in contrasting evolutions of the tonic (both of which target IV): first I⇨ (B♮-D♭-F-A♭ at 61), then I➔ (B♮-D-F-G at 142). The cadence supplied in 7.2 borrows material from Chopin’s cadence in measures 40 and 41, while completing the descending background line left dangling after

in

measures 8 and 9. The at the downbeat of hypothetical measure 16 (reminiscent of 82) “belongs” at the end of measure 15, where it appears in 7.3. Any notion of a parallel relationship between the phrases of measures 1–8 and 9– (16) would be difficult to develop in the context of Hood’s erratic application of Roman numerals: whereas no IV numeral appears below the subdominant of measures 6 and 7 in any of her graphs, a iv appears below the minor subdominant of 151 in her graph 2H (though not in graph 1F or 1G, which also incorporate Roman numerals). Explanations for how Chopin proceeds from I to IV might indeed take several courses. Yet before proceeding to that investigation, I suggest that some revision in the hierarchical relationships among pitches that Hood displays is in order. Graph 1F shows a bass descent from E♭ through D♭ to C in

measures 13 through 15. To my ears the line possesses a more uniformly chromatic character, with the final note of each beat within measures 13 and 14 serving as the principal note, in coordination with the likewise chromatic soprano, as follows: B♭

A

A♭

G

E♭ > D

D > C♯

D♭ > C

C > B♮

Two intervals of the tonic triad (whose third shifts from B♭ to B♮ over the course of the passage) are traversed: B♭ to G, and D to B♮. An interpretation of the chordal progression would need to accommodate the following:

g

A➔

f

G➔

One might regard these chords as the first two cycles of an obstinate sequence whose next chord, e♭, fails to emerge owing to the interaction between the g and G➔ chords, resulting in a succession instead to c, as follows:

G Minor:

I (

)

I➔

IV

Or, one might regard f as a chromatic upper-third substitution for D in a tonicprolonging

I

II➔

I➔

tonic expansion. The f enhances the “dominant-emulating” quality of the G➔ chord by being “pre-dominant emulating,” so that measures 14 and 15 take on the aspect of

IV

V7

I

in what some would interpret as a brief tonicization of the C Minor subdominant. None of these notions coordinate with Hood’s hierarchical interpretation of the bass, from which the Roman numeral analysis in her graph 2H is derived. After twelve measures of music during which only one Roman numeral has been applied, suddenly two measures are annotated by eight numerals (some surrounded by parentheses or single quotation marks) in the context of three keys. Though these numerals are correct insofar as they indicate root and quality for a range of stacked-third chords, they do not succeed in conveying what I regard to be the measures’ essential feature: the evolution of the meek diatonic minor tonic (which Hood displays as i within parentheses and as

of V within single quotes,

thereby diminishing its hierarchical importance) into a surging, iv-targeting I➔ (which she labels as

of iv without discernible connection to the preceding

minor tonic). Finally, whereas my perception of how what has occurred thus far conforms to the conventions of a parallel period guides my ears to expect that after the IV of 151, V♯ will follow (in accord with the prior succession from IV♮ to V♯ during measures 7 and 8), Hood’s analysis is silent concerning measure 15’s F♯[G♭]-A-C-E♭ chord (exactly the same evolved state as in measure 8, though in a different inversion). That brings us to the fateful moment of bass A♭’s arrival (triggering F♯’s enharmonic shift to a G♭ role, in accord with Chopin’s spelling), which both prevents closure in measure 16 and directs the progression on a more expansive course, to be explored below.

Chopin’s expanded A2 section (measures 8|9–41)

Chopin’s expanded A2 section (measures 8|9–41) Two common continuations from IV are available within Chopin’s tonal syntax. Perhaps the dominant will follow directly; or perhaps the path to the dominant will be expanded through a 5–6 shift applied to the subdominant. In G Minor, subdominant C-E♭-G’s 6phase chord might emerge as diatonic C-E♭-A; or, a more colorful “Neapolitan” variant (C-E♭-A♭) might sound instead. Chopin chose this latter alternative (as displayed in 7.4), going so far as to briefly tonicize A♭ Major. (The initial statement of the A♭ chord in measures 15 and 16 is already surging as I➔ towards IV within the tonicizing progression in A♭ Major, as is conveyed by the parentheses around 8 to the right of “A♭ Major: I” in 7.4.)

Example 7.4 Analysis of Prelude in G Minor (op. 28/22), mm. 8|9–41 The two continuations from G Minor’s IV under consideration – dominant D-F♯-A and lowered supertonic A♭-C-E♭ – are antipodally related (that is, their roots are separated by a diminished fifth or augmented fourth). This is an ideal context for the mehrdeutig deployment of a diminished seventh chord.8 The four pitch classes on the fourth and fifth eighth notes of measure 15 might have been spelled either as F♯-A-C-E♭ (an evolved state of G Minor’s V♯ chord, which Chopin could have confirmed by resolving ninth E♭ to D, as occurs in 7.2) or as C-E♭-G♭-B (an evolved stated of a ♭II chord surging within its

own tonicization, which Chopin does confirm by resolving ninth B [A] to A♭ at the end of measure 15 and by undertaking a chromatically filled-in voice exchange – – over the bar line between measures 15 and 16). As 7.2 and 7.3 demonstrate, the first interpretation would lead to a PAC in G Minor at the normative point, the phrase’s eighth measure. In contrast, 7.4, which corresponds to what Chopin actually composed, shows how the ♭II alternative results in a longer route to the PAC. Once a cadence during the phrase’s eighth measure is decisively rejected, Chopin seems in no hurry to reach his goal: the phrase expands from the normative eight to an astonishing thirty-three measures by means of the already mentioned tonicization as well as several internal repetitions and expansions, acknowledged by 7.4’s grid of measure numbers and by a hairpin symbol. The more developed harmonization stems in part from Chopin’s decision to replace the single-arpeggiation bass (G–D) of A1 with a double-arpeggiation bass (G–D–G–D–G) during A2. Whereas the “Neapolitan” version of IV6 proceeds to V7 and then I to support the span from through

to during the opening segment of A2, the path from to

proceeds by way of incomplete upper neighbor C, which is presented in the soprano register during measure 24, supported by the supertonic harmony. After a repetition of this portion of the structure, the A (= ) is transferred downwards, not to the register in which the descent to

transpired during A1, but instead (in the middle of measure 34) to the

register of the initial sounding of Kopfton D a seventh below Middle C (in measure 4). From that low A, prolonged through measure 40 via embellishing chords (including the potent C♯-E♭-G-B♭ of measure 39, mentioned above), the background line’s concluding G emerges by stepwise descent, supported by the PAC tonic. Doublings of G an octave and two octaves higher bring closure concurrently in all of the registers in which portions of the fundamental line have sounded during the prelude. Hood’s graph 1F contains a remarkable analysis that highlights our widely divergent views of the work’s harmonic dimension. She deploys only three analytical symbols to provide the basic harmonic sense of measures 9 through 22: i N i. (In her work, N stands for Neapolitan; the latter i is followed by an Arabic 6 to

convey that the tonic chord appears in its first inversion.) Though my 7.4 incorporates equivalent symbols – I ♭II I – my contextualization of the Neapolitan chord contrasts Hood’s in important ways. Note first that our difference of opinion regarding the arrival point of the phrase’s initial tonic chord emerges once more: Hood places the tonic in measure 9, whereas I place it in measure 12. Yet we agree that, one way or another, the phrase establishes the G Minor tonic before the Neapolitan arrives. Though I acknowledge that ♭II is tonicized, I nevertheless regard it as the asserted 6 phase of a hierarchically deeper chord – namely, IV, whose attainment is emphasized through the transformation of the minor tonic into a surging I➔. In Hood’s Graph 1F this IV chord lacks a label (as is also the case in the more detailed Graph 1G, though in Graph 2H a iv appears among the twenty symbols – numerals, N, and +6 – that annotate this fourteen-measure passage). Likewise, in my view a harmony that is hierarchically deeper than ♭II precedes the tonic resolution – namely,

. (The three bass noteheads for this passage

connected to a beam in 7.4 are G, D, and G.) Hood displays evidence of some sympathy for that view in her graph 1B (though, again, no V label appears). I am not in a position to decide whether the competing hierarchies displayed in 1B and 1F amount to an assertion that the Neapolitan imposes a shift in the relationship among these various chords (in accord with the “ambiguity” theme of Hood’s article); or whether, instead, the annotation of the latter graph with harmonic symbols is in need of repair. I also note a significant discrepancy between the presence of Roman numeral i at measures 34–35 in graphs 1A through G and its absence in graph 2H.9 Again, is this an inadvertent omission; or is Hood intending to juxtapose two quite different readings of the closing measures, fostering the notion of ambiguity? (Though neither version matches what I display in 7.4, graph 2H is far closer to my view. However, I suspect that Hood would quickly add V and i numerals, to conform with the other graphs, if the discrepancy were brought to her attention.)10 Though other issues could be addressed (for example, Hood’s +6 label, in the context of C Minor, for what I interpret as the initial statement of the ♭II chord at the end of measure 15), by now it is clear that there is little common ground between our interpretations, despite our use of similar analytical strategies.

Readers may wish to extend the comparison of our perspectives beyond this single brief prelude, placing Hood’s recent monograph alongside mine for a double dose of invigorating Chopin study.

8

Prelude in C♯ Minor (op. 45) ◈ in response to Jean-Jacques Eigeldinger and to Charles J. Smith Jean-Jacques Eigeldinger’s lifelong dedication to Chopin has enriched the musician’s library with important books, articles, and scores. He edited all of the preludes (both op. 28 and op. 45) for the recent Peters Urtext edition and has displayed his musicological acumen in a wide-ranging article on the Prelude in C♯ Minor, op. 45.1 Though devoted in large part to contemplations regarding Chopin’s interactions with Delacroix’s views on painting and his indebtedness to Beethoven, that essay offers a sophisticated analytical study of the prelude as well. (Eigeldinger acknowledges the contribution of Georges Starobinski in its formulation.) Another noteworthy analysis of that work, by Charles J. Smith, has appeared in a volume of essays, intended for students, by a range of luminaries in the field of analysis, edited by Deborah Stein.2 In that Smith has held a special interest in both Chopin and in harmonic analysis throughout his career, the opportunity to explore his reading of the prelude here is especially welcome.

The Prelude in C♯ Minor’s introduction (measures 1–5) The opening measures of the Prelude in C♯ Minor only gradually come into focus as an establishment of the C♯ tonic, confirmed by the potent G♯>C♯ bass succession over the bar line between measures 4 and 5, supporting a PAC in that key. Parallel progressions of chords were featured often in Baroque thoroughbass treatises.3 Yet once harmonic thinking began to emerge as a central component of musical speculation, their analytical treatment turned out to be especially problematic.4 Though certainly one could concoct a Roman numeral label for each chord within Chopin’s progression, in my view that exercise would be pointless, since many of the internal chords do not fulfill the roles that they would in harmonically asserted contexts. (Though the labels I VII VI V IV III II, for example, may succeed in indicating where within tonal space the various chords of a parallel progression reside, they do so at the expense of syntactic sense. Any harmonic system that can blithely accommodate VII proceeding to VI, or IV to III, is so watered down as to be of no value.) I propose instead that Chopin pursues a focused and nuanced downward linear initiative for three measures, broken off (at 41) just before the phrase’s concluding V➔ I cadence, where the logical next chord within the pattern – E♯-G♯-C♯ (displayed conjecturally in 8.1a) – is replaced by E♮-G♯-C♯ (which here functions as a cadential whose bass G♯ is tardy), embellished by a suspension (quarter note A) and retained for half a measure to help break the momentum of the descending progression. Chopin’s writing divides the preceding descending seventh (which in retrospect will be interpreted as a broad connection between I and ♮II) into three thirds. Note how the A and f♯ chords become nodal points through the insertion of downbeat neighboring chords, thereby expanding the domain of each within the stepwise descent from one to three quarter notes. Consequently the model in 8.1a displays three levels of activity: the foundational c♯ to D♮ (traversing a descending seventh that projects I to ♮II), the segmentation of that seventh into three thirds (with internal nodal points at A and f♯), and local passing chords that connect nodal points and neighboring chords that prolong the two internal nodal points.

Example 8.1 Prelude in C♯ Minor (op. 45) (a) Analysis of mm. 1–3; (b) Analysis of mm. 1–5. In that music analysts for good reason have come to regard the ♮II (“Neapolitan”) chord as a normal occurrence within minor-key contexts, some care in assessing how it comes about here is in order. (This assessment will prove to be crucial for our understanding of a later passage from the prelude.) I propose that Chopin is proceeding in this descending path not according to diatonic precepts (even if A and f♯ coincide with diatonic chords within C♯ Minor), but instead in an obstinate manner. As such, he is not bound by the dictates imposed by the C♯ Minor key signature, which favors seven specific pitch classes. When thinking outside the diatonic realm, the numbers from 0 to 11 (with C = 0) offer a neutral means of displaying pitch interactions, in a modulo 12 framework free from the hierarchical differentiations imposed by key-based (modulo 7) thinking. Chopin’s descending triads thus may be represented as follows:

8 4 —————

4

1 —————

1 —————

1

9 —————

9 —————

9

6 —————

6 2

m

M

m

M

Note especially that each chord’s third and fifth hold over from the preceding chord, and that the chordal qualities alternate between minor (m) and major (M). Once the descending trajectory has run its course (as determined by the composer), the endpoint is thrust back into the context of diatonic tonal space, which must somehow make sense of it according to the conventional relationships within the key. Though in this case the chord that is thrust back is not diatonic, it happens to coincide with the common “Neapolitan” variant of the supertonic. The graph displayed in 8.1b thus interprets chromatic D♮ as a frequently encountered and therefore unremarkable wobbly note resulting in ♮II, with diatonic pitch D♯ restored (as it almost always is) during the dominant harmony that follows. Minor-key tonality ultimately prevails: D♮ is subservient to D♯, and the major dominant is the principal structural event between the perimeter tonic harmonies, as indicated by the beamed bass notes, C♯–G♯–C♯ (Schenker’s “sacred triangle”). The graph displays one unusual feature: because the soprano melody’s descending seventh during the parallel progression places the endpoint chords in contrasting registers, a foundational linear connection emerges between the first chord’s lowest sounding pitch, E (which I propose serves as the Kopfton), and the ♮II chord’s highest pitch, D♮, which proceeds via the D♯ wobble correction to tonic C♯, completing a third-progression. After the cadence, the Kopfton is reinforced (indeed, in this unusual context it needs some reinforcement) through the bass melody’s projection of an apex E in three successive registers – at the middle and end of measure 5 and the end of measure 6, and then repeated. Eigeldinger interprets Chopin’s opening melody not as a descending seventh followed by cadential gestures, as I do, but instead extends a bit further, to a

descending octave, split into two tetrachords: C♯–G♯ and F♯–C♯ (p. 246). To support his tetrachord interpretation, he directs readers to measures 80 and 81, where those tetrachords (plural) allegedly recur (note 29).5 Exploring the latter assertion first will provide some useful perspective for an assessment of the former. The G♯-C♯-E-G♯ chord that boldly brings the cadenza to an end at 801 would lead listeners to expect a specific continuation: the dominant’s root G♯ will be retained while the three remaining pitches of

will sooner or later fall into

place (or will be imagined to fall into place if not literally stated). Nothing through measure 82 hints at any progress in achieving that result. Instead, the dominant’s third (B♯), imagined fifth (D♯), and seventh (F♯) emerge concurrently at 831. Between measures 80 and 83 Chopin presents a descending arpeggiation touching upon all of the cadential chord’s members: G♯>E>C♯>G♯. During this arpeggiation he incorporates at each nodal point exactly the same sort of embellishment as was deployed at the two internal nodal points during the introduction: half-step lower neighbors. The following stages convey my conception of how Chopin constructed this intriguing melody: G♯

