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.
Standard Bosanquet–Wilson
This mapping is "Preset 8 — 31-ET Bosanquet" in the official Lumatone manual.
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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 Myna mapping is the most efficient one, while still giving 5-limit chords easy to play shapes. Though, the resulting 4L 3s MOS has a very awkward 7:1 step ratio.
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Valentine
The Universe of Music 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). This layout is inspired by the ultra-compressed version of the Lumatone mapping for porcupine, but 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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