Probabilistic Modeling of Hierarchical Music Analysis

Hierarchical music analysis, as exemplified by Schenkerian analysis, describes the structure of a musical composition by a hierarchy among its notes. Each analysis defines a set of prolongations, where musical objects persist in time even though others are present. We present a formal model for representing hierarchical music analysis, probabilistic interpretations of that model, and an efficient algorithm for computing the most probable analysis under these interpretations. We represent Schenkerian analyses as maximal outerplanar graphs (MOPs). We use this representation to encode the largest known data set of computer-processable Schenkerian analyses, and we use these data to identify statistical regularities in the human-generated analyses. We show that a dynamic programming algorithm can be applied to these regularities to identify the maximum likelihood analysis for a given piece of music.