There are many conceivable ways to map 31edo onto the onto the Lumatone keyboard. Only one, however, agrees with the Standard Lumatone mapping for Pythagorean.
Diatonic
This is "Preset 8 — 31-ET Bosanquet" in version 1.0 of the official Lumatone manual, and "Preset 8 — 31-EDO Bosanquet" in version 1.21.
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Double-Bosanquet
As in the Lumatone mapping for neutral thirds scales, this cuts the chromatic semitones in the "vertical" direction in half, so neutral intervals appear in between minor and major intervals. This makes neutral intervals easier to access, but puts octaves all over the place.
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Anti-Double-Bosanquet
This is a flipped version of Double-Bosanquet which results in octaves being closer to horizontal. The step shape normally mapped to major seconds is here mapped to neutral seconds.
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Myna
If you want maximum range while still having access to all notes, the 3L 1s Myna mapping is the most efficient one, covering eight full (and almost level) octaves while still giving 5-limit chords easy to play shapes. However, the 4L 3s MOS has a 7:1 step ratio, making it very lopsided.
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Orwell
The Orwell mapping comes close in range to Myna, covering six full octaves using its 4L 1s MOS, but makes the diatonic scale hard to play.
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Valentine
TheUniverseOfMusic has used the Valentine mapping, demonstrated in Her Gentle Touch (2025). (In this video, even notes are mapped to red keys, and odd notes are mapped to purple keys, each outlining a Valentine 15L 1s scale.) This layout is inspired by the ultra-compressed version of the Lumatone mapping for porcupine, but is even more compressed. Octaves are in horizontal rows, but stretched out over a large distance (which would be even longer if the layout were not made extremely compressed), so that the range is just slightly over 3 octaves (not counting some gamut fragments in the upper left and lower right corners), while notes are repeated multiple times vertically (at a slant), which allows an easy reach for octaves and other intervals that would require very long fingers if only available purely horizontally.
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Squares
The 3L 2s mapping for Squares uses 11 steps (the supermajor third or diminished fourth) as the generator. The range is seven octaves, though each successive octave is located noticeably lower than the previous. Other adjacent key intervals are 7\31 (~7/6 subminor third) and 9\31 (~11/9 neutral third), so this mapping may be of interest to those playing in Myna and Mohajira, respectively, especially if they need to switch quickly between Squares and either or both of these temperaments. Also adjacent is 2\31, allowing this mapping to serve as a rotated and compressed version of the Valentine mapping, although the available vertical space is insufficient to make good use of Valentine; the octave slant would make Valentine awkward even with more vertical space, and single-step movements and the diatonic scale are hard to play.
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