Probabilistic Multilabel Graphical Modelling of Motif Transformations in Symbolic Music

2026-03-27

AI Summary

This study investigates the occurrence patterns and structural relationships of motivic variants within their local contexts in symbolic music. To this end, it introduces—for the first time—a multi-label conditional random field (CRF)–based probabilistic graphical model that represents motivic transformations as multi-label variables. The model integrates multi-source musical features, including melodic, rhythmic, and harmonic attributes, to uniformly capture contextual dependency patterns in Beethoven’s piano sonatas. This approach not only offers an interpretable account of co-occurrence regularities and stylistic variation structures among motivic transformation families but also establishes the first quantitative analytical framework for symbolic music corpora that supports joint multi-label modeling of compositional practices.

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.

Problem

• motif transformations
• symbolic music
• musical context
• stylistic variation
• multilabel modeling

Innovation

• multilabel graphical model
• motivic transformation
• Conditional Random Field
• symbolic music analysis
• probabilistic modeling