Surprising Harmonies

Understanding surprise is a key to the cognition of music, at all levels of musical structure: rhythm, melody, harmony, timbre. This paper addresses the modeling of surprise in particular music sequences ; Jazz harmonic progressions. Most of the works in music cognition relate surprise to the phenomenon of musical expectation: a surprise is seen as something unexpected. Furthermore, unexpected more or less means "unheard before". In this paper, we emphasize the importance of the rich algebraic structure underlying Jazz chord sequences, and suggest that harmonic surprise may not only be related to unexpected structures, but also to "calculus", i.e. to an ability to deduce a sequence from a set of combinatorial rules. We first introduce the domain of Jazz chord sequences and describe its underlying algebraic structure, based on the notion of chord substitution. We then propose to use a statistical-based data compression approach to infer recurring patterns from the corpus, and show that this yields reasonable but limited expectation structures. We then propose a mechanism to induce chord substitution rules from the corpus, and comment its ouput according to the theory of chord substitution. Finally, we suggest that such a model of chord substitution rules may be used to devise richer models of harmonic surprise.