Deriving Representative Structure from Music Corpora

2025-02-21

AI Summary

Modeling the hierarchical structural complexity of Western music remains challenging. Method: This paper introduces Structural Temporal Graphs (STGs) as a unified representation for individual pieces and formalizes the corpus-level structural summarization task as a doubly NP-hard Generalized Median Graph Extension problem. We propose a novel hybrid algorithm integrating Satisfiability Modulo Theories (SMT) solvers with nested simulated annealing, guaranteeing theoretically sound generation of a central STG that balances structural plausibility and corpus representativeness. Contribution/Results: Our graph-isomorphism–based structural distance metric is empirically validated to effectively discriminate musical structural differences. The computed central STG accurately captures the aggregate structural characteristics of the corpus, establishing a new paradigm—multigranular, interpretable, and computationally tractable—for music analysis and serving as a foundational model for structural music understanding.

Technology Category

• Machine Learning: Structured Learning
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Reasoning under Uncertainty: Graphical Models

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Web Mining and Content Analysis: Bridging structured and unstructured data
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies

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 dually 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.

Problem

• Hierarchical meta-representation of musical structure
• NP-hard combinatorial optimization problem
• Structural distance and centroid STG derivation

Innovation

• Hierarchical meta-representation STG
• Simulated annealing structural distance
• Combined SMT solvers annealing