Formalization of Voice-Leadings and the Nabla Algorithm

摘要

This work presents some concepts related to voice-leadings and proposes a formalization of them. The aim is to teach voice-leadings in a systematic way by using elements of mathematical music theory. Within this formalization, we defined the nabla distance of a chord progression. This distance is a measure of how close the voices are among them. One of its applications is to produce voice-leadings with nice properties, especially for jazz music. The nabla distance has been implemented in the form of an application, the V application. This application computes the optimal voice-leading for a given chord progression.