  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...). 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 that there is not a unique probability
distribution that best describes the usage of the different codewords by each
composer.
