The abstraction of musical structures as mathematical objects in a geometrical space is one of the major accomplishments of contemporary music theory. The author generalizes the concept of musical spaces as networks and derives compositional design principles via network topology analysis. This approach provides a framework for analysis and quantification of similarity of musical objects and structures and suggests a way to relate such measures to human perception of different musical entities. Finally, network analysis provides alternative ways of interpreting the compositional process by quantifying emergent behaviors with well-established statistical mechanics. Interpreting the latter as probabilistic randomness in the network, the author develops novel compositional design frameworks.

中文翻译：

---

广义音乐空间中的网络拓扑

将音乐结构抽象为几何空间中的数学对象是当代音乐理论的主要成就之一。作者将音乐空间的概念概括为网络，并通过网络拓扑分析得出组合设计原则。这种方法为分析和量化音乐对象和结构的相似性提供了一个框架，并提出了一种将这些度量与人类对不同音乐实体的感知联系起来的方法。最后，网络分析通过使用完善的统计力学量化突发行为，提供了解释组合过程的替代方法。将后者解释为网络中的概率随机性，作者开发了新颖的组合设计框架。