Fractal patterns in music

John McDonough and Andrzej Herczyński

Chaos, Solitons & Fractals, 2023, vol. 170, issue C

Abstract: If aesthetic preferences are affected by the fractal geometry of nature, scaling regularities would be expected to appear in all art forms, including music. While a variety of statistical tools have been proposed to analyze time series in sound, no consensus has yet emerged regarding the most meaningful measure of complexity in music or how to discern fractal patterns in compositions in the first place. Here, we offer a new approach based on the self-similarity of melodic lines recurring at various temporal scales. In contrast to the statistical analyses advanced in recent literature, the proposed method does not depend on averaging within time-windows and is distinctively local. The corresponding definition of the fractal dimension is based on the temporal scaling hierarchy and depends on the tonal contours of musical motifs. The new concepts are tested on musical “renditions” of the Cantor Set and the Koch Curve, and then applied to a number of carefully selected masterful compositions spanning five centuries of music making.

Keywords: Fractals; Fractal dimension; Self-similarity; Scaling; Time series; Music (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:170:y:2023:i:c:s0960077923002163

DOI: 10.1016/j.chaos.2023.113315

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