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Correlation dimension of woodwind multiphonic tones.
1Systematic Musicology Program, School of Music, University of Washington, Seattle 98195.
The Journal of the Acoustical Society of America
|October 1, 1991
Summary
Woodwind multiphonics exhibit phase-locked frequencies, suggesting complex dynamics. Analysis reveals some multiphonic tones possess a strange attractor, indicating chaotic behavior in musical instrument oscillations.
Area of Science:
- Acoustics
- Musical Instrument Physics
- Nonlinear Dynamics
Background:
- Multiphonics in woodwind instruments produce multiple simultaneous pitches.
- Previous studies suggest complex oscillatory regimes in musical instruments.
Purpose of the Study:
- To investigate the spectral properties and dynamical complexity of woodwind multiphonics.
- To determine if multiphonic tones exhibit characteristics of deterministic chaos.
Main Methods:
- Spectral analysis of saxophone and clarinet multiphonic tones.
- Phase-space reconstruction using time-series embedding.
- Calculation of correlation dimension (D) using Grassberger-Procaccia algorithm.
Main Results:
- Multiphonic spectra show phase-locked frequencies with ratios of small integers.
- Broadband spectral components are present beyond noise.
- Correlation dimension values indicate complex dynamics, with some multiphonics showing evidence of a strange attractor.
Conclusions:
- Woodwind multiphonics display phase-locked spectral components.
- Quantitative analysis supports the presence of strange attractors in some multiphonic tones, suggesting chaotic dynamics.