Zipf's law and the creation of musical context
Ziv, N. & Eitan, Z. (2007). Themes as prototypes: Similarity judgments and categorization tasks in musical contexts. Musicae Scientiae, Discussion Forum 4A, 99-133.
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. ...