Computational modeling of structural repetition in music

Humans experience repetition in music in ways that extend far beyond the recurrence of surface material. What we hear as repeated patterns may appear very different on the surface, yet at the same time, this sense of repeat can also break with certain tiny changes to the surface. This thesis provides a computational account for musical repetition by putting interpretation at the center. It specifically proposes that the experience of repetition comes from using the same causal explanation. This new perspective, termed structural repetition, systematically explains variations in music as instantiating and composing reusable generative explanations. This thesis progressively builds toward a model that infers program-like structure directly from musical observations, treating structural repetition as the reuse of learned programs that achieves optimal compression. The first stage identifies reusable components within a given corpus of tree-structured reductive analyses. The second stage extends the previous approach by relaxing the input to the raw sequential data of a single piece. It introduces Template programs and recasts the detection of structural repeat in sequences as minimal program inference using a weighted-deduction algorithm. The final stage scales this framework to allow the joint discovery of piece-specific programs and a library of reusable abstractions across works. It combines deductive parsing with library learning over E-graphs to deal with the vast search space. Taken together, these contributions bridge theoretically posited musical structures with modern ideas and techniques in computational cognitive science. By formalizing structural repetition as program reuse, the model makes abstract analytical concepts explicit, computable, and learnable from data. The resulting framework establishes a computational basis for understanding how listeners construct, revise, and generalize program-like generative representations of musical structure, providing a candidate algorithmic-level description on the perception and learning of structural repetition.