Tonnetz

A modern rendering of the Tonnetz. The A minor triad is in dark blue, and the C major triad is in dark red. Interpreted as a torus, the Tonnetz has 12 nodes (pitches) and 24 triangles (triads).

In musical tuning and harmony, the Tonnetz (German for 'tone net') is a conceptual lattice diagram representing tonal space first described by Leonhard Euler in 1739.[1] Various visual representations of the Tonnetz can be used to show traditional harmonic relationships in European classical music.

  1. ^ Euler, Leonhard (1739). Tentamen novae theoriae musicae ex certissismis harmoniae principiis dilucide expositae (in Latin). Saint Petersburg Academy. p. 147.