音调和谐与动态分数网络的拓扑结构
Tonal harmony and the topology of dynamical score networks
摘要：
我们引入动态分数网络的概念，用于音调组成的表示和分析：分数被解释为一个动态网络，其中每个和弦是一个节点，每个进展链接连续的和弦。该网络可以被视为非平稳信号的时间序列，因此，可以使用时间序列分析和变化点检测来划分该网络以用于音调区域的自动识别，而不依赖于与预定参考集或广泛语料库的比较。我们证明了音调和谐的基本特征，中心性，指涉性，方向性和层次性，自然地出现在网络拓扑结构及其无标度属性。最后，通过这些图上的路线优化算法求解最小长度路径提供了谐波序列的抽象，其可以被概括为音调组成设计的生成模型的概念。
英文摘要：
We introduce the concept of dynamical score networks for the representation and analysis of tonal compositions: a score is interpreted as a dynamical network where every chord is a node and each progression links successive chords. This network can be viewed as a time series of a non-stationary signal, and as such, it can be partitioned for the automatic identification of tonal regions using time series analysis and change point detection without relying on comparisons with pre-determined reference sets or extensive corpora. We demonstrate that the essential features of tonal harmony, centricity, referentiality, directedness and hierarchy, emerge naturally from the network topology and its scale-free properties. Finally, solving for the minimal length path through a route optimization algorithm on these graphs provides an abstraction of harmonic sequences that can be generalized for the conception of generative models of tonal compositional design.
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