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Zipf's law is a paradigm describing the importance of different elements incommunication systems, especially in linguistics. Despite the complexity of thehierarchical structure of language, music has in some sense an even morecomplex structure, due to its multidimensional character (melody, harmony,rhythm, timbre...). Thus, the relevance of Zipf's law in music is still an openquestion. Using discrete codewords representing harmonic content obtained froma large-scale analysis of classical composers, we show that a nearly universalZipf-like law holds at a qualitative level. However, in an in-depthquantitative analysis, where we introduce the double power-law distribution asa new player in the classical debate between the superiority of Zipf's (power)law and that of the lognormal distribution, we conclude not only thatuniversality does not hold, but that there is not a unique probabilitydistribution that best describes the usage of the different codewords by eachcomposer.

Lognormals, Power Laws and Double Power Laws in the Distribution of Frequencies of Harmonic Codewords from Classical Music