量化西方古典音乐中和声与新异性的演化
Quantifying the evolution of harmony and novelty in western classical music
AI总结：
本文通过改进效应中心算法逐小节提取局部调性，量化调性不确定性与调转换的多样性和新异性，揭示西方古典音乐和声演化趋势，并解释古典时期创新先降后升的现象。
摘要：
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以及普通公众。理解音乐的历史发展可能有助于我们理解感知与认知，同时也能为文化传播、创造力和创新过程提供洞见。本文提出了一项与和声相关的音乐特征研究，并记录了这些特征在西方古典音乐中四百多年间的演化方式。我们开发了“效应中心”（center of effect）算法的一种变体，用于为一组给定音符判定最可能的调性，从而将一首音乐作品表示为逐小节计算的局部调序列。我们提出了量化调性不确定性以及调性转换中多样性和新异性的度量方法。我们给出具体示例来展示这些概念所代表的特征，并论证它们如何与和声复杂度相关，以及如何用于研究和声的演化。我们确认了音乐学家和科学家先前报告的若干观察结果和趋势，但在古典时期存在一些差异。我们报告了古典时期早期和声转换创新的下降，随后在古典时期晚期出现急剧上升；我们为这一发现给出了一种与音乐理论家论述相一致的解释。最后，我们讨论了该方法在跨文化研究中的局限性，以及未来研究中对更具表现力但仍可处理的乐谱表示以及大规模且可靠的音乐语料库的需求。
英文摘要：
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.
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