Lumatone mapping for 23edo

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There are many conceivable ways to map 23edo onto the onto the Lumatone keyboard. However, as both of its fifths are about as far away from just as possible, neither the sharp or the flat versions of the Standard Lumatone mapping for Pythagorean work particularly well.

Antidiatonic

The flat fifth is slightly closer, however, which produces the following layout. However, as 23edo is a mavila temperament, its best fifths are both quite dissonant and the chromatic semitone goes in the opposite direction to usual. In fact, all 4 of its first prime harmonics are tuned almost as badly as is possible with its step size.

13
16
17
20
0
3
6
18
21
1
4
7
10
13
16
22
2
5
8
11
14
17
20
0
3
6
0
3
6
9
12
15
18
21
1
4
7
10
13
16
4
7
10
13
16
19
22
2
5
8
11
14
17
20
0
3
6
5
8
11
14
17
20
0
3
6
9
12
15
18
21
1
4
7
10
13
16
9
12
15
18
21
1
4
7
10
13
16
19
22
2
5
8
11
14
17
20
0
3
6
10
13
16
19
22
2
5
8
11
14
17
20
0
3
6
9
12
15
18
21
1
4
7
10
13
16
17
20
0
3
6
9
12
15
18
21
1
4
7
10
13
16
19
22
2
5
8
11
14
17
20
0
3
6
4
7
10
13
16
19
22
2
5
8
11
14
17
20
0
3
6
9
12
15
18
21
1
4
7
10
17
20
0
3
6
9
12
15
18
21
1
4
7
10
13
16
19
22
2
5
8
11
14
4
7
10
13
16
19
22
2
5
8
11
14
17
20
0
3
6
9
12
15
17
20
0
3
6
9
12
15
18
21
1
4
7
10
13
16
19
4
7
10
13
16
19
22
2
5
8
11
14
17
20
17
20
0
3
6
9
12
15
18
21
1
4
7
10
13
16
19
22
2
17
20
0
3
6
4
7

Mavila (Superdiatonic) + Baldy (Amsochromic)

Still using the 23edo flat fifth ~3/2 for mavila temperament, an alternative to the antidiatonic mapping is the superdiatonic mapping, having a 7L 2s scale (3:1 step ratio), with the generator 13\23 being reached by moving four keys right plus one key down-right. This reduces the range from just under five octaves to about 3½ octaves, although it keeps them nearly level — rising gently enough to support division into multiple manuals. It also supports a 6L 5s scale (3:1 step ratio) if the mildly sharp directly-approximated Pythagorean whole tone ~9/8 is used as a generator instead, although this causes the octaves to slope down enough to prevent vertical division into two contiguous manuals; this generator (4\23) is reached by moving one key right plus one key down-right, which is easier than reaching the mavila generator. This mapping is demonstrated on the left Lumatone in David Wise's Aquatic Ambience (1993 via Donkey Kong Country (1994) – microtonal cover in 23edo by Stephen Weigel (right) and Vito Sicurella (left) on Lumatones (2026, from UnTwelve 2025); the color scheme is for the superdiatonic scale, but different between the left and right halves of the layout to represent division into two horizontal zones for different soft synthesizers. This layout is used on the left Lumatone; for the right Lumatone layout, see Oolong (Smitonic) below.

0
3
1
4
7
10
13
22
2
5
8
11
14
17
20
0
3
6
9
12
15
18
21
1
4
7
21
1
4
7
10
13
16
19
22
2
5
8
11
14
22
2
5
8
11
14
17
20
0
3
6
9
12
15
18
21
1
20
0
3
6
9
12
15
18
21
1
4
7
10
13
16
19
22
2
5
8
21
1
4
7
10
13
16
19
22
2
5
8
11
14
17
20
0
3
6
9
12
15
18
19
22
2
5
8
11
14
17
20
0
3
6
9
12
15
18
21
1
4
7
10
13
16
19
22
2
0
3
6
9
12
15
18
21
1
4
7
10
13
16
19
22
2
5
8
11
14
17
20
0
3
6
9
12
7
10
13
16
19
22
2
5
8
11
14
17
20
0
3
6
9
12
15
18
21
1
4
7
10
13
17
20
0
3
6
9
12
15
18
21
1
4
7
10
13
16
19
22
2
5
8
11
14
1
4
7
10
13
16
19
22
2
5
8
11
14
17
20
0
3
6
9
12
11
14
17
20
0
3
6
9
12
15
18
21
1
4
7
10
13
18
21
1
4
7
10
13
16
19
22
2
5
8
11
5
8
11
14
17
20
0
3
6
9
12
12
15
18
21
1
4
7
10
22
2
5
8
11
6
9

