There are many conceivable ways to map 24edo 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. Since it is highly composite, many other mappings will also fail to cover the whole gamut.
Neutral thirds
One way to map 24edo onto the Lumatone is by using the neutral third, which is one-half of the perfect fifth, as a generator, making these layouts of potential interest for Mohajira and Arabic, Turkish, and Persian music.
Standard
The official Lumatone manual contains a rotated version of a Lumatone mapping for neutral thirds scales as "Preset 6 — 24-ET Isomorphic" in version 1.0 and "Preset 7 — 24-EDO Isomorphic" in version 1.21.
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Inverted
The above layout has a potential disadvantage, in that each successive octave is now located substantially lower on the keyboard than the previous one, eventually requiring a jump of hand position where it wraps around to the top again. Inverting the direction of the chroma keeps octaves closer to horizontal, but going down to move pitch upward can seem counterintuitive.
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Compressed
Bryan Deister has used the 3L 1s layout, as demonstrated in In Your Hands (microtonal 24edo) (alt layout) (2024). The octaves rise just slightly while moving to higher pitches, and the range is somewhat over eight octaves. Although rotated left from the usual orientation, the notes of a standard diatonic scale (within each ring of fifths) are within easy reach of each other.
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Semiquartal
The 4L 1s layout, which uses 2+1⁄2 semitones (one-half of the perfect fourth) as the generator, also has a wide range, keeps octaves close to horizontal, makes the diatonic scale relatively easy to play, and puts the chroma in the right direction on the vertical axis, so it may be preferable. The rightward generator 5\24 functions as ~15/13 and ~22/19 (being in between these, and representing both highly accurately), and as expected for Semaphore temperament, is half of a fourth (~4/3, also represented highly accurately); four of them function as ~9/5 and ~16/9, and five of them with octave reduction produce the slightly flat al-Farabi quarter tone (~33/32) that 24edo is famous for. The range is just under seven octaves. Bryan Deister uses this in 24edo jam (2025) with a different zero point and the edges cut off due to only using one midi channel.
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Expanding this mapping to 5L 4s makes the diatonic scale easy to play, but puts octaves all over the place.
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Barton + Diatonicized Chromaticism
If you want to keep octaves completely horizontal, you need to use the 2L 5s (step ratio 7:2) Barton mapping, which makes more xenharmonic combinations of notes easy to play and familiar diatonic chords difficult. In particular, if one can work with several keys worth of backtracking for the small step (quarter-tone = 1\24), this mapping also supports Ivan Wyschnegradsky's Diatonicized Chromaticism (11L 2s) scale. One problem (apart from the required backtracking) is that Ivan Wyschnegradsky composed for the full 88 note range of each of two (or sometimes four) pianos, while the range of this mapping is just one note short of five octaves; however, since each note is represented at least twice, one approach to work around this problem would be to shift this layout so as to produce two manuals, of which the lower manual would be for the bass octaves and the upper manual for the treble octaves, with two octaves of overlap between the right two octaves of the lower manual and the left two octaves of the upper manual to ensure an easy transition between the divisions of the range.
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