There are many conceivable ways to map 40edo onto the onto the Lumatone keyboard. Only one, however, agrees with the Standard Lumatone mapping for Pythagorean.
Diatonic
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Blackwood
Compressed, forward chroma
If you want a wider range, the blackwood mapping is the most efficient as long as you don't mind the sharp fifth being easier to play than the flat one.
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Expanded, reverse chroma
If 40edo is mapped for blackwood with a reverse chroma, the range is much less than in the forward-chroma version (at 4¼ octaves), but the flat (patent) fifth ~3/2 (23\40) is much easier to reach (by moving three keys right plus one key down-right from the root note). The slightly sharp classic major third ~5/4 (13\40) is even easier to reach, at one key right plus one key down-right from the root note (this is the same as in the forward chroma version). Bryan Deister has used this mapping in 40edo improv (2026).
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