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

arXiv: https://arxiv.org/abs/2609.36460 · HTML: https://mlsanity.com/paper/2609.36460/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 25 references that are in the map.
- First posted on arXiv 29 Sep 2026.

## Builds on (most cited first, 8 of 8)

- [Distributed Representations of Words and Phrases and their Compositionality](https://mlsanity.com/paper/1310.4546/) (2013)
- [MorpheuS: generating structured music with constrained patterns and tension](https://mlsanity.com/paper/1812.04832/) (2018)
- [A Tutorial on Deep Learning for Music Information Retrieval](https://mlsanity.com/paper/1709.04396/) (2017)
- [From Context to Concept: Exploring Semantic Relationships in Music with Word2Vec](https://mlsanity.com/paper/1811.12408/) (2018)
- [Chord Embeddings: Analyzing What They Capture and Their Role for Next Chord Prediction and Artist Attribute Prediction](https://mlsanity.com/paper/2102.02917/) (2021)
- [Pitchclass2vec: Symbolic Music Structure Segmentation with Chord Embeddings](https://mlsanity.com/paper/2303.15306/) (2023)
- [Learning and Evaluating Musical Features with Deep Autoencoders](https://mlsanity.com/paper/1706.04486/) (2017)
- [Exploring Latent Spaces of Tonal Music using Variational Autoencoders](https://mlsanity.com/paper/2311.03621/) (2023)

## Abstract (arXiv)

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.