Author: O'Donnell, Shaugn J.
Title: Transformational Voice Leading in Atonal Music
Institution: City University of New York
Begun: October 1994
Completed: March 1997
Throughout much of modern history two central concerns of music theorists have been "vertical" pitch structures (chords or simultaneities) and the "horizontal" connections (voice leading) among them. In the study of twentieth-century music the former has received extensive coverage, while the latter remains substantially less explored. Over the last two decades, a small, but growing, number of theoretical and analytical works attempt to redress this imbalance, and "Transformational Voice Leading in Atonal Music" is my contribution to that effort.
As a point of departure I explore the analytical ramifications of interpreting operational mappings as contrapuntal voices. Finding that transposition and inversion cannot sufficiently account for the point-to-point motions of most musical surfaces, I probe the recent theoretical literature for alternative transformations. In particular, Klumpenhouwer networks and three singleton transformations (Forte's "unary transformations," Lewin's "if-only," and Straus's "near-transformations") inspire me to develop and generalize a number of original "dual transformations." These theoretical tools coalesce in a voice-leading model that combines the mappings generated by dual transformations with those implied by recursive Klumpenhouwer networks. This transformational model offers multiple interpretations of musical passages that I organize into non-hierarchical levels of voices called "adjacencies" and "recursive structure."
The remainder of the dissertation tests the analytical viability of my voice-leading model, with its emphasis on dual transformations and Klumpenhouwer networks, in the context of a wide variety of twentieth-century atonal musical literature. The nine analytical essays examine substantial excerpts or complete compositions by Babbitt, Bartok, Ives, Skryabin, Stravinsky, and Webern.
Keywords: transformations, voice leading, analysis, Klumpenhouwer networks, Babbitt, Bartok, Ives, Skryabin, Stravinsky, Webern
Chapter 1 Transformational Techniques
1.1 Transformations and Mappings
1.2 Similarity, Networks, and Singleton Transformations
1.3 Klumpenhouwer Networks
1.4 Dual Transformations
Chapter 2 Analyses I: Homophonic Applications
2.1 Bela Bartok, Concerto for Piano and Orchestra No. 2, II
2.2 Igor Stravinsky, Three Pieces for String Quartet, III
2.3 Alexander Skryabin, Prelude, Op. 74, No. 4
2.4 Charles Ives, "Serenity"
2.5 Charles Ives, "The Cage"
Chapter 3 Analyses II: Linear and Polyphonic Applications
3.1 Anton Webern, Five Pieces for String Quartet, II
3.2 Anton Webern, Five Pieces for String Quartet, III
3.3 Milton Babbitt, Semi-Simple Variations
3.4 Igor Stravinsky, Movements for Piano and Orchestra, I
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