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).
"Double-Bosanquet"
This is called "Double-Bosanquet" since the diatonic scale is the same as in the Bosanquet-Wilson layout, except with rows of non-diatonic pitches inserted every other row. In other words it has exactly 2x as many pitches as Bosanquet, and if you removed all the half-sharps, half-flats etc. and slid the remaining rows together, it would become Bosanquet.
Pros:
- Some familiarity to users of the standard Bosanquet layout, since major seconds have the same shape.
- Good ergonomics for major seconds.
Cons:
- Because of the angle of the octave direction (rising up away from the player toward the left and descending towards the player on the right), this doesn't even include 4 complete octaves of the diatonic scale. (With equal temperaments this is alleviated somewhat because octaves will be available in alternate, enharmonic locations. For example, in 31edo Gv is the same as F, so an octave of F is available there.)
"Anti-double-Bosanquet"
Here is a reflected version of the above, which results in compact scales and the angle of the octave interval being fairly close to horizontal (perfect horizontal is impossible with this system):
Pros:
- Over 5 complete octaves.
- Neutral seconds have good ergonomics, because they have the same shape that major seconds do in Bosanquet-Wilson.
Cons:
- Worse ergonomics for major seconds.
- May be unfamiliar or confusing to people familiar with normal Bosanquet.
- In particular the "sharp" direction is now down toward the player (not up away from the player as in normal Bosanquet), which may be confusing.