history-diagrams · tymoczko2006-geometry-chords

Musicians have been investigating these questions for almost three centuries. The circle of fifths (fig. S1), first published in 1728 (4), depicts efficient voice leadings among the 12 major scales. The Tonnetz (fig. S2), originating with Euler in 1739, represents efficient voice leadings among the 24 major and minor triads (2, 5).