论文标题
拓扑音乐分析的框架（TMA）
A Framework for Topological Music Analysis (TMA)
论文作者
论文摘要
在本文中，我们描述并讨论了将不同的拓扑数据分析（TDA）技术应用于传统西方符号中的音乐片段的框架。我们首先考虑不同维度的欧几里得空间中的不同点，这些点与分数中的音乐事件相对应，并获得其持续的同源性特征。然后，我们介绍了两个可以与和弦序列相关的简单络合物家族，并利用同源性来计算其显着特征。最后，我们展示了将所述方法应用于J.S.的三个Brandenburg协奏曲的分析和风格比较的结果。墨西哥作曲家Armando Luna的Bach和两个涂鸦。
In the present article we describe and discuss a framework for applying different topological data analysis (TDA) techniques to a music fragment given as a score in traditional Western notation. We first consider different sets of points in Euclidean spaces of different dimensions that correspond to musical events in the score, and obtain their persistent homology features. Then we introduce two families of simplicial complexes that can be associated with chord sequences, and leverage homology to compute their salient features. Finally, we show the results of applying the described methods to the analysis and stylistic comparison of fragments from three Brandenburg Concertos by J.S. Bach and two Graffiti by Mexican composer Armando Luna.
