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Universality in the tail of musical note rank distribution

Author

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  • Beltrán del Río, M.
  • Cocho, G.
  • Naumis, G.G.

Abstract

Although power laws have been used to fit rank distributions in many different contexts, they usually fail at the tails. Languages as sequences of symbols have been a popular subject for ranking distributions, and for this purpose, music can be treated as such. Here we show that more than 1800 musical compositions are very well fitted by the first kind two parameter beta distribution, which arises in the ranking of multiplicative stochastic processes. The parameters a and b are obtained for classical, jazz and rock music, revealing interesting features. Specially, we have obtained a clear trend in the values of the parameters for major and minor tonal modes. Finally, we discuss the distribution of notes for each octave and its connection with the ranking of the notes.

Suggested Citation

  • Beltrán del Río, M. & Cocho, G. & Naumis, G.G., 2008. "Universality in the tail of musical note rank distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(22), pages 5552-5560.
    • Handle: RePEc:eee:phsmap:v:387:y:2008:i:22:p:5552-5560
    DOI: 10.1016/j.physa.2008.05.031
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    References listed on IDEAS

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    1. James B. McDonald, 2008. "Some Generalized Functions for the Size Distribution of Income," Economic Studies in Inequality, Social Exclusion, and Well-Being, in: Duangkamon Chotikapanich (ed.), Modeling Income Distributions and Lorenz Curves, chapter 3, pages 37-55, Springer.
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    1. Nowak, Przemysław & Santolini, Marc & Singh, Chakresh & Siudem, Grzegorz & Tupikina, Liubov, 2024. "Beyond Zipf’s law: Exploring the discrete generalized beta distribution in open-source repositories," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 649(C).
    2. Elio Roca-Flores & Gerardo G. Naumis, 2021. "Assessing statistical hurricane risks: nonlinear regression and time-window analysis of North Atlantic annual accumulated cyclonic energy rank profile," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 108(3), pages 2455-2465, September.
    3. Alvarez-Martinez, R. & Martinez-Mekler, G. & Cocho, G., 2011. "Order–disorder transition in conflicting dynamics leading to rank–frequency generalized beta distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(1), pages 120-130.

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