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On Pitch-Class Set Cartography: Relations between Voice-Leading Spaces and Fourier Spaces

On Pitch-Class Set Cartography: Relations between Voice-Leading Spaces and Fourier Spaces Recent music-theoretical research has proposed two ways of mapping the pitch-class set universe. Fourier spaces, constructed by Quinn, relate sets to one another based upon their composition from members of interval cycles, reflecting what might be called "harmonic quality." Voice-leading spaces, generalized by Callender, Quinn, and Tymoczko, illustrate voice-leading relationships between sets. Though many researchers have noted hints of a relationship between these two types of space, their exact relation remains murky. One way of relating these two spaces involves associating voice leading with motion through Fourier space. Voice-leading displacements of each of the six interval classes can be associated with specific changes of position in each of the six Fourier spaces for twelve-tone equal temperament. Likewise, displacement spaces, showing all of the sets that can be related by voice-leading displacements of a particular interval class, model predictable motion through each of the Fourier spaces. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Music Theory Duke University Press

On Pitch-Class Set Cartography: Relations between Voice-Leading Spaces and Fourier Spaces

Journal of Music Theory , Volume 52 (2) – Sep 1, 2008

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Publisher
Duke University Press
Copyright
Duke University Press
ISSN
0022-2909
eISSN
1941-7497
DOI
10.1215/00222909-2009-016
Publisher site
See Article on Publisher Site

Abstract

Recent music-theoretical research has proposed two ways of mapping the pitch-class set universe. Fourier spaces, constructed by Quinn, relate sets to one another based upon their composition from members of interval cycles, reflecting what might be called "harmonic quality." Voice-leading spaces, generalized by Callender, Quinn, and Tymoczko, illustrate voice-leading relationships between sets. Though many researchers have noted hints of a relationship between these two types of space, their exact relation remains murky. One way of relating these two spaces involves associating voice leading with motion through Fourier space. Voice-leading displacements of each of the six interval classes can be associated with specific changes of position in each of the six Fourier spaces for twelve-tone equal temperament. Likewise, displacement spaces, showing all of the sets that can be related by voice-leading displacements of a particular interval class, model predictable motion through each of the Fourier spaces.

Journal

Journal of Music TheoryDuke University Press

Published: Sep 1, 2008

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