We set out to perform a cluster analysis of harmonic structures (specifically, chord-to-chord transitions) in the McGill Billboard dataset, to determine whether there is evidence of multiple harmonic grammars and practices in the corpus, and if so, what the optimal division of songs, according to those harmonic grammars, is. We define optimal as providing meaningful, specific information about the harmonic practices of songs in the cluster, but being general enough to be used as a guide to songwriting and predictive listening. We test two hypotheses in our cluster analysis — first that 5–9 clusters would be optimal, based on the work of Walter Everett (2004), and second that 15 clusters would be optimal, based on a set of user-generated genre tags reported by Hendrik Schreiber (2015). We subjected the harmonic structures for each song in the corpus to a K-means cluster analysis. We conclude that the optimal clustering solution is likely to be within the 5–8 cluster range. We also propose that a map of cluster types emerging as the number of clusters increases from one to eight constitutes a greater aid to our understanding of how various harmonic practices, styles, and sub-styles comprise the McGill Billboard dataset.

中文翻译：

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McGill Billboard数据集中和谐的聚类分析

我们着手对McGill Billboard数据集中的谐和结构（特别是和弦和弦过渡）进行聚类分析，以确定语料库中是否存在多种和声语法和实践的证据，如果是，最佳选择根据那些和声语法，歌曲的划分是。我们将“最佳”定义为提供有关集群中歌曲的和声实践的有意义的特定信息，但又具有足够的通用性，可以用作歌曲创作和预测性聆听的指南。我们在聚类分析中检验了两个假设：第一，根据Walter Everett（2004）的研究，最佳5–9个聚类，第二，根据一组用户生成的类型标签，最佳15个聚类。亨德里克·施雷伯（Hendrik Schreiber）（2015）。我们对语料库中每首歌曲的谐波结构进行了K均值聚类分析。我们得出结论，最佳聚类解决方案可能在5-8个聚类范围内。我们还建议，随着簇的数量从一增加到八个而出现的簇类型图，可以更好地帮助我们理解各种谐波实践，样式和子样式如何构成McGill Billboard数据集。