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Normalizing Musical Contour Theory

Normalizing Musical Contour Theory The advent of the numerical representation of contour was a watershed in the development of musical contour theory. Both Michael L. Friedmann and Robert D. Morris pioneered the practice by mapping pitches in ascending registral order onto the subset of nonnegative integers from 0 to n − 1, where n equals cardinality. This notation identifies pitches solely by their relative height, thereby eschewing any reference to specific interval size and effectively transforming pitches in pitch space into contour pitches in contour space. The variable end-point mechanism this procedure entails, however, often yields counterintuitive and inconsistent results when comparing contour segments (csegs) of different cardinalities. In some instances, it falsely implies that an expansion or contraction of contour space has transpired. In other cases, it grossly misrepresents the phenomenological disposition of certain members of a given cseg yet remains perfectly true to that of others. This article addresses the analytical pitfalls of the integer-based contour labeling system by instead adopting a normalized scheme that maps pitches onto evenly distributed subsets of the real numbers from 0 to 1 inclusive. This not only systematically eliminates the distortions and inconsistencies that crop up with respect to mixed cardinality csegs but also provides a considerably more nuanced metric for intervallic distances in contour space. Using analytical case studies juxtaposing the two notational systems, this article demonstrates how the normalized representation of contour both enhances and extends the analytical capabilities of musical contour theory by more effectively modeling the transformational implications embedded therein. contour pitch melody rhythm normalization analytical notation http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Music Theory Duke University Press

Normalizing Musical Contour Theory

Journal of Music Theory , Volume 60 (1) – Apr 1, 2016

Normalizing Musical Contour Theory


the advent of the numerical representation of contour was a watershed in the development of musical contour theory. Elizabeth West Marvin (1995, 149­50) has cited three distinct advantages that numerical representation offers over the various graphic notations of contour found in earlier studies by Arnold Schoenberg (1967), Ernst Toch ([1948] 1977), Charles Seeger (1960), and Mieczyslaw Kolinski (1965), among others. First, Marvin (1995, 149­50) observes that "numerical representation . . . conveys at least as much information, is more compact and easier to reproduce and discuss, and can easily be converted to graphic form if necessary." Second, by virtue of its greater precision, numerical representation has enabled the creation of equivalence classes and sophisticated similarity measurements that would not be so easily conceivable in strictly graphic terms. Third, numerical represenI wish to thank Joseph N. Straus for his constructive feedback on an earlier draft of this article. Journal of Music Theory 60:1, April 2016 DOI 10.1215/00222909-3448746 © 2016 by Yale University Published by Duke University Press Journal of Music Theory JOURNAL of MUSIC THEORY Schultz Example 1 oe oe Example 1. Integer representation of contour as a cseg, in Olivier Messiaen's Quatuor pour la fin du temps, movement 7, m. 17 tation allows for a more generalized approach to contour that is not restricted to just modeling pitches in time but can also be applied to duration, dynamSchultz Example 2 ics, tone color, and other potentially relevant musical parameters. Theoe oe b numericalbrepresentation system in current mainstream use, which oe oe oe & was pioneered by Michael L. Friedmann (1985) and Robert D. Morris (1987), maps4 2 0from low to high onto the subset of integers from 0 to n - 1, 1 3 cseg = pitches where n equals the cardinality of the set. Thus the contour of the melodic ÷4 segment displayed in Example 1 is represented by mapping the...
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Publisher
Duke University Press
Copyright
Copyright © Duke Univ Press
ISSN
0022-2909
eISSN
1941-7497
DOI
10.1215/00222909-3448746
Publisher site
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Abstract

The advent of the numerical representation of contour was a watershed in the development of musical contour theory. Both Michael L. Friedmann and Robert D. Morris pioneered the practice by mapping pitches in ascending registral order onto the subset of nonnegative integers from 0 to n − 1, where n equals cardinality. This notation identifies pitches solely by their relative height, thereby eschewing any reference to specific interval size and effectively transforming pitches in pitch space into contour pitches in contour space. The variable end-point mechanism this procedure entails, however, often yields counterintuitive and inconsistent results when comparing contour segments (csegs) of different cardinalities. In some instances, it falsely implies that an expansion or contraction of contour space has transpired. In other cases, it grossly misrepresents the phenomenological disposition of certain members of a given cseg yet remains perfectly true to that of others. This article addresses the analytical pitfalls of the integer-based contour labeling system by instead adopting a normalized scheme that maps pitches onto evenly distributed subsets of the real numbers from 0 to 1 inclusive. This not only systematically eliminates the distortions and inconsistencies that crop up with respect to mixed cardinality csegs but also provides a considerably more nuanced metric for intervallic distances in contour space. Using analytical case studies juxtaposing the two notational systems, this article demonstrates how the normalized representation of contour both enhances and extends the analytical capabilities of musical contour theory by more effectively modeling the transformational implications embedded therein. contour pitch melody rhythm normalization analytical notation

Journal

Journal of Music TheoryDuke University Press

Published: Apr 1, 2016

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