William A. Sethares
Dept. of Elec. and Comput. Eng., Univ. of Wisconsin, Madison, WI 53706-1691
A relationship between tuning (or scale) and timbre (or spectrum) based on the perceptual results of Plomp and Levelt [J. Acoust. Soc. Am. 38, 548--560 (1965)] was presented by Sethares [J. Acoust. Soc. Am. 94, 1218--1228 (1993)]. This relationship can be used to determine an appropriate scale in which a given timbre sounds most consonant, or to design timbres for play in specified scales. This presentation gives sound demonstrations using stretched and compressed timbres, scales related to FM (and other) timbres, and timbres designed specifically for play in 10-tone equal temperament. The notion of an adaptive tuning is an extension in which the tuning of notes are allowed to vary in real time so as to iteratively maximize a measure of consonance. Sound examples that demonstrate the evolution of notes in an adaptive tuning are presented. Examples include complex tonal clusters that slowly evolve towards consonance, adaptation of nonharmonic notes to related scales, and automatic ``correction'' of out-of-tune harmonic notes. The sound demonstrations provide concrete auditory evidence of the validity of the theoretical results.