Lumatone mapping for 24edo: Difference between revisions

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Forgot to add the generator for Bryan Deister's layout -- fixing this.
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There are many conceivable ways to map [[24edo]] onto the [[Lumatone]] keyboard. However, the [[Standard Lumatone mapping for Pythagorean]] is not one of them because there are two mutually-exclusive rings of fifths.
{{Lumatone mapping intro}}


The official Lumatone manual contains a rotated version of a [[Lumatone mapping for neutral thirds scales]] as "Preset 6 — 24-ET Isomorphic".
== 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, Persian|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. This layout is demonstrated on the official Lumatone youtube channel. [https://www.youtube.com/watch?v=3okSkgpCcqc Learning Lumatone: Episode 23 - "24-EDO Basics"]
{{Lumatone EDO mapping|n=24|start=0|xstep=4|ystep=-1}}
{{Lumatone EDO mapping|n=24|start=0|xstep=4|ystep=-1}}


=== 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.
{{Lumatone EDO mapping|n=24|start=0|xstep=3|ystep=1}}


However, 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.  
=== Emphasizing Neutral Seconds ===
{{Lumatone EDO mapping|n=24|start=0|xstep=3|ystep=1}}
Another neutral thirds mapping uses a [[6L 3s]] scale (3:2 step ratio) to make [[24edo]] neutral seconds (3\24) more easily accessible, as demonstrated by [[Bryan Deister]] in [https://www.youtube.com/shorts/3ZvbKIGBLoY ''24edo groove''] (2026). The range is only four octaves, but the octaves are close enough to level that the layout could be split into two manuals with some keys to spare, although the slight downwards octave slope would make them noticeably lopsided.
{{Lumatone EDO mapping|n=24|start=0|xstep=3|ystep=-1}}


=== Compressed ===
[[Bryan Deister]] has used the [[3L 1s]] (7:3 step ratio) layout, as demonstrated in [http://www.youtube.com/shorts/ZnAl6EN_wq4 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.
{{Lumatone EDO mapping|n=24|start=2|xstep=7|ystep=-4}}


The semiquartal ([[5L 4s]]) layout, which uses 2.5 semitones as the generator, has a wider range, keeps octaves closer to horizontal, makes the diatonic scale relatively easy to play, and naturally puts the chroma in the right direction on the vertical axis, so it may be preferable.
== Semiquartal ==
The [[4L 1s]] layout, which uses {{frac|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 [https://www.youtube.com/shorts/Mjzfb_-3kS4 ''24edo jam''] (2025) with a different zero point and the edges cut off due to only using one midi channel.
{{Lumatone EDO mapping|n=24|start=15|xstep=5|ystep=-1}}
{{Lumatone EDO mapping|n=24|start=15|xstep=5|ystep=-1}}




[[Bryan Deister]] has used the following layout (as demonstrated in [https://www.youtube.com/shorts/ZnAl6EN_wq4 In Your Hands (microtonal 24edo) (alt layout)]). The octaves rise just slightly while moving to higher pitches, and the range is somewhat over eight octaves.  The generator is half a fifth, making this layout of potential interest for [[Mohajira]].  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.
Expanding this mapping to [[5L 4s]] makes the diatonic scale easy to play, but puts octaves all over the place.
{{Lumatone EDO mapping|n=24|start=2|xstep=7|ystep=-4}}
{{Lumatone EDO mapping|n=24|start=0|xstep=4|ystep=-3}}
 
== 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.
{{Lumatone EDO mapping|n=24|start=0|xstep=2|ystep=5}}
 


{{Lumatone mapping navigation}}
{{Navbox Lumatone}}

Latest revision as of 08:43, 4 March 2026

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. This layout is demonstrated on the official Lumatone youtube channel. Learning Lumatone: Episode 23 - "24-EDO Basics"

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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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Emphasizing Neutral Seconds

Another neutral thirds mapping uses a 6L 3s scale (3:2 step ratio) to make 24edo neutral seconds (3\24) more easily accessible, as demonstrated by Bryan Deister in 24edo groove (2026). The range is only four octaves, but the octaves are close enough to level that the layout could be split into two manuals with some keys to spare, although the slight downwards octave slope would make them noticeably lopsided.

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Compressed

Bryan Deister has used the 3L 1s (7:3 step ratio) 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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11
13
15
12
14
16
18
20
22
0
2
4
6
8
10
12
14
16
18
20
22
0
2
19
21
23
1
3
5
7
9
11
13
15
17
19
21
23
1
3
5
7
9
11
13
15
0
2
4
6
8
10
12
14
16
18
20
22
0
2
4
6
8
10
12
14
16
18
20
22
0
2
9
11
13
15
17
19
21
23
1
3
5
7
9
11
13
15
17
19
21
23
1
3
5
7
9
11
13
15
20
22
0
2
4
6
8
10
12
14
16
18
20
22
0
2
4
6
8
10
12
14
16
18
20
22
9
11
13
15
17
19
21
23
1
3
5
7
9
11
13
15
17
19
21
23
1
3
5
20
22
0
2
4
6
8
10
12
14
16
18
20
22
0
2
4
6
8
10
9
11
13
15
17
19
21
23
1
3
5
7
9
11
13
15
17
20
22
0
2
4
6
8
10
12
14
16
18
20
22
9
11
13
15
17
19
21
23
1
3
5
20
22
0
2
4
6
8
10
9
11
13
15
17
20
22


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