Here are some tuning files intended for use with a Lumatone. They're all rank 2 temperaments, in fact all linear temperaments so far, except for one rank 2 tuning that isn't a temperament. Rank 2 fits the two-dimensional nature of the keyboard. Other than that, they don't depend on any specific properties of the Lumatone. Feel free to use them if you have some other keyboard with similar flexibility.
Default presets are correct for the keyboard I have and the original printing of the manual. They might change in future.
Preset 4 repeats about 19 notes. The colouring is for meantone but it will also work with magic. Meantone is a hugely important European temperament class and the basis of common practice notation.
Magic temperament has better approximations to meantone, but is a bit more complicated. It doesn't temper out the syntonic comma and, in the 19 note scale, there are no comma shifts. This means you only get one tuning for each pitch in a major key and that can be difficult to work around because it means not all chords are correctly tuned. I have a ZynAddSubFX configuration file for magic with the pitches required for my interpretation of John Coltrane's Countdown chords assuming the blue keys in Preset 4 match the white notes on a piano. Those blue keys form a diatonic scale with the best approximations of 5-limit harmony given the constraints.
We've already seen magic. You can get 22 notes of it with Preset 5.
Orwell is another temperament class that's good in the 11-limit.
Singly positive tunings are generated by a single chain of fifths and that fifth is slightly sharp of 12-tone equal temperament. You get 29 notes with Preset 7. The colors are suitable for fifth-generated scales, and the diatonic scale in the middle is a single chain of fifths, which isn't the best approximation to 5-limit harmony.
29 notes per octave is too many for 5 octaves within the MIDI range. Preset 7 uses two different channels and my ZynAddSubFX configuration file for 29 notes of andromeda will work with it. If you change the instrument, you need to change it on both channels.
We've already seen meantone. Preset 8 can expand it to 31 notes. Miracle can be very accurate in the 31-limit. Orwell also works with 31 notes. The symmetrical mappings here work if start them on MIDI pitch 24 with the 31-note orwell Lumatone mapping I just linked and I'm about to link to a ZynAddSubFX configuration file for 31 notes of orwell. Pianoteq users will want a different 31-note orwell Lumatone mapping that works with the way Pianoteq tunes its channels.
The ZynAddSubFX configuration file for 31 notes of meantone uses two channels to cover the full 5 octaves. If you change the instrument, you need to change it on both channels.
We've already seen singly positive tunings and miracle. There isn't a default preset with 41 notes so you can download my Lumatone mapping for 41 based on an original by Cam Taylor. You can use it with the ZynAddSubFX configuration file for 41 notes of andromeda .
We've already seen singly positive tunings and orwell. 53 notes come with a new problem: they require 3 channels. Furthermore, Preset 9 works in such a way that, but a limitation of ZynAddSubFX's key shift, some of the channels need to be tuned in the instrument settings rather than the part.
I think I can find a keyboard mapping that only needs the minimal 3 channels and key shifts. For now, I have a ZynAddSubFX configuration file for 53 notes of andromeda that will work with Preset 9. I over-engineered it and set 6 channels where I think you only need 5. If you change the instrument, you need to change it on the first 5 channels, and you also need to fiddle with the octaves on channels 4 and 5.