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SOME NON-ISOMORPHISMS BETWEEN PITCH AND TIME

SOME NON-ISOMORPHISMS BETWEEN PITCH AND TIME atic” (1971, 91). Stockhausen (1959) goes much further, for if pitches and rhythms both involve periodic phases between successive impulses, then both are instances of the same basic phenomenon, but in different octaves. Indeed, Stockhausen drew explicit parallels between the overtone series for pitch and categorical values for duration. In the realm of 12-tone compositional theory and method there have been various attempts at translating pitch and pitch-class relationships to the temporal domain—indeed, this is a basic tenet of multi-serialism. Thus, to choose an obvious example, Babbitt (1972) gives a systematic account of how row elements and intervals can (as well as cannot) be related to metric position and relative duration. Shifting to more recent music theory, Lewin has discussed pitch-time isomorphisms in specific analytical contexts (1981) and as a feature of his well-known models for interval systems (1987).1 The notions of consonance and dissonance have been applied to metrical relationships, as in Yeston 1976 and (especially) Krebs 1987, 1997. Finally, Pressing (1983) has explicitly claimed that there is a cognitive isomorphism (grounded in musical substance) between the interval pattern of the diatonic scale and certain non-western rhythmic patterns. At first blush the intuitions of these composers and http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Music Theory Duke University Press

SOME NON-ISOMORPHISMS BETWEEN PITCH AND TIME

Journal of Music Theory , Volume 46 (1-2) – Jan 1, 2002

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Publisher
Duke University Press
Copyright
Copyright 2002 by Yale University
ISSN
0022-2909
eISSN
1941-7497
DOI
10.1215/00222909-46-1-2-127
Publisher site
See Article on Publisher Site

Abstract

atic” (1971, 91). Stockhausen (1959) goes much further, for if pitches and rhythms both involve periodic phases between successive impulses, then both are instances of the same basic phenomenon, but in different octaves. Indeed, Stockhausen drew explicit parallels between the overtone series for pitch and categorical values for duration. In the realm of 12-tone compositional theory and method there have been various attempts at translating pitch and pitch-class relationships to the temporal domain—indeed, this is a basic tenet of multi-serialism. Thus, to choose an obvious example, Babbitt (1972) gives a systematic account of how row elements and intervals can (as well as cannot) be related to metric position and relative duration. Shifting to more recent music theory, Lewin has discussed pitch-time isomorphisms in specific analytical contexts (1981) and as a feature of his well-known models for interval systems (1987).1 The notions of consonance and dissonance have been applied to metrical relationships, as in Yeston 1976 and (especially) Krebs 1987, 1997. Finally, Pressing (1983) has explicitly claimed that there is a cognitive isomorphism (grounded in musical substance) between the interval pattern of the diatonic scale and certain non-western rhythmic patterns. At first blush the intuitions of these composers and

Journal

Journal of Music TheoryDuke University Press

Published: Jan 1, 2002

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