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Complexity measures of music

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  • Pease, April
  • Mahmoodi, Korosh
  • West, Bruce J.

Abstract

We present a technique to search for the presence of crucial events in music, based on the analysis of the music volume. Earlier work on this issue was based on the assumption that crucial events correspond to the change of music notes, with the interesting result that the complexity index of the crucial events is μ ≈ 2, which is the same inverse power-law index of the dynamics of the brain. The search technique analyzes music volume and confirms the results of the earlier work, thereby contributing to the explanation as to why the brain is sensitive to music, through the phenomenon of complexity matching. Complexity matching has recently been interpreted as the transfer of multifractality from one complex network to another. For this reason we also examine the mulifractality of music, with the observation that the multifractal spectrum of a computer performance is significantly narrower than the multifractal spectrum of a human performance of the same musical score. We conjecture that although crucial events are demonstrably important for information transmission, they alone are not sufficient to define musicality, which is more adequately measured by the multifractality spectrum.

Suggested Citation

  • Pease, April & Mahmoodi, Korosh & West, Bruce J., 2018. "Complexity measures of music," Chaos, Solitons & Fractals, Elsevier, vol. 108(C), pages 82-86.
    • Handle: RePEc:eee:chsofr:v:108:y:2018:i:c:p:82-86
    DOI: 10.1016/j.chaos.2018.01.021
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    References listed on IDEAS

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    1. Kantelhardt, Jan W. & Zschiegner, Stephan A. & Koscielny-Bunde, Eva & Havlin, Shlomo & Bunde, Armin & Stanley, H.Eugene, 2002. "Multifractal detrended fluctuation analysis of nonstationary time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 316(1), pages 87-114.
    2. Grigolini, Paolo, 2015. "Emergence of biological complexity: Criticality, renewal and memory," Chaos, Solitons & Fractals, Elsevier, vol. 81(PB), pages 575-588.
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    Cited by:

    1. Ramirez-Aristizabal, Adolfo G. & Médé, Butovens & Kello, Christopher T., 2018. "Complexity matching in speech: Effects of speaking rate and naturalness," Chaos, Solitons & Fractals, Elsevier, vol. 111(C), pages 175-179.
    2. McDonough, John & Herczyński, Andrzej, 2023. "Fractal patterns in music," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    3. Chichigina, Olga A. & Valenti, Davide, 2021. "Strongly super-Poisson statistics replaced by a wide-pulse Poisson process: The billiard random generator," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
    4. Korosh Mahmoodi & Bruce J. West & Paolo Grigolini, 2018. "Self-Organized Temporal Criticality: Bottom-Up Resilience versus Top-Down Vulnerability," Complexity, Hindawi, vol. 2018, pages 1-10, March.

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