Synthesizing Composite Hierarchical Structure from Symbolic Music Corpora
This work addresses the challenge of holistic music analysis for researchers and musicians by providing a unified hierarchical representation, though it is incremental in applying existing optimization techniques to a new domain.
The authors tackled the problem of analyzing music compositions at multiple granularities by proposing a hierarchical meta-representation called the structural temporal graph (STG), and they developed a method to derive a representative structural summary of a music corpus, achieving accurate differentiation between pieces and characterization of corpora in experiments.
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.