There are many conceivable ways to map 38edo onto the onto the Lumatone keyboard. However, it has 2 mutually-exclusive rings of fifths, so the Standard Lumatone mapping for Pythagorean is not one of them. Even the b val does not generate a diatonic or antidiatonic scale.
The bb val fifth is very flat indeed, generating a very lopsided 2L 5s scale having a 9:4 step ratio or a 2L 7s scale (with backtracking) having a 5:4 step ratio.
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Neutral thirds
Instead, as slicing the perfect fifth in two results in an essentially perfect 11/9, it makes a lot of sense to use a neutral thirds mapping. The versions below present a tradeoff familiar for Neutral Thirds mappings, between rotating the notes of the diatonic scale or incurring a considerable slope of the octaves that causes vertical wraparounds.
Rotated (Opossum + Ptolemy)
A rotated version yields a range of five octaves but for a few missing notes in the bottom octave (or top octave, depending upon the placement of note 0), with octaves sloping down mildly. This version lends itself to Opossum and Ptolemy.
Or if you want greater range while still reaching a lot of good intervals in few steps while only incurring a gentle downward slope of octaves, the Astrology mapping works well.
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Bison + Hemisensi + Hemikleismic
It is possible to map 38df to support scales 4L 2s (7:5 step ratio, and proceeding overall down-right) and 7L 1s (5:3 step ratio, with the small step proceeding right + up-right), supporting temperaments bison, hemisensi, and hemikleismic. Bryan Deister has demonstrated this layout in waltz in 38edo [short] (2026), motivated by the wish to reverse major and minor thirds but without needing a super-flat fifth. This yields a range of a bit over 4¾ octaves, but with a severe downwards slope that incurs vertical wraparounds.
