Mathematical model of modulation in traditional Chinese music: theory and computational implementation

Modulation is an important component of musical composition and performance that enhances the emotional experience of the listener. Like Western classical music, traditional Chinese music also features modulation. However, compared to the concrete rules of modulation in Western classical music, traditional Chinese music theory currently lacks a similarly solid and deep analytical model. This manuscript describes a mathematical model of modulation that can be used to model modulation in traditional Chinese music. First, historical context behind what is currently called traditional Chinese music is provided. Next, 118 instances of modulation from 35 different traditional Chinese musical works are analyzed to propose a new mathematical model of modulation called Honeray's criterion. This model uses Mazzola's gesture theory to provide a novel model of modulation in traditional Chinese music. Lastly, after explaining this criterion's logical components, a Python implementation capable of determining whether a given modulation satisfies Honeray's criterion is provided.