Polyspectra as measures of sound texture and timbre
Abstract 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 partiais, a...