Polyspectra as measures of sound texture and timbre

In this work aperiodicities in the waveform of musical sounds, are investigated, with a focus on fluctuations (jitter) in frequency that occur during the stable (sustained) portion of the sound. The existence of statistical independence between fluctuations of different harmonics brings a sense of separability among the sound components, and this puts the problem in the border area between timbre and texture. In the paper it is shown that coherence of fluctuations is strongly related to nonlinear properties of the time series model of the sound. By application of higher order statistical (HOS, polyspectral) methods, we analyze and model this phenomena. Our main result is demonstrating the important correspondence between HOS features, and texture and timbre properties, specifically the classification into instrument families of string, woodwind, and brass instruments. It is shown that the appearance of higher order cumulants is directly related to the number of statistically dependent partíais, and this property seems to be characteristic of instrumental families. We also show that at least approximate resynthesis of the bispectral properties of the sound can be achieved by controlling the statistical dependence/independence of the frequency modulating jitters among the different partíais. From a broader perspective, the method of analysis seems to be applicable to additional sound domains. For instance, in the final part of the paper our methods are applied to the classification of man-made noises and other complex, noninstrumental sounds. A musical discussion of the notion of sound texture is also presented.