There are many conceivable ways to map 39edo onto the onto the Lumatone keyboard. Only one, however, agrees with the Standard Lumatone mapping for Pythagorean.
Diatonic
Although not as imbalanced as the diatonic scale for 37edo (step ratio 7:1), the diatonic scale for 39edo is still fairly imbalanced (step ratio 7:2).
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Augmented + immunity
Bryan Deister has used a porcupine-inspired layout for 39edo, as demonstrated in 39edo jam (2025). To take advantage of the fact that 39edo is at the intersection of augmented and immunity, the rightward generator is 5\39, half of a 6/5 minor third as 12/11~11/10 (but much closer to 12/11). This enables a modmos derived from 1L 6s by shrinking the large step from 9\39 to 8\39 and expanding one of the small steps from 5\39 to 6\39, to enable chords such as 12/11 (somewhat sharp, at 5\39) – 6/5 (slightly flat, at 10\39) – 11/8 (near-just, at 18\39) – 3/2 (mildly sharp, 23\39) – 18/11 (moderately sharp, at 28\39) – 9/5 (near-just, at 33\39). Playing this chord uses almost the same geometry of depressed keys as that for playing a diatonic scale in a diatonic mapping (but has a very different sound effect), save when proceeding to the next octave. The range is slightly over 6 octaves overall (which slant moderately downwards), but with the first and last octaves missing some notes due to clipping in the upper left and lower right corners of the layout.
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Triforce
Since it is its optimal patent val, the triforce mapping is also a particularly good way to organise the intervals of 39edo.
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Amity
The Lumatone mapping for amity is also above average at putting good intervals close together, and makes chromatic runs much easier than the previous two layouts.
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Familia
Related to amity is familia. Bryan Deister has demonstrated a 3L 4s (10:3 step ratio) layout for this, in 39edo improv (2025). Right by 1 key (10\39) is a somewhat flat classic minor third ~6/5, while down-right by 1 key (3\39) functions both as an inconsistently mapped sharp diptolmeic chromatic semitone (~25/24) and an inconsistently mapped flat ptolemaic diatonic semitone (~16/15), which means that right 1 key + down-right 1 key (total 13\39) yields a sharp (400 ¢) classic major third ~5/4). The range is six octaves, although the octaves slope down enough to cause a vertical wraparound.
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Semiquartal (immunity)
The immunity mapping gives excellent range (over 6⅓ octaves), but the resulting 5L 4s scale has a 7:1 step ratio, which makes it very lopsided; on the other hand, the octaves slope up in this mapping more gently than they slope down on the previous four mappings.
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Biyatismic
Bryan Deister has used a biyatismic layout with a 7L 1s scale (5:4 step ratio) for 39edo, as demonstrated in Tilt Your Head Down - 39edo [short] (2026). The rightward generator 4\39 is a combination of the Alpharabian tendoneutral second ~12/11 and the undecimal submajor second ~11/10, and two of these make a near-just classic minor third ~6/5, with the biyatisma (121/120) being tempered out. Although biyatismic is technically rank-3 or rank-4, it functions here as a rank-2 temperament, filling in several useful intervals by rightward progression and octave-reduction: four of these generators make a near-just septimal tritone ~10/7; five of them make a flat pentacircle minor sixth ~11/7 or a somewhat sharp septimal minor sixth ~14/9; and six of them make a flat septimal major sixth ~12/7. After octave-reduction, nine of them make a slightly sharp classic whole tone ~10/9; ten of them make a flat Alpharabian artoneutral third ~11/9; eleven of them make a flat fourth ~4/3; twelve of them make a slightly flat Axirabian paraminor fifth ~16/11; and thirteen of them make a flat classic minor sixth ~8/5. The range is just under four octaves, and the octaves slant up.
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