Oolong (Smitonic)

An alternative for 23edo to using either (highly inaccurate) fifth as a generator is stacking the much more accurate (only slightly flat) classic minor third ~6/5, as in oolong temperament, having a 4L 3s scale (5:1 step ratio); the generator 6\23 is reached by moving one key right plus one key down-right. This results in a moderate downwards slope of the octaves, but the range is 5¾ octaves, still with a generous allocation of repeated notes to mitigate vertical wraparounds. This mapping is demonstrated on the right Lumatone in David Wise's Aquatic Ambience (1993 via Donkey Kong Country (1994) – microtonal cover in 23edo by Stephen Weigel (right) and Vito Sicurella (left) on Lumatones (2026, from UnTwelve 2025). This layout is used on the right Lumatone; for the left Lumatone layout, see Mavila (Superdiatonic) + Baldy (Amsochromic) above.

0
5
1
6
11
16
21
20
2
7
12
17
22
4
9
21
3
8
13
18
0
5
10
15
20
2
17
22
4
9
14
19
1
6
11
16
21
3
8
13
18
0
5
10
15
20
2
7
12
17
22
4
9
14
19
1
6
14
19
1
6
11
16
21
3
8
13
18
0
5
10
15
20
2
7
12
17
15
20
2
7
12
17
22
4
9
14
19
1
6
11
16
21
3
8
13
18
0
5
10
11
16
21
3
8
13
18
0
5
10
15
20
2
7
12
17
22
4
9
14
19
1
6
11
16
21
17
22
4
9
14
19
1
6
11
16
21
3
8
13
18
0
5
10
15
20
2
7
12
17
22
4
9
14
5
10
15
20
2
7
12
17
22
4
9
14
19
1
6
11
16
21
3
8
13
18
0
5
10
15
21
3
8
13
18
0
5
10
15
20
2
7
12
17
22
4
9
14
19
1
6
11
16
9
14
19
1
6
11
16
21
3
8
13
18
0
5
10
15
20
2
7
12
2
7
12
17
22
4
9
14
19
1
6
11
16
21
3
8
13
13
18
0
5
10
15
20
2
7
12
17
22
4
9
6
11
16
21
3
8
13
18
0
5
10
17
22
4
9
14
19
1
6
10
15
20
2
7
21
3

Sephiroth

The first harmonics that are decently tuned are 9, 13, 15, 17, and 21. The most efficient way to reach these is the sephiroth mapping, which forms a neat 16:17:21:26:32 chord with −3 generators.

6
13
8
15
22
6
13
3
10
17
1
8
15
22
6
5
12
19
3
10
17
1
8
15
22
6
0
7
14
21
5
12
19
3
10
17
1
8
15
22
2
9
16
0
7
14
21
5
12
19
3
10
17
1
8
15
22
20
4
11
18
2
9
16
0
7
14
21
5
12
19
3
10
17
1
8
15
22
6
13
20
4
11
18
2
9
16
0
7
14
21
5
12
19
3
10
17
1
8
15
17
1
8
15
22
6
13
20
4
11
18
2
9
16
0
7
14
21
5
12
19
3
10
17
1
8
3
10
17
1
8
15
22
6
13
20
4
11
18
2
9
16
0
7
14
21
5
12
19
3
10
17
1
8
19
3
10
17
1
8
15
22
6
13
20
4
11
18
2
9
16
0
7
14
21
5
12
19
3
10
19
3
10
17
1
8
15
22
6
13
20
4
11
18
2
9
16
0
7
14
21
5
12
12
19
3
10
17
1
8
15
22
6
13
20
4
11
18
2
9
16
0
7
12
19
3
10
17
1
8
15
22
6
13
20
4
11
18
2
9
5
12
19
3
10
17
1
8
15
22
6
13
20
4
5
12
19
3
10
17
1
8
15
22
6
21
5
12
19
3
10
17
1
21
5
12
19
3
14
21

A-Team

Also quite effective is the A-Team mapping, which turns the harmonic sequence 16:18:21 and its inversion into easy to play consonant cluster chords that only require a single finger to hit all three notes.

