Title: Optimizing Tonal Economy in Chord-Sequence Analysis: Integrating Modulation Expenses with Tonal Lexicons

Abstract

This research investigates the method of assigning local tonalities to chord progressions, a process essential for harmonic analysis, musical composition, and jazz improvisation. While conventional dynamic-programming techniques focus on minimizing modulations, they often result in an excessive number of tonal centers. We evaluate this transition-centric objective against two alternatives: pure minimum-vocabulary analysis and tonal parsimony. The latter approach prioritizes minimizing the number of modulations lexicographically, followed by minimizing the count of distinct tonalities. Although this combined objective presents combinatorial challenges, we present exact algorithms that leverage the constraints of the standard 24-tone major/minor system. Testing on 31,032 sequences from the LMD Chords dataset reveals that tonal parsimony maintains the optimal transition count while reducing the tonal vocabulary in 55.8% of instances. When applied with weighted jazz-substitution closure, the method decreases the mean number of tonalities from 3.802 to 3.206 and reduces modulations from 16.728 to 12.141. Furthermore, analysis of 1,555 annotated jazz standards shows that this approach enhances chord-scale compatibility to 95.6%, demonstrating its viability for professional-scale harmonic analysis.

Source: arXiv Generated at: 2026-06-03 00:00:00 UTC