Statistical Properties of Tonal Harmony in Bach ’ s Chorales
Statistical Properties of Tonal Harmony in Bach ’ s Chorales
复制标题
巴赫合唱曲中音调和声的统计特性
DOI：
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
I. Cross
中科院分区：
文献类型：
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作者：
M. Rohrmeier;I. Cross
本研究的目的是提供经验性的计算结果，以了解调性和和声结构。它分析方面的音调和谐和和声模式的基础上，统计，计算语料库分析巴赫的合唱。这是使用专门为此目的开发的一种新的启发式分割方法进行的。对单pc集、和弦类和pc集转换的分布分析揭示了两种调式中非常不同的结构模式，其中许多但不是全部雅阁标准音乐理论。此外，发现最频繁的和弦过渡表现出很大程度的不对称性，或定向性，对于两个pc集合A，B，过渡频率f（A→B）和f（B→A）可能在很大程度上不同。一元词和二元词的分布遵循Zipf分布，即频率大致按照1/x衰减，这意味着音乐结构的大部分由几个频繁的元素支配。研究结果提供了证据的一个潜在的谐波语法，导致不同的统计模式。随后的层次聚类分析的pc集的基础上各自的前因和后果的模式发现，这一信息足以组和弦成有意义的功能组，只对内在的统计理由，而不考虑音高
This study aims to contribute empirical computational results to the understanding of tonality and harmonic structure. It analyses aspects of tonal harmony and harmonic patterns based on a statistical, computational corpus analysis of Bach’s chorales. This is carried out using a novel heuristic method of segmentation developed specifically for that purpose. Analyses of distributions of single pc sets, chord classes and pc set transitions reveal very different structural patterns in both modes, many, but not all of which accord with standard music theory. In addition, most frequent chord transitions are found to exhibit a large degree of asymmetry, or, directedness, in way that for two pc sets A,B the transition frequencies f(A→B) and f(B→A) may differ to a large extent. Distributions of unigrams and bigrams are found to follow a Zipf distribution, i.e. decay in frequency roughly according to 1/x which implies that the majority of the musical structure is governed by a few frequent elements. The findings provide evidence for an underlying harmonic syntax which results in distinct statistical patterns. A subsequent hierarchical cluster analysis of pc sets based on respective antecedent and consequent patterns finds that this information suffices to group chords into meaningful functional groups solely on intrinsic statistical grounds without regard to pitch