Zipf's law and the creation of musical context

Abstract

This article discusses the extension of the notion of context from linguistics to the domain of music. In language, the statistical regularity known as Zipf's law — which concerns the frequency of usage of different words — has been quantitatively related to the process of text generation. The connection is established by Simon's model, on the basis of a few assumptions regarding the accompanying creation of context. This model captures the essential mechanism of repetition of perceptual elements, which underlies the construction of a structured, comprehensible message. Here, it is shown that the statistics of note usage in musical compositions are compatible with the predictions of Simon's model. This result, which gives objective support to the conceptual likeness of context in language and music, is obtained through automatic analysis of the digital versions of several compositions. As a by-product, a quantitative measure of context definiteness is introduced, and used to compare tonal and atonal works.