“Neither Tonal Nor Atonal”?: Harmony and Harmonic Syntax in György Ligeti’S Late Triadic Works
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ABSTRACT “Neither Tonal nor Atonal”?: Harmony and Harmonic Syntax in György Ligeti’s Late Triadic Works Kristen (Kris) P. Sha!er 2011 A number of works from the latter part of György Ligeti’s career are saturated by ma- jor and minor triads and other tertian harmonies. Chief among them are Hungarian Rock (1978), Passacaglia ungherese (1978), “Fanfares” (Étude no. 4 for piano, 1985), and the last three movements of Síppal, dobbal, nádihegedűvel (2000). Ligeti claims that his triadic structures are “neither ‘avant-garde’ nor ‘traditional,’ neither tonal nor atonal,” and analysts commonly characterize these pieces as making use of the “vocabulary” but not the “syntax” of tonal music. The most proli"c of these analysts refers to Ligeti’s triads as “context-free atonal harmony . without a sense of harmonic function or a sense of history” (Searby 2010, p. 24). However, to date, no detailed analysis of Ligeti’s triadic sequences has been presented in support of these claims. This dissertation seeks to provide such an analysis in evaluation of these claims. This dissertation takes as its analytical starting point a de"nition of harmonic syntax based largely on the writings of Leonard Meyer and Aniruddh D. Patel: harmonic syntax in- volves principles or norms governing the combination of chords into successions with those chords, or the kinds of progressions between them, being categorized into at least two cate- gories of stability and instability. With this de"nition in mind, this dissertation explores the six movements named above, seeking to answer two primary research questions: 1) do these works present what we might call harmonic syntactic structures?; and 2) to what extent are those syntactic structures based in tonal procedures? i ABSTRACT ii Chapter 2 presents a statistical analysis of the triadic structures of the six most heav- ily triadic works from the latter part of Ligeti’s career, comparing the results to analyses of two tonal corpora. This analysis provides evidence of meaningful, non-random structure to the ordering of Ligeti’s harmonic successions in these movements, as well as signi"cant rela- tionships between the structures of these movements and the representative tonal works. Speci"cally, Ligeti’s late triadic pieces evidence guiding principles for the ordering of chords into successions, and there is reason to believe that these principles may have their founda- tion—at least in part—in tonal harmonic practice. Further analysis is required to "nd catego- ries of stability and instability, or to establish a link of more than correlation between Ligeti’s structures and those of tonal practice. The results of this study also raise speci"c questions about the harmonic structures of individual movements, to be explored in subsequent analysis. Chapters 3–5 explores these questions and other features of the harmonic structures of these six movements through direct analysis of the scores of these movements and, where appropriate and available, the precompositional sketches preserved for these movements. The analyses of Chapters 3–5 con"rm the conclusion of Chapter 2 that there are meaningful syntactic structures in these movements. Both principles for the ordering of chords into suc- cessions and categories of stability and instability can be found in these movements, though these principles and categories are not the same for each movement. In sum, we can say with con"dence that in these six movements, Ligeti composed meaningful harmonic successions, that those successions can be said to be syntactic, that the structures of those successions and the properties of those syntaxes have a strong relation- ship with some fundamental aspects of the successions and syntax of common-practice to- nal music, that Ligeti was aware of that relationship, that Ligeti intended that relationship, ABSTRACT iii and that understanding that relationship is fundamental to understanding the harmonic and formal structures of these works. Chapter 6 explores the con#ict between this conclusion and Ligeti’s pronouncement that his triadic music is “neither tonal nor atonal.” Ligeti’s use of both tonal and atonal ele- ments in his late music can be seen in large part as a response to problems about form and syntax that arose within the serialist tradition, which Ligeti has been addressing in his com- positions and articles since the late 1950s. In the latter part of his career, in spite of the fact that he continues to write music in line with his earlier writings on form and syntax, Ligeti desires to be seen as a “late” composer—both in