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Single-Voice Transformations: A Model for Parsimonious Voice Leading
Author(s): Brandon Derfler (Author)
- Publisher: Cambridge Scholars Publishing
- Publication Date: 15 Mar. 2010
- Edition: 1st
- Language: English
- Print length: 215 pages
- ISBN-10: 1443818607
- ISBN-13: 9781443818605
Book Description
This study demonstrates how smooth voice leading in music can be effectively modeled using concepts from abstract algebra. Minute voice-leading displacements are explained as iterations of the basic operation, the single-semitone transformation (SST). The SST is a type of transformation in which only a single voice in a chord is transposed by a semitone. Unlike previous music theoretic studies, the SST model does not rely on twelve-tone operations on sets to determine voice-leading paths. SST-succession classes can then be defined; they allow SSTs to be generalized as parsimonious voice-leading relations between pair-ordered set classes. Voice leading between chords of different “sizes” can be obtained through split and fuse operations. Once a mathematical basis for smooth voice-leading is formalized, 3D graphical representations in the form of lattices of parsimoniously related chord types can be developed. The study compares the single-voice transformational model to transformational theories of atonal voice leading and to recent work in the emergent field of neo-Riemannian theory. The final chapter examines music from tonal, atonal, and “post-atonal” stylistic periods by Chopin, Scriabin, Webern, Paul Lansky, and John Adams, showing the new voice-leading model’s versatility as an analytical tool.
Editorial Reviews
Review
Brandon Derfler’s Single-Voice Transformations: A Model for Parsimonious Voice Leading explores neo-Riemannian and parsimonious voice-leading relations among generalized types of set classes. It summarizes very clearly the bewildering variety of terminology and ideas in this area, and goes on to develop an approach based on n-tuples of pitch-classes for chords, related to one another by single-semitone transformations (the parsimonious aspect here) assembled into a direct product group that acts on the chord-tuples. This is a mathematical treatment that is more correct and superior to previous approaches. The thesis includes some very impressive online 3-dimensional virtual reality fly-through models of the geometry of chord types under these relations. A must-read for anyone interested in this area of music theory research. –John Rahn, Professor of Music, University of Washington, Editor, Perspectives of New Music
About the Author
Brandon Derfler holds an MA degree in Musicology from the University of North Carolina at Chapel Hill and a PhD in Music Theory from the University of Washington. His publications have appeared in GAMUT, Indiana Theory Review, and Perspectives of New Music. He is Associate Provost at the Academy of Music Northwest.
