New hexachordal theorems in metric spaces with a probability measure

Abstract

The Hexachordal Theorem is an intriguing combinatorial property of the sets in Z/12Z discovered and popularized by the musicologist Milton Babbitt (19162011). 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. Mathematics Subject Classification (2020). Primary: 00A65; Secondary: 28A75, 05C12, 60Dxx.