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Dynamical systems theory for music dynamics.

Jean Pierre Boon1, Olivier Decroly

  • 1Physique Nonlineaire et Mecanique Statistique, Universite libre de Bruxelles, Campus Plaine CP 231, B-1050 Bruxelles, Belgium.

Chaos (Woodbury, N.Y.)
|September 1, 1995
PubMed
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Dynamical systems theory reveals music

Area of Science:

  • Music analysis
  • Dynamical systems theory
  • Time series analysis

Background:

  • Music can be represented as time series of pitch variations.
  • Dynamical systems theory offers tools for analyzing temporal patterns.

Purpose of the Study:

  • To apply dynamical systems theory to analyze temporal dynamics in music.
  • To evaluate global and local dynamics and complexity in musical pieces.

Main Methods:

  • Constructing phase space portraits from pitch time series.
  • Evaluating dimensionality as a measure of global musical dynamics.
  • Performing spectral analysis to obtain power spectra.
  • Defining information entropy to quantify local dynamics and complexity.

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Main Results:

  • Dimensionality measures global musical dynamics.
  • Spectral analysis reveals power spectra (approximately f(-nu)) similar to red noise (nu approximately 2).
  • Information entropy quantifies local dynamics and musical complexity, with no clear analytical link to global dynamics.

Conclusions:

  • Dynamical systems theory provides a framework for analyzing musical temporal dynamics.
  • Measures of global and local dynamics can be derived from musical time series.
  • Musical complexity, measured by entropy, does not show a direct analytical relationship with global dynamics.