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Fractal patterns in music

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  • McDonough, John
  • Herczyński, Andrzej

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.

Suggested Citation

  • McDonough, John & Herczyński, Andrzej, 2023. "Fractal patterns in music," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    • Handle: RePEc:eee:chsofr:v:170:y:2023:i:c:s0960077923002163
    DOI: 10.1016/j.chaos.2023.113315
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    References listed on IDEAS

    as
    1. Sanyal, Shankha & Banerjee, Archi & Patranabis, Anirban & Banerjee, Kaushik & Sengupta, Ranjan & Ghosh, Dipak, 2016. "A study on Improvisation in a Musical performance using Multifractal Detrended Cross Correlation Analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 67-83.
    2. Pease, April & Mahmoodi, Korosh & West, Bruce J., 2018. "Complexity measures of music," Chaos, Solitons & Fractals, Elsevier, vol. 108(C), pages 82-86.
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