Post-Tonal Affinities in Piano Works of Bartók, Chen, and Crumb

by Monica Kang (Author)
Monographs 227 Pages


The book explores cellular pivots as a new means of progression, functional tonality having disappeared in much of contemporary music. Béla Bartók can be seen as a kind of father figure to the other two composers, Chen Yi and George Crumb, in terms of their stylistic, technical, and even philosophical connections. The musical affinities of all three composers reflect a larger body of post-tonal music. Cell constructions and their pivotal motions span the gamut from traditional/asymmetrical to more abstract/symmetrical formations. This study provides insight into universal principles of the post-tonal era and reveals a broader evolution of the musical language as represented by the three composers.

Table Of Contents

  • Cover
  • Title
  • Copyright
  • About the author
  • About the book
  • This eBook can be cited
  • Contents
  • Preface
  • Acknowledgements
  • Chapter 1 From Late Romanticism to the Post-Tonal Era
  • Chapter 2 Cells and Their Pivotal Functions: Basic Structures and Terminology
  • Chapter 3 Folk Tunes and Their Transformations in Bartók’s
  • Chapter 4 Toward Further Abstraction in Bartók’s
  • Chapter 5 Programmatic Soundscapes in Bartók’s
  • Chapter 6 Pentatonic Folk Sources for Basic Cells: Chen’s
  • Chapter 7 More Abstract Octatonic Contexts: Cellular Pivots in Chen’s
  • Chapter 8 Crumb’s
  • Chapter 9 From Art to Music: Cellular Procedures within Crumb’s
  • Chapter 10 Melodic/Harmonic Transformations Inspired by a Jazz Tune in Crumb’s
  • Chapter 11 Conclusion: Cellular Pivots in Post-Tonal Context
  • Bibliography
  • Index
  • Series index


In musical contexts of the post-tonal era, the concept of the pitch cell replaces the traditional triadic construction and its harmonic function as the primary means of integrating the large-scale fabric. In serving as anchors for departure and return, cells acquire the burden of pivotal function among various pitch collections.

The intention of this study is to provide new insights into post-tonal music through exploration of pivotal cell functions primarily in the solo piano music of three composers—Béla Bartók (1881–1945), Chen Yi (b. 1953), and George Crumb (b. 1929)—including the most recently published piano works by the latter two composers. Analyses of eleven works provide a microcosmic perspective of the compositional techniques of many other contemporary composers. These range from earlier masters such as Debussy, Scriabin, Stravinsky, and Schoenberg, to more recent ones, including Cage, Takemitsu, and Penderecki, among others. In addition to the basic compositional focuses, discussions extend to comparable works by other composers to provide a broader perspective.

Bartók can be seen as a kind of father figure for the other two composers of this study, Chen and Crumb, both of whom explicitly referred to him as influential in their compositional development. In Bartók’s music, cellular pivots occur in compositions heavily influenced by traditional folk material, as exemplified by Eight Improvisations on Hungarian Peasant Songs, Op. 20. While much of Bartók’s style reveals the essence of his Hungarian and other Eastern European sources, Chen’s reflects the essence of her Chinese heritage, as in Duo Ye, Guessing, Ba Ban, and Ji-Dong-Nuo. These respective sources provide the intrinsic qualities of the individual composers, yet reveal certain commonalities in their musical idioms. In contrast, Crumb’s compositions tend to be more abstract, i.e., beyond the parameters of any national source, as exemplified in Makrokosmos, Volume I and A Little Suite for Christmas, A.D. 1979, his Eine Kleine Mitternachtmusik based on Monk’s jazz tune. Therefore, cellular interactions in Crumb, while having affinities with the technical approaches of the other two composers, occur as part of a more abstract musical conception. Within their respective oeuvres, a greater relative degree of abstraction can be observed in Bartók’s Mikrokosmos and Out of Doors and Chen’s Northern Scenes. Through piano works of all three composers, this study therefore surveys the application of pitch cells in contrasting contexts that range from authentic folk tunes to more abstract material. These contexts incorporate a gamut of constructions, from traditional/asymmetrical collections (pentatonic, diatonic/modal, polymodal, and nondiatonic Romanian folk mode) ← 9 | 10 → to more abstract/symmetrical collections (whole-tone, octatonic, and chromatic), all integrated by means of cellular pivots.

