Musical Polygons

摘要

Iread with fascination Michael Sewell's article describing a 'Coffee break problem' [1]. It reminded me of a problem that Brian 'Benny' Leonard (computational fluid dynamicist and musician; see e.g. [2,3]) raised in a coffee break during a visit to the Met Office,namely: 'How many different (musical) chord types are there?' Somewhat surprisingly, the musical chord problem and Michael Sewell's coffee break problem turn out to be remarkably similar. Here we give some methods of calculating the solution to these problems.