Tonnetz-Driven Graph Wedgelet for Harmonic Complexity Reduction in Music Scores

2026-07-09

AI Summary

This work addresses the challenge of simplifying complex musical scores while preserving essential harmonic relationships and graph structure. The authors propose a structure-preserving simplification method that constructs a heterogeneous graph encompassing notes, lyric syllables, and accompaniment events. By introducing a harmony-distance–based splitting criterion in six-dimensional Tonnetz space, the approach recursively minimizes L² reconstruction error using a binary wedgelet partition tree and an adaptive greedy algorithm to produce piecewise-constant approximations of piano subgraphs. Experiments on symbolic scores by three composers demonstrate that the resulting simplified scores significantly reduce complexity while effectively retaining the original harmonic structure, achieving both readability and playability.

Abstract

Heterogeneous graph built on notes, lyric syllables, and accompaniment events is a natural representation of symbolic music score, providing a substrate for both philological analysis and computational tasks. Music features are therefore well-captured by graph geometry and its properties. This representation has proved effective for analytical tasks as cadence detection, voice separation, and stylistic classification. In the present work, the reduction of harmonic complexity of a music score on graph, by preserving task-relevant information, relation between notes, and graph structure is investigated. A compression scheme for the piano subgraph of vocal-pianistic scores, built on binary wedge partitioning trees, is proposed. The wedges are generated through a fully adaptive greedy algorithm that recursively minimizes the $L^2$-error within a six-dimensional Tonnetz embedding of musical notes. The partitioning process employs a splitting criterion based on harmonic distance, resulting in regions that accurately reflect the intrinsic harmonic relationships among notes. The reconstructed music scores obtained through piecewise-constant functions and the mean values of the notes inside each wedge are used as a new simplified scores human-readable and playable. Some experiments on a corpus of symbolic music scores of three different composers are performed to assess the proposed approach.

Problem

• harmonic complexity reduction
• music score
• graph representation
• Tonnetz
• symbolic music

Innovation

• Tonnetz
• graph wedgelet
• harmonic complexity reduction
• adaptive greedy algorithm
• symbolic music score