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Correlation dimension of woodwind multiphonic tones.

Correlation dimension of woodwind multiphonic tones. A multiphonic is a regime of oscillation of woodwind musical instruments that is perceived as two or more simultaneously sounding pitches. The frequencies fl,m of the line spectral components of a measured woodwind multiphonic tone fit a biperiodic spectrum at low- to mid-playing levels. For the saxophone and clarinet multiphonics investigated, the two basis frequencies of the biperiodic spectrum are phase locked, that is, their ratio is equal to a ratio of small integers. A broadband spectrum is present in multiphonic spectra that exceeds instrumentation noise and window leakage associated with signal processing. The correlation dimension D of P. Grassberger and I. Procaccia [Physica D 9, 189-208 (1983)] is measured by embedding a single measured time series in higher-dimensional space, so as to reconstruct the phase space of the dynamical system. The time delay used in the dimensional reconstruction is chosen using information theory. For the particular multiphonics analyzed, the correlation dimension ranges from 2.5 to 2.9 for the saxophone and from 1.3 to 2.2 for the clarinet. One clarinet multiphonic shows possible additional dynamical complexity at small length scales in the embedding space, with a correlation dimension of 3.3. These results give quantitative evidence that some, but not all, multiphonic tones possess a strange attractor. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png The Journal of the Acoustical Society of America Pubmed

Correlation dimension of woodwind multiphonic tones.

The Journal of the Acoustical Society of America , Volume 90 (4 Pt 1): -1688 – Jan 7, 1992

Correlation dimension of woodwind multiphonic tones.


Abstract

A multiphonic is a regime of oscillation of woodwind musical instruments that is perceived as two or more simultaneously sounding pitches. The frequencies fl,m of the line spectral components of a measured woodwind multiphonic tone fit a biperiodic spectrum at low- to mid-playing levels. For the saxophone and clarinet multiphonics investigated, the two basis frequencies of the biperiodic spectrum are phase locked, that is, their ratio is equal to a ratio of small integers. A broadband spectrum is present in multiphonic spectra that exceeds instrumentation noise and window leakage associated with signal processing. The correlation dimension D of P. Grassberger and I. Procaccia [Physica D 9, 189-208 (1983)] is measured by embedding a single measured time series in higher-dimensional space, so as to reconstruct the phase space of the dynamical system. The time delay used in the dimensional reconstruction is chosen using information theory. For the particular multiphonics analyzed, the correlation dimension ranges from 2.5 to 2.9 for the saxophone and from 1.3 to 2.2 for the clarinet. One clarinet multiphonic shows possible additional dynamical complexity at small length scales in the embedding space, with a correlation dimension of 3.3. These results give quantitative evidence that some, but not all, multiphonic tones possess a strange attractor.

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ISSN
0001-4966
DOI
10.1121/1.401656
pmid
1960272

Abstract

A multiphonic is a regime of oscillation of woodwind musical instruments that is perceived as two or more simultaneously sounding pitches. The frequencies fl,m of the line spectral components of a measured woodwind multiphonic tone fit a biperiodic spectrum at low- to mid-playing levels. For the saxophone and clarinet multiphonics investigated, the two basis frequencies of the biperiodic spectrum are phase locked, that is, their ratio is equal to a ratio of small integers. A broadband spectrum is present in multiphonic spectra that exceeds instrumentation noise and window leakage associated with signal processing. The correlation dimension D of P. Grassberger and I. Procaccia [Physica D 9, 189-208 (1983)] is measured by embedding a single measured time series in higher-dimensional space, so as to reconstruct the phase space of the dynamical system. The time delay used in the dimensional reconstruction is chosen using information theory. For the particular multiphonics analyzed, the correlation dimension ranges from 2.5 to 2.9 for the saxophone and from 1.3 to 2.2 for the clarinet. One clarinet multiphonic shows possible additional dynamical complexity at small length scales in the embedding space, with a correlation dimension of 3.3. These results give quantitative evidence that some, but not all, multiphonic tones possess a strange attractor.

Journal

The Journal of the Acoustical Society of AmericaPubmed

Published: Jan 7, 1992

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