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ON COHERENCE AND SAMENESS, AND THE EVALUATION OF SCALE CANDIDACY CLAIMS

ON COHERENCE AND SAMENESS, AND THE EVALUATION OF SCALE CANDIDACY CLAIMS The finite pitch-class space of 12-tone equal temperament 1/12 2/12 3/12 4/12 5/12 6/12 7/12 8/12 9/12 10/12 11/12 1 • • • • • • • • • • • (°) The infinite pitch class space defined by the set of real numbers ρ, 0 ≤ ρ < 1 1 Example 1. Finite and infinite pitch-class spaces. while the boundary between “scale” and “ordinary pitch-class set” is necessarily porous, it is still possible to formalize the radar we use to decide if we have crossed it. The methods will prove applicable to a variety of actual scales including diatonic, pentatonic, and chromatic systems, as well as many scales in non-Western musics. These methods are also suitable for investigating existing microtonal scales, and for formulating new ones. The term scale comprises a constellation of related notions. We understand a scale to be a series of pitches bounded by an interval of recurrence, ordinarily the octave. A scale sometimes serves as a kind of tone bank, or pitch repository, providing pitch-class material for scales of smaller cardinalities. The Arabic maqam system of 17 notes to the octave comes to mind in this context as well as the 22 srutis http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Music Theory Duke University Press

ON COHERENCE AND SAMENESS, AND THE EVALUATION OF SCALE CANDIDACY CLAIMS

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
10.1215/00222909-46-1-2-1
Publisher site
See Article on Publisher Site

Abstract

The finite pitch-class space of 12-tone equal temperament 1/12 2/12 3/12 4/12 5/12 6/12 7/12 8/12 9/12 10/12 11/12 1 • • • • • • • • • • • (°) The infinite pitch class space defined by the set of real numbers ρ, 0 ≤ ρ < 1 1 Example 1. Finite and infinite pitch-class spaces. while the boundary between “scale” and “ordinary pitch-class set” is necessarily porous, it is still possible to formalize the radar we use to decide if we have crossed it. The methods will prove applicable to a variety of actual scales including diatonic, pentatonic, and chromatic systems, as well as many scales in non-Western musics. These methods are also suitable for investigating existing microtonal scales, and for formulating new ones. The term scale comprises a constellation of related notions. We understand a scale to be a series of pitches bounded by an interval of recurrence, ordinarily the octave. A scale sometimes serves as a kind of tone bank, or pitch repository, providing pitch-class material for scales of smaller cardinalities. The Arabic maqam system of 17 notes to the octave comes to mind in this context as well as the 22 srutis

Journal

Journal of Music TheoryDuke University Press

Published: Jan 1, 2002

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