E

C♯

G♯

G♯>F D♯B♯D♮ E♯

The persistence of third-relationships during the main section of the prelude further supports this reading.6 Eigeldinger has put his finger on an important point by suggesting that the introduction wavers between C♯ Minor and A Major (p. 246). He directs our attention especially to the pitch D♮, which differentiates A Major’s diatonic pitch collection from that of C♯ Minor. As an experiment, perform the introduction as written until 42, substituting D♮ for D♯ at that point. You will discover that the following B♯ will want to shift to diatonic B♮ and that the low bass note E (instead of G♯) will sound right. Letting those notes proceed according to their inclinations, one ends up cadencing on A at 51. Indeed, the introduction’s nodal c♯, A, f♯, and D♮ chords are all diatonic in A Major, and if Chopin had in fact proceeded as in our experiment, one likely would regard the initiating c♯ chord as tonic A’s upperthird chord. The descent would in that case be interpreted as a filling in of the A>D♮ fifth, corresponding to I ( ) IV. It is only through the strength of Chopin’s cadence that an analyst may, instead, retrospectively assign the initiating c♯ chord – despite its brevity and weak metrical placement – the structural role of initiating

tonic. As stated at the outset, “the opening measures of the Prelude in C♯ Minor only gradually come into focus as an establishment of the C♯ tonic.” Smith’s analysis takes the unusual tack of comparing Chopin’s composition to the narrative trajectory of a thriller movie, proposing that just as the film audience tries to resolve the various plot entanglements and figure out who the culprit is, so also auditors of Chopin’s prelude will ponder it as a puzzle that needs to be resolved. I don’t buy it. As Smith suggests, sometimes the key to resolution is “hidden in plain sight” (p. 240). In this case the introduction is that key.7 If one does not suitably come to terms with its nuances before proceeding to the main body of the work, the complications that arise likely will be perplexing. I do not think that Chopin intended to obfuscate what he was doing: the introduction pursues a straightforward course in a direct and uncluttered presentation. Nevertheless, Smith (following Eigeldinger’s lead) proceeds to segment the melody into tetrachords rather than trichords, and consequently his reading of the passage does not sufficiently correlate with the contour of the work’s main section (to be explored below) for him to recognize the latter as a gargantuan variant of the former. Smith’s annotated score 20.1 (p. 243) contains a curious – and telling – use of curved arrows. During the first four chords, the initial c♯ is the target of an arrow that curves leftwards from the fourth chord; whereas during the fifth through eighth chords the initial A is the target of no arrow, while the eighth chord’s arrow curves to the right, targeting the ninth chord. Compare that inconsistent reading with 8.1a, where the fourth and eighth chords perform equivalent roles as expanders of the nodal points that immediately precede them. Though Smith yearns for a D♮ chord in measure 4 (a chord that is crucial to his plot denouement later in the work), I contend that such a D♮ chord is a conspicuous part of the prelude’s fabric at the end of measure 3.8 The plot thus may be summarized as follows: after the initial tonic, a descent in thirds through A and f♯ proceeds as far as D♮, which (following the conventions of the “Neapolitan” chord’s usage) leads to a V➔ I cadence. As we shall see, the main section of the work at first pursues the same trajectory, reiterating the introduction’s c♯, A, f♯, and D♮ nodal points (measures 6|7 through 18) and thus giving auditors a second chance at

comprehending this essential component of the plot, after which multiple wobbly notes transform the second through fourth chords, so that ultimately D♯ (II➔) rather than D♮ (♮II) precedes the main section’s V➔ I cadence in measures 66 and 67 (which, as we shall see, Smith relegates to the status of a retransition). Smith gives considerable weight to chords that he regards as tonicized. In his fig. 20.5 (p. 248) he shows a triangular relationship among the introduction’s c♯, A, and tonicized f♯ (to which D is appended off to the side). An arrow points directly from f♯ back to c♯. My 8.1b accounts for all of those chords (with a contrasting reading of their hierarchical relationships) and notably includes one that is absent from Smith’s account: the G♯ dominant, a member of the introduction’s foundational sacred triangle, C♯–G♯–C♯.9

The Prelude in C♯ Minor’s main section

The Prelude in C♯ Minor’s main section (measures 5–67) During the prelude’s introduction a brief though dense linear passage connects I (measure 1) and ♮II (measure 3) prior to the V➔ I cadence. Chopin’s construction of the prelude’s main section pursues a similarly modest agenda, now astonishingly expanded: between the I of measures 5 through 8 and the II➔ of measure 65, Chopin passes back and forth among the nodal points established during the introduction, even as they undergo chromatic mutation. (See 8.2.) The extraordinary size of this connective passage stems not only from the fact that Chopin now pursues a roundabout course, with multiple ups and downs along the descending-seventh trajectory, but also from the substitution of multiplechord progressions for the individual chords that connect or expand nodal points during the introduction. For example, a connective b chord comes between the c♯ and A nodal points during measure 1. In descending from c♯ to A during measure 7 through measure 13 that b chord indeed recurs (measure 11), though now it resides within a segment of the descending circle of fifths: c♯ F♯➔ B/b E➔ A. The G♮ connective chord that passes between A and f♯ during the introduction is replaced by a more dynamic C♯➔ during 141. (Note that its context retains the sense of stepwise descent between soprano pitches A and F♯, now incorporating diatonic G♯, along with a lower sixth in the alto register.) Though the D♮ chord emerges directly after f♯, its prolongation during measures 15 through 18 incorporates vestiges of the G♯-B-E connective chord of measure 3: the E at the end of measure 15 passes between the melody’s F♯ and D♮, whereas the embellishes

of measure 17

. Likely a shorter composition would have resulted if this D♮ chord

(asserted as ♮II) had proceeded to dominant G♯, as was the case during the introduction. Chopin instead backtracks to f♯ in measure 19 – creating some distance from the chord that during the introduction resided at the juncture of the linear initiative and the concluding harmonic initiative. The prolongation of this chord, including a modal shift to F♯ at measure 31 and a mutation to F♮ at measure 55, is one of the principal features of the main section, followed by the definitive descent to D♯➔ at measure 65. (One may trace the progress of the f♯ chord’s evolution in 8.2, noting especially how f♯, F♯, or F♮ resides at the internal phrase boundaries, indicated by the bar lines.) One might even regard all the

material between the f♯ of measure 19 and the F♯ of measure 64 as a parenthetical passage.

Example 8.2 Analysis of Prelude in C♯ Minor (op. 45), mm. 5–67. At first it seems that the prolongation might be of brief duration, since the new phrase that begins at measures 20|21 inaugurates, starting on f♯, the same circular progression that earlier led from c♯ to A. Listeners are poised for a D♮ arrival at 271. Chopin indeed is prepared to confirm that D♮ with a five-measure tonicizing expansion deploying a local I– IV–V–I harmonic progression (compensating for the absence of even an embellishingchord expansion at the D♮ nodal point during the introduction). This progression does in fact transpire, though down a third, since B♭ unexpectedly displaces the D♮ goal at 271. Its cadence measure (31) offers yet another surprise: a further drop – now from B♭ to G♭ – occurs. This G♭ is confirmed via a similar five-measure expansion (transposed), which cadences successfully in measure 35. It may appear that Chopin has managed to move from a sharp key (F♯ Minor) to a very flat key (G♭ Major). Yet ultimately G♭ will be accepted as F♯, even if the notation in flats persists for some time in the score. This is a thorny and controversial issue. In my view, the passage’s obstinate chord progression should be interpreted outside the realm of diatonic tonality. In a modulo 12 context (already called into service during our discussion of the introduction’s obstinate progression), the following grid aptly represents the “descending in thirds” progression: 1

9 —————

9

6 —————

6

5

2 —————

2

1

10 —————

10 6

m

M

M

M

In a modulo 12 context an octave may be traversed (here as 6>2>10>6) with no enharmonic seam. Whereas the introduction’s obstinate progression alternates between minor and major chords each of which shares two pitches with its predecessor, here a midcourse shift in the relationship between adjacent chords results in the juxtaposition of three major triads (starting with the elided 2-6-9 of measure 27), connected by only one common tone. Once that modulo 12 progression concludes, the goal chord is thrust back into the diatonic context. In this case accommodation is easy: the progression has come full circle, from a minor to a major chord rooted on F♯. The emergence of the enharmonic G♭ spelling comes about through the use of modulo 7 notation (wherein three “major thirds” span an augmented seventh) to convey a modulo 12 conception. The trajectory proceeds upwards from F♯ at the onset of the next phrase, which begins at measures 36|37. (This discussion will be presented in terms of sharps, corresponding to my 8.2, not the flats of Chopin’s score.) Whereas each of the section’s first two phrases was inaugurated with the traversal of a descending major third, navigated via a segment of the circle of fifths (c♯ to A in the first, and f♯ to (D♮) in the second), now an obstinate ascending 5–6 sequence is set in motion to chug upwards a major third (F♯ to A♯), with D♯➔ (F♯’s chromaticized 6-phase chord) in measure 39 targeting the passing chord G♯ (measure 42) and E♯➔ (G♯’s chromaticized 6-phase chord) in measure 47 targeting goal A♯. Yet A♯ is not one of the nodal points introduced during the introduction, and so Chopin revises course mid-sequence by shifting E♯➔ down a half step to E➔ (measure 53), thereby targeting nodal A. Yet, just as the goal chord of measure 27 is elided and displaced by a chord a major third lower, so also is this A goal (measure 55) elided and displaced by F♮. Thus we have ended up “in the cracks” (outside the

confines of the initially established nodal points) after all. This wayward F♮ nevertheless is treated to the same sort of chordal expansion as was the F♯ arrival of measure 31. We now seem even further from tonal resolution than was the case at that point. The section’s final phrase sets things aright and achieves the long-awaited goal with surprising alacrity. First the usurping F♮ chord is simply hoisted up a half step to the legitimate nodal F♯ (measure 64), the oddity of the voice leading (three simultaneous wobbly-note resolutions!) mitigated by the concurrent sounding of a descending passing note (E) in the bass. F♯’s major quality (acquired in measure 31) is not relinquished. The presence of pitch A♯ as third of the F♯ chord leads to the substitution of II➔ for the introduction’s ♮II as the progression continues downwards its final third. Of course, either incarnation of the supertonic may serve as the predecessor of V♯. That dominant (measure 66) in turn targets the tonic goal (measure 67), bringing to a close the extraordinary twelvefold expansion of an idea that during the introduction transpired in just five measures. It is understandable that Chopin elected to present a large chunk of this sharp-key composition using flats. He has thereby spared performers (including many amateurs) from having to read numerous frightfully spelled chords, such as the E♯➔ chord (with suspended ninth) at 491, whose appropriate spelling would be E♯-B♯-F -G -B♯. Granted, an enharmonic shift is required at some point in order for the section to end where it started – in C♯ Minor, rather than D♭ Minor. The logical spot for that shift within one’s analysis would be during the modulo 12 equal subdivision of the octave (measures 21 through 31): from f♯ to F♯, rather than f♯ to G♭. In his ex. 2 (p. 247) Eigeldinger instead copies Chopin’s flat notation at that point. Sharps are restored at measure 51’s E-A-C♯ chord. Undertaking a cosmetic (and therefore distracting and potentially misleading) enharmonic shift while concurrently charting chordal associations in an analysis is exceedingly dangerous. Consequently my analytical diagrams generally do not follow composers when they employ spellings of convenience. (Theory-savvy readers of technical analyses should be able to handle a few double-sharps!) Given that chords related by a third have been a pervasive feature of the entire composition, it is reasonable that Chopin pursues an ascending-third trajectory from the stable F♯ chord of measure 37. Yet what should that initiative’s goal be?

Earlier the relationship between A and f♯ was established. Does the conversion of f♯ into F♯ warrant targeting upper-third a♯ (or A♯) instead? Or should A be maintained nevertheless? The ascending 5–6 sequence that Chopin employs could lead to either goal, depending upon how the 6-phase chords are constructed. F♯ D♯➔ G♯ (an elaboration of F♯5–6 G♯5) is a good start in either case. But should G♯’s 6-phase chord be E➔ (G♯-B-E, surging towards A) or instead E♯➔ (G -B♯E♯, surging towards either a♯ or A♯)? The score bears witness that Chopin wove indecisiveness on this point into the fabric of the work: he initially selects the latter trajectory (measure 49) but soon shifts to the former (measure 54). Thus two potential fifth-relationships are juxtaposed: E♯➔ A♯ and E➔ A. When goal A is displaced by F♮, a descending third-relationship is implied: A (imagined) to F♮. Eigeldinger’s spelling of E♯ as F (his annotation for measures 47 through 63 – during which the cosmetic enharmonic shift from sharps to flats occurs – reads “F A F”) equates the initiating and closing elements of this complex and fascinating passage, a reading that not only betrays an insensitivity to the difference between descending fifth (ascending fourth: E♯F♮) relationships but that then proceeds by claiming that the home key of C♯ Minor is “symmetrically divided into three enharmonic thirds”: c♯, F, and A (p. 246). Whereas I accept A as one of the work’s main players (what I have referred to as a nodal point along the c♯>D♮ trajectory, whose D♮ will be replaced by D♯ in measure 65), I reject Eigeldinger’s F: as E♯ it is an internal element of a sequential progression, and as F at the cadence it is a temporary usurper of F♯, whose restoration in measure 64 is accomplished before further progress in the tonal trajectory occurs. Indeed, the equal subdivision of an octave is featured occasionally in music of this era: Chopin in fact pursues it in the 6–(2)–10–6 passage of measures 21 through 31, as I have noted above. But to pick a C♯ here, an A there, and an F somewhere else and claim that these are the “poles around which the piece’s harmony is constructed” (p. 246) distorts their compositional roles within Chopin’s prelude. As the juxtaposition of 8.1b and 8.2 makes clear, the bass C♯–G♯–C♯ sacred triangle plays a foundational harmonic role both in the introduction and in the main section, and in both contexts some sort of supertonic (♮II or II➔),

achieved via a descent in thirds, serves as the principal connector between the tonic and the dominant. As is typical of tonal music in general, the bulk of Chopin’s creative energy here is devoted to what comes between the initial I and the cadential V♯. In claiming that the D♮ chord of measures 15 through 18 “is established without any functional raison d’être” (p. 246), Eigeldinger neglects its potential to continue immediately to V➔, a scenario that Chopin passes over in favor of a longer and far more captivating build-up to the supertonic (II➔) in measure 65. If the prelude’s main section is in fact a “gargantuan variant” of the introduction, as I have proposed above, then there is a significant structural connection between the cadences on tonic c♯ in measures 4–5 and 66–67. (Play them one after the other to hear how they rhyme.) My reading of the form gives them comparable status: as close of the introduction and of the main section. The latter is divided into four parts (indicated by bar lines in 8.2), set off by a rather amorphous halt on F♯ in measure 19 and dynamic (and equivalently formulated) cadences on F♯ in measure 35 and on its usurper, F♮, in measure 59. (Eigeldinger’s ex. 2 likewise presents the expanse from c♯ in measure 5 to c♯ in measure 67 as a single multi-sectional entity, though his internal bar lines do not in all cases coincide with mine. He annotates the goal c♯ chord with the word “Reprise,” which I take to imply a dovetailing of the end of the main section with the onset of its modified repetition.) Smith proposes a contrasting view of the form, which he classifies as rounded binary (p. 242).10 Though he divides what I call the main section into the same four parts as I do, my first two parts correspond to his first section, my third part to his middle section, and my fourth part to his retransition (p. 241).11 Consequently what follows the cadence of measure 67 is for him a more vital part of the formal design than it is for me. (In my view a one-part form has fully run its course by the cadence of measure 67 and will be reprised in an abbreviated version that retains all essential deep structural features; whereas Smith’s middle section, which cadences in F Major, requires the material after measure 67 to re-assert the tonic and to balance the open-ended first section.) As the remainder of this essay will help clarify, I propose that the prelude is organized as a set of four distinct passes through the same structural “theme”: the introduction, the main section, its modified repetition, and the coda. That view is

