Lumatone mapping for neutral thirds scales
Neutral third scales could conceivably be mapped onto the Lumatone keyboard in different ways. The important intervals which could be mapped to adjacent hexagons in certain directions include the whole step, the diatonic semitone, and the half-apotome which is half of a usual / modifier. In this article the symbols ^ and v are used for half-sharp and half-flat (other symbols are sometimes available in different software).
Here is one possible mapping of the neutral thirds system, which results in compact scales and the angle of the octave interval being fairly close to horizontal (perfect horizontal is impossible with this system):
[WORK IN PROGRESS]
G
A
B
C
D
E
F
G
A
B
C
Av
Bv
Cv
Dv
Ev
F^
G^
A^
B^
C^
D^
E^
C
D
E
F
G
A
B
C
D
E
F
Dv
Ev
Fv
Gv
Av
Bv
C^
D^
E^
F^
G^
F
G
A
B
C
D
E
F
G
A
B
Gv
Av
Bv
Cv
Dv
Ev
F^
G^
A^
B^
C^
A
B
C
D
E
F
G
A
B
C
D
E
Cv
Dv
Ev
Fv
Gv
Av
Bv
C^
D^
E^
F^
D
E
F
G
A
B
C
D
E
F
G