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