论文标题
音乐风格分析：通过持久同源性对间隔过渡图的研究
Musical Stylistic Analysis: A Study of Intervallic Transition Graphs via Persistent Homology
论文作者
论文摘要
最近已应用拓扑数据分析来研究音乐作品的风格特征和趋势。该领域的一个有用的工具是持续的同源性。在本文中，我们开发了一种新颖的方法来表示加权的有限图形作为有限的度量空间，然后使用持久同源物来提取有用的特征。我们将此方法应用于从给定音乐片段的俯仰转变信息获得的加权定向图，并将这些技术用于研究风格趋势。特别是，我们有兴趣使用这些工具来进行定量的风格比较。作为第一个说明，我们分析了海顿，莫扎特和贝多芬的一系列弦乐四重奏，并讨论了这些作曲家对风格探索和多样性的不同方法的可能含义。我们观察到海顿在风格上是最保守的，其次是莫扎特，而贝多芬是最具创新性的，扩展和修改了弦乐四重奏作为音乐形式。最后，我们还通过给定的作曲家比较了不同类型的变异性，即Minuets，Allegros，Prestos和Adagios，并得出结论，Minuet是弦乐四重奏运动的最稳定形式。
Topological data analysis has been recently applied to investigate stylistic signatures and trends in musical compositions. A useful tool in this area is Persistent Homology. In this paper, we develop a novel method to represent a weighted directed graph as a finite metric space and then use persistent homology to extract useful features. We apply this method to weighted directed graphs obtained from pitch transitions information of a given musical fragment and use these techniques to the study of stylistic trends. In particular, we are interested in using these tools to make quantitative stylistic comparisons. As a first illustration, we analyze a selection of string quartets by Haydn, Mozart and Beethoven and discuss possible implications of our results in terms of different approaches by these composers to stylistic exploration and variety. We observe that Haydn is stylistically the most conservative, followed by Mozart, while Beethoven is the most innovative, expanding and modifying the string quartet as a musical form. Finally we also compare the variability of different genres, namely minuets, allegros, prestos and adagios, by a given composer and conclude that the minuet is the most stable form of the string quartet movements.
