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Music walk, fractal geometry in music

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  • Su, Zhi-Yuan
  • Wu, Tzuyin

Abstract

In this study, sequences of musical notes from various pieces of music are converted into one-variable random walks (here termed ‘music walks’). Quantitative measurements of the properties of each musical composition are then performed by applying Hurst exponent and Fourier spectral analyses on these music-walk sequences. Our results show that music shares the similar fractal properties of a fractional Brownian motion (fBm). That is, music displays an anti-persistent trend in its tone changes (melody) over decades of musical notes; and music sequence exhibits generally the 1/fβ-type spectrum (fractal property), with apparently two different β values in two different temporal scales.

Suggested Citation

  • Su, Zhi-Yuan & Wu, Tzuyin, 2007. "Music walk, fractal geometry in music," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 380(C), pages 418-428.
    • Handle: RePEc:eee:phsmap:v:380:y:2007:i:c:p:418-428
    DOI: 10.1016/j.physa.2007.02.079
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    Cited by:

    1. Banerjee, Archi & Sanyal, Shankha & Roy, Souparno & Nag, Sayan & Sengupta, Ranjan & Ghosh, Dipak, 2021. "A novel study on perception–cognition scenario in music using deterministic and non-deterministic approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 567(C).
    2. Zunino, L. & Pérez, D.G. & Kowalski, A. & Martín, M.T. & Garavaglia, M. & Plastino, A. & Rosso, O.A., 2008. "Fractional Brownian motion, fractional Gaussian noise, and Tsallis permutation entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(24), pages 6057-6068.
    3. Fossion, R. & Donado, F. & Jaguey-Hernández, Y. & Tapia-Ignacio, C., 2023. "Application of Fourier analysis to an ellipsoidal particle on a granular magnetic bath," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 630(C).

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