Using Tonnetz Tone Mesh to Understand Jazz Harmony

The "negative harmony" bit (i.e. pitch class inversion) works here by 180 degree rotation exactly the same way it works on string instruments. (We can imagine a musical instrument based on this Tonnetz mesh).

For instance if you take a C major scale pattern laid out somewhere on the first four strings of the guitar (we avoid the inconsistency of the G to B string being a major third) and you rotate it 180, you get a Phrygian pattern:

Ionian:

  -*---*-*-
  -*-*---*-
  ---*---*-

Phrygian:

  -*---*---
  -*---*-*-
  -*-*---*-

The intervals are different in this mesh but the rotation inverts them the same way.