Exploration of procedures surrounding the application of these pivotal cells reveals some processes to be either unique or common. Affinities among the various pieces and their composers include actual compositional influences that pass from older to newer generations, and procedures that become common practice in the post-tonal genre. The book provides insights into all-encompassing concepts and principles that occur in the post-tonal era and reveals a broader evolution of the musical language as represented by the three composers. ← 10 | 11 →


I am grateful to Elliott Antokoletz for his encouragement in this endeavor as mentor and friend. No words can describe how fortunate I am to have been under the wing of this knowledgeable Bartók scholar, who has been more than generous with his time and energy. His help was invaluable in seeing this project from its inception to fruition. I am also extremely grateful to Chen Yi and George Crumb for their warm-hearted and helpful conversations about their music. Much appreciation is extended toward Gregory Allen, James Buhler, Sophia Gilmson, Martha Hilley, and Thomas O’Hare for their crucial suggestions regarding various technical and editorial matters.

I acknowledge the publishers—Boosey & Hawkes, Inc., C.F. Peters Corporation, and Carl Fischer Music/Theodore Presser Company—for their kind permission to reproduce the musical excerpts included in this book. Credit is given as follows:

Mikrokosmos by Béla Bartók. Copyright 1940 by Hawkes & Son (London), Ltd. [Definitive Corrected Edition Copyright 1987 by Hawkes & Son (London), Ltd.] Reprinted by Permission.

Out of Doors by Béla Bartók. Copyright 1927 by Boosey & Sons, Inc. Copyright Renewed. Reprinted by Permission.

Ba Ban by Chen Yi. Copyright 2006 by Theodore Presser Company. All Rights Reserved.

Duo Ye by Chen Yi. Copyright 2000 by Theodore Presser Company. All Rights Reserved.

Guessing by Chen Yi. Copyright 2000 by Theodore Presser Company. All Rights Reserved.

Ji-Dong-Nuo by Chen Yi. Copyright 2007 by Theodore Presser Company. All Rights Reserved.

Northern Scenes by Chen Yi. Copyright 2015 by Theodore Presser Company. All Rights Reserved.

Eine Kleine Mitternachtmusik by George Crumb. Copyright 2001 by C.F. Peters Corporation. Used by permission.

A Little Suite for Christmas, A.D. 1979 by George Crumb. Copyright 1980 by C.F. Peters Corporation. Used by permission.

Makrokosmos, Volume I by George Crumb. Copyright 1974 by C.F. Peters Corporation. Used by permission. ← 11 | 12 → ← 12 | 13 →

Chapter 1
From Late Romanticism to the Post-Tonal Era

Compositions of the twentieth and twenty-first centuries are vastly divergent in terms of style, but many share a commonality in their lack of functional tonality. Generally categorized as post-tonal, these pieces may use traditional tonal elements in unconventional ways, such as employing nonfunctional harmonies or combining multiple collections (i.e., hybrid modes, bi/poly-tonality/modality). They may rely on a new system like the twelve-tone matrix or be completely atonal. Within this post-tonal context, this study primarily explores the solo piano music of three composers of varied stylistic backgrounds—Béla Bartók, Chen Yi, and George Crumb—who are inextricably connected in terms of the development of a new musical language. Throughout the book, we will also connect them to other contemporary composers and trends to provide a broader perspective.

The selection of this triad of composers stems from their aesthetic, philosophical, and musical relationship with Bartók as a kind of father figure. Both Chen and Crumb explicitly refer to Bartók as influential in their musical development.1 Bartók’s compositions synthesize various influences from Eastern European folk sources and composers ranging from Wagner, Liszt, Brahms, Strauss, and Debussy in the early years and more generally, composers rooted in the German tradition. Bartók referred to the influence of Bach for counterpoint, Beethoven for form, and Debussy for sonority.2 Chen and Crumb also synthesize elements from other sources in addition to Bartók. Chen derives inspiration from Eastern Asian folk sources and various contemporary Western composers: Schoenberg, Debussy, Messiaen, Stravinsky, Shostakovich, Lutosławski, and others from a broad spectrum of styles. Crumb is prominently influenced by Mahler, Debussy, and others who have experimented with timbre: Berio, Boulez, Cage, Cowell, and Ives, among others. Spanning the generation of composers after Bartók, the compositional output of these three composers projects a certain compositional lineage from the Hungarian composer while also synthesizing a diversity of influences. Together they create a microcosm of a post-tonal musical literature.

With the dissolution of traditional tonality, a modern harmonic language—along with new means of organization and progression—arose in post-tonal mu ← 13 | 14 → sic. We explore this transformation through the concept of the cell, which is a set of pitch classes based on particular intervallic content. The cell in post-tonal music replaces the traditional harmonic role of the triad. Cells are defined as a “microcosmic set of fixed intervallic context, statable either as a chord or as melodic figure or as a combination of both”,3 which may either be ordered (serial) or unordered.

