Lognormals, Power Laws and Double Power Laws in the Distribution of Frequencies of Harmonic Codewords from Classical Music
arXiv:2110.08200 · doi:10.1038/s41598-022-06137-3
Abstract
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.
33 pages
References in corpus (11)
- Power-law distributions in empirical data
- Collaborative Tagging and Semiotic Dynamics
- Languages cool as they expand: Allometric scaling and the decreasing need for new words
- Parameter estimation for power-law distributions by maximum likelihood methods
- Zipf's law for word frequencies: word forms versus lemmas in long texts
- Testing statistical laws in complex systems
- Text mixing shapes the anatomy of rank-frequency distributions: A modern Zipfian mechanics for natural language
- The brevity law as a scaling law, and a possible origin of Zipf's law for word frequencies
- The arrow of time across five centuries of classical music
- Tail of the distribution of fatalities in epidemics
- Heaps' Law and Vocabulary Richness in the History of Classical Music Harmony