Direct Estimation of Multidimensional Tonal Dissimilarity
Thomas Carvellas, Bruce A. Schneider · The Journal of the Acoustical Society of America · 1972
Magnitude estimates were obtained for the dissimilarity of pure tones varying in frequency and intensity. In Expt. 1, a spatial embedding for a set of seven tones was determined by assuming the magnitude estimates represented distances in a two-dimensional space whose coordinate axes were pitch and loudness. Embeddings were determined for both Euclidean and “city-block” distance functions. A linear relation was consistently observed between the projections of the tones on dimensions of pitch and loudness and their values on Stevens's mel and sone scales, with the city-block projections usually yielding higher correlations. In Expt. 2, 11 tones were used and the magnitude estimates of dissimilarity were compared to the tightly constrained “monotone” distances derived from the rank-order properties of the dissimilarities. The agreement observed between the magnitude estimates and the monotone predicted distances strongly supports a distance interpretation for the dissimilarities.