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.
0
4
3
7
11
15
19
2
6
10
14
18
22
2
6
5
9
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17
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1
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17
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8
12
16
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0
4
8
12
16
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0
4
8
7
11
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23
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7
11
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23
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7
11
15
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23
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10
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18
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6
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6
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2
6
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1
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1
5
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1
8
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7
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7
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2
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6
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9
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1
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1
5
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7
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10
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5
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16
20
0
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12
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3
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11
15
10
14
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.
0
3
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16
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14
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8
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19
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6
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3
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0
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11
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2
0
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7
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9
12
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.
2
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9
1
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0
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1
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8
1
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21
4
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.
15
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14
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3
2
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14
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10
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20
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7
21
2
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12
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18
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9
14
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11
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15
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1
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2
7
12
17
5
10
15
20
1
6
11
16
0
5
10
15
20
14
19
Expanding this mapping to 5L 4s makes the diatonic scale easy to play, but puts octaves all over the place.
0
4
1
5
9
13
17
22
2
6
10
14
18
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2
23
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7
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21
1
5
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10
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19
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7
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16
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0
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3
7
11
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1
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