There are many conceivable ways to map 14edo onto the onto the Lumatone keyboard. However, it has no generators that create a diatonic or antidiatonic scale that covers the whole gamut, so the Standard Lumatone mapping for Pythagorean is not one of them. Due to its composite nature, only two generators work at all to produce single period mos scales.
Whitewood
The closest thing to a diatonic scale is the whitewood mapping, which puts the naturals in a straight line and the second unconnected circle of fifths above and below.
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Beep
In terms of approximating simple consonant intervals and giving them comfortable fingerings, the beep mapping is the most efficient, although they still sound quite dissonant compared to 12edo.
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Smate
The smate mapping is most effective if you want to maximise range, although you should still probably expand it from 1L 1s to 2L 1s to make chords easier to finger, as 11 octaves is still beyond the range of human hearing.
