The sensory consonance and dissonance of musical intervals is dependent on the spectrum of the tones. The dissonance curve gives a measure of this perception over a range of intervals, and a musical scale is said to be related to a sound with a given spectrum if minima of the dissonance curve occur at the scale steps. While it is straightforward to calculate the dissonance curve for a given sound, it is not obvious how to find related spectra for a given scale. This paper introduces a “symbolic method” for constructing related spectra that is applicable to scales built from a small number of successive intervals. The method is applied to specify related spectra for several different tetrachordal scales, including the well-known Pythagorean scale. Mathematical properties of the symbolic system are investigated, and the strengths and weaknesses of the approach are discussed.
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October 1997
October 01 1997
Specifying spectra for musical scales
William A. Sethares
William A. Sethares
Department of Electrical and Computer Engineering, University of Wisconsin, Madison, Wisconsin 53706-1691
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J. Acoust. Soc. Am. 102, 2422–2431 (1997)
Article history
Received:
July 05 1996
Accepted:
June 03 1997
Citation
William A. Sethares; Specifying spectra for musical scales. J. Acoust. Soc. Am. 1 October 1997; 102 (4): 2422–2431. https://doi.org/10.1121/1.419604
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