incompatible with Smith’s interpretation of the passage leading to the cadence in measures 66–67 (for me the site of the work’s background Urlinie descent) as a retransition. Despite our disagreement regarding the prelude’s form, Smith’s fig. 20.3 (which he calls the “Schematic form”) and my 8.2 have much in common over the course of what I call the main section until the final part, between F♮ and c♯ (measures 59 through 67), where his representation goes blank while mine robustly includes three of the section’s seven open noteheads and two of its four Roman numerals. This is an intensified replication of our disagreement regarding measure 4, discussed above. Whereas Smith’s focus emphasizes tonicized keys (going so far as to omit the structural dominant, which is labeled as V7/c♯ in his score 20.6), my perspective intermixes chords derived from modulo 12 progressions, chords modified by multiple wobbly notes, and structural harmonies regardless of whether or not they are reinforced by local progressions that incorporate their leading tones. I regard tonicization and structural depth as distinct notions that often do not correlate.12 Given the roster of chords left after his selective purging, it is not surprising that Smith has appended a listing of two chordal cycles to his fig. 20.3: B♭–D–F♯ and F–A–C♯. (They are presented in triangular diagrams in his fig. 20.4 as well.) His commentary explains: “This C♯–A–F cycle … accounts for the overall shape of the prelude’s beginning (C♯ minor to A) and end (F back to C♯ minor); in contrast, the D–B♭–G♭ cycle is the source for the harmonic motion through the middle” (p. 247). Whereas the latter corresponds to my 6–2–10–6 cycle (modulo 12) for measures 21 through 31, the former, which Eigeldinger endorses as well (as we have seen), falls apart for me because all of the various A(♯) and F(♯) chords above the open parentheses in 8.2 serve as nodal points (with or without wobbly-note mutation) along the path between the hierarchically deeper I and II➔.13

The modified repetition of the Prelude in C♯

The modified repetition of the Prelude in C♯ Minor’s main section (measures 67–84) After the PAC that is achieved in measure 67, the prelude could proceed directly to the coda (jumping from 671 to 842) with no injury to the form. Instead, Chopin electively repeats the structure that has just been presented, now in a much tidier (though, due to the cadenza, still very impressive) manner. A repeat of the initial c♯-to-A motion transpires during measures 67 through 75. (See 8.3.) Then Chopin takes advantage of a nifty trick of the trade: adding F to A-C♯-E results in II⇨. Thus the progression avoids entirely the intricate and extended navigation among mutating nodal points that characterizes the main section’s initial statement. The written-out cadenza briefly postpones the denouement, in the process accomplishing a shift from II⇨ to II➔ (thus bringing this progression into a closer alliance with that of the earlier main section, where II➔ occurs in measure 65).14 From the cadenza’s initiating D♯⇨ chord (which Chopin spells enharmonically using easier-to-read G♮ in place of F ), the second through ninth four-note groupings work downwards by half steps. The ninth chord in the series (eight half-steps below the starting point) incorporates a mutation: presented by Chopin as F♮-B-D♮-G♯ rather than as F♮-BC♯-G♯. From that point he works his way back up again, achieving C♯-G♮-E-B♭ (which represents D♯➔: F -A♯-C♯-E) in the middle of the thirteenth four-note grouping. That chord returns and is prolonged at the end of the cadenza, where the correct spelling is employed. Bass F at the start of the final four-note grouping resolves to the dominant’s G♯ (three octaves lower) at 801. A three-measure expansion of the cadential chord (measures 80 through 82) precedes a staid V➔ I close. Though the rhyme with measures 4–5 and 66–67 is inexact, the effect is one of increased stability due to the downbeat arrival of soprano . Yet eighth notes rise again from the depths, initiating a brief coda.

Eigeldinger tacitly confirms the formal redundancy of this section by giving it hardly any attention in his analysis. The word “Reprise” in his ex. 2 suffices.15 The annotations in Smith’s score 20.8 demonstrate one of my principal concerns with conventional harmonic analysis: the use of widely divergent symbols for essentially the same harmonic function. The cadenza connects two very similar chords: A-C♯-E-F and F -A♯-C♯-E, both of which target V♯. My notational practice, either with Arabic numerals (as displayed in 8.3) or with arrows (II⇨➔), emphasizes that a mere wobbly note differentiates those two sonorities. Smith’s conventional analysis instead makes them seem disparate: Ger versus vii°7/V. (If one agrees with me that their shared root is D♯, then the “= A7” in Smith’s annotation will seem curious as well.) Equally problematic, in my view, is the label i for the chord of measures 80 through 82 (Smith’s 81 through 83), though so much ink has been spilt on that issue over the years that I will hold my peace.

Example 8.3 Analysis of Prelude in C♯ Minor (op. 45), mm. 67–84.

The Prelude in C♯ Minor’s coda (measures 84–91) Whereas the penultimate left-hand pitch in the cadential measure 67 is G♯, an accented A emerges at that location in the counterpart measure 84. This A of course brings to mind the various A major chords that have initiated progressions away from tonic c♯ in the preceding regions of the prelude (measures 1, 13, and 75). In those earlier contexts A led either to f♯ (on the way to D♮ or D♯➔) or directly to D♯⇨. Now, with the help of the G♮ that emerges in measure 85, A➔ targets D♮ directly. (See 8.4.) Listeners thus may admire the range of similar though distinct trajectories that Chopin juxtaposes in this work. Yet there is something even more delicious to savor: the chord of measure 85 (spelled A-C♯E-G♮) is the enharmonic equivalent of the chord of measure 76 (spelled A-C♯-E-F ). Consequently alert listeners might develop a special interest in finding out how Chopin will proceed after measure 85: will A➔ lead to ♮II; or will D♯⇨ lead to V♯? Chopin chooses the ♮II route, thereby restoring the introduction’s version of the dominant preparation. The PAC that follows brings the progression to a close, with lingering echoes of Kopfton E in the post-cadential measures.

Example 8.4 Analysis of Prelude in C♯ Minor (op. 45), mm. 84–91.

9

Ballade in F Minor (op. 52) ◈ in response to Laufer Edward Edward Laufer’s detailed analysis of Chopin’s Ballade in F Minor appears in a book devoted to sonata forms.1 Given the venue, Laufer focuses especially on the work’s form and motivic associations. I am not persuaded by his formal assessment, which has appeared with some frequency in the literature devoted to this ballade. I propose that Chopin instead pursues a creative variant of an A1 A2 binary form, with multiple repetitions of A1, incorporating variation and internal expansion, accounting for the bulk of the work, followed by a single A2 statement near the end. (Laufer refers to the latter as a coda.) Since my focus is on harmony, I will not dwell on our disagreement regarding the form, but instead will glean as much as I can about harmonic matters from Laufer’s generous graphs. Though his examples are dense – to the point of sometimes exceeding what might reasonably be squeezed onto a page2 – Laufer’s use of Roman numerals is uncommonly sparse. Consequently I sometimes reconstruct the implied harmonic progressions through an assessment of the graphs’ pitch content and of the associations indicated by slurs and beams.

The introduction and the initial statement of A1 (measures 1–22) The Ballade in F Minor’s A1 section presents a conventional trajectory from a minor tonic (introduced at 82) to its major dominant (attained at 222).3 This trajectory is presented four times over the course of the ballade (incorporating progressively more extraordinary elaborations and expansions), after which a tonic-cadencing A2 finally commences at measure 211. Consequently a cadential dominant and the onset of a fresh tonic are juxtaposed multiple times: at measures 22–23, 57–58, 151–152, and 202–211. That same juxtaposition is deployed at the juncture of the introduction and the initial A1: a C major dominant is tonicized from the opening measure through the fermata chord of 72, thereby coordinating with what precedes each of the later A-section onsets. Gradually emerging out of a misty repeated octave G, the introduction’s tonicized C chord soon surges towards IV, whose 6 phase leads the progression onwards to V♮ and then I.4 (See 9.1.) The entire progression is repeated during measures 4 and 5, followed by fragments that extend the introduction for an additional two measures. The establishment of G (F Minor’s ) at the top of the texture as the introduction begins is critical. Whereas G is emphasized from the outset during the dominant-focused introduction, during each statement of A1 or A2 it serves as the successor of Kopfton A♭, which first emerges (in the same register as the introduction’s G) during 131. As 9.1 shows, Chopin’s melody juxtaposes a pair of unfolded thirds over the course of the ballade’s first thirteen measures: G down to leading tone E♮ during the dominant introduction, followed by tonic resolution F up to Kopfton A♭ during the opening measures of the A1 section. (As often is the case in minor-key compositions, an upper-third chord – A♭-C-E♭ – plays a role in the prolongation of the initial F-A♭-C tonic.)

Example 9.1 Analysis of Ballade in F Minor (op. 52), mm. 1–13. During the initial statement of A1 (measures 7|8 through 22), IV comes between Ispace (which eventually surges, targeting IV) and the cadential

. (See 9.2.) Tonic F’s

minor seventh, E♭, sounds in a consonant context during an excursion to the tonic’s upperthird chord (A♭-C-E♭ in measures 12 through 15). E♭’s ultimately dissonant character is unleashed through the restoration of tonic root F and the shift from A♭ to A♮ during 161. (An E♭-G(♭)-B♭-(D♭) embellishing chord separates the A♭ chord from the F tonic both upon arrival and upon departure.) The upward melodic unfolding from F reaches Kopfton A♭ during the prolongation of the upper-third chord.

Example 9.2 Analysis of Ballade in F Minor (op. 52), mm. 7|8–22. Once attained, the subdominant is prolonged via a tonicization of B♭ Minor, supporting a local third-progression from D♭ down to B♭, as is displayed in 9.2. This tonicization likewise proceeds to an upper-third chord (again aided by an intervening embellishing chord). The progression continues with II7 and then

within B♭ Minor.

Though prolonged for several measures, the F dominant does eventually resolve to B♭, at which point B♭’s role as IV within the broader F Minor progression is fulfilled by the continuation to dominant C. The sketch proposes that what conventionally might occur as a stepwise connection between Kopfton A♭ (during 131 and 141) and its incomplete upper neighbor B♭ (at 162 and 221) here coordinates with a registral shift, so that the seventh A♭>B♭ (broken up into three thirds) is traversed instead of the second A♭F fourth was traversed (bound by a slur in 9.2, measures 16 through 18). That fourth plays a role in both parts of the expansion displayed in 9.3. The shift from F to G♭ (tentatively touched upon at 371, then decisively embraced in measure 38) begins an ascending trajectory that reaches B♭ in measure 46. (Note the slur, incorporating an internal downward registral shift, below the staff in 9.3.) Whereas the G♭ chord might have served as ♭II (a chromatic variant of IV’s 6-phase chord), offering an alternative route to the goal C major dominant, instead an A♭-C♭-E♭-(G♭) passing chord leads back to the B♭ subdominant, which is subsequently embellished by F-A♮-C-E♭ in measure 49. Then during the circle of fifths the same filled-in fourth, highlighted by the beam above the staff in measures 50 through 57 of 9.3, reverts to the descending direction. Mapping 571 of 9.3 onto 221 of 9.2, we should not be surprised that the C dominant (supporting

) that follows in measure 22 also

emerges in measure 57. Will a fresh start, beginning in measure 58, lead to success in achieving the longedfor PAC goal in the context of A2? Or will Chopin instead undertake an even more daring expansion of the A1 structure?

Two issues regarding hierarchical relations surface during a comparison of my 9.3 and Laufer’s ex. 7–4. First, I hear the soprano G♭ introduced in measure 38 extending through measure 45, noting that a descending G♭>E♭ third is answered by an ascending D♮E♭ slur and parenthetical reinstatement of G♭ below E♭.) Instead, I suggest that G♭ here resolves as a 9♭–8 suspension, confirmed by Chopin’s alto-register F during 562. (Laufer’s reading of a G♭ prolongation until the downbeat of measure 57 is presented most clearly in his ex. 7–4 c.)

The third statement of A1 (measures 58–151) At a basic level the tonal tale that the A1 section tells is unremarkable: after its initial stabilization the tonic surges, targeting the subdominant, which, after a tonicizing expansion, proceeds to the dominant for a half cadence. In an idiosyncratic organizational plan, Chopin repeats A1 several times, maintaining approximately the same structural framework for the tonic, for its surge, and for the dominant arrival, while developing the internal subdominant prolongation in ever more wondrous ways. During the first three statements of A1 this burgeoning content is anchored by straightforward and repeated presentations of the subdominant chord in a characteristic register (as first stated during 162 and 221). The following account of how those subdominant expansions transpire during the first three A1 sections will guide our discussion. First statement: 162–221 The foundational state of the subdominant tonicization, featuring a third-progression (D♭>C>B♭) supported by a harmonic progression within the tonicized key of B♭ Minor [9.2]. Second statement: 311–362 A reprise of the foundational state of the subdominant tonicization. 362–571 A fresh expansion of the subdominant, featuring a fourth-progression (B♭>A♭>G♭>F) supported by a descending circle of fifths within the tonicized key of B♭ Minor [9.3]. Third statement: 661–992 What begins as a straightforward reprise of the foundational state of the subdominant tonicization is transformed into an extended traversal of the D♭>C>B♭ third-

progression, incorporating an interruption and a shift to B♭ Major [9.4]. 992–1452 A fresh expansion during which B♭ Minor is restored, again traversing a thirdprogression (D♮>C>B♭), this time with C supported by a dominant whose prolongation incorporates a segment of an obstinate ascending circle of thirds (FE♭ line beamed in measures 172 through 176 of his exx. 7.8a and 7.8d should continue with an imagined D♭ in measure 177, corresponding to a cadence on the D♭ tonic.

(See 9.6.) That tonic then surges, leading to the arrival of IV at 1822 (not 1812, as Laufer proposes). A similar surge of IV’s 6-phase chord (as II➔) heralds the arrival of V at 1842. (Observe how in both cases the surge coordinates with a long crescendo marking, so that the resolutions occur at moments of peak intensity, just as a decrescendo begins.) Laufer instead extends the IV5–6 trajectory through measure 189. A key factor in my reading is the assumption that the embellishing chord B♭-D♭-F-G♮ at 1871 “should” resolve to C-E♭-A♭ (an inverted dominant). That chord’s E♭ is elided during 1872. Instead, F is retained as an anticipation of the following downbeat chord’s F.9 Whereas I regard measure 211 as a new beginning (finally, the onset of A2!), Laufer places that measure at the end of his fig. 7.8 graphs. He proposes both that the Urlinie reaches goal there and that a coda commences there. (Note that in his fig. 7.9a – but not 7.9b through 7.9d – the goal F appears within parentheses. In his fig. 7.10 the parentheses recur, and the chord is annotated as follows: “evades strong close on .”) Given my reading of the ballade’s deep structure thus far as consisting of four distinct melodic descents from to

, each supported by the

harmonic trajectory from I to V♮, I propose that the A♭ of 2111 serves as the initiation point for a descent that attains the Urlinie’s goal at 2231 (to be explored below).