The evolution of styles from Bartók to Chen and Crumb can be traced from folk-influenced material to more abstract pitch collections, from traditional to modern idioms. Bartók investigated folk music, ranging from Hungarian, Slovakian, and Romanian sources, and later, Arab, Bulgarian, Turkish, and Serbo-Croatian.4 He uses cells as a means of progression within contexts that are often imbued by the essence of Eastern European folk sources. Hence, he often utilizes traditional modal constructions, which can generate and interact with more abstract, symmetrical pitch constructions derived from the interval cycles.5 Among the most prevalent are whole-tone and octatonic collections. Albeit abstract, these constructions often appear to have significant transformational connections with the modal folk sources. Chen similarly derives ideas from her Chinese heritage, using cells to progress between sections of folk and abstract materials. Whereas Bartók uses authentic folk tunes more extensively, Chen tends toward a more consistent context of abstract formations. Both still retain the essence of the original folk songs. In contrast, Crumb’s focus on timbre and sonority demands the use of cells in an almost entirely abstract context. Hence, his compositions are least likely to be based on a core of folk music. Even quotations of existing excerpts or motivic use of popular tunes are treated in a more abstract manner. Each composer’s use of cells are compared and contrasted in terms of progression and linkage within the context of traditional/folk and abstract compositions. There are many parameters to be considered in musical analysis. The present study focuses primarily on pitch relations as the basis of musical progression, the potential of these cells as pivotal links.

Cells not only serve as links within the music of these three composers but also often supply a common thread in a broader body of post-tonal music. The study of the cellular thread in a range of pitch constructions and compositional techniques can be adequately exemplified in works by Bartók, Chen, and Crumb. ← 14 | 15 → The compositions were selected as exemplars of these technical procedures, which contribute to the aesthetic flow of the musical syntax.

Context: Breaking Away from the Ultra-Chromaticism of German Late-Romantic Music

What brought the establishment of post-tonal music? Harmonic transformations by means of non-diatonic infiltrations in German late-Romantic music led to a new type of chromaticism. The dissolution of the major and minor scale system brought a more pervasive use of certain types of pitch collections, such as whole-tone, octatonic, and other non-functional symmetrical constructions that are derived from interval cycles.6 At the same time, interest in folk music brought the use of pentatonic and modal scales by composers of varied national backgrounds. Interactions among these collections create a polymodal chromatic complex, which forms the building blocks of post-tonal music. A diversity of compositional styles is reflected in the myriad of post-tonal composers. The music of Arnold Schoenberg (1874–1951), Claude Debussy (1862–1918), and Igor Stravinsky (1882–1971), as well as Béla Bartók, is addressed in this initial chapter to best demonstrate the new procedures within post-tonal music. We center our analytical discussion on one of the most influential composers from the early twentieth century—Bartók, who also exhibits a kinship to Debussy and in certain ways, Stravinsky. Bartók, like Debussy and Stravinsky, is a core influence on many post-tonal composers.

The reaction against the ultra-chromaticism of late-Romantic music led to the breakdown of traditional tonality and a new concept of the chromatic continuum. This led to the equalization of the twelve tones. In the tonal world, dissonance served as a means to express emotional intensity and existential angst, which was reflected in the writings of Friedrich Nietzsche and paintings by Vincent van Gogh and Edvard Munch. In music, Richard Wagner’s innovative use of abrupt tonal shifts in addition to extreme chromaticism paved the way into the twentieth century for Gustav Mahler and Richard Strauss.7 This move away from ← 15 | 16 → tonal functionality, which led to the emancipation of dissonance in Schoenberg, is one of the two trends toward a new chromatic idiom, the other trend based on pentatonic and diatonic modality. Schoenberg defined his free-atonal idiom:


ISBN (Softcover)
Publication date
2016 (August)
Folk sources Modality polymodality Pitch-set transformations Cells
Frankfurt am Main, Berlin, Bern, Bruxelles, New York, Oxford, Wien, 2016. 227 pp.

Biographical notes

Monica Kang (Author)

Monica Kang received her Doctor of Musical Arts degree in Piano Performance from The University of Texas at Austin. She also holds dual bachelor degrees in math and music from Northwestern University. Her research focuses on the affinities between music and other disciplines.


Title: Post-Tonal Affinities in Piano Works of Bartók, Chen, and Crumb