Lumatone mapping for 23edo: Difference between revisions

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There are many conceivable ways to map [[23edo]] onto the [[Lumatone]] keyboard. Only one, however, agrees with the [[Standard Lumatone mapping for Pythagorean]].
{{Lumatone mapping intro}} The flat fifth is slightly closer, however, which produces this layout:
{{Lumatone EDO mapping|n=23|start=13|xstep=3|ystep=1}}
{{Lumatone EDO mapping|n=23|start=13|xstep=3|ystep=1}}




However, as 23edo is a [[mavila]] temperament, it's best fifths are 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. The first harmonics that are decently tuned are 9, 13, 15, 17 & 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.
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. 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.
{{Lumatone EDO mapping|n=23|start=6|xstep=7|ystep=-5}}
{{Lumatone EDO mapping|n=23|start=6|xstep=7|ystep=-5}}




Also quite effective is the [[Subgroup_temperaments#A-team|A-team]] mapping, which turns the harmonic sequence 16:18:21 and it's inversion into easy to play consonant cluster chords.
Also quite effective is the [[Subgroup_temperaments#A-team|A-team]] mapping, which turns the harmonic sequence 16:18:21 and its inversion into easy to play consonant cluster chords.
{{Lumatone EDO mapping|n=23|start=20|xstep=5|ystep=-1}}
{{Lumatone EDO mapping|n=23|start=20|xstep=5|ystep=-1}}


{{Navbox Lumatone}}
{{Navbox Lumatone}}

Revision as of 18:13, 14 March 2025

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. 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. 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


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


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