Learned chord embeddings reveal tonal structure and tension patterns
Emergent Tonal Structure in Learned Chord Embeddings and Its Relation to Tonal Tension
SoundArtificial IntelligenceMachine Learning
Summary
Understanding how chords relate to each other in music helps explain feelings like tension and resolution. The authors studied computer models that learn chord relationships from music data without explicit music theory input. They found that when the model is trained with data shifts representing musical transposition, it captures well-known musical structures and tension patterns. These embeddings align moderately with human perceptions of tension in music and offer a new way to analyze tonal music.
What this means in practice
- •For music software developers: Enhance music analysis tools with embeddings that capture tonal relationships and tension patterns automatically.
- •For digital audio workstation teams: Integrate chord embedding models to assist composers by suggesting harmonically coherent chord progressions reflecting tonal tension.
Authors
Maral Ebrahimzadeh, Gilberto Bernardes, Sebastian Stober
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.