There are many conceivable ways to map 56edo onto the onto the Lumatone keyboard. Only one, however, agrees with the Standard Lumatone mapping for Pythagorean.
Diatonic
This is the highest EDO in which the standard Bosanquet–Wilson mapping gives you access to all notes in the gamut in each octave, except where chopped off at the left and right edges (note 1 in the lowest octave, and notes 48, 50, 52, and 55 in the highest octave). Each note appears exactly only once with no skips or repetitions.
8
18
11
21
31
41
51
4
14
24
34
44
54
8
18
7
17
27
37
47
1
11
21
31
41
51
0
10
20
30
40
50
4
14
24
34
44
54
8
18
3
13
23
33
43
53
7
17
27
37
47
1
11
21
31
41
51
52
6
16
26
36
46
0
10
20
30
40
50
4
14
24
34
44
54
8
18
55
9
19
29
39
49
3
13
23
33
43
53
7
17
27
37
47
1
11
21
31
41
51
48
2
12
22
32
42
52
6
16
26
36
46
0
10
20
30
40
50
4
14
24
34
44
54
8
18
5
15
25
35
45
55
9
19
29
39
49
3
13
23
33
43
53
7
17
27
37
47
1
11
21
31
41
51
28
38
48
2
12
22
32
42
52
6
16
26
36
46
0
10
20
30
40
50
4
14
24
34
44
54
5
15
25
35
45
55
9
19
29
39
49
3
13
23
33
43
53
7
17
27
37
47
1
28
38
48
2
12
22
32
42
52
6
16
26
36
46
0
10
20
30
40
50
5
15
25
35
45
55
9
19
29
39
49
3
13
23
33
43
53
28
38
48
2
12
22
32
42
52
6
16
26
36
46
5
15
25
35
45
55
9
19
29
39
49
28
38
48
2
12
22
32
42
5
15
25
35
45
28
38
Pajara
The 2L 8s mapping for Pajara mapping has a smaller range and some repeated notes, but makes 5-limit chords easier to play.
23
28
31
36
41
46
51
34
39
44
49
54
3
8
13
42
47
52
1
6
11
16
21
26
31
36
45
50
55
4
9
14
19
24
29
34
39
44
49
54
53
2
7
12
17
22
27
32
37
42
47
52
1
6
11
16
21
0
5
10
15
20
25
30
35
40
45
50
55
4
9
14
19
24
29
34
39
8
13
18
23
28
33
38
43
48
53
2
7
12
17
22
27
32
37
42
47
52
1
6
11
16
21
26
31
36
41
46
51
0
5
10
15
20
25
30
35
40
45
50
55
4
9
14
19
24
24
29
34
39
44
49
54
3
8
13
18
23
28
33
38
43
48
53
2
7
12
17
22
27
32
37
42
47
42
47
52
1
6
11
16
21
26
31
36
41
46
51
0
5
10
15
20
25
30
35
40
45
50
55
9
14
19
24
29
34
39
44
49
54
3
8
13
18
23
28
33
38
43
48
53
2
7
27
32
37
42
47
52
1
6
11
16
21
26
31
36
41
46
51
0
5
10
50
55
4
9
14
19
24
29
34
39
44
49
54
3
8
13
18
12
17
22
27
32
37
42
47
52
1
6
11
16
21
35
40
45
50
55
4
9
14
19
24
29
53
2
7
12
17
22
27
32
20
25
30
35
40
38
43
Bidia (+ Diminished + Charismic + Semitonismic)
Bryan Deister has demonstrated a 4L 4s (9:5 step ratio) mapping for 56edo, in Curious Light - DOORS (microtonal cover in 56edo) (2025). Right + down-right divides the octave into slices of 14\56; as an interval in its own right, this is the same as the minor third of 12edo, which functions as ~19/16 and ~25/21 (both being near-just). Down-right alone is 5\56, which is the minimal form generator for Bidia; it functions as the classic diatonic semitone ~16/15, the large septendecimal semitone ~17/16, and the small septendecimal semitone ~18/17, meaning that the charisma 256/255 and the semitonisma 289/288 are both tempered out; two of them make a rather sharp whole tone ~9/8; three of them (passing the quarter-octave) make a mildly sharp classic minor third ~6/5, although the afore-mentioned quarter-octave (12edo-style) minor third is easier to reach; in contrast, the near-just classic major third ~5/4 is very easy to reach with just two moves rightwards, and a down-right move from this reaches the moderately flat fourth ~4/3; two more down-right moves reaches the rather sharp fifth ~3/2. The efficiency is almost as good as that of the diatonic mapping, with no missed notes and one repeated note per octave; the overall range is somewhat under five octaves, with no notes chopped off by the left and right edges before reaching the end of overall range. The cost of this is that octaves slant downwards.
0
9
5
14
23
32
41
1
10
19
28
37
46
55
8
6
15
24
33
42
51
4
13
22
31
40
2
11
20
29
38
47
0
9
18
27
36
45
54
7
7
16
25
34
43
52
5
14
23
32
41
50
3
12
21
30
39
3
12
21
30
39
48
1
10
19
28
37
46
55
8
17
26
35
44
53
6
8
17
26
35
44
53
6
15
24
33
42
51
4
13
22
31
40
49
2
11
20
29
38
4
13
22
31
40
49
2
11
20
29
38
47
0
9
18
27
36
45
54
7
16
25
34
43
52
5
18
27
36
45
54
7
16
25
34
43
52
5
14
23
32
41
50
3
12
21
30
39
48
1
10
19
28
37
41
50
3
12
21
30
39
48
1
10
19
28
37
46
55
8
17
26
35
44
53
6
15
24
33
42
17
26
35
44
53
6
15
24
33
42
51
4
13
22
31
40
49
2
11
20
29
38
47
40
49
2
11
20
29
38
47
0
9
18
27
36
45
54
7
16
25
34
43
16
25
34
43
52
5
14
23
32
41
50
3
12
21
30
39
48
39
48
1
10
19
28
37
46
55
8
17
26
35
44
15
24
33
42
51
4
13
22
31
40
49
38
47
0
9
18
27
36
45
14
23
32
41
50
37
46