terms of his own career, and in terms of the broader history of music. Thus, while composing music that draws heavily on both tonal and atonal musics of the past, he shifts his rhetoric and states that his music is “neither tonal nor atonal.” The tension between these two strains in his output is fundamental to a complete, nuanced understanding of Ligeti’s music and aesthetic ideology. “Neither Tonal nor Atonal”?: Harmony and Harmonic Syntax in György Ligeti’s Late Triadic Works A Dissertation Presented to the Faculty of the Graduate School of Yale University in Candidacy for the Degree of Doctor of Philosophy by Kristen (Kris) P. Sha!er Dissertation Director: Ian Quinn December 2011 ©2012 by Kris Sha!er All rights reserved. http://kris.sha!ermusic.com for Ciaran and Finn TABLE OF CONTENTS Illustrations ix Acknowledgements xvi I. “Neither Tonal nor Atonal?” 1 II. A Statistical Root-Motion Analysis of Ligeti’s Late Triadic Works 15 De"nitions and Methods 15 Null Hypothesis 25 Tonal Syntax 32 Tonal Corpus One: The Bach Chorales 32 Tonal Corpus Two: Rock Music 43 Statistical Syntactic Structures in Ligeti’s Triadic Works 49 Summary 56 III. Analysis – The 1978 Harpsichord Works 58 Hungarian Rock 59 Passacaglia ungherese 71 Form and General Structural Properties 71 The Construction of the Ground 77 The Perception of Dissonance in a Cycle of Consonances 84 Acoustic and Contextual “Consonance”; Syntax and Form 93 Summary 107 IV. Analysis – Étude for Piano no. 4, “Fanfares” 109 Form 110 The Analytical Literature 116 Analysis 123 V. Analysis – Síppal, dobbal, nádihegedűvel 147 V. “Alma álma” 147 VI. “Keserédes” 161 VII. “Szajkó” 171 vii CONTENTS viii VI. Conclusions 189 Appendix 1. Pro"ler Software 210 Appendix 2. Bach Chorales Progression Totals by Root Interval and Chord Quality 213 References 219 ILLUSTRATIONS FIGURES 1.1. Mm. 1–20 of “Fanfares” 1 2.1. Ligeti’s Passacaglia ungherese, mm. 1–11 18 2.2. Ligeti’s Hungarian Rock, mm. 1–11 18 2.3 End of Ligeti’s Hungarian Rock 19 2.4 Ligeti’s “Fanfares,” mm. 1–4 20 2.5 Ligeti’s “Fanfares,” mm. 45–48 21 2.6 Ligeti’s Síppal, dobbal, nádihegedűvel, movement V, mm. 1–9 22 2.7 Ligeti’s Síppal, dobbal, nádihegedűvel, movement VI, mm. 1–13 23 2.8 Ligeti’s Síppal, dobbal, nádihegedűvel, movement VII, mm. 1–9 24 2.9. Probability pro"les for chord-root distribution in Ligeti’s triadic movements, 28 arranged according to the circle of "fths 2.10. Probability pro"les for root-progression distributions and root-progression 29–30 distributions of 10,000 randomly ordered chords of the same root-occurrence probability pro"le 2.11. Chord-root (pitch-class) distribution pro"le for J.S. Bach’s four-part chorales 33 2.12. Chord-root (pitch-class) distribution pro"le for J.S. Bach’s four-part chorales, 33 arranged according to the circle of "fths 2.13. Chord-root (scale-degree) distribution pro"le for J.S. Bach’s four-part chorales, 35 arranged according to the circle of "fths 2.14. Root-progression pro"le for the actual successions of chords found in J.S. Bach’s 37 four-part chorales and root-progression pro"le for a random ordering of chords with the same zeroth-order probability pro"le as the scale-degree chord-root distribu- tion pro"le for J.S. Bach’s four-part chorales ix ILLUSTRATIONS x 2.15. Root-progression pro"le for the actual successions of chords found in J.S. Bach’s 41 four-part chorales, arranged according to distance on the circle of "fths 2.16. Chord-root distribution pro"les for J.S. Bach’s four-part chorales and de Clercq & 44 Temperley’s 5 x 20 corpus, arranged according to the circle of "fths 2.17. Root-progression pro"les for the actual successions of chords found in J.S. Bach’s 45 four-part chorales and the 5 x 20 corpus, arranged according to distance on the circle of "fths 2.18. Root-progression pro"les for the actual successions of chords found in J.S. Bach’s 46 four-part chorales (with chord substitutions) and the 5 x 20 corpus, arranged according to distance on the circle of "fths 2.19. Root-progression pro"les for the 5 x 20 corpus and de Clercq & Temperley’s 46 extended 200-song corpus, arranged according to distance on the circle of "fths 2.20. Probability pro"les for root-progression distributions of Ligeti’s triadic 49 movements, arranged according to distance on the circle of "fths 3.1. Root-interval probability pro"le for Hungarian Rock, arranged according to 59 distance on the circle of "fths 3.2. Root-interval probability pro"le for the successions of chords found in de Clercq 59 & Temperley’s 200-song rock corpus, arranged according to distance on the circle of "fths 3.3. Four-bar ground of Hungarian Rock 61 3.4. One-bar ostinato bass of Hungarian Rock 61 3.5. Root-interval probability pro"le for mm. 178–184 62 3.6.