用更少调性表达和弦序列，让音乐分析更简洁准确
Tonal parsimony in chord-sequence analysis: combining modulation cost and tonal vocabulary
- 联合优化调性切换次数与不同调性的数量
- 在3.8个调性基础上降低至3.2个，调性切换减少约27%
- 适合音乐分析、作曲与爵士即兴创作专业人士使用
我们研究将局部调性分配给和弦序列的任务，该任务对和声分析、作曲及爵士即兴演奏均有帮助。标准动态规划方法仅最小化调性转换，但可能引入过多调性中心。本文对比了仅最小化转换的方案、纯最小词汇量分析，以及同时最小化调性切换次数和不同调性数量的调性简约策略（tonal parsimony）。尽管该联合目标在一般情况下为组合难题，但本文针对固定的24种大小调体系给出精确算法。在31,032条LMD Chords序列上，调性简约在保持转换数最优的同时，在55.8%的情况下减少了调性词汇量；结合加权爵士替换闭合规则后，平均调性数从3.802降至3.206，平均调性切换数从16.728降至12.141。在1,555条标注爵士标准曲上，调性匹配度提升至95.6%，支持可扩展的专业级和声分析。
原文摘要 · Abstract (English)
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.
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