论文标题
音调和谐与动态得分网络的拓扑结构
Tonal harmony and the topology of dynamical score networks
论文作者
论文摘要
我们介绍了动态得分网络的概念，以表示和分析音调组成：分数被解释为一个动态网络，每个和弦都是节点，每个进步都链接连续的和弦。该网络可以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更改点检测来自动识别音调区域，而无需与预定的参考集或广泛的COLPORA进行比较。我们证明，音调和谐，中心性，参考性，定向性和层次结构的基本特征自然而然地来自网络拓扑及其无规模的属性。最后，在这些图上求解通过路由优化算法的最小长度路径提供了谐波序列的抽象，这些序列可以推广到音调组成设计的生成模型的概念中。
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.
