Emergent Tonal Structure in Learned Chord Embeddings and Its Relation to Tonal Tension

2026-09-28

AI Summary

This study investigates whether data-driven chord embeddings can effectively capture tonal structure and tension. Leveraging a Skip-gram model trained on symbolic music corpora, this work introduces transposition-based data augmentation to learn chord embeddings and systematically evaluates their tonal organization, functional properties, and alignment with human perception through geometric spatial analysis. Results demonstrate that transposition augmentation endows the embedding space with a circle-of-fifths topology and transposition equivariance, substantially enhancing geometric stability and interpretability. Building upon these structural properties, we propose a distance-based tension metric that effectively captures tonal tension patterns consistent with human cognitive perception.

Abstract

Several tonal pitch spaces and computational models have been proposed to analyze tonal structure in Western tonal music, many of them grounded in principles from music theory and used to support tonal analysis with important implications for tonal tension. In parallel, data-driven methods such as skip-gram have been used to learn chord embeddings from symbolic corpora, but their ability to recover tonal structure and its relation to tonal tension remains underexplored. In this work, we investigate how skip-gram chord embeddings reflect tonal structure and whether they provide a useful basis for analyzing structural aspects of tonal tension. Using chord sequences with and without transposition-based augmentation, we evaluate the learned spaces from geometric, functional, and tension-related perspectives. We show that augmented embeddings exhibit strong transposition equivariance, recover a clear circle-of-fifths structure, and support interpretable shifts between key-related regions of the learned space. We then derive embedding-based measures from chord-to-key distance and contextual chord-distance relations, and show that they capture meaningful aspects of tonal tension structure through correspondence with matched tonal measures and moderate alignment with human tension profiles. Across analyses, transposition-based augmentation generally improves the stability, tonal coherence, and interpretability of the learned space.

Problem

• chord embeddings
• tonal structure
• tonal tension
• skip-gram
• music information retrieval

Innovation

• Chord Embeddings
• Skip-gram
• Tonal Tension
• Transposition Augmentation
• Circle of Fifths