Probabilistic Multilabel Graphical Modelling of Motif Transformations in Symbolic Music

TL;DR

This paper introduces a probabilistic multilabel graphical model to analyze and interpret motif transformations in symbolic music, specifically applied to Beethoven's piano sonatas, capturing structural and stylistic variations.

Contribution

It develops a multilabel Conditional Random Field framework for modeling motivic transformations, integrating multiple musical features for interpretability and analysis.

Findings

Model effectively captures motif transformation patterns.

Framework reveals co-occurrence of transformation families.

Enables quantitative analysis of musical structure and style.

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.