Entropy, Probabilistic Harmonic Space, and the Harmony of Antonio Carlos Jobim

This paper introduces a theoretical framework derived from a deep and detailed harmonic analysis of songs composed by Antonio Carlos Jobim, focusing on two components, namely, “semantic” (related to the idea of chord type) and “syntactic” (involving binary relations between contiguous chords). The research is mainly focused on investigating the correlations between compositional style (here related to the harmonic construction) and the concepts of probability, expectance, and, especially entropy, being the latter defined as a measure of uncertainty or “surprise” of events along time. After a bibliographical review of these topics and their applications to music, a section exposes Markov Chains, a mathematical tool used to formalize the “semantic-syntactic” harmonic relations statistically inferred in the analyzed corpus of Jobim’s works. Then it follows the formalization of a probabilistic harmonic space and the concept of probabilistic index, directly associated with the entropy of the observed binary relations. This approach opens a new analytical perspective, also allowing the generalization of the presented theoretical and methodological technology for the examination of other repertoires and posterior comparison, presenting then as a new mean of investigation on the nature of style.