I have used Touch Tonnetz app on iOS which uses the inverted Tonnetz layout. Different systems show different inversions. The Touch Tonnetz follows what is used as the layout on Wikipedia. Basically upside down triangles are Major and upright triangles are Minor so fifths go from left to right and fourths go from right to left. I also used the same tuning for the notes. This was a headache to map.
I also found I wanted a bass note so added a chromatic layout of the 12 tone system which appears within the 31 tone to give a strong fundamental for harmonic progression. Ergonomically it works best in the way I have laid it out to the left and can be played with left thumb or little finger.
This allows me to explore Neo-Riemannian theory with 31 EDO. I actually use Fokker 31.scl - his just intonation tuning but the Equal Temperament 31 works well also.
Traditionally Tonnetz used just intonation so had no enharmonic equivalents as we see with 12 EDO. 31 EDO allows for this just tuning layout.
The Dbb, Dx, Gbb and Ax included to the right are what were missing from the Tonnetz. Harmonically they are interesting and are included for consistency with having all 31 notes in 31EDO.
31 Tonnetz MPE.senselmap (9.2 KB)
Fokker 31.zip (322 Bytes)
