There are many conceivable ways to map 37edo onto the onto the Lumatone keyboard. Only one, however, agrees with the Standard Lumatone mapping for Pythagorean.
Diatonic
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Antidiatonic
Since the perfect fifth is so sharp, you lose little accuracy by using the flat fifth as a generator instead, which can be interpreted as near equalised mavila, or more accurately but complexly as undecimation.
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Diatonicized Chromaticism via Rotated Antidiatonic
Bryan Deister has demonstrated a rotated antidiatonic (2L 5s) mapping in 37edo (2025), using the Mavila (sub-)fifth (21\37) as a generator. This yields a range of over five octaves, although the note 0 positions alternate between middle and near/far. (In the demonstration video, active keys on the Lumatone are cut back at both the left and right edges to yield exactly five octaves.) With this mapping, notes of the 11L 2s scale line up in pairs of row segments (of 6\37 offset from each other by the large MOSstep 3\37, and cut by the small MOSstep 2\37), which may make this mapping attractive for users wishing to play Ivan Wyschnegradsky's Diatonicized Chromatic scale in a tuning system different from 24edo, while still retaining respectable (though not full piano) range.
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Porcupine
However, none of these are the most efficient when it comes to comfortably fingering simple chords. If you want an arrangement that makes it easy to play the best note combinations together, the 1L 6s mapping for Porcupine is considerably superior.
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Others
If you want to maximise your range, the Gariberttet mapping is probably the clearest arrangement that gives access to the full gamut.
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