Revision as of 04:50, 10 July 2026 by Lucius Chiaraviglio(talk | contribs)(Add Bryan Deister's Diminished (Demolished) + Würschmidt mapping; edit description of the existing Würschmidt mapping to take this into account; fix section heading for Machine now that Bryan Deister has more than 1 mapping on this page)
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 diminished temperament (as above), the Würschmidt mapping is a good way to maximise your range (a bit over eight octaves, nearly level) and make consonant chords easy to reach.
21
2
22
3
12
21
2
14
23
4
13
22
3
12
21
15
24
5
14
23
4
13
22
3
12
21
7
16
25
6
15
24
5
14
23
4
13
22
3
12
8
17
26
7
16
25
6
15
24
5
14
23
4
13
22
3
12
0
9
18
27
8
17
26
7
16
25
6
15
24
5
14
23
4
13
22
3
1
10
19
0
9
18
27
8
17
26
7
16
25
6
15
24
5
14
23
4
13
22
3
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
22
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
22
3
12
21
2
11
20
1
10
19
0
9
18
27
8
17
26
7
16
25
6
15
24
13
22
3
12
21
2
11
20
1
10
19
0
9
18
27
8
17
26
7
16
13
22
3
12
21
2
11
20
1
10
19
0
9
18
27
8
17
4
13
22
3
12
21
2
11
20
1
10
19
0
9
4
13
22
3
12
21
2
11
20
1
10
23
4
13
22
3
12
21
2
23
4
13
22
3
14
23
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.
