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2004, 21

O.P. Skljarov

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

language: Russian

received 30.10.2004, published 04.12.2004

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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.

10 pages, 3 figures

Сitation: O.P. Skljarov. Fractals and large-scale temporal structure of the acoustical speech signal and music. Electronic Journal “Technical Acoustics”,, 2004, 21.


[1] Feigenbaum M. J., Kadanoff L. P., Shenker S. J. Quasi periodicity in dissipate systems: renormalisation group approach. Physica, 1983, vol. 5D, 239–248.
[2] Скляров О. П. Элементы теории ритма речи на основе физической феноменологии его нарушений. Автореф. дисс... доктора физ.-мат. наук. Санкт-Петербургский Университет, СПб, 1999.
[3] Skljarov O. P. Neurodynamical Route to Chaos and Normal Speech vs. Stuttering. Proceedings of Int. Conf. “Control of Oscillations and Chaos”, St. Petersburg, 2000, 449–452.
[4] Заславский Г. М., Сагдеев Р. З. Введение в нелинейную физику: от маятника до турбулентности и хаоса. М.: «Наука», 1988.
[5] Шустер Г. Детерминированный хаос. М., «Мир», 1988.
[6] Скляров О. П. V/U-ритм речи при чтении как индикатор состояния функции речевого дыхания у заикающихся. Электронный журнал «Техническая акустика», http://www.ejta.orgta, 2004, 16.
[7] Grassberger P., Procaccia I. On the Characterization of Strange Attractors, Phys. Rev. Lett., 1983, vol. 50, 346–354.
[8] Скляров О. П. Онтогенез речи и сценарий развития ее V-ритмов. Электронный журнал «Техническая акустика»,, 2004, 7.


Oleg Skljarov received the BS degree in 1970, and the PhD degree in 1975 from Physical Faculty of the St.Petersburg State University (Russia). In 1975-1982, he worked at State Optical Institute as a scientific researcher. In 1982-1990 he was a chief of scientific sector in the Acoustical Department of the Telecommunication Company. Since 1990, he was been a Senior Scientific Researcher at Institute of Ear, Throat, Nose & Speech. In 2000 he received the Doctoral degree of Physical-and-Mathematical Sciences from St. Petersburg State University. His research interests included soft computing (neural networks and dynamical chaos); critical behaviour of speech rhythm in both theory and applied aspect (correction of the stuttering); and non-linear phenomena in both biology and acoustics of speech