The A2 section (measures 211–239)

The A2 section (measures 211–239) The triplet sixteenth notes that pervade the A2 section complete the gradual enlivenment of rhythmic content that has characterized the ballade. The A2 section, whose structure unfolds beginning in measure 211 (as shown in 9.7), is loosely related to its A1 predecessors: the Kopfton (now stated at the outset) is supported by the tonic harmony, with a pervasive deployment of II at diverse structural levels (contrasting the tonicized IV favored in the initial statements) proceeding to V♮ (with C-F-G to C-E♮-G in measure 218 echoing the earlier occurrence of that distinctive construction in measures 201 and 202). Yet certainly a sense of novelty prevails. Finally we achieve a breakthrough, extending beyond the confines of the dominant-cadencing A1 to A2’s long-anticipated PAC tonic, presented fortissimo at 2231, with reiterations at 2251 and 2271 (where the minor tonic’s third finally is correctly spelled as A♭). Though an impressive hierarchical nesting of chordal activity is documented in 9.7, that visualization actually is somewhat simplified from Chopin’s version, since a chord-dense parenthetical passage, reminiscent of those in the vicinity of measures 196 through 200, emerges between

(at 2184) and

(at

2224). I regard it as a written-out manifestation of something that otherwise might have been improvised, serving to heighten the already considerable intensity in the final approach to the cadence.

Example 9.7 Analysis of Ballade in F Minor (op. 52), mm. 211–239.

The chordal progression in measures 215 and 216 may seem baffling. The middleground C major dominant harmony attained at the end of measure 214 is here embellished by a chord spelled as F-B♮-D♮-A♭. To get back to C, Chopin traverses a segment of the modulo 12 division of the octave into six equal parts, each spanning two half steps. The forzando markings highlight two successive -2 shifts, shown in 9.7. By this means we arrive at the diminished seventh chord corresponding to dominant C, which is fully restored with the resolution of D♭ to C in the bass (a conversion to a less evolved state of V) during 2161.10 In this construction, the E♮-D♭-G-B♭ chord at the end of 2151 serves as a local connective chord (filling in the first whole step) rather than as a resolution. The prominence of II during the harmonic progressions (at various levels) that are integrated to form A2’s structure contrasts the tonicized IV within the various manifestations of A1. As soon as the PAC is achieved (at 2231) Chopin boldly substitutes IV for II during two quick reiterations of a tonic-affirming progression. Whereas the minor tonic of 82 eventually surges (as F-A♮-C-E♭ during 161), the surge in measure 223 (spelled as A♮-C-E♭-G♭) gets under way breathtakingly soon after the moment of cadence. Chopin has spelled that juxtaposition not with A♭ to A♮ (as was the case during the A1 surge), but instead as G♯ to A♮. Whereas some analysts (including Laufer) would argue that Chopin here elides the minor tonic entirely (until 2271), intending G♯ as an accented passing note between the dominant’s G and a major tonic’s A♮, I support the alternative view that, since Chopin frequently employs quirky spellings, one should not give too much weight to the curious G♯ here. As a listener (not watching the score), I acknowledge the expected cadence on the minor tonic and then am jolted by the surprising and vigorous surge towards IV. In either reading, the IV (with soprano B♭) that emerges in measure 224 corresponds to that of measure 22. As such, the melodic third from B♭ down to G should be expected in coordination with the dominant’s arrival. (Contrasting the earlier presentations, here IV’s 6-phase chord emerges between IV and V♮.) Yet in this case E♮F at the cadence. (Thus the structural G is placed within parentheses in 9.7.) Chopin responds to that lacuna by emphasizing a G>F second following the cadence (measure 227). After several reiterations, a long tonic-affirming cascade descends to the downbeat of measure 237, followed by a final cadential gesture that reinstates the I5–6 II approach to the dominant, Chopin’s final word on the matter.

Though Laufer’s paucity of Roman numerals makes an assessment of his reading of the work’s harmonic dimension especially challenging, I question his interpretation of measure 212, based upon the notes included in his graph (ex. 7.10a). I suggest that I6 (or VI), rather than I, sounds at the downbeat of that measure. Perhaps Chopin delayed sounding D♭ in the bass to avoid forming parallel fifths against the melody’s GD♯>D♮>…>B>A♮>G♮>F♯), whereas during the middle either the listener will imagine a pitch (C♯ during measure 106) or a pitch sounds but is covered by other chord members. The harmonic analysis that annotates the presentation of this voice leading in 10.5 reveals a boldly realized double traversal of the basic I IV V I progression. The initial tonic surges towards IV, that IV’s 6-phase chord takes on a “Neapolitan” flavor, and the dominant that follows is attained by simply adding leading tone E♯ to the Neapolitan’s pitches (resulting in V⇨, and consequently not alleviating the G♮ wobble). The tonic that resolves that dominant evolves gradually into I➔ during measures 106 through 108, proceeding to a IV♮ whose D♮ extends into the domain of V➔, where eventually G♯ shifts to G♮, resulting in a second V⇨ approach to the tonic. Indeed, Chopin has reserved some of the Barcarolle’s most memorable harmonic writing for the coda! A concluding melody begins in measure 113, notably on the same A♯ that introduced the Kopfton in measure 4. The progression’s initial I-space supports the ascending arpeggiation A♯A♭ during the second ending.) In his “Idiosyncrasies of Phrase Rhythm in Chopin’s Mazurkas,” in The Age of Chopin: Interdisciplinary Inquiries, ed. H. Goldberg (Bloomington: Indiana University Press, 2004), pp. 95–105 , Carl Schachter explores this tonic pillar in detail, essentially agreeing with Schenker’s reading of the high C of measure 10 while questioning (p. 98) his relative neglect of the C at 21, which conforms in register to the mazurka’s other structurally deep pitches. 8. It is so labeled in standard editions of the mazurkas, including the National Edition used in creating this chapter. 9. This mazurka’s juxtaposition of keys is not unique in Chopin’s oeuvre. Other examples that have been widely discussed include the Scherzo (op. 31), addressed by William Kinderman in his “Directional Tonality in Chopin,” in Chopin Studies, ed. J. Samson (Cambridge University Press, 1988), pp. 59–75 and by Harald Krebs in his “Tonal and Formal Dualism in Chopin’s Scherzo, Op. 31,” Music Theory Spectrum 13 (1991), pp. 48–60 , and the Ballade (op. 38), addressed by Jonathan Bellman in his Chopin’s Polish Ballade: Op. 38 as Narrative of National Martyrdom (Oxford

University Press, 2010) and by Kevin Korsyn in his “Directional Tonality and Intertextuality: Brahms’s Quintet Op. 88 and Chopin’s Ballade Op. 38,” in The Second Practice of Nineteenth-Century Tonality, ed. W. Kinderman and H. Krebs (Lincoln: University of Nebraska Press, 1996), pp. 45–83 . 10. The notion of “reaching-over” is a common voice-leading principle, an essential component of the Schenkerian perspective. (See my Tonal Analysis: A Schenkerian Perspective, chapter 7.) 11. For a contrasting interpretation, see David Kopp’s analysis in his Chromatic Transformations in Nineteenth-Century Music (Cambridge University Press, 2002), pp. 235–240 . I do not concur that the tonic pillar “projects tonal ambiguity for much of its duration” (p. 236): the juxtaposition of antipodal C♯ and G♮ chords (a focus of my analysis) is a strong signal of tonic B, with only its mode (major versus minor) as yet indeterminate. 12. Compare with Haydn/Mozart, 1.5. 13. The mazurka begins in the middle of a harmonic progression. Taking into account measure 22, which presents an E major chord to lead back to the opening material (in a written-out repeat), it would be appropriate to regard the initial II as an asserted IV6. Note especially the 5–6 connection between tenor-register B at 222 and C♯ during 231 (= 11). For this reason, and by noting how bass B at 21–2 is reiterated by bass B during 31, I regard the initial E-G♯ dyad as representing C♯-E-G♯ (with the C♯ arriving half a beat later) rather than as representing E-G♯-B with C♯ serving as a neighbor to IV’s fifth, B. 14. Once introduced to these notions, my students at the University of Minnesota began referring to ⇨ as a “supersurge,” while ➔ remained a “surge” or, more precisely, a “simple surge.” 15. Note Chopin’s persistence in incorporating an upper third in the vicinity of the Kopfton ’s arrival. D♯D♯ here (measures 16 and 17) corresponds to DD in measures 2 through 4 of opus 7/1.

16. Compare with Schubert, 1.23. 17. This division of structural content does not coincide with the pillar’s division into two halves, each repeated: measures 5 through 8 recur as 9 through 12, and measures 13 through 20 recur as 21 through 28. Chopin transcends that surface division by extending the ascending arpeggiation into the second half. 18. Chopin’s misspelling comes about as a result of his substituting easy-to-read A♮-C♯E♮ in the preceding harmony for the correct spelling, B -D♭-F♭. Further pertinent considerations will emerge in the exploration of this mazurka’s structure in chapter 2. 19. As 1.11 reveals, the fifth-progression’s E♭, C, and B♭ are all embellished by an upper fourth or third. Chopin offsets the neglect of D♭ (resulting from its delayed arrival within the beat) later, during the mazurka’s B section: D♭C♯ is pursued. (Compare with TAH, 6.20.) In his “Harmonic Complexity and Form in Chopin’s Mazurkas,” Ostinato rigore: Revue internationale d’études musicales 15 (2000), pp. 102–103 , Joel Lester labels this chord as vii7/D♯ and describes the passage as “a fleeting instance” of “motion by dominants around the circle of fifths.”

23. See Edward T. Cone’s “Ambiguity and Reinterpretation in Chopin,” in Chopin Studies 2, ed. J. Rink and J. Samson (Cambridge University Press, 1994), pp. 142–143 . 24. Though Schenker provides a detailed analysis of this mazurka in FC (his fig. 75), it is difficult to determine which route he endorses for the fifth-progression between B and E. Observe that his graph is inconsistent in its placement of the internal G and F♯ during A1 and A2. In the former (corresponding to measures 1 through 4), the placement of G before the arrival of dominant root B would seem to favor an imaginative insertion, though no parentheses are placed around his G notehead. In the latter (corresponding to measures 57 through 60), the placement of G above the dominant root B would seem to correspond to the G of 593. I propose that his version for A1 endeavors to recompose the passage in accordance with the second species of counterpoint (wherein G would serve as a passing note above bass A), subjected to a considerable shift in Chopin’s realization, where that passing note is delayed until after

the dominant root arrives. That is, the foundational state

may shift (via

the unaccented passing note of species counterpoint being transformed into the accented

passing note of free composition) to create a “cadential ” context, as

;

or even further, so that A lingers to sound against the dominant root, as

. 25. Compare G, which here neglects to descend to F♯, with D♭ (which neglects to descend to C) in 1.6, m. 5. Carl Schachter, in “The Prelude in E Minor Op. 28 No. 4: Autograph Sources and Interpretation,” in Chopin Studies 2, ed. J. Rink and J. Samson (Cambridge University Press, 1994), pp. 161–182 , takes a literalist approach (as does Schenker in FC, fig. 75). Schachter’s ex. 9.4 (p. 168) displays the melody pitch E at 73 as an anticipation of that in measure 8. (The intervening G – a crucial note for me – is omitted from his graph.) He adds a special annotation above the bass beam: “No V!”

Whereas my graph projects an imagined diatonic within the descending fifthprogression from , Schachter’s descent (like Schenker’s) incorporates the earlier ♮ . An intriguing analysis by Franz Eibner in part concurs with my reading. See his “Über die Akkorde im Satz Chopins,” in Chopin-Jahrbuch 1970, ed. F. Zagiba (Vienna: Notring der wissenschaftlichen Verbände Österreichs, 1970), pp. 3–24 . The initial chord is analyzed as E Minor’s tonic and is provided only with the Roman numeral I (once with to the right, in his fig. 7 on p. 23). He comments as follows: “Durch den Dominantklang am Beginn ist nur die IV. Stufe (von T. 2) ‘tonikalisiert’ worden und also muß dieser Dominantklang in der ganzen Kadenz die I. Stufe der Haupttonart repräsentieren” (p. 6). His fig. 4 (p. 20) displays both a parenthetical D♯ below G at the end of measure 7 and a parenthetical bass B for the final beat of that measure, under which he places the Roman numeral V within square brackets. (His fig. 5 on p. 21 provides additional perspective, including an indication that the melody’s G at the end of measure 7 serves as an “Antizipationston.”) He reads the Kopfton as , supplied within square brackets and annotated with the word “Ellipse” in his fig. 6 (p. 22). (The G is connected to the F♯ of the mazurka’s B section, graphed in his fig. 7 on p. 23.) Though in disagreement with Schenker’s reading of the Kopfton as , which Eibner addresses in his n. 3 on pp. 18–19, his choice has the advantage of not raising the expectation of a G between A and F♯. I remain unpersuaded, however, due to the prominence of the initial B, its clear voice-leading descent to A in measures 2 and 6, and the relationship between the A section’s fifth and the B section’s (inverted to

sixth

), to be explored in chapter 2.

26. This D♮-F♯-A embellishment of a C♯ chord corresponds to the A♭-C-E♭ embellishment of a G chord in opus 17/2, mm. 39ff. Its exotic flavor inspired Dmitri Tymoczko to interpret the mazurka’s mode initially as “phrygian.” See his A Geometry of Music, pp. 312–313.

27. Schenker alternates between two notational practices for interruption in FC. (See editor Ernst Oster’s note 7 on p. 37 of the example volume.) I have adopted the one that I prefer. For a more detailed introduction to this important topic, see my Tonal Analysis: A Schenkerian Perspective, chapter 4. 28. I have placed the D♮ in the bass, in conformity with 143. The parentheses around the C♭ above this D♮ indicate merely that it is displayed in a higher register than where it occurs in the score. 29. Whereas Schenker (FC, fig. 106, ex. 2c) proposes a local ascending C♯C>B♮ (followed by B♭>A♮>A♭) will lead to an IAC. If instead (and as I recommend) the performer leads downwards to the fifth note of each measure, then the melodic path leads to the F at 162 (as displayed by the stemmed notes in 1.22) for a PAC. 33. In his A Geometry of Music, pp. 288–290, Dmitri Tymoczko presents within his fig. 8.5.9 a root progression similar to mine, though flawed in two ways: first, I propose that it should commence with the A chord of measure 4, not the G♯ chord of measure 5; and second, he omits an analysis for the G♯ chord of 83. (The latter is not a printer’s error, because his commentary explicitly notes the exceptional “descending semitone” D to C♯.) Both of these points of contention relate to my willingness to allow imperfect fifths into my circle. His G♯ … D span contains only perfect fifths, avoiding my preceding A–D♯ and following D–G♯. Compare with ex. 362 in Felix Salzer’s Structural Hearing: Tonal Coherence in Music, 2 vols. (New York: Boni, 1952; reprint edn., New York: Dover, 1962) . Though Salzer’s model suitably starts on the A chord, he omits the D♯ chord of measure 5. In addition, he makes it appear as if a harmonic progression proceeds from III in measure 4 through V (which would be displayed as V♯ in my notation) in measure 9 (III and V are connected by an arrow) to I, contrasting my view that the initial upward trajectory breaks off after III, with a fresh start in measure 9. 34. Though Chopin’s slurring in measures 13 and 14 would support a reading that maintains the tonic until 151 (with the D-A-F♮-B chords functioning as local embellishments), his slurs so often counter his mazurkas’ structures that I here am willing to discount them. One might instead view their presence (in coordination with the dynamic markings) as helping to emphasize the subdominant statement on three consecutive downbeats. The progression proceeds beyond IV only on the third try. In performance the third-beat A chords should seem like a backtracking to the position of measure 12. 35. The 5–6 shift that often transpires during IV is realized here as (8)–7–6. (The 7 sounds from the outset.) The G♯ that arrives at 152 prevents the descending parallel fifths that would have occurred had A functioned instead as IV’s chordal seventh.

