Stochastic properties of musical time series

Corentin Nelias and Theo Geisel ()
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Corentin Nelias: Max Planck Institute for Dynamics and Self-Organization
Theo Geisel: Max Planck Institute for Dynamics and Self-Organization

Nature Communications, 2024, vol. 15, issue 1, 1-11

Abstract: Abstract Musical sequences are correlated dynamical processes that may differ depending on musical styles. We aim to quantify the correlations through power spectral analysis of pitch sequences in a large corpus of musical compositions as well as improvised performances. Using a multitaper method we extend the power spectral estimates down to the smallest possible frequencies optimizing the tradeoff between bias and variance. The power spectral densities reveal a characteristic behavior; they typically follow inverse power laws (1/f β-noise), yet only down to a cutoff frequency, where they end in a plateau. Correspondingly the pitch autocorrelation function exhibits slow power law decays only up to a cutoff time, beyond which the correlations vanish. We determine cutoff times between 4 and 100 quarter note units for the compositions and improvisations of the corpus, serving as a measure for the degree of persistence and predictability in music. The histogram of exponents β for the power law regimes has a pronounced peak near β = 1 for classical compositions, but is much broader for jazz improvisations.

Date: 2024
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DOI: 10.1038/s41467-024-53155-y

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