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Self-Similarity Of Classical Music Networks

Author

Listed:
  • VITOR ROLLA

    (VISGRAF Lab, Institute for Pure and Applied Mathematics — IMPA, Rio de Janeiro, RJ 22460-320, USA)

  • PABLO RIERA

    (��Laboratorio de Inteligencia Artificial Aplicada, Universidad de Buenos Aires, Buenos Aires C1428EGA, USA)

  • PEDRO SOUZA

    (VISGRAF Lab, Institute for Pure and Applied Mathematics — IMPA, Rio de Janeiro, RJ 22460-320, USA)

  • JORGE ZUBELLI

    (��Mathematics Department, Khalifa University of Science Technology, Al Saada St., Zone 1, Abu Dhabi)

  • LUIZ VELHO

    (VISGRAF Lab, Institute for Pure and Applied Mathematics — IMPA, Rio de Janeiro, RJ 22460-320, USA)

Abstract

We present an in-depth analysis of the fractal nature of 21 classical music pieces previously shown to have scale-free properties. The musical pieces are represented as networks where the nodes are musical notes and respective durations, and the edges are its chronological sequence. The node degree distribution of these networks is analyzed, looking for self-similarity. This analysis is done in the full network, in its fractal dimensions, and its skeletons. The assortativeness of the pieces is also studied as a fractal property. We show that two-thirds of these networks are scale-invariant, i.e. scale-free in some dimension or their skeleton. In particular, two pieces were given attention because of their exceptional tendency for fractality.

Suggested Citation

  • Vitor Rolla & Pablo Riera & Pedro Souza & Jorge Zubelli & Luiz Velho, 2021. "Self-Similarity Of Classical Music Networks," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(02), pages 1-7, March.
    • Handle: RePEc:wsi:fracta:v:29:y:2021:i:02:n:s0218348x21500419
    DOI: 10.1142/S0218348X21500419
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