Close-up of the Tonnetz

Let's take a closer look at the Tonnetz and its properties. First off, the triangles defined by three adjacent points represent major and minor chords. As you can see, isometries (geometric transformations) in the Tonnetz correspond to modulations (changes to a nearby key) in music.

Again, the Tonnetz can be tesselated/tiled indefinitely to fill a plane. Its sides connect with the sides of other Tonnetze. So picture the keys going on forever, as they do in music theory.