SPECIFYING SPECTRA FOR MUSICAL SCALES

The sensory consonance and dissonance of musical intervals is dependen t on the spectrum of the tones. The dissonance curve gives a measure o f this perception over a range of intervals, and a musical scale is sa id to be related to a sound with a given spectrum if minima of the dis sonance curve occur at the scale steps. While it is straightforward to calculate the dissonance curve for a given sound, it is not obvious h ow to find related spectra for a given scale. This paper introduces a ''symbolic method'' for constructing related spectra that is applicabl e to scales built from a small number of successive intervals. The met hod is applied to specify related spectra for several different tetrac hordal scales, including the well-known Pythagorean scale. Mathematica l properties of the symbolic system are investigated, and the strength s and weaknesses of the approach are discussed. (C) 1997 Acoustical So ciety of America. [S0001-4966(97)05509-4] PACS numbers: 43.75.Bc, 43.7 5.Cd [WJS].