Music, Mathematics, and Magnetic Ordering - Abstract

Richard Krantz, Jack Douthett and John Clough
Bridges: Mathematical Connections in Art, Music, and Science (1999)
Pages 295–296


Consider the problem of seating a dichotomous group (say, five scientists and three musicians) about a round table so as best to intermingle the two constituencies. There is an intuitive solution (up to rotation), at least for small numbers. The distribution of the seven months with 31 days among the 12 months of the year appeals to a similar intuition. Many Western musical scales and chords (considered as a selection from the 12 notes of the equal-tempered scale) reflect comparable distributions--called Maximally Even (ME) sets [1]. These musical patterns (and corresponding extra-musical patterns: seating arrangements, etc.) are well defined mathematically in terms of intervals between pairs of selected notes: specific intervals (measured by counting over the full 12-note scale) associate in a particular way with generic intervals (measured by counting only the selected notes). The definition of ME applies recursively to account for three-note chords (triads) drawn from the Western diatonic scale, as well as the seven-note gram as of ancient Indian music [2]. More generally, any set of notes (or extramusical circular distribution) may be characterized in terms of its degree of evenness (minimal through maximal) through further interval analysis [3].