36. I suspect that Chopin’s ear was bothered by the prospect of a soprano B>G♯ leap coinciding with the bass D>C♯ step (creating “hidden fifths” in the exposed outer voices). Consequently he called upon C♯ (related to the C♯s of 133 and 143) as a substitute for G♯ at 153. The unusual situation at the cadence also in part justifies my rejection of what might seem to many as a clear instance of Kopfton . (This issue will be touched upon again when the remainder of the mazurka is assessed in chapter 2.) 37. The written-out repeat of the juxtaposed I and III phrases is facilitated by some transitional chords (during 83) that do not recur during measure 16. They are not displayed in 1.24. 38. For the written-out repeat of a1, the mediant’s C from 82 corresponds to the imagined Kopfton, with a C>B>A third-progression extending from that point through 122. 39. Though I do not regard C-E-G at 73 as a harmonically asserted chord (it is instead an unfurled embellishment of the tonic), this situation corresponds to what some analysts call a plagal cadence. 40. In 1.26 I propose that a sequential progression – A♭>E♭CF♯>E followed by B>A>G♯ followed by G♯>F♯>E, all displayed in 1.27, measures 5 through 22) give more the sense of a tonic reinstatement than of a mediant expansion.

Chapter 2: Between the tonic pillars

Chapter 2: Between the tonic pillars 1. The bass E♭>B♭ fourth is a meaningful interval in the context of E♭ Minor, whereas the upper strand’s G♭>D♮ fourth is not. The latter span, which incorporates the conventional modal shift from diatonic D♭ to leading tone D♮ near the cadence, is justified because it follows – in upper tenths – the contour set by the bass. 2. Chopin is having some fun in this mazurka by juxtaposing G➔C during the A section and D➔G during the B section. Could this be interpreted as I➔ IV V➔ I in G Major? The Dal segno senza Fine instruction in fact may be intended to eradicate the memory of which chord is first established as the tonic. My term “tonic pillar” reflects the observation that a mazurka’s A section invariably establishes the tonic key. To argue that this mazurka is in G Major would require both that the tonic pillar correspond instead to the B section role and that Chopin’s C Major key signature is bogus. (The least conventional of Chopin’s mazurkas in this regard is opus 30/2. See 2.5.) 3. The analysis of this mazurka by Nicholas Meeùs in his “Questions de méthode: La Mazurka op. 7 no. 5 de Chopin,” Analyse musicale 32 (1993), pp. 58–63 , embraces such doubt. 4. The earlier components of the circle of fifths coordinate with descending filled-in melodic thirds at two distinct structural levels. For example, a surface E♭>D♭>C third occurs within measure 13, while a broader third transpires between 132 and 143. (Only the latter is displayed in 2.4.) I propose that though A♭>G>F in measure 19 will at first seem to be of the former type, it ultimately performs (speedily) the role of the latter type. 5. The sounding of D♭ (rather than D♮) at 193 creates a motivic connection with the D♭>C over the bar line between measures 1 and 2, strengthening my assertion that the unfolded A♭A♭ D♭>C F>E♭.) Consequently measure 25 ought not to be interpreted as background V within a broad I III♮ V7 I progression. 8. In fact, Edward Laufer proposed such a reading for this mazurka in his lecture “Parenthetical Passages,” delivered at the Mannes College of Music Schenker Symposium in 1985. Ex. 19 of his handout displays bass open noteheads on G♯ (at 121), B (at 261), C♯ (at 412 or 452), and D♯ (at 433 or 473) before the close on G♯. (His Roman numeral analysis is I III5−6 IV V I.) 9. Though certainly one could deploy the Roman numeral ♭VI 5 ♭ at measure 20 in 2.8 (in keeping with Schenker’s practice in FC), I here instead account for that sonority by means of symbols to the right of the I numeral: the wobble from E to E♭ and back (3♮– ♭–♮) and the chromatic neighbor A♭ embellishing G (5–6♭–5). By this means I emphasize that chord’s alliance with the initial tonic and acknowledge that it does not lead anywhere harmonically. 10. A descending circle of fifths supports this fifth-progression. Observe how the already surging tonic E➔ that opens the A1 tonic pillar (measure 1) is echoed by the already surging G♯➔ that initiates the circle of fifths (measure 33). These chords also share an upper-neighbor embellishment (BB and D♯D♯). (The relationship between these neighboring motions was more emphatically projected in the original version of measure 33, where the E occurs on beat 3 in a rhythmic context exactly matching that of measure 1. The original and revised versions are juxtaposed in Jeffrey Kallberg’s “The Problem of Repetition and Return in Chopin’s Mazurkas,” in Chopin Studies, ed. J. Samson (Cambridge University Press, 1988), p. 14, ex. 6 .) Though the dominant is tonicized during the B section, the cover tone D♯’s upward tendency as leading tone eventually is fulfilled: the opening of the A2 tonic pillar’s theme coincides with D♯’s resolution pitch E in measures 57–58. 11. Reinforcing the tonic’s dominant-emulating impact, the preceding dominant is supertonic-emulating in its minor quality. Compare with Haydn/Mozart, 6.4c.

12. Though of no apparent consequence initially, the tinge of C♯ Minor supplied by A♮ in measure 53 sets the stage for the surprising turn of events beginning in measure 65. 13. Compare the addition of B♯ to D♮-F♯-A here (measure 72) and the addition of E♯ to G♮-B-D♮ in 1.8 (measure 12). That example’s resulting II⇨ is a more characteristic context for this evolved chordal formation than is this mazurka’s V⇨. 14. Though it may appear that the circular motion proceeds uniformly as B➔ E A➔ D G➔ C during measures 37 through 42, in my view the prior establishment of A as the local tonic places the B➔ E A➔ segment within its domain (extending from minor A to surging A➔), so that the progression extends beyond the tonic only with the arrival of D in measure 40, coinciding with the onset of the fifth-progression descending from Kopfton E. 15. In the context of A1, the content of measures 1 through 3 embellishes the initial tonic. The harmonic progression begins with I, not V♮. At the juncture of B and A2, the prior establishment of V♮ imbues equivalent content (measures 41 through 43) with an asserted dominant function, extending the B section’s harmonic goal into the domain of A2, preceding the re-emergence of the tonic. 16. Chopin’s spelling of II⇨ as D♯-G♮-A-C♯ at 493 is incorrect, of course. Yet in this case F ’s upward resolution to G♯ is elided, resulting in the direct succession to the dominant’s seventh, F♯. Consequently the “incorrect” G♮ reflects the line’s atypical downward orientation. 17. Compare with a similar lower-third shift in Schubert’s Piano Sonata in B♭ Major (D. 960), mvmt. 4, measures 41 through 62, which I address in my “Conspicuous 6-Phase Chords in the Closing Movement of Schubert’s Piano Sonata in B-Flat Major (D. 960),” in Rethinking Schubert (Oxford University Press, in press). 18. Two examples in Joyce Yip’s “Tonal and Formal Aspects of Selected Mazurkas of Chopin” (Ph.D. dissertation, University of Michigan, 2010) – numbered 2–4 (p. 188) and 6–1 (p. 263) – are derived from an analysis of this mazurka by Edward Laufer, presented in a talk entitled “A Different Reading for the Same Music” that he delivered at Queens College in 1993. (Similar graphs appear in his handout for the lecture

“Parenthetical Passages,” delivered at the Mannes College of Music Schenker Symposium in 1985.) Whereas he proposes a connection of the A chords at 213 and 243, I instead regard the former as an internal element within a circular progression whose endpoints correspond to the shift from A to A➔. Laufer’s title refers to his intriguing proposal that whereas the chord of measure 1 embellishes that of measure 2 (thus establishing the tonic at the outset), the chord of measure 26 may be regarded as dependent upon that of measure 25 (as its upper fifth), resulting in a bold DB♭ third is a counterpart to the a1 region’s CC>B♭ in measure 15. In FC, fig. 30a, Schenker proposes that the D♭ neighbor is prolonged: D♭>C♭>B♭ instead of D♭>C♭>B♭. 22. Though the accented C♭ at 40b3 might be understood merely as an anticipation of the following downbeat, it instead might be regarded as a last-moment shift of the A section’s key to A♭ Minor, with which the upcoming F♭ Major relates as diatonic I6. F♭ has been a prominent feature of the local harmonic fabric even in A♭ Major, from the downbeat of measure 1 onwards. See Patrick McCreless’s “The Pitch-Class Motive in

Tonal Analysis: Some Historical and Critical Observations,” Res musica 3 (2011), pp. 59–63 , for thoughtful commentary on Chopin’s deployment of F♭ in this mazurka from both Schoenbergian and Schenkerian perspectives. 23. During his analysis of this mazurka and commentary on Schenker’s reading in Phrase Rhythm in Tonal Music (New York: Schirmer, 1989; reprint edn., Ann Arbor: Musicalia, 2007), p. 220 , William Rothstein proposes: “Chopin’s … slurs are an analytical minefield. No composer so frequently slurred against the phrase structure of his music rather than in support of that structure.” Here the slur ends not in measure 48, coinciding with the close of the antecedent phrase, but instead during the following measure, after the first three notes of the consequent phrase.

24. In some compositions it is challenging to decide whether or serves as the Kopfton. Though I regard as the better reading in this case, I acknowledge that I have received prodding from an anonymous external reviewer to instead choose . My reading is worked out in 2.18, where A and G♯ play prominent roles at various stages. Anyone intrigued by this conundrum might wish to create an alternative analysis based on Kopfton and then to compare the two interpretations. Which elements of the composition are emphasized when is regarded as the Kopfton, and which are emphasized when is? How might a performance of the mazurka suitably project one or the other of these readings? 25. Compare with TAH, 6.19 through 6.21. 26. It is important not to assume a direct correlation between tonicization and structural depth. Though C Minor is tonicized during the b region’s initial measures, root C falls within the tonal path from tonic A♭ to dominant E♭ (represented by the inverted dominant harmony of measure 16). Though neither tonicized nor presented in root position, that dominant is hierarchically deeper than the preceding mediant. (Note that its imagined root E♭ is the only element of the b region that is attached to the middleground bass beam in 2.21.) Consequently I do not concur with the reading of the

basic harmonic progression for the mazurka’s A1 section (measures 1 through 24) as I … iii … I, as is proposed by John Rink in his “Tonal Architecture in the Early Music,” in The Cambridge Companion to Chopin, ed. J. Samson (Cambridge University Press, 1992), pp. 78–97, ex. 8 (p. 90) . 27. Felix Salzer offers a reading that calls upon neither of these assertions in his Structural Hearing: Tonal Coherence in Music, 2 vols. (New York: Boni, 1952; reprint edn., New York: Dover, 1962), ex. 361 . 28. Compare with a similar parallel progression in TAH, 7.14c. 29. Note that the coda’s E>D♯>D>C third was stated several times during the b section (measures 37–42). 30. Chopin misspells the chord at 283. E♮ stands for F♭, minor ninth of an E♭➔ chord that is derived from that which occurred at 203. 31. This notion is explored in my Tonal Analysis: A Schenkerian Perspective, section 1.3. 32. Though the chord of 523 is spelled as B-D♯-F♯, the melodic A>G>F♯ third of measures 48–52 serves to extend A, so that B-D♯-F♯(-A) is understood as B7. The imagined seventh, A, resolves to VI➔’s third, G♯, at 531. 33. Though the pitches at these two locations correspond, the C chord during the A1 section proceeds to the dominant, whereas that during the B section is part of a backand-forth motion that embellishes the tonic, as is conveyed by the Arabic numerals just below the bass beam in 2.26.

34. Whereas a conventional cadential in measure 35 embellishes the consequent phrase’s dominant, the corresponding chord during the antecedent (measure 31) serves as a common-tone diminished seventh. Chopin might have spelled it more appropriately as A♯-C♯-E♮-G, with the lower three pitches ascending by minor second to resolution on B♮-D-F-G in measure 32. Concurrently ninth A♭ displaces the dominant root. All this occurs above a tonic pedal point. Perhaps Chopin’s spelling in flats was motivated

by a desire to avoid a concurrent C and C♯. (My colleague David Grayson, a pupil of Nadia Boulanger, related to me her observation that Chopin often misspelled his chords, but that Schumann did not.) For an exemplary account of Chopin’s often quirky orthography, see part I, chapter 2, of Maciej Gołąb’s Chromatyka i tonalnoséc w muzyce Chopina (Cracow: Polskie Wydawnictwo Muzyczne, 1991) ; as Chopins Harmonik: Chromatik in ihrer Beziehung zur Tonalität, trans. B. Hirszenberg (Cologne: Bela Verlag, 1995) . 35. The means by which the G♯ chord is attained offers insight into why Chopin lowers B♯ to B♮ during measures 79 and 142. Since the G♯ triad is a half step “too high” for the G Major context, the B♮ of measure 142 might be perceived as an effort to attain G♮-B♮D♮ within the downward cascade of chords. The triad’s unyielding G♯ and D♯ prevent the achievement of that outcome. 36. Compare with a passage by Schubert in my “Conspicuous 6-Phase Chords,” exx. 4 and 5. 37. Compare with 2.14, mm. 16 through 24.

Chapter 3: Irregular pillars in the mazurkas

Chapter 3: Irregular pillars in the mazurkas 1. Though Schenker’s readings of this mazurka’s tonic pillars harbor several contradictions, he does not waver from displaying the Kopfton as . See FC, fig. 76, ex. 5; fig. 83, ex. 2; and fig. 119, ex. 11. Unfortunately most of these interpretations are neither detailed nor adequately annotated by measure numbers. However, it appears that for the most part he proposes a PAC close after four measures, though he offers a contrasting reading at measure 20. In “Parenthetical Passages,” a lecture delivered at the Mannes College of Music Schenker Symposium in 1985, Edward Laufer presented an analysis in which measures 3 and 4 project and 8 project

, while the equivalent measures 7

. For him, what occurs between those pairs of measures

consequently constitutes a parenthetical passage. I instead espouse the view that each of the three regions within the mazurka’s A1 and A2 sections offers four measures of content, followed by a four-measure varied repetition. Measure 24 exceptionally departs from that design, to conclude the tonic pillar with a PAC. Compare this structure (including how repeat signs are deployed) with that which prevails during the two-pillar Mazurka in E♭ Minor (opus 6/4), analyzed in 1.15 and 2.1.

2. Though an interpretation of 182 through 192 as

(reinforced by a

voice exchange) is tempting, Chopin’s slurring, which matches that of the a1 pillar, binds the and tonic chords within measure 18. Thus I propose that I-space persists through the end of measure 18, maintaining the model of measures 2 and 6. 3. Though each measure of the introduction begins with the interval of a perfect fifth, none of those fifths are structurally significant. Instead Chopin alternates between and neighbors

, with both E♮ and B♮ consistently delayed by suspensions. The tonic

harmony emerges in measure 9, not measure 2 or measure 4.

