Triadic comparisons of musical intervals.

An analysis is made of the perception of musical intervals. Two kinds of stimuli were used; intervals consisting of two simultaneous simple tones (sinusoids) and intervals consisting of two simultaneous complex tones (fundamental plus harmonics). Subjects judged the stimuli by the method of triadic comparisons in an incomplete balanced design. Multidimensional analysis was performed according to Kruskal's MDSCAL program. The following results were obtained: (a) In both the space of simple-tone intervals (S) and the space of complex-tone intervals (C) musical intervals are ordered according to their width (frequency difference between fundamental tones). This ordering appears to follow a scale which is bowed upwards in the centre; extremely narrow and extremely wide intervals are therefore more similar than would be expected on the basis of their width alone, (b) In addition, the intervals in C are ordered along a dimension which is related to the complexity of the frequency ratio of the fundamental tones. This is much less true for S. (c) In S, on the other hand, intervals are differentiated on a dimension which is interpreted as indicating their resemblance to certain normative reference intervals. Attention is given to a number of methodological issues.