Tonal parsimony in chord-sequence analysis: combining modulation cost and tonal vocabulary
For researchers and practitioners in harmonic analysis and jazz improvisation, this provides a tractable method to reduce unnecessary tonal centers in chord-sequence analysis.
The authors introduce tonal parsimony, a lexicographic objective that minimizes modulations then distinct tonalities, for assigning local tonalities to chord sequences. On 31,032 chord sequences, it reduces tonal vocabulary in 55.8% of cases while preserving transition optimality, and on 1,555 jazz standards improves chord-scale agreement to 95.6%.
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.