Music is a complex socio-cultural construct, which fascinates researchers in diverse fields, as well as the general public. Understanding the historical development of music may help us understand perceptual and cognition, while also yielding insight in the processes of cultural transmission, creativity, and innovation. Here, we present a study of musical features related to harmony, and we document how they evolved over 400 years in western classical music. We developed a variant of the center of effect algorithm to call the most likely for a given set of notes, to represent a musical piece as a sequence of local keys computed measure by measure. We develop measures to quantify key uncertainty, and diversity and novelty in key transitions. We provide specific examples to demonstrate the features represented by these concepts, and we argue how they are related to harmonic complexity and can be used to study the evolution of harmony. We confirm several observations and trends previously reported by musicologists and scientists, with some discrepancies during the Classical period. We report a decline in innovation in harmonic transitions in the early classical period followed by a steep increase in the late classical; and we give an explanation for this finding that is consistent with accounts by music theorists. Finally, we discuss the limitations of this approach for cross-cultural studies and the need for more expressive but still tractable representations of musical scores, as well as a large and reliable musical corpus, for future study.

翻译：音乐是一种复杂的社会文化建构，吸引着不同领域的研究者及公众的兴趣。理解音乐的历史发展有助于我们理解感知与认知过程，同时也能揭示文化传播、创造力和创新机制。本文针对与和声相关的音乐特征展开研究，系统记录了西方古典音乐四百年间这些特征的演变过程。我们提出了一种改进的中心效应算法（center of effect algorithm）变体，用以推断给定音符集合最可能的调性，从而将音乐作品逐小节地表示为局部调性序列。我们开发了量化指标来表征调性不确定性、调性转换的多样性及新颖性。通过具体实例阐释这些概念所代表的特征，论证它们与和声复杂性的关联性及其在研究和声演变中的应用价值。研究证实了音乐学家和科学家先前报告的若干观察结果与发展趋势，但在古典主义时期存在部分差异。我们发现古典主义早期调性转换的创新性呈现下降趋势，而古典主义晚期则急剧上升；我们基于音乐理论家的论述对此发现给出了合理解释。最后，本文讨论了该方法在跨文化研究中的局限性，并指出未来研究需要更具表现力且易于处理的乐谱表征方式，以及大规模可靠的音乐语料库。