Mathematical Music Theory

In this post you’ll find a basic explanation of the mathematical problem I plan to solve as my undergraduate’s thesis project, besides its connection to music.

After giving that post a read, I invite you to play around with the musical functions defined in such article, via these web apps I’ve created:

• https://lucio-cornejo.shinyapps.io/Unidirectional_minimal_voice_leading_graph

• https://lucio-cornejo.shinyapps.io/MVL_and_CMD

A quick summary of my mathemusical research is to find conditions, either necessary or sufficient, for when, given a chord and some transposition of it, does there exist a minimal voice leading between such chords such that all the trajectories which define such voice leading have the same direction, that is, all downward or all upward trajectories.