The dimensions of tonal experience: A nonmetric multidimensional scaling approach

Subjects were required in each trial to directly compare two pairs of tones and indicate which pair of tones had the greater subjective difference or dissimilarity. Eleven tones differing in both intensity and frequency were employed. Subjects made binary comparisons among the 55 tone pairs which can be formed from the set of 11 tones. These paired comparisons of tonal intervals were used to determine a two-dimensional Euclidean representation for tonal experience. Loudness and pitch appeared as orthogonal dimensions in this representation. However, a 45-deg rotation of loudness and pitch axes produced axes which could be identified as volume and density. This relationship suggested that volume and density were simple functions of pitch and loudness. Volume and density predictions based on this two-dimensional representation were shown to provide a good account of the data from three experiments on volume and density.