On the emergence of Zipf's law in music
arXiv:1902.06678 · doi:10.1016/j.physa.2020.124309
Abstract
Zipf's law is found when the vocabulary of long written texts is ranked according to the frequency of word occurrences, establishing a power-law decay for the frequency vs rank relation. This law is a robust statistical property observed even in ancient untranslated languages. Interestingly, this law seems to be also manifested in music records when several metrics---functioning as words in written texts---are used. Even though music can be regarded as a language, finding an accurate equivalent of the concept of words in music is difficult because it lacks a functional semantic. This raises the question of which is the appropriate choice of Zipfian units in music, which is extensive to other contexts where this law can emerge. In particular, this is still an open question in written texts, where several alternatives have been proposed as Zipfian units besides the canonical use of words. Seeking to validate a natural election of Zipfian units in music, in this work we find that Zipf's law emerges when a combination of chords and notes are chosen as Zipfian units. Our results are grounded on a consistent analysis of the statistical properties of music and texts, complemented with theoretical considerations that combine different reference models, including a simple model inspired in the Lempel-Ziv compression algorithm that we have devised to explain the emergence of Zipf's law as the consequence of languages evolving into more efficient forms of communication.
arXiv commentPublished in Physica A: Statistical Mechanics and its Applications
References in corpus (19)
- Power laws, Pareto distributions and Zipf's law
- The origin of bursts and heavy tails in human dynamics
- Long-Term Clustering, Scaling, and Universality in the Temporal Occurrence of Earthquakes
- Measuring the evolution of contemporary western popular music
- Beyond word frequency: Bursts, lulls, and scaling in the temporal distributions of words
- Scale-free Networks Well Done
- Zipf's Law Leads to Heaps' Law: Analyzing Their Relation in Finite-Size Systems
- Large-scale analysis of Zipf's law in English texts
- Zipf's law unzipped
- Estimating the entropy of binary time series: Methodology, some theory and a simulation study
- Statistical laws in linguistics
- Zipf law in the popularity distribution of chess openings
- Testing statistical laws in complex systems
- The distinct flavors of Zipf's law in the rank-size and in the size-distribution representations, and its maximum-likelihood fitting
- Log-log Convexity of Type-Token Growth in Zipf's Systems
- Rank-frequency relation for Chinese characters
- Innovation and Nested Preferential Growth in Chess Playing Behavior
- Investigation of the Zipf-plot of the extinct Meroitic language
- The Dependence of Frequency Distributions on Multiple Meanings of Words, Codes and Signs