Universality in the tail of musical note rank distribution

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

Physica A: Statistical Mechanics and its Applications, 2008, vol. 387, issue 22, 5552-5560

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.

Keywords: Ranking distributions; Power law distribution; Multiplicative processes; Music (search for similar items in EconPapers)
Date: 2008
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:387:y:2008:i:22:p:5552-5560

DOI: 10.1016/j.physa.2008.05.031

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