Probabilistic Multilabel Graphical Modelling of Motif Transformations in Symbolic Music

arXiv stat.ML / 3/30/2026

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Key Points

The paper proposes a probabilistic framework to analyze how musical motifs transform while retaining identity-like characteristics within their surrounding context in symbolic music.
It represents motif transformations as multilabel variables by comparing each motif instance to a reference occurrence in its local context, yielding consistent labeling across transformation families.
The authors introduce a multilabel Conditional Random Field that models how motif-level musical features affect transformation occurrence and how transformation families co-occur.
They apply the approach to Beethoven’s piano sonatas by integrating multiple datasets covering melodic, rhythmic, harmonic, and motivic information into a unified representation.
The goal is an interpretable, distributional account of motivic transformation patterns that bridges computational modeling with music-theoretical interpretation for quantitative study of structure and stylistic variation.

Abstract

Motifs often recur in musical works in altered forms, preserving aspects of their identity while undergoing local variation. This paper investigates how such motivic transformations occur within their musical context in symbolic music. To support this analysis, we develop a probabilistic framework for modeling motivic transformations and apply it to Beethoven's piano sonatas by integrating multiple datasets that provide melodic, rhythmic, harmonic, and motivic information within a unified analytical representation. Motif transformations are represented as multilabel variables by comparing each motif instance to a designated reference occurrence within its local context, ensuring consistent labeling across transformation families. We introduce a multilabel Conditional Random Field to model how motif-level musical features influence the occurrence of transformations and how different transformation families tend to co-occur. Our goal is to provide an interpretable, distributional analysis of motivic transformation patterns, enabling the study of their structural relationships and stylistic variation. By linking computational modeling with music-theoretical interpretation, the proposed framework supports quantitative investigation of musical structure and complexity in symbolic corpora and may facilitate the analysis of broader compositional patterns and writing practices.