Abstract
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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