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

We study the assignment of local tonalities to chord sequences, a task useful for harmonic analysis, composition, and jazz-oriented improvisation. Standard dynamic-programming approaches minimize modulations but can introduce unnecessarily many tonal centers. We compare this transition-only objective with pure minimum-vocabulary analysis and with tonal parsimony, which minimizes lexicographically the number of modulations and then the number of distinct tonalities. Although this joint objective is combinatorially hard in general, we give exact algorithms exploiting the fixed 24-tonality major/minor universe. On 31,032 LMD Chords sequences, tonal parsimony preserves the transition optimum while reducing tonal vocabulary in 55.8% of cases. With weighted jazz-substitution closure, it lowers mean tonalities from 3.802 to 3.206 and modulations from 16.728 to 12.141. On 1,555 annotated jazz standards, it improves compatible chord-scale agreement to 95.6%, supporting tractable professional-scale harmonic analysis.

We propose a continuous measure of tonal ambiguity that extends the established concept of uniqueness. While uniqueness is widely regarded as necessary for tonality, it cannot (i) discriminate among sets that possess it, (ii) capture hierarchical organization in modes of limited transposition, or (iii) account for temporal unfolding. To address these limitations, we introduce a companion measure, grounded in information theory, that quantifies tonal ambiguity on a continuous scale. The measure applies across pitch-class sets and tuning systems, expanding analytic coverage of tonal relationships and offering a practical tool for theory and analysis.

Chord progressions encapsulate important information about music, pertaining to its structure and conveyed emotions. They serve as the backbone of musical composition, and in many cases, they are the sole information required for a musician to play along and follow the music. Despite their importance, chord progressions as a data domain remain underexplored; existing datasets lack the scale, structural annotation, and metadata diversity required for rigorous evaluation of music understanding models. In this work, we present Chordonomicon, the largest dataset of its kind, containing over 666,000 song-level symbolic chord progressions, annotated with structural parts (verse, chorus, bridge, etc.), genre, and release date, created by scraping various sources of user-generated progressions and associated metadata, showing strong similarity to well-established prior datasets. Beyond the dataset itself, we propose a reproducible benchmark suite for next chord prediction, evaluating three sequence modeling architectures (RNN, GRU, LSTM) across multiple context window sizes and data scales under strict exact-match evaluation. Our experiments reveal that structural part annotations consistently improve prediction performance. Chordonomicon is released as an open benchmark, providing split methodology, baselines, and evaluation protocols to enable fair and reproducible comparison for future work on chord prediction, classification, generation, and beyond.