Synthesizing Composite Hierarchical Structure from Symbolic Music Corpora

TL;DR

This paper introduces the structural temporal graph (STG), a hierarchical data structure for analyzing and summarizing the complex multi-level structure of musical compositions across a corpus.

Contribution

It proposes a novel unified hierarchical representation (STG) and a method to derive representative structural summaries of music corpora using optimization and graph isomorphism techniques.

Findings

Structural distance effectively differentiates music pieces.

Centroid STGs accurately characterize music corpora.

The approach combines simulated annealing and SMT solvers for structural analysis.

Abstract

Western music is an innately hierarchical system of interacting levels of structure, from fine-grained melody to high-level form. In order to analyze music compositions holistically and at multiple granularities, we propose a unified, hierarchical meta-representation of musical structure called the structural temporal graph (STG). For a single piece, the STG is a data structure that defines a hierarchy of progressively finer structural musical features and the temporal relationships between them. We use the STG to enable a novel approach for deriving a representative structural summary of a music corpus, which we formalize as a nested NP-hard combinatorial optimization problem extending the Generalized Median Graph problem. Our approach first applies simulated annealing to develop a measure of structural distance between two music pieces rooted in graph isomorphism. Our approach then combines the formal guarantees of SMT solvers with nested simulated annealing over structural distances to produce a structurally sound, representative centroid STG for an entire corpus of STGs from individual pieces. To evaluate our approach, we conduct experiments verifying that structural distance accurately differentiates between music pieces, and that derived centroids accurately structurally characterize their corpora.