Abstract

We propose a complex network approach to the harmonic structure underpinning western tonal music. From a database of Beethoven’s string quartets, we construct a directed network whose nodes are musical chords and edges connect chords following each other. We show that the network is scale-free and has specific properties when ranking algorithms are applied. We explore the community structure and its musical interpretation, and propose statistical measures stemming from network theory allowing to distinguish stylistically between periods of composition. Our work opens the way to a network approach of structural properties of tonal harmony.

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中文翻译：

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贝多芬四重奏的谐波结构：一种复杂的网络方法

摘要

我们提出了一种复杂的网络方法来处理支撑西方音调音乐的谐波结构。从贝多芬弦乐四重奏的数据库中，我们构建了一个有向网络，其节点是音乐和弦，边连接和弦。我们展示了网络是无标度的，并且在应用排名算法时具有特定的属性。我们探索社区结构及其音乐解释，并提出源自网络理论的统计措施，允许在风格上区分作曲时期。我们的工作为色调和谐的结构特性的网络方法开辟了道路。

图形摘要