4. Compare with Chopin’s construction in 1.9. Note how the G♮-B-D♮ chord of measure 6 there eventually takes on an E♯, thereby projecting root C♯. 5. Though initially the pitch F♭ serves as a wobble within the D♭ chord, in the broader context it is transformed into the major dominant’s third, E♮. The diatonic context would be whole step F>E♭. Here the F is lowered and the E♭ is raised, resulting in the juxtaposition of the enharmonically equivalent pitches F♭ and E♮. 6. Chopin’s particular approach to the tonic 6-phase chord in this mazurka resembles that employed by Mozart in the Trio of his Symphony in G Minor (K. 550), analyzed in Haydn/Mozart, 9.2. 7. I offer a detailed exploration of the subtonic–dominant connection in my “Schenker, Schubert, and the Subtonic Chord,” in A Music-Theoretical Matrix: Essays in Honor of Allen Forte (Part II), ed. D. C. Berry, Gamut: Online Journal of the Music Theory Society of the Mid-Atlantic 3 (2010), pp. 127–166 . 8. See also my discussion of this passage in TAH, pp. 70–75, which includes commentary on Schenker’s reading of the passage (FC, fig. 54, ex. 6). 9. Indeed this turn of events is unusual and thus susceptible to a range of analytical responses. Michael Klein calls it a “dark subdominant … (with an added sixth)” and interprets this passage as residing within a coda in his “Chopin’s Dreams: The Mazurka in C♯ Minor, Op. 30, No. 4,” 19th-Century Music 35 (2011–2012), p. 255 . This article (pp. 238–260) offers a range of intriguing ideas that readers are encouraged to explore as a complement to the harmonic focus of my work.

10. Given the pillar’s broad harmonic trajectory from I to V♯ (supporting to ), the melodic attempt to reignite the tonic (potently colliding with the dominant during measure 33) is, in my view, doomed to failure. (The restoration of the tonic – transformed into I♯ – is deferred until the fourth measure of the B section.) Consequently I regard the melody’s A at 333 as ultimately bending to the dominant’s will: instead of igniting a reinstatement of I by means of an AC>C♭>B♭ and B♭>B [A♮]>A♭[G♯]. 8. Compare with the embellishment of II during the Mazurka in C Major (op. 24, no. 2), measure 13 [1.4]. 9. Bass C [B♯] at 331 comes after two-measure units that emphasize E♭ [D♯] (the circle’s fourth element) and D♭ [C♯] (a passing chord). Though initially the attentive listener will regard C as the third of a chord rooted on A♭ (the circle’s fifth element), the downward trajectory from E♭ through passing D♭ does ultimately lead to C as root, taking into account the transformation that transpires during measures 33 through 35. Consequently the structural melodic line, which has descended from Kopfton G through F to E♭, now detours upwards through E♮ to incomplete neighbor F in measure 37 (in a trajectory divided between the soprano and bass) before reaching goal D in conjunction with the dominant. (See 4.3.) 10. Chopin rejects the D♭-F-A♭ sonority twice during this passage: first, the circle of fifths is abandoned just as the A♭➔ chord is targeting a D♭ arrival; and second, the minor IV’s chromatic 6-phase chord, F-A♭-D♭, is auditioned during measure 38 but

rejected, with the D♮ of measure 40 successfully leading from IV onwards to V♮. (Though D♭ is chromatic if F-A♭-C is interpreted as IV in C Minor, the onset of an F Minor tonicization would instead support CC, echoing the GG sounded during A1’s opening tonic presentation.) 11. Though Schenker’s and my conceptions of the A1 section’s second part correlate to some extent, we disagree on numerous points. Again looking principally at Five Graphic Music Analyses, note how our interpretations of the path from root C to root F are similar, even if I make more of the interior E♮-G-B♭-C chord than he does and interpret the melodic line as emanating from Kopfton G rather than E♭. I regard his assertion of ’s arrival at measure 27 to be untenable. The I⇨ chord that immediately precedes root F could contain either an imagined C or an imagined D♭ (displacing C). Either way, the D♮ of measure 27 is a neighboring note that resolves to the C at that measure’s close. D is a member neither of the C chord nor of the F chord. How, then, can it be regarded as the onset of ? Looking next at measure 28, Schenker acknowledges the addition of minor seventh A♭ to the B♭ major chord in his foreground graph (p. 58), yet he does not follow through on assessing the repercussions of that surge-inducing act – namely, the succession from B♭➔ to E♭. During measures 29 through 33 he and I present opposing hierarchies for the chord pairs. From his perspective root A♭ takes hold at measure 29, whereas in my view the circle of fifths proceeds normatively to E♭ before the arrival of A♭ (realized by a chord in first inversion) in measure 33. Though he has moderated the potent seismic shifts that raise A♭➔ to C➔ in measures 33 through 35 through the extensive use of parenthetical notes in his foreground graph, we both understand that this activity is leading the progression towards IV, though I find it curious that the IV numeral is postponed until measure 40 in his foreground graph – at the point where IV shifts to its 6 phase. 12. See Schenker’s foreground graph in Five Graphic Music Analyses, p. 58. 13. Five Graphic Music Analyses, p. 58. 14. Though not identical, the structure here closely resembles that of 264 through 274.

15. Diminished seventh chords in measures 66 and 68 soften the stark voice leading displayed in 4.3. That in measure 66 targets the chord of measure 67 as that in measure 64 targets the chord of measure 65. Because the descent of the chords is not evenly spaced (a major second from D♭ to C♭, but a minor second from C♭ to B♭), the chord of measure 68 does not function like those of measures 64 and 66. Instead it anticipates the upcoming subtonic. 16. Though this ♭II offers fulfillment after the frustrations noted in the vicinity of measures 33, 38, and 65, Schenker’s graph of the entire movement in FC, fig. 12, erases it, displaying instead a diatonic II with at measure 72. Readers mystified by such seeming errors may gain insight into Schenker’s thinking by comparing the two graphs labeled “1. Schicht” and “2. Schicht” in Five Graphic Music Analyses, pp. 54–55. 17. See TAH, p. 313, n.14, for samples of creative diminished-seventh usage on display in August Swoboda’s Harmonielehre (Vienna: Haykul, 1828) , tab. V. The date and place of publication tantalizingly encourage the hypothesis of a direct encounter with its contents (or even with the author himself) during Chopin’s two visits to Vienna preceding his migration to Paris. For an account of Chopin’s documented or presumed exposure to music theory during his Warsaw years (including notions derived from Albrechtsberger and from Kirnberger), see the exemplary account in part I, chapter 1, of Maciej Gołąb’s Chromatyka i tonalnoséc w muzyce Chopina (Cracow: Polskie Wydawnictwo Muzyczne, 1991) ; as Chopins Harmonik: Chromatik in ihrer Beziehung zur Tonalität, trans. B. Hirszenberg (Cologne: Bela Verlag, 1995) . 18. Phipps cites a motion to an F minor chord in measures 36–37 to support his assertion. Note, however, that there the bass is E♮ (sounded at 351), which targets resolution pitch F (presented in multiple registers during measure 37). In contrast, the bass D♭ (measures 65 and 66) is disinclined to ascend to F, though Phipps displays exactly that hypothetical resolution (his ex. 13).

Chapter 5: Nocturne in C♯ Minor (op. 27, no. 1)

Chapter 5: Nocturne in C♯ Minor (op. 27, no. 1) 1. It was recommended to me in 1976 by my first Schenkerian analysis instructor, John Rothgeb. 2. The Music Forum was published in New York by Columbia University Press. Salzer’s article is found on pp. 283 through 297 of volume 2. His analysis is discussed in Alison Hood’s “Intraopus Connections in Chopin’s Nocturnes, Opus 27,” in The Sources of Chopin’s Style: Inspirations and Contexts, ed. A. Szklener (Warsaw: Narodowy Instytut Fryderyka Chopina, 2005), pp. 371–385 . Hood incorporates additional commentary from John Rink’s 1989 Cambridge University dissertation, “The Evolution of Chopin’s ‘Structural Style’ and Its Relation to Improvisation,” which I have not been able to access. 3. The Oster Collection: Papers of Heinrich Schenker (housed at the New York Public Library for the Performing Arts at Lincoln Center), file 32, item 51. The archive includes several intriguing graphs by Ernest Oster of a passage from the nocturne (file 32, item 46). Oster’s placement of the abbreviation “recap.” at measure 84 concurs with my reading, in contrast to Salzer’s assertion of a formal division at measure 65. 4. It would be reasonable to propose that measures 7 and 8 should be read as III5−6 IV, with the internal III6 asserted locally as I➔. My analysis in 5.1 instead juxtaposes two continuations from the same starting point: from minor tonic to the mediant between 31 and 71 as a means of expanding the initial tonic, then a tonic restoration proceeding to a contorted dominant between 73 and 94. Chopin’s excursion to the mediant extends the first phrase into a fifth measure, requiring some compensatory compression: the second phrase begins now in the middle of measure 7, rather than at its outset. 5. In the second and fourth of these statements, C♯ is embellished by an excursion up to E (as C♯A. The passing note B♭ seems at first to attach itself structurally to the C♮ chord (at 63), forming a C➔ surge towards F♮. Chopin indeed may be playing with listeners’ expectations by projecting the first two chords of a I

♮II5♮ V progression, a chromatic variant of the first phrase’s

I5–6 II➔ V. Yet by the downbeat of measure 7 that potentiality loses its viability, and the deeper connection between E and A becomes paramount. 17. Concerning this thorny issue, see TAH, 7.6 (including the commentary regarding Progression 3 on p. 175). 18. Continuing the discussion of slurring begun in note 12, the score that Lerdahl provides as fig. 3.1 contains a bass slur beginning at the B of 84 and extending through the E of 93. Again, that does not correspond to the recent Urtext editions, where a single

long slur extends from 51 through the final chord. Though I disagree in some details with Schenker’s unpublished analysis of the prelude (see note 5 above), his jottings for measures 5 through 8 twice show a progression from I through III (sic) to V, supporting a structural descent from to . 19. Aldwell and Schachter, Harmony and Voice Leading, pp. 628–629. 20. Dmitri Tymoczko offers an alternative analysis of this phrase in his A Geometry of Music: Harmony and Counterpoint in the Extended Common Practice (Oxford University Press, 2011), pp. 218–219 . Our widely divergent views on harmonic analysis are apparent even in some basic statistics: my example (6.3) employs three Roman numerals (one chromatically modified) and four letters indicating roots (two of which coincide with Roman numerals), all in E Major; his example (6.6.2) employs sixteen Roman numerals in the keys of E, C, F, d, A♭, and then E again. (My strongest objections relate to both passing chords, labeled as ii , and to the chord with suspensions labeled as iii within parentheses.) We both read the phrase as continuing to E Major’s dominant at the end of measure 8, contrasting Lerdahl’s close on the preceding G♯ [A♭] chord. 21. Aldwell and Schachter, Harmony and Voice Leading, pp. 590–591. 22. Though Lerdahl’s commentary acknowledges the exceptional nature of this passage – “modulates to a distant place, returning home at the last moment” and “remarkable for its pitch-space journey” (pp. 89–91) – his fig. 3.8b conveys neither a veering away from an intended course (in the way that my crossing out a chord, highlighted within a box, does in 6.4) nor even that there is an intended course targeting C. In addition, the juxtaposition of G and V/E appears to grant the G a higher hierarchical status than the structural dominant. Note that the B dominant chord of 114, because it resides within the tonal sphere of goal E, is absent from the representations in his figs. 3.5 and 3.6; and though a V appears and is circled in his fig. 3.8b, it there pales in comparison with the bold presentation of circled E, a, F, g, and G. My discomfort with this visual presentation corresponds exactly to a similar sentiment expressed in my assessment of

the early nineteenth-century author Gottfried Weber’s analytical procedure in TAH (p. 147 and 6.7). 23. A whole step in one voice occurs at the prelude’s outset: B>A in measures 1 and 2. Consequently a parallel progression of diminished – rather than minor – chords ensues. Given their role in filling in a broader tonic expanse, there is no one “correct” way to spell the progression’s internal chords. In fact, Chopin shows no predilection even to spell them using a sixth and a third above the bass, as I have done in 6.5. 24. Parallel progressions of diminished seventh chords descending in half steps were sufficiently commonplace by the beginning of the nineteenth century to be featured in the harmony textbook used at the Conservatoire National de Musique in Paris: CharlesSimon Catel’s Traité d’harmonie [1802]. See TAH, 3.11b. 25. One might propose an alternative hypothesis in which the surging I➔ is asserted earlier – at the end of measure 3 (G♯-B-D-F♮, with B locally embellished by neighbor C) – and then prolonged through the end of measure 8. (This hypothesis is closely allied with Schenker’s reading, published in London and Rodman, “Musical Genre,” p. 119.) One could accommodate that view by spelling the third tenor note in 6.5 as G♯ and adjusting the slurring. However, I do not hear measure 3 as anything other than an interior element of an expansive downward glide. Thus I stand by my reading as presented in 6.5. 26. Though a minority opinion during the nineteenth century, this perspective is not without historical precedent: see TAH, 3.4b and 7.14c. Dmitri Tymoczko’s A Geometry of Music, fig. 8.5.5 (p. 287), offers the antithesis of my perspective: seventeen analytical symbols in a total of five keys over the course of the phrase. 27. Two distinct levels of hierarchy are at play here. Several bona fide passing chords (such as E-G-C♯-A♯[B♭] in measure 4) connect the perimeter tonic chords of measures 1 and 8; while at the surface level the gradual falling-into-place of those various passing chords results in a range of incidental simultaneities that perform a connective role between the individual passing chords. For example, E-G♯-D-B at the beginning of measure 4 should not be interpreted as I➔ even though the ultimate goal of the

descending parallel progression is, in fact, a form of I➔. (On this point, I disagree with Schenker’s analysis in the Oster Collection, cited above.) 28. Note the lovely motivic association between G>F♯ and C>B in measure 12. The latter occurs twice (corresponding to the BC>B triplet should be interpreted as a layering of neighboring embellishments: C embellishes B, whereas D embellishes C. It makes no sense from a Schenkerian perspective to process the triplet – as London and Rodman do – as a filledin unfolding of the third

, since D♯ – not D♮ – is a member of the dominant harmony

prolonged since measure 10.) The C>B neighbor reiterates the bass motion of measures 9 through 12 and is then taken up by the melody during measure 13, as in measure 1. 29. London and Rodman, “Musical Genre.” 30. Regarding the critical G♯-B-D-F♮ chord at the end of measure 8, Lerdahl’s vii°/a reading (in his fig. 3.20b) is similar to my surging tonic (I➔) reading. We agree that it is a chord that potently targets the A minor chord of measure 9. In my view London and Rodman’s “Schenkerian” reading misses the point: the ♭vii7 label in their ex. 1 (presented instead as “vii7” within quotation marks in their commentary on p. 102) pertains to the D-F♮-A-C chord of 81, from which they proceed directly to measure 9’s iv6, omitting consideration of the G♯-B-D-F♮ chord altogether at this level. (They propose a subdominant prolongation from 51 through 92.) In the succeeding paragraph of their commentary they do mention the I➔ chord, labeling it vii°7/iv. It appears in the foreground layer of their ex. 1 as a connective chord between ♯vii7 and iv6. Since they were attempting to construct a Schenkerian analysis of the work, it is curious that they did not take into account that Schenker employed only one Roman numeral for all of measures 7 and 8: I♯ below a D-F♮-G♯-B chord. (Though Schenker’s analysis in the Oster Collection is sketchy, on this point the perspective is clear: the measure numbers 7–8 sit squarely underneath a I♯3 numeral – not off to the side, as in the botched London and Rodman transcription.) 31. Schachter, “The Prelude in E Minor,” and Schachter, “The Triad as Place and Action.”

32. That third is traversed both in an interior strand during measures 18 through 20, as indicated by the slurred noteheads in 6.6, and in the upper register (where a beam is employed) during measures 18 through 24. 33. London and Rodman, “Musical Genre,” p. 104. 34. Schachter, “The Prelude in E Minor.” 35. Though his Roman numeral analysis does not acknowledge F♯’s presence in the chord, I think Schachter would agree with me that by this point the IV Stufe has shifted to what I refer to as its 6 phase, with F♯ serving as the sixth above root A. (The Arabic 6 at measure 16 of Schachter’s 1994 graph instead indicates that the iv chord initially sounds in an inverted state.)

