Dissertation Index

Author: Derfler, Brandon

Title: Single-Voice Transformations: A Model for Parsimonious Voice Leading

Institution: University of Washington

Begun: September 2003

Completed: November 2007


This study proposes a transformational model for voice leading in which parsimony is privileged above all other factors. Voice-leading displacements are explained as multiple iterations of the basic operation, the single-semitone transformation (SST). The SST is a type of single-voice transformation (SVT) in which only a single voice in a chord is transposed by a semitone. The SVT group Gm is a direct product group G1 X G2 X ... X Gm acting on a set (chord) C of order m where G = Tn, the group of musical transpositions, and C is sorted into voices expressed as an m-tuple . An SVT is any element of Gm such that all but one of the entries in the direct product vector are the identity: . The SST is a specialized SVT in which the non-trivially transposing vector entry = T1. The SVT model does not rely on TTOs on sets to determine voice-leading paths, as is commonly the case in previous studies. SST-succession classes are defined; they allow SSTs to be generalized as parsimonious voice-leading relations between pair-ordered set classes. Voice leading between chords of differing cardinalities is obtained through split and fuse operations; these are formalized mathematically and generalized as parsimonious voice-leading relations between pair-ordered set classes called split- and fuse-succession classes. 3D graphical representations of interlocking SST-succession classes and split-succession classes involving trichordal and tetrachordal SCs are developed. The study concludes with comparisons of the single-voice transformational model to recent work in neo-Riemannian theory and with analyses of music from tonal, atonal, and post-atonal stylistic periods by Chopin, Scriabin, Webern, Paul Lansky, and John Adams.

Keywords: transformational theory, neo-Riemannian theory, voice leading


Chapter 1: IntroductionChapter 2: Some Transformational Models of Voice-Leading Space
Chapter 3: The Single-Voice-Transformation Model
Chapter 4: Graphical Representations of Parsimonious Voice-Leading Spaces
Chapter 5: The SST Model and Neo-Riemannian Theory
Chapter 6: Analyses
Appendix A: Summary of [SSTi]-Relations Between Trichordal and Tetrachordal Equivalence-Class Pair-Successions
Appendix B: Chart of [SSTi] Subscripts Relating Trichordal and Tetrachordal Equivalence-Class Pair-Successions


Brandon Derfler
601 N 42nd St.
Seattle, WA 98103
(206) 632-1025

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