Regensburg 2025 – wissenschaftliches Programm
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DY: Fachverband Dynamik und Statistische Physik
DY 8: Focus Session: Nonlinear Dynamics and Stochastic Processes – Advances in Theory and Applications II
DY 8.5: Vortrag
Montag, 17. März 2025, 16:15–16:30, H43
Stochastic Properties of Musical Time Series: Measuring Musical Variability — Corentin Nelias and •Theo Geisel — Max Planck Institute for Dynamics and Self-Organization, Göttingen, Germany
Music philosophers and psychologists have argued that emotions and meaning in music depend on an interplay of expectation and surprise. We aimed to quantify the variability of musical pieces empirically by considering them as correlated dynamical processes. Using a multitaper method we determined power spectral density (PSD) estimates for more than 550 classical compositions and jazz improvisations down to the smallest possible frequencies [1]. The PSDs typically follow inverse power laws (1/fβ-noise) with exponents near β=1 for classical compositions, 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 abruptly. We determined cutoff times between 4 and 100 quarter note units serving as a measure for the degree of persistence and predictability in music. They tend to be larger in Mozart’s compositions than in Bach’s, which implies that the anticipation and expectation of the musical progression tends to last longer in Mozart’s than in Bach’s compositions
[1] C. Nelias, T. Geisel, Nature Comm. 15, 9280 (2024)
Keywords: music; empirical musicology; timeseries analysis; stochastic properties; 1/f-noise