To study the perceptual structure of musical timbre and the effects of musical training, timbral dissimilarities of synthesized instrument sounds were rated by professional musicians, amateur musicians, and nonmusicians. The data were analyzed with an extended version of the multidimensional scaling algorithm CLASCAL (Winsberg & De Soete, 1993), which estimates the number of latent classes of subjects, the coordinates of each timbre on common Euclidean dimensions, a specificity value of unique attributes for each timbre, and a separate weight for each latent class on each of the common dimensions and the set of specificities. Five latent classes were found for a three-dimensional spatial model with specificities. Common dimensions were quantified psychophysically in terms of log-rise time, spectral centroid, and degree of spectral variation. The results further suggest that musical timbres possess specific attributes not accounted for by these shared perceptual dimensions. Weight patterns indicate that perceptual salience of dimensions and specificities varied across classes. A comparison of class structure with biographical factors associated with degree of musical training and activity was not clearly related to the class structure, though musicians gave more precise and coherent judgments than did non-musicians or amateurs. The model with latent classes and specificities gave a better fit to the data and made the acoustic correlates of the common dimensions more interpretable.

Timbre spaces represent the organization of perceptual distances, as measured with dissimilarity ratings, among tones equated for pitch, loudness, and perceived duration. A number of potential acoustic correlates of timbre-space dimensions have been proposed in the psychoacoustic literature, including attack time, spectral centroid, spectral flux, and spectrum fine structure. The experiments reported here were designed as direct tests of the perceptual relevance of these acoustical parameters for timbre dissimilarity judgments. Listeners presented with carefully controlled synthetic tones use attack time, spectral centroid, and spectrum fine structure in dissimilarity rating experiments. These parameters thus appear as major determinants of timbre. However, spectral flux appears as a less salient timbre parameter, its salience depending on the number of other dimensions varying concurrently in the stimulus set. Dissimilarity ratings were analyzed with two different multidimensional scaling models (CLASCAL and CONSCAL), the latter providing psychophysical functions constrained by the physical parameters. Their complementarity is discussed.

The dependency of the timbre of musical sounds on their fundamental frequency (F 0 ) was examined in three experiments. In experiment I subjects compared the timbres of stimuli produced by a set of 12 musical instruments with equal F 0 , duration, and loudness. There were three sessions, each at a different F 0 . In experiment II the same stimuli were rearranged in pairs, each with the same difference in F 0 , and subjects had to ignore the constant difference in pitch. In experiment III, instruments were paired both with and without an F 0 difference within the same session, and subjects had to ignore the variable differences in pitch. Experiment I yielded dissimilarity matrices that were similar at different F 0 's, suggesting that instruments kept their relative positions within timbre space. Experiment II found that subjects were able to ignore the salient pitch difference while rating timbre dissimilarity. Dissimilarity matrices were symmetrical, suggesting further that the absolute displacement of the set of instruments within timbre space was small. Experiment III extended this result to the case where the pitch difference varied from trial to trial. Multidimensional scaling ͑MDS͒ of dissimilarity scores produced solutions ͑timbre spaces͒ that varied little across conditions and experiments. MDS solutions were used to test the validity of signal-based predictors of timbre, and in particular their stability as a function of F 0 . Taken together, the results suggest that timbre differences are perceived independently from differences of pitch, at least for F 0 differences smaller than an octave. Timbre differences can be measured between stimuli with different F 0 's.

A timbre space represents the mental organization of sound events at equal pitch, loudness, and duration. The geometric distance between two timbres corresponds to their degree of perceived dissimilarity. The dimensions of such a three-dimensional space, established by Krumhansl [l] for a set of 21 synthesized sounds, were investigated with respect to their acoustic characteristics. Several acoustical parameters based on the temporal and frequency properties of the sounds were calculated. The high degree of correlation of several parameters with the perceptual axes lend support to previous interpretations of the qualitative character of two perceptual dimensions and their semantic attributes. The perceptual dimensions "brightness" and "rapidity of attack" tum out to be quantitatively explainable by the center of gravity of the sound spectrum (CGS) and the rise t h e on a logarithmic scale (LTM), respectively. The third dimension, initially called "spectralJEux" corresponds partially to the standard deviation of the timeaveraged harmonic amplitudes from a spectral envelope (IRR). A new verbal descritor, "spectralJine structure" seems to fit better with the results of acoustic analyses.