Fractals and large-scale temporal structure of the acoustical speech signal and music

In paper the Hausdorff dimensionality and Kolmogorov entropy for sequences of durations of voice segments in speech (V-rhythm) are considered. The Hausdorff dimensionalities and Kolmogorov entropy are calculated with the help of experimentally determined V-rhythms for samples of both normal speech, and speech at a stammering. These calculations are possible due to introduction into consideration generalized Renyi's dimensionality and generalized Renyi's entropy. It is demonstrated in paper, that the V-rhythm of speech forms fractal structure, and the Hausdorff dimensionality is more than topological dimensionality. The fractal dimensionality of normal speech is more than fractal dimensionality of speech samples consisting of fluency disorders. Besides it is shown, that Kolmogorov entropy of V-rhythm of normal speech is positive and is finite quantity. It is necessary and sufficient condition of existence of the determined chaos in V-rhythm structure. The lower limit of the estimation for Kolmogorov entropy for fluency disorders is negative. It indicates to the regularity of the temporal structure of the disorders in speech. It is shown by an example of Vivaldi and Paganini composition, that the Hausdorff dimensionalities of music are lower than dimensionality of the fluency disorders in speech. It allows to compare the structure of music V-rhythm with structure of the V-rhythm of early phonetics in children.