Chapter 7: Prelude in G Minor (op. 28, no. 22)

Chapter 7: Prelude in G Minor (op. 28, no. 22) 1. Analyzing Schubert (Cambridge University Press, 2011). 2. Interpreting Chopin: Analysis and Performance (Farnham: Ashgate, 2014) . 3. “Ambiguity of Tonal Meaning in Chopin’s Prelude Opus 28, No. 22,” Festschrift for Steve Larson, Music Theory Online 18/3 (September 2012) . A revised version of this article appears on pages 111 through 124 of Interpreting Chopin. 4. This relationship between B♭ and A is replicated later, in measures 24 and 32 (treble clef). The gesture collides with the dominant’s embellishing chord (B♭-E♭-G) during 342. 5. In that an evolution of the ⇨ type occurs most often in the context of II⇨ proceeding to a major dominant, it is opportune that the subdominant to which I⇨ proceeds is of major quality (atypical in a minor-key context). 6. Hood employs the word “ambiguous” or one of its derivatives a total of twenty-six times within her six-page essay. Indeed, when I was younger I found many passages in Chopin’s music ambiguous, though I did not extol ambiguity as an important compositional feature. As I have aged I have found less and less of the music that I study to be ambiguous. I regard this as a sign that my analytical acumen has developed (to the point that I now willingly publish my analyses, something I refrained from doing during that earlier phase of my career). Certainly some readers (including Hood) might suggest instead that an undesirable rigidity has invaded my thinking – that I too summarily reject alternative readings that might hold potential. Though I do not celebrate ambiguity as Hood does, I appreciate the sincerity of her conviction. 7. Hood’s graphs and her commentary present somewhat different conceptions. Her paragraph 16 asserts: “The vii°7 at the beginning of measure 8 encourages us to hear the A as part of a dominant-functioning harmony. Yet, at the same time, because B♭–A–G sounds as an upbeat (as it did previously) we can also hear it as prolonging tonic harmony, so the A is heard as a passing tone that resolves to G … it can now be interpreted in two mutually-exclusive ways.” Whereas I am using the comparatively

unambiguous context of measures 8 and 9 to come to terms with measures 0 and 1, she is imposing her interpretation of measures 0 and 1 upon measures 8 and 9 even though, as she acknowledges, the chordal accompaniment does not support it. A review of the graphs from chapters 1 and 3, above, reveals that thirteen of the forty-three mazurkas explored there do not begin on a tonic chord. Whereas I suggest that this prelude conforms to that 30 percent option, Hood is endeavoring to hear the work in terms of the alternative 70 percent option, despite Chopin’s instructive presentation within measures 8 and 9. 8. Mehrdeutigkeit (multiple meaning) is explored in TAH, pp. 155–161. 9. Compounding my confusion, the score labeled A2 in Hood’s ex. 2 places a I numeral (why capital?) at the end of measure 33 (note that the bar line between measures 32 and 33 was inadvertently omitted) rather than where I think it was intended – below the G at the end of measure 34. 10. Certainly the author of an article whose title begins with the word “Ambiguity” should be extra careful in proofreading, lest unintended additional instances of ambiguity divert the reader’s attention, as it has mine. The remarks in this chapter correspond to the article’s state on October 12, 2012, not to the version later published in Interpreting Chopin (after Harmony in Chopin went into production).

Chapter 8: Prelude in C♯ Minor (op. 45)

Chapter 8: Prelude in C♯ Minor (op. 45) 1. “Chopin and ‘La note bleue’: An Interpretation of the Prelude Op. 45,” Music & Letters 78 (1997), pp. 233–253 ; as “Chopin et ‘la note bleue’: Une interprétation du Prélude opus 45,” in Eigeldinger, J.-J., L’univers musical de Chopin (Paris: Fayard, 2000), pp. 169–188 . 2. “‘Rounding Up the Usual Suspects?’: The Enigmatic Narrative of Chopin’s C-sharp Minor Prelude,” in Engaging Music: Essays in Music Analysis, ed. D. Stein (Oxford University Press, 2005), pp. 236–252 . 3. See TAH, 3.2. 4. Ibid., 3.3, 3.4, and 3.5. 5. When working on this article, Eigeldinger regarded the prelude’s cadenza as occurring in measure 80. Yet in the subsequent Peters edition (2003), which he edited, the cadenza is counted as a continuation of measure 79. (The latter view conforms to the National Edition as well.) Consequently I have tacitly lowered all of the article’s measure numbers higher than 79 by one in my commentary. 6. Eigeldinger hears echoes of his tetrachords (with some chromatic inflection, and curiously breaking off in the middle of the second one) in the forthcoming main section’s bass. In note 29 he asks readers to ponder the following series of stepwisedescending bass pitches: C♯ (51), B (91), A (131), G♮ (171), F♯ (191), and E (231). I reject the placement of G♮ within this series, in that the G♮ chord resides within the domain of a hierarchically deeper D♮ chord; and I can make sense of E only as an internal component of an F♯>E>D♮ third whose goal D♮ is elided at 271 (as will be explained in due course). I will argue that the C♯-to-D♮ contour of this region corresponds to the C♯-to-D♮ seventh introduced during the introduction. 7. Readers will find the relationship I propose between the introduction and the main section of this prelude reminiscent of the correlation I draw between the introduction and exposition of Schubert’s Symphony in B Minor (“Unfinished”), movement 1. See Schubert, chapter 7.

8. Smith acknowledges this D♮ chord without assigning it a significant role (p. 251). In his score 20.1 he places the following symbol underneath measure 4 (not measure 3): [➔D?]. 9. In that editor Deborah Stein introduces Smith’s essay by informing readers that he “has long been interested in … the theories of Heinrich Schenker” (p. 236), impressionable young readers (the book’s intended audience) might assume that there is something Schenkerian about Smith’s analysis. That assumption would be incorrect. Any Schenker-influenced reading would acknowledge the foundational role of I V♯ I within the introduction, as conveyed in 8.1b. 10. Though the bold type in which the words rounded binary form are printed prods readers to look up the term in the glossary provided at the end of the volume in which Smith’s essay appears, the definition found there (p. 331) and the formal description of the prelude in his essay do not correspond. 11. Smith’s word “retransition” corresponds to the German word “Rückleitung” in Hugo Leichtentritt’s analysis of the prelude. See his Analyse der Chopin’schen Klavierwerke, 2 vols. (Berlin: M. Hesse, 1921–1922), vol. 1, pp. 177–179 . 12. As I did also in my critique of Lerdahl (note 22 on pp. 274–275), I trace my discomfort with this visualization back to a similar sentiment expressed in my assessment of the early nineteenth-century author Gottfried Weber’s analytical procedure in TAH (p. 147 and 6.7). 13. It is important to keep in mind that the F♮ chord of measures 55 through 63 is a wobble-infiltrated mutation of F♯, and not a misspelled E♯ chord. Consequently Smith’s application of the word “mediant” in his n. 16 (p. 241) is entering dangerous territory, in my view. Likewise, Gunner Rischel’s Roman numeral III (within the progression III IV II V I) is off the mark. (See his “Tonal analyse,” Musik & Forskning 14 (1988–1989), p. 127 .) 14. The cadenza’s emphasis upon the D♯ nodal point in part compensates for the brevity of that chord (measure 65) during the initial presentation of the main section.

15. In the glossary of Engaging Music, the volume in which Smith’s essay appears, editor Deborah Stein distinguishes two different meanings for the word “Reprise”: “a repeated section” or “the repetition of opening material later in the piece” (p. 331). In the context of my one-part form, I use the word in the former sense; in the context of his idiosyncratic rounded binary form, Smith uses it in the latter sense. I suspect that Eigeldinger intends the “repeated section” meaning as well, though the terseness of his commentary leaves that open to question.

Chapter 9: Ballade in F Minor (op. 52)

Chapter 9: Ballade in F Minor (op. 52) 1. Laufer’s essay, “On Chopin’s Fourth Ballade,” is published in Keys to the Drama: Nine Perspectives on Sonata Form, ed. G. Sly (Farnham: Ashgate, 2009), pp. 157–175 . Another substantial account of the ballade (from a contrasting perspective) that readers might wish to pursue concurrently is Michael Klein’s “Chopin’s Fourth Ballade as Musical Narrative,” Music Theory Spectrum 26 (2004), pp. 23–55 . 2. Before proceeding to publication, Laufer presented his analysis at the Fourth International Schenker Symposium (Mannes College of Music, New York, March 17, 2006). The longhand examples were printed on pages that measure 11 by 17 inches. Typeset for publication with no changes in layout, the same examples were reduced so as to fit onto pages that measure approximately 6 by 9 inches. 3. My reading of the work embraces this conventional flow from the tonic to the dominant. In his “Chopin’s Modular Forms” in Variations on the Canon: Essays on Music from Bach to Boulez in Honor of Charles Rosen on His Eightieth Birthday, ed. R. Curry, D. Gable, and R. L. Marshall (University of Rochester Press, 2008), pp. 198–199 , Robert P. Morgan proposes that the theme ends instead with “a full cadence in iv” followed by a “brief, half-measure transition back to V of F minor following the end of the theme.” That perspective coincides with Laufer’s analysis, to be explored below. 4. In his “Ambiguity and Reinterpretation in Chopin,” Chopin Studies 2, ed. J. Rink and J. Samson (Cambridge University Press, 1994), pp. 140–160 , Edward T. Cone savors Chopin’s treatment of the ballade’s initial C chord: what may at first seem to function as the dominant of an F tonic arriving in measure 2 (displayed as one of two analytical hypotheses in his ex. 8.1) is tonicized for several measures, after which it reveals its role as dominant – of the F tonic that emerges in measure 8. Cone projects the conviction that Chopin “wished us to hear” the passages as “deliberately ambiguous” (p. 141). I endorse an alternative perspective on this issue. Whereas for many analysts a chord such as C-E♮-G-B♭ automatically will be labeled as V7 (either as a dominant or as an “applied” dominant, here V7/IV), I am comfortable with such a chordal configuration emerging at any point where a descending-fifth root succession occurs. Chromatic

pitches often are incorporated so as to enhance the forward momentum generated when a chord surges, without concurrently signaling diatonic pitch content within any key. Consequently when listening I embrace the energetic initiative of a I➔ or II➔ or VI➔ without concurrently expecting that the chords they target will function as a tonic at any level. Clearly this is a matter that defies resolution. Though Cone’s strongly worded conviction – that a “convincing analysis” “must reveal” such an intention – is reasonable, certainly others may pursue alternative perspectives with equal justification. 5. Since the cadence will be a major point of contention between Laufer and me, I mention here that Lauri Suurpää’s analysis in “The Path from Tonic to Dominant in the Second Movement of Schubert’s String Quintet and in Chopin’s Fourth Ballade,” Journal of Music Theory 44 (2000), pp. 468–469 , similarly proposes an interruption at

. Suurpää does not acknowledge Chopin’s establishment of A♭ as the Kopfton prior to the cadence. Instead he proposes a novel – and in my view doubtful – structural reading, ascending from to . (The establishment of as the Kopfton in the context of a mediant chord, as I propose occurs in measure 13, is demonstrated by Schenker in FC, fig. 38a and fig. 40, ex. 10.) For a reading more in line with Laufer’s, see William Rothstein’s “Ambiguity in the Themes of Chopin’s First, Second, and Fourth Ballades,” Intégral 8 (1994), p. 25 , where he proposes that “the dominants in question are not typical half cadences. The large-scale harmonic progression of each variation – basically I-(III)-IV-V7– closes into the tonic at the beginning of the next variation, so that a chain of overlapping progressions results.” My subtly different reading proposes that a hierarchically deep C, E♮, and G during the second half of measure 22 collide with a foreground B♭ that serves as a local voice-leading connection to the following I. 6. Though what ensues in measures 23ff. turns out to be a modified repetition of A1 rather than A2, listeners might reasonably surmise that the work has embarked upon the post-interruption half of a binary structure at that point. 7. The flourish of notes following the fermata chord in measure 134 suggests that Chopin might likewise have intended the fermatas of measure 7 as an invitation to some improvised embellishment. Nowadays any deviation from the printed score during a

performance attracts inordinate attention, since many members of the audience have heard numerous live or recorded performances of the work already. Clearly that state of affairs was not in play during Chopin’s lifetime. A modern performer might at least privately (and perhaps even publicly) seek to regain that spontaneity through tasteful additions to the printed score in contexts such as measure 7. 8. Laufer’s correlation of the D♭ tonicization to the already established B♭ subdominant echoes a reading presented by Carl Schachter in his review of Jim Samson’s The Music of Chopin, Music Analysis 8 (1989), p. 190 . On the other hand, Laufer and I disagree with Schachter regarding how Chopin leads onwards from D♭: we interpret the prominent chromatic line A♭A♮>G, and D♮>C>B♭), the upper strand appears awkwardly as A♭>G♭>E♮. Using modulo 12 numbers that line would be represented without enharmonic seam as 8>6>4. One attains the downbeat embellishing chord within the prevailing F Minor key (modulo 7), enters the domain of modulo 12 for the -2-2 parallel progression, and then thrusts the goal chord back into the modulo 7 environment.

Chapter 10: Barcarolle in F♯ Major (op. 60)

Chapter 10: Barcarolle in F♯ Major (op. 60) 1. “The Barcarolle: Auskomponierung and Apotheosis,” in Chopin Studies, ed. J. Samson (Cambridge University Press, 1988), pp. 195–219 . Readers also should consult David Kopp’s “On Performing Chopin’s Barcarolle,” Music Theory Online 20/4 (2014) , which appeared after the present book went to press. 2. The parallel progression’s upper line, which traverses all the diatonic steps within a G♯>G♯ octave, is highly embellished, particularly with incomplete upper neighbors following the principal pitches, beginning with the last pitch in measure 1: F♯seventh), and so a uniform descent ensues. During the prolongation of the tonic’s upper-third chord during the B section, the three principal strands connect different elements of the prolonged chord (fifth>root, third>fifth, and root>third). Consequently the line emanating from E♯ gets off to a slow start, since it has a shorter distance to cover. The interior strand does not pursue a maximally linear course, which would be C >(B♯)>A♯>(G♯)>F♯>E♯. (Chopin omitted the notes enclosed within parentheses.) 7. The proposed broad F♯E♯ (fourth and sixth soprano noteheads of measure 29). The situation is complicated by the linear activity of the interior strands. Whereas internal A♯>G♯>F♯ in measure 28 reinforces the F♯>E♮>D♯ above (both connecting members of the F♯➔ and the following B chords), the D♯ of an E♮>D♯>C♯ third (seventh to fifth within the F♯➔ chord) collides with the sounding of F♯ during 283, and that third’s C♯ (the note to which D♯ passes) sounds only an octave lower. 8. Rink lists what I refer to as the B section as a ‘Development’ – single quotes included – in his formal synopsis of the Barcarolle (his fig. 1). 9. I explore this issue in detail in TAH, pp. 162–165, incorporating analyses of a passage from Chopin’s Prelude in D♭ Major by Schenker and by Schoenberg [6.21a–b]. The C♭ in the Prelude’s measure 9 is the equivalent of the E♮ in the Barcarolle’s measure 17. 10. As suggested above, a comparison with 3.6a, an analysis of the Mazurka in B Major (op. 63, no. 1) – just three opus numbers after the Barcarolle! – is encouraged. 11. Rink’s presentation of the A♯➔ chord of 94 in his foreground graph (example 9) is botched: whereas the chord’s A♯, C , and E♯ are all accounted for, the magic is missing

because F♯’s ascent to G♯ is neglected. All the pitches of A♯⇨ in 302 are accounted for in his fig. 11. 12. The chromatic variants of an upper-third chord were introduced in Schubert, pp. 59– 60. For F♯ Major’s upper-third A♯-C♯-E♯, the first chromatic variant is A♯-C -E♯, the second is A♮-C♯-E♮, and the third is A♮-C♮-E♮. 13. Likely some Schenkerian analysts would instead interpret this passage as III5−6 (with the 6-phase chord unfurled into position) proceeding to II➔. The correlation with Chopin’s treatment of the B section’s upper-third chord has influenced my willingness to posit a full-fledged return of I in measure 76. As with the tonic chord of 174, its duration is breathtakingly brief. Nevertheless, it represents the completion of broad tonic prolongation, in this case embellished by an uncommonly potent and extended upper-third chord. 14. As commonly occurs in the shift of a minor third, the diminished-seventh sonority is called into service. From E-G♯-B-D♮ in measure 72 Chopin proceeds to G♯-B-D♮-F♮ at the end of measure 75. Resolution to A♮-C♯-E♮ seems imminent. Yet in terms of what follows, this chord behaves as if its spelling had been E♯-G♯-B-D♮, representing C♯➔. That alternative interpretation is confirmed by the arrival of root C♯ at 761.

