The Tonnetz (opens in new tab)

In 1739, Leonhard Euler devised a “tone net” to represent graphically the traditional harmonic relationships in European classical music. In the version above, the dark blue triangle at the center is an A minor triad; the red triangle to its right is the relative major, C; and the red triangle below it is the parallel major, A. Every such pattern is mirrored in all the other keys. The tones are numbered from 0 (A♭) to 11 (G). Major triads are red, and minor are blue. The thinnest lines denote...