22
8
4
13
22
8
17
0
9
18
4
13
22
8
17
5
14
0
9
18
4
13
22
8
17
3
1
10
19
5
14
0
9
18
4
13
22
8
17
3
6
15
1
10
19
5
14
0
9
18
4
13
22
8
17
3
12
2
11
20
6
15
1
10
19
5
14
0
9
18
4
13
22
8
17
3
12
7
16
2
11
20
6
15
1
10
19
5
14
0
9
18
4
13
22
8
17
3
12
21
3
12
21
7
16
2
11
20
6
15
1
10
19
5
14
0
9
18
4
13
22
8
17
3
12
21
17
3
12
21
7
16
2
11
20
6
15
1
10
19
5
14
0
9
18
4
13
22
8
17
3
12
21
7
17
3
12
21
7
16
2
11
20
6
15
1
10
19
5
14
0
9
18
4
13
22
8
17
3
12
3
12
21
7
16
2
11
20
6
15
1
10
19
5
14
0
9
18
4
13
22
8
17
3
12
21
7
16
2
11
20
6
15
1
10
19
5
14
0
9
18
4
13
12
21
7
16
2
11
20
6
15
1
10
19
5
14
0
9
18
12
21
7
16
2
11
20
6
15
1
10
19
5
14
21
7
16
2
11
20
6
15
1
10
19
21
7
16
2
11
20
6
15
7
16
2
11
20
7
16

Didacus/Isra-related Machinoid

Bryan Deister has demonstrated a 5L 1s (4:3 step ratio) mapping for 23edo in 23edo (2023), although with MIDI note numbering offset relative to what is shown here. The rightward generator 4\23 corresponds to a somewhat sharp directly-approximated Pythagorean whole tone ~9/8, as in didacus and isra; however, unlike these temperaments, it brings up a different set of intervals, all in the 2.9.15.21.33.13.17 subgroup (same as as used for the table of intervals on the 23edo page, and required to get ~9/8 and most of the following intervals to map correctly). Two of these generators make a near-just undecimal (pentacircle) major third ~14/11; three of them make a mildly sharp greater septimal tritone ~10/7; four of them make a somewhat flat lesser tridecimal neutral sixth ~13/8; and five of them make a mildly flat undecimal neutral seventh ~11/6. The range is a bit over five octaves, and the octaves slope upwards.

15
19
18
22
3
7
11
17
21
2
6
10
14
18
22
20
1
5
9
13
17
21
2
6
10
14
19
0
4
8
12
16
20
1
5
9
13
17
21
2
22
3
7
11
15
19
0
4
8
12
16
20
1
5
9
13
17
21
2
6
10
14
18
22
3
7
11
15
19
0
4
8
12
16
20
1
5
1
5
9
13
17
21
2
6
10
14
18
22
3
7
11
15
19
0
4
8
12
16
20
0
4
8
12
16
20
1
5
9
13
17
21
2
6
10
14
18
22
3
7
11
15
19
0
4
8
7
11
15
19
0
4
8
12
16
20
1
5
9
13
17
21
2
6
10
14
18
22
3
7
11
15
19
0
18
22
3
7
11
15
19
0
4
8
12
16
20
1
5
9
13
17
21
2
6
10
14
18
22
3
10
14
18
22
3
7
11
15
19
0
4
8
12
16
20
1
5
9
13
17
21
2
6
21
2
6
10
14
18
22
3
7
11
15
19
0
4
8
12
16
20
1
5
13
17
21
2
6
10
14
18
22
3
7
11
15
19
0
4
8
1
5
9
13
17
21
2
6
10
14
18
22
3
7
16
20
1
5
9
13
17
21
2
6
10
4
8
12
16
20
1
5
9
19
0
4
8
12
7
11
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