15. This

embellishment stems from

at 64.

16. See, for example, the progression explored in 6.4. 17. Though foreground Roman numerals are not provided, it appears that Rink intends a tonicization of C♯ Major via what I would label as I➔ IV♮ V7 I. 18. Rink’s positioning of a PAC under his measure number 91 in ex. 3 is not borne out by the content of that measure in Chopin’s score. The cadence is indisputably at 931, as he proposes in his ex. 7 (contradicting his exx. 1 and 3). 19. Bass D♮>C♯>B♯ during measure 101 coordinates with the tenor register’s B♯B♮>A♯[B♭]. Chopin inaugurates the succession to II⇨ before that third’s traversal is complete. Consequently between the harmonic entities D♯-F -A♯-C♯ and D♮-F♯-A♮-B♯ (a normative succession from a surging I6 to an evolved II⇨) the pitches D♮, G♮, and B♮ happen to sound at the same time. That is a purely incidental consequence of these colliding voice-leading initiatives, in no sense asserting a ♮II5♮ (“Neapolitan”) function, which Rink proposes (with his label ♭II ) as the harmonic support for background (p. 210).

List of references to music examples 1.1 5, 7, 12, 73 1.2 12, 44 1.3 9, 12, 23, 31, 74 1.4 12, 41, 79, 83, 269 1.5 12, 49 1.6 12, 14, 81, 256 1.7 49 1.8 50 1.9 11, 32, 86 1.10 27, 60, 257 1.11 29, 30, 41, 74 1.12 52 1.13 54 1.14 56 1.15 32, 42 1.16 67 1.17 25, 53 1.18 69 1.19 31, 65 1.20 41, 45 1.21 77 1.22 32, 62 1.23 37, 41, 71, 84 1.24 39, 41, 58

1.25 37, 84 1.26 41, 86 1.27 63 2.1 50 2.3 50, 53, 95 2.4 53 2.6 53, 83 2.15 160 2.16 114 2.18 73, 74 2.19 74 3.2 96, 98, 99, 101, 236 3.3 99, 101, 236 3.4 11, 236 3.5 111, 236 3.6 236, 283 3.7 236 3.8 236 3.10 273 6.4 236, 283

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Index of Chopin’s works Ballades op. 38 (F Major), 254 op. 52 (F Minor), 213–232 Barcarolle op. 60 (F♯ Major), 233–252 Étude op. 10, no. 2 (C Minor), 145–156 Grande Valse brillante op. 18 (E♭ Major), 253 Mazurkas op. 6, no. 1 (F♯ Minor), 32, 43, 71, 73–74 op. 6, no. 2 (C♯ Minor), 4–5, 7, 43, 73–74 op. 6, no. 3 (E Major), 106–109 op. 6, no. 4 (E♭ Minor), 22–23, 42–44, 264 op. 6, no. 5 [a.k.a. op. 7, no. 5] (C Major), 5–6, 43, 44–45 op. 7, no. 1 (B♭ Major), 6–7, 43, 74, 255 op. 7, no. 2 (A Minor), 26–27, 43, 64–65, 160 op. 7, no. 3 (F Minor), 95–98, 123 op. 7, no. 4 (A♭ Major), 16–17, 43, 74–75 op. 17, no. 1 (B♭ Major), 91–95 op. 17, no. 2 (E Minor), 27–29, 43, 45–47 op. 17, no. 3 (A♭ Major), 23–24, 43, 67 op. 17, no. 4 (A Minor), 29–30, 43, 77 op. 24, no. 1 (G Minor), 109–111 op. 24, no. 2 (C Major), 7–8, 43, 79–81, 269 op. 24, no. 3 (A♭ Major), 8–9, 14, 43, 47–49 op. 24, no. 4 (B♭ Minor), 9–10, 12, 43, 81–84

op. 30, no. 1 (C Minor), 96–98 op. 30, no. 2 (F♯ Minor), 10–12, 43, 49–50, 259 op. 30, no. 3 (D♭ Major), 6, 12–13, 43, 50–52 op. 30, no. 4 (C♯ Minor), 11, 98–101 op. 33, no. 1 (G♯ Minor), 17–18, 43, 52–53, 273 op. 33, no. 2 [a.k.a. op. 33, no. 3] (C Major), 24–25, 43, 53–54 op. 33, no. 3 [a.k.a. op. 33, no. 2] (D Major), 25, 43, 67–70 op. 33, no. 4 (B Minor), 130–133 op. 41, no. 1 [a.k.a. op. 41, no. 2] (E Minor), 18–20, 43, 54 op. 41, no. 2 [a.k.a. op. 41, no. 3] (B Major), 116–119, 273, 274 op. 41, no. 3 [a.k.a. op. 41, no. 4] (A♭ Major), 119–120 op. 41, no. 4 [a.k.a. op. 41, no. 1] (C♯ Minor), 20–21, 43, 56–58 without opus 42A (A Minor), 101–104 without opus 42B (A Minor), 32–35, 43, 58–60 op. 50, no. 1 (G Major), 35–37, 43, 84 op. 50, no. 2 (A♭ Major), 37–39, 43, 86 op. 50, no. 3 (C♯ Minor), 111–116 op. 56, no. 1 (B Major), 11, 13–14, 43, 86–90 op. 56, no. 2 (C Major), 15, 43, 60–62, 265 op. 56, no. 3 (C Minor), 133–136 op. 59, no. 1 (A Minor), 136–142 op. 59, no. 2 (A♭ Major), 120–124 op. 59, no. 3 (F♯ Minor), 124–129 op. 63, no. 1 (B Major), 104–106, 283 op. 63, no. 2 (F Minor), 31, 43, 62–63 op. 63, no. 3 (C♯ Minor), 39–41, 43, 63–64 Nocturne op. 27, no. 1 (C♯ Minor), 157–165

Preludes op. 28, no. 4 (E Minor), 166–167, 176–186 op. 28, no. 9 (E Major), 166–176 op. 28, no. 15 (D♭ Major), 283 op. 28, no. 22 (G Minor), 187–197 op. 45 (C♯ Minor), 198–212 Scherzo op. 31 (B♭ Minor), 254

Index of names and concepts Aldwell, E., 167, 173, 176, 273 antecedent/consequent, 21, 22–23, 25, 26, 29, 30, 31, 41, 58, 62, 65, 67, 77, 86, 108, 116, 122, 158, 172, 187, 189, 191, 216, 220, 262, 266 antipode, 13, 14, 26–27, 131, 141, 151, 194, 220, 254 applied dominant, 18, 255, 280 arrow symbols (➔ and ⇨), 4, 12, 13–14, 255 augmented sixth chords, 12, 14, 132, 150, 183, 212, 248, 265, 266 Beach, D., 257 Beethoven, L. van, 198 Bellman, J., 254 Boulanger, N., 263 bullet symbol, 7 Burkhart, C., 266 Catel, C.-S., 275 chromatic variant, 48, 63, 67, 69–70, 88, 114, 116, 123, 164, 246, 259–260, 283 circle of fifths, 10, 13, 27, 29, 32, 39, 41, 43, 48, 49, 50, 52, 59–60, 65, 67, 81, 84, 88, 90, 94, 96–98, 99, 101, 105, 116, 118, 119, 123, 124, 128, 129, 135, 149, 150–151, 162–164, 171, 172, 173, 204, 206, 217–218, 219, 221, 237, 240, 242, 244, 248, 258, 259, 260–261, 267, 269, 274 circle of thirds, 199, 205, 219 collision, 7, 39, 48, 101, 109, 110, 134, 153, 171, 173, 265, 277, 281, 283, 284 common-tone diminished seventh chord, 155, 263, 272 Cone, E. T., 255, 280 Cortot, A., 273 Delacroix, E., 198

dominant emulation, 4 Edlund, B., 167 Eibner, F., 256–257 Eigeldinger, J.-J., 198–212, 273 Ekier, J., 266, 273 elision, 6, 8, 9, 18, 31, 35, 39, 48, 73, 81, 86, 94, 111, 123, 137, 150, 201, 206, 229, 231, 237, 255, 257, 261, 266, 267, 278 embellishing chord, 9, 17, 20, 30, 31, 45, 47, 54, 63, 73, 75, 79, 81, 84, 88, 95, 96, 99, 101, 104, 108, 109, 111, 116, 120, 122, 123, 124, 126, 128, 129, 134, 136, 142, 145, 150, 153, 163, 183, 186, 190–191, 196, 199, 205, 211, 214, 215, 216, 218, 221, 228, 229, 231, 234, 242, 246, 253, 258, 263, 264, 265, 277 enharmonic equivalence, 14, 67, 70, 77, 79–81, 88, 101, 110, 115, 116, 123, 124, 129, 131, 150, 153, 155, 161, 167, 171, 173, 176, 183, 205, 206, 207, 208, 211, 212, 220, 223, 245, 255, 263, 264, 265, 266, 267, 271, 273, 281, 283 equal subdivisions of the octave, 173, 208, 223, 231 essential dissonance, 233 Gołąb, M., 263, 270 hidden fifths, 258 Hood, A., 187–197, 270 hypermeter, 116, 118 idiosyncratic progression, 79, 175, 176, 237 incidental dissonance, 153, 233, 281, 284 interruption, 21–23 Jackendoff, R., 166 Kallberg, J., 260 Kinderman, W., 254 Klein, M., 265, 279 Kopp, D., 254

Korsyn, K., 254 Krebs, H., 254 Laufer, E., 213–232, 260, 261, 264 Leichtentritt, H., 279 Lerdahl, F., 166–186 Lester, J., 255, 257 London, J., 167, 180–181, 185–186, 276 lower-third chord, 69, 246 lowered supertonic see ♭II Lydian mode, 79 McCreless, P., 262 Mehrdeutigkeit, 148, 194, 268, 277 modal mixture see parallel keys modulo 7 vs. modulo 12, 70, 81, 101, 115–116, 123, 200, 205–206, 207, 281 Morgan, R. P., 280 Mozart, W. A., 264 multiple meaning see Mehrdeutigkeit Neapolitan sixth see ♭II obstinate progression, 13, 70, 115, 174, 176, 177, 193, 200, 205, 206, 219, 220 Oster, E., 271 Oster Collection, 254, 271, 272, 273, 276 parallel fifths, 29, 178, 232, 258 parallel keys, 42, 45, 56, 70, 77, 94, 116, 123, 132, 136, 161, 163, 274 parallel octaves, 13, 54, 67 parallel progression, 77, 101, 177, 179, 182, 198–199, 220, 233, 237, 275, 281, 282 parenthetical passage, 122, 165, 205, 228, 231, 264 passing chord, 177, 218, 257, 275

peculiar juxtapositions, 63 Phipps, G. H., 145–156 Picardy third, 86, 129, 135 reaching-over, 11, 14, 15, 32, 41, 95, 249, 267 registral shift, 4, 29, 47, 49, 83, 116, 168, 215, 218, 233, 234, 242, 244–245, 252 Rink, J., 233–252, 262, 270 Rischel, G., 279 Rodman, R., 167, 180–181, 185–186, 276 Rothstein, W., 255, 262, 280 Salzer, F., 157–165, 258, 263 Samson, J., 3 Schachter, C., 167, 173, 176, 181, 185–186, 254, 256, 265, 273, 276, 281 Schenker, H., 145, 152, 167, 169, 185, 200, 253–254, 255–256, 257, 260, 262, 264, 265, 268, 269, 270, 271, 273, 274, 275, 276, 278, 280, 283 Schoenberg, A., 145, 147, 262, 283 Schubert, F., 261, 263, 278 Sechter, S., 145, 148 seismic shift, 133–135, 141, 142, 151, 152, 153, 267, 269 sequence, 4, 11, 31, 59–60, 64, 79–81, 106, 114, 122–123, 128, 129, 141, 150, 169, 170, 174–175, 176, 193, 206, 207, 208, 237–239, 259, 267, 268, 273 Smith, C. J., 198–212 species counterpoint, 4, 5, 10, 12, 16, 29, 54, 256 Starobinski, G., 198 Stein, D., 278, 279 surge, 8–9 Suurpää, L., 280 Swoboda, A., 270

tonic pillar, 3, 91, 259 tonicization, 42, 45, 47, 53, 54, 60, 73, 75, 79, 83, 86, 88, 96, 99, 101, 106, 108, 114, 128, 150, 160, 164, 166, 194, 196, 203, 205, 210, 213–214, 215, 216, 217, 218, 219, 221, 224, 225, 226, 228–229, 241, 244–245, 250, 253, 260, 261, 262–263, 271, 280, 281, 283 twelve-note chromatic space see modulo 7 vs. modulo 12 Tymoczko, D., 257, 258, 261, 274, 275 unfurling, 6, 53, 54, 58, 63, 79, 99, 104, 106, 111, 115, 163, 168, 176 upper-third chord, 53, 54, 81, 99, 106, 109, 114–115, 161, 163, 164, 193, 214, 215, 221, 223, 228, 241, 242–244, 246, 282, 283 voice exchange, 30, 39, 161, 162, 194–195, 264, 284 Wagner, R., 181 Weber, G., 275, 279 wobbly note, 15, 19, 24, 27, 31, 32, 39, 48, 50, 53, 58–59, 69, 73, 86, 88, 99, 104, 114, 115, 116, 122, 131, 136, 141, 157, 163, 164, 171, 200, 203, 207, 212, 218, 220, 237, 241, 251, 260, 262, 264, 267, 273, 279 Yip, J., 261 5–6 shift (5- and 6-phase chords), 5, 7–8, 24, 25, 30, 37, 44, 45, 47, 49, 52, 54, 56, 64, 69, 70, 75, 79, 84, 86, 88, 94, 96, 98, 110, 111, 115, 122, 124, 126, 132, 133, 135, 141, 163, 168, 169, 170, 172, 174, 176, 177, 182, 194, 214, 218, 221, 223, 226, 228, 229, 231, 232, 233, 234, 237, 239, 241, 246, 251, 253, 254, 258, 259, 264, 265, 266, 269, 271, 276, 283 ♭II, 26–27, 31, 58, 69–70, 75, 88, 99, 130–131, 133, 150, 151, 153, 157, 176, 194–195, 196, 197, 200–201, 203, 207, 212, 218, 223, 241, 251, 267, 270, 271, 284