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Approximate Set TheoryChord Categories, Voicings, and Interval Cycles

Approximate Set TheoryChord Categories, Voicings, and Interval Cycles This article describes an approximate set theory modeling intuitions shared by musicians such as Cowell, Schoenberg, Messiaen, and Persichetti. The author considers five approximation strategies, showing that in each case the result resembles an exact seven-tone set theory. Since most seven-tone sets are interval cycles, approximate twelve-tone sets are approximately cyclic as well. The theory explains how to highlight this cyclic structure using voicings, modeled by intervals in the intrinsic scale formed from a chord's own notes. This connection to voicing is what gives approximate chord categories much of their significance. The approach is most useful for chords with five or fewer notes and works tolerably for hexachords, but it breaks down with larger collections. This is not a failure of the model but a reflection of the fact that quality space contracts as cardinality increases. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Music Theory Duke University Press

Approximate Set TheoryChord Categories, Voicings, and Interval Cycles

Journal of Music Theory , Volume 67 (1) – Apr 1, 2023

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Copyright
Copyright © 2023 by Yale University
ISSN
0022-2909
eISSN
1941-7497
DOI
10.1215/00222909-10232057
Publisher site
See Article on Publisher Site

Abstract

This article describes an approximate set theory modeling intuitions shared by musicians such as Cowell, Schoenberg, Messiaen, and Persichetti. The author considers five approximation strategies, showing that in each case the result resembles an exact seven-tone set theory. Since most seven-tone sets are interval cycles, approximate twelve-tone sets are approximately cyclic as well. The theory explains how to highlight this cyclic structure using voicings, modeled by intervals in the intrinsic scale formed from a chord's own notes. This connection to voicing is what gives approximate chord categories much of their significance. The approach is most useful for chords with five or fewer notes and works tolerably for hexachords, but it breaks down with larger collections. This is not a failure of the model but a reflection of the fact that quality space contracts as cardinality increases.

Journal

Journal of Music TheoryDuke University Press

Published: Apr 1, 2023

References