Lognormals, power laws and double power laws in the distribution of frequencies of harmonic codewords from classical music
Serra-Peralta, Marc (Universitat Autònoma de Barcelona. Departament de Física)
Serrà, Joan (Dolby Laboratories (Barcelona))
Corral, Álvaro (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Data:	2022
Resum:	Zipf's law is a paradigm describing the importance of different elements in communication systems, especially in linguistics. Despite the complexity of the hierarchical structure of language, music has in some sense an even more complex structure, due to its multidimensional character (melody, harmony, rhythm, timbre, etc. ). Thus, the relevance of Zipf's law in music is still an open question. Using discrete codewords representing harmonic content obtained from a large-scale analysis of classical composers, we show that a nearly universal Zipf-like law holds at a qualitative level. However, in an in-depth quantitative analysis, where we introduce the double power-law distribution as a new player in the classical debate between the superiority of Zipf's (power) law and that of the lognormal distribution, we conclude not only that universality does not hold, but also that there is not a unique probability distribution that best describes the usage of the different codewords by each composer.
Ajuts:	Ministerio de Economía y Competitividad FIS2015-71851-P Ministerio de Economía y Competitividad PGC-FIS2018-099629-B-I00 Agencia Estatal de Investigación CEX2020-001084-M
Drets:	Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, la comunicació pública de l'obra i la creació d'obres derivades, fins i tot amb finalitats comercials, sempre i quan es reconegui l'autoria de l'obra original.
Llengua:	Anglès
Document:	Article ; recerca ; Versió publicada
Matèria:	Mathematics and computing ; Nonlinear phenomena
Publicat a:	Scientific reports, Vol. 12 (February 2022) , art. 2615, ISSN 2045-2322

DOI: 10.1038/s41598-022-06137-3
PMID: 35173194

14 p, 13.1 MB

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