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 this layout:
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
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.
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). 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
