Modeling the Multiscale Structure of Chord Sequences Using Polytopic Graphs

Chord sequences are an essential source of information in a number of MIR tasks. However, beyond the sequential nature of musical content, relations and dependencies within a music segment can be more efficiently modeled as a graph. Polytopic Graphs have been recently introduced to model music structure so as to account for multiscale relationships between events located at metrically homologous instants. In this paper, we focus on the description of chord sequences and we study a specific set of graph configurations, called Primer Preserving Permutations (PPP). For sequences of 16 chords, PPPs account for 6 different latent systems of relations, corresponding to 6 main structural patterns (Prototypical Carrier Sequences or PCS). Observed chord sequences can be viewed as distorted versions of these PCS and the corresponding optimal PPP is estimated by minimizing a description cost over the latent relations. After presenting the main concepts of this approach, the article provides a detailed study of PPPs across a corpus of 727 chord sequences annotated from the RWC POP database (100 pop songs). Our results illustrate both qualitatively and quantitatively the potential of the proposed model for capturing long-term multiscale structure in musical data, which remains a challenge in computational music modeling and in Music Information Retrieval.