Effect of Phase on the Timbre of Complex Tones

Abstract

Applying a digital computer both for signal generation and response processing, some experiments were carried out in which comparisons were made of the timbres of complex tones. The tones had equal loudness and pitch but different phase and amplitude patterns of the harmonics. The stimuli were presented successively in triads, and the subject's task was to select the most similar and most dissimilar pairs. The results were analyzed with Kruskal's multidimensional-scaling program. In general terms, the most important findings are: (1) the timbre difference between a tone consisting of only sine or cosine terms and a tone consisting of alternative sine and cosine terms represents the maximal possible effect of phase on timbre; (2) the maximal effect of phase on timbre is quantitatively smaller than the effect of changing the slope of the amplitude pattern by 2 dB/oct and is less for higher than for lower frequencies; (3) the effect of phase on timbre appears to be independent of the effect of amplitude pattern and of the loudness factor.