New hexachordal theorems in metric spaces with a probability measure

Abstract

The hexachordal theorem is an intriguing combinatorial property of the sets in $\mathbb{Z}/12\mathbb{Z}$, discovered and popularized by the musicologist Milton Babbitt (1916–2011). It has been given several explanations and partial generalizations. Here we enhance how this phenomenon can be understood by giving both a geometrical and a probabilistic perspective.