Generalizations of Euler’s Tonnetz

The picture above by Konstanze Rietsch shows a Tonnetz of type G₂. This is an infinite tessellation of 30°–60°–90° triangles whose edges are labelled by musical notes (shown on the right) in an infinitely repeating pattern. The 12 edges meeting at a point are labelled clockwise by the notes in a circle of fifths: C, G, D, A, and so on, going up by a per…