Geometry and Harmony

David Rappaport
Renaissance Banff: Mathematics, Music, Art, Culture (2005)
Pages 67–72


A musical scale can be viewed as a subset of notes or pitches taken from a chromatic universe. Given integers (N,K) N > K we use particular integer partitions of N into K parts to construct distinguished sets, or scales. We show that a natural geometric realization of these sets have maximal area, so we call them maximal area sets. We then discuss properties of maximal area sets for the integer pairs (12,5) (12,6) (12,7) and (12,8) with the obvious relevance to our normal chromatic collection of 12 pitches.