There are many conceivable ways to map 28edo onto the onto the Lumatone keyboard. However, it has 4 mutually-exclusive rings of fifths, so the Standard Lumatone mapping for Pythagorean is not one of them.
Whitewood
The Whitewood mapping is perhaps the most diatonic-like mapping that covers all notes. Bryan Deister demonstrates this mapping in 28edo improvisation (2022).
20
24
23
27
3
7
11
22
26
2
6
10
14
18
22
25
1
5
9
13
17
21
25
1
5
9
24
0
4
8
12
16
20
24
0
4
8
12
16
20
27
3
7
11
15
19
23
27
3
7
11
15
19
23
27
3
7
26
2
6
10
14
18
22
26
2
6
10
14
18
22
26
2
6
10
14
18
1
5
9
13
17
21
25
1
5
9
13
17
21
25
1
5
9
13
17
21
25
1
5
0
4
8
12
16
20
24
0
4
8
12
16
20
24
0
4
8
12
16
20
24
0
4
8
12
16
7
11
15
19
23
27
3
7
11
15
19
23
27
3
7
11
15
19
23
27
3
7
11
15
19
23
27
3
18
22
26
2
6
10
14
18
22
26
2
6
10
14
18
22
26
2
6
10
14
18
22
26
2
6
5
9
13
17
21
25
1
5
9
13
17
21
25
1
5
9
13
17
21
25
1
5
9
16
20
24
0
4
8
12
16
20
24
0
4
8
12
16
20
24
0
4
8
3
7
11
15
19
23
27
3
7
11
15
19
23
27
3
7
11
14
18
22
26
2
6
10
14
18
22
26
2
6
10
1
5
9
13
17
21
25
1
5
9
13
12
16
20
24
0
4
8
12
27
3
7
11
15
10
14
Diminished (Demolished) + Würschmidt
It is possible to generate 28edo using its near-just classic major third ~5/4 represented by 9\28 (one key right plus one key down-right) as in Würschmidt temperament, producing a 3L 1s scale with a 9:1 step ratio, or by dividing the octave into four parts and using its quarter-octave-reduced form of the major third as a near-just septimal minor semitone ~21/20 represented by 2\28 as in demolished temperament (a variety of diminished temperament), producing a 4L 4s scale with a 5:2 step ratio (in which the 5\28 is a near-just diatismic whole tone ~17/15, and the quarter-octave 7\28 is the flat classic major third ~6/5). Bryan Deister has used this mapping in 28edo groove (2026). The octaves slope up with the rows, and the range is seven complete octaves except for a missing note 27 in the highest octave, with a few repeated notes to mitigated vertical wraparounds.
6
13
8
15
22
1
8
3
10
17
24
3
10
17
24
5
12
19
26
5
12
19
26
5
12
19
0
7
14
21
0
7
14
21
0
7
14
21
0
7
2
9
16
23
2
9
16
23
2
9
16
23
2
9
16
23
2
25
4
11
18
25
4
11
18
25
4
11
18
25
4
11
18
25
4
11
18
27
6
13
20
27
6
13
20
27
6
13
20
27
6
13
20
27
6
13
20
27
6
13
22
1
8
15
22
1
8
15
22
1
8
15
22
1
8
15
22
1
8
15
22
1
8
15
22
1
3
10
17
24
3
10
17
24
3
10
17
24
3
10
17
24
3
10
17
24
3
10
17
24
3
10
17
24
19
26
5
12
19
26
5
12
19
26
5
12
19
26
5
12
19
26
5
12
19
26
5
12
19
26
14
21
0
7
14
21
0
7
14
21
0
7
14
21
0
7
14
21
0
7
14
21
0
2
9
16
23
2
9
16
23
2
9
16
23
2
9
16
23
2
9
16
23
25
4
11
18
25
4
11
18
25
4
11
18
25
4
11
18
25
13
20
27
6
13
20
27
6
13
20
27
6
13
20
8
15
22
1
8
15
22
1
8
15
22
24
3
10
17
24
3
10
17
19
26
5
12
19
7
14
Würschmidt
Since the 5th harmonic is easily the best tuned interval, if you don't need easy access to diminished temperament (as above), the Würschmidt mapping is a good way to maximise your range (a bit over eight octaves, nearly level, although the bass octave is missing note 4) and make consonant chords easy to reach.
12
21
13
22
3
12
21
5
14
23
4
13
22
3
12
6
15
24
5
14
23
4
13
22
3
12
26
7
16
25
6
15
24
5
14
23
4
13
22
3
27
8
17
26
7
16
25
6
15
24
5
14
23
4
13
22
3
19
0
9
18
27
8
17
26
7
16
25
6
15
24
5
14
23
4
13
22
20
1
10
19
0
9
18
27
8
17
26
7
16
25
6
15
24
5
14
23
4
13
22
12
21
2
11
20
1
10
19
0
9
18
27
8
17
26
7
16
25
6
15
24
5
14
23
4
13
22
3
12
21
2
11
20
1
10
19
0
9
18
27
8
17
26
7
16
25
6
15
24
5
14
23
4
13
13
22
3
12
21
2
11
20
1
10
19
0
9
18
27
8
17
26
7
16
25
6
15
24
5
14
13
22
3
12
21
2
11
20
1
10
19
0
9
18
27
8
17
26
7
16
25
6
15
4
13
22
3
12
21
2
11
20
1
10
19
0
9
18
27
8
17
26
7
4
13
22
3
12
21
2
11
20
1
10
19
0
9
18
27
8
23
4
13
22
3
12
21
2
11
20
1
10
19
0
23
4
13
22
3
12
21
2
11
20
1
14
23
4
13
22
3
12
21
14
23
4
13
22
5
14
Machine
Bryan Deister has used a layout for 28edo that was inspired by the layout for 29edo (rather than being made for any specific temperament), as demonstrated in minuet in 28edo (2025). The right-moving generator is a somewhat sharp Pythagorean whole tone (~9/8, or near-just 17/15, 5\28). The up-moving generator is an almost-just tridecimal supraminor second (~14/13, 3\28). The range is a bit over five octaves, with octaves alternating near/far and middle with an overall small upwards slant. Although this layout was not designed for any particular temperament, it so happens that the right-moving generator matches Machine.
4
9
6
11
16
21
26
3
8
13
18
23
0
5
10
5
10
15
20
25
2
7
12
17
22
27
2
7
12
17
22
27
4
9
14
19
24
1
6
11
4
9
14
19
24
1
6
11
16
21
26
3
8
13
18
23
0
1
6
11
16
21
26
3
8
13
18
23
0
5
10
15
20
25
2
7
12
3
8
13
18
23
0
5
10
15
20
25
2
7
12
17
22
27
4
9
14
19
24
1
0
5
10
15
20
25
2
7
12
17
22
27
4
9
14
19
24
1
6
11
16
21
26
3
8
13
7
12
17
22
27
4
9
14
19
24
1
6
11
16
21
26
3
8
13
18
23
0
5
10
15
20
25
2
19
24
1
6
11
16
21
26
3
8
13
18
23
0
5
10
15
20
25
2
7
12
17
22
27
4
8
13
18
23
0
5
10
15
20
25
2
7
12
17
22
27
4
9
14
19
24
1
6
20
25
2
7
12
17
22
27
4
9
14
19
24
1
6
11
16
21
26
3
9
14
19
24
1
6
11
16
21
26
3
8
13
18
23
0
5
21
26
3
8
13
18
23
0
5
10
15
20
25
2
10
15
20
25
2
7
12
17
22
27
4
22
27
4
9
14
19
24
1
11
16
21
26
3
23
0
