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.

翻译：我们研究为和弦序列分配局部调性的任务，该任务在和声分析、作曲以及爵士即兴演奏中具有实用价值。标准动态规划方法虽能最小化调性转换，但可能引入过多的不必要调性中心。我们将这种仅针对调性转换的目标函数与纯最小调性词汇分析及调性简约性进行对比。调性简约性通过字典序方式优先最小化调性转换次数，再最小化不同调性的数量。尽管该联合目标函数在一般情况下具有组合复杂性，我们利用固定的24调性大/小调体系提出了精确算法。在31,032个LMD和弦序列上，调性简约性在保留最优调性转换结果的同时，于55.8%的案例中减少了调性词汇量。通过加权的爵士替代闭合处理，平均调性数量从3.802降至3.206，调性转换次数从16.728降至12.141。在1,555首带注释的爵士标准曲中，该方法将兼容的和弦-音阶一致性提升至95.6%，支持可计算的专业级和声分析。