Formalization of Voice-Leadings and the Nabla Algorithm

  • Isaac del PozoEmail author
  • Francisco GómezEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11502)


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 \(\nabla \) application. This application computes the optimal voice-leading for a given chord progression.


Voice-leadings Chord progressions Matrix algebra Distance functions Nabla distance Optimal voice-leadings 


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.GetafeSpain
  2. 2.Universidad Politécnica de MadridGetafeSpain

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