However, to the size of the edo, this mapping does not quite cover all the notes. In addition, the best approximation to 5/4 is the quadruply diminished or pentuply augmented 6th, which is extremely awkward to play with the root and 5th. The second best is shared with 12edo and is a triply augmented unison, which is slightly more ergonomic but still a tough stretch to play as a chord one-handed.
6
17
10
21
32
43
54
3
14
25
36
47
58
6
17
7
18
29
40
51
62
10
21
32
43
54
0
11
22
33
44
55
3
14
25
36
47
58
6
17
4
15
26
37
48
59
7
18
29
40
51
62
10
21
32
43
54
60
8
19
30
41
52
0
11
22
33
44
55
3
14
25
36
47
58
6
17
1
12
23
34
45
56
4
15
26
37
48
59
7
18
29
40
51
62
10
21
32
43
54
57
5
16
27
38
49
60
8
19
30
41
52
0
11
22
33
44
55
3
14
25
36
47
58
6
17
9
20
31
42
53
1
12
23
34
45
56
4
15
26
37
48
59
7
18
29
40
51
62
10
21
32
43
54
35
46
57
5
16
27
38
49
60
8
19
30
41
52
0
11
22
33
44
55
3
14
25
36
47
58
9
20
31
42
53
1
12
23
34
45
56
4
15
26
37
48
59
7
18
29
40
51
62
35
46
57
5
16
27
38
49
60
8
19
30
41
52
0
11
22
33
44
55
9
20
31
42
53
1
12
23
34
45
56
4
15
26
37
48
59
35
46
57
5
16
27
38
49
60
8
19
30
41
52
9
20
31
42
53
1
12
23
34
45
56
35
46
57
5
16
27
38
49
9
20
31
42
53
35
46
Other Mappings
Of the mappings that cover all the notes, the 7L 1s scale (of Sevond temperament) generated by 8/63 and the 3L 5s one generated by 23/63 are highly efficient, with the second of those keeping octaves closer to horizontal.
Sevond
38
46
45
53
61
6
14
44
52
60
5
13
21
29
37
51
59
4
12
20
28
36
44
52
60
5
50
58
3
11
19
27
35
43
51
59
4
12
20
28
57
2
10
18
26
34
42
50
58
3
11
19
27
35
43
51
59
56
1
9
17
25
33
41
49
57
2
10
18
26
34
42
50
58
3
11
19
0
8
16
24
32
40
48
56
1
9
17
25
33
41
49
57
2
10
18
26
34
42
50
62
7
15
23
31
39
47
55
0
8
16
24
32
40
48
56
1
9
17
25
33
41
49
57
2
10
14
22
30
38
46
54
62
7
15
23
31
39
47
55
0
8
16
24
32
40
48
56
1
9
17
25
33
41
37
45
53
61
6
14
22
30
38
46
54
62
7
15
23
31
39
47
55
0
8
16
24
32
40
48
5
13
21
29
37
45
53
61
6
14
22
30
38
46
54
62
7
15
23
31
39
47
55
28
36
44
52
60
5
13
21
29
37
45
53
61
6
14
22
30
38
46
54
59
4
12
20
28
36
44
52
60
5
13
21
29
37
45
53
61
19
27
35
43
51
59
4
12
20
28
36
44
52
60
50
58
3
11
19
27
35
43
51
59
4
10
18
26
34
42
50
58
3
41
49
57
2
10
1
9
Unidentified temperament
47
53
58
1
7
13
19
0
6
12
18
24
30
36
42
11
17
23
29
35
41
47
53
59
2
8
16
22
28
34
40
46
52
58
1
7
13
19
25
31
27
33
39
45
51
57
0
6
12
18
24
30
36
42
48
54
60
32
38
44
50
56
62
5
11
17
23
29
35
41
47
53
59
2
8
14
20
43
49
55
61
4
10
16
22
28
34
40
46
52
58
1
7
13
19
25
31
37
43
49
48
54
60
3
9
15
21
27
33
39
45
51
57
0
6
12
18
24
30
36
42
48
54
60
3
9
2
8
14
20
26
32
38
44
50
56
62
5
11
17
23
29
35
41
47
53
59
2
8
14
20
26
32
38
25
31
37
43
49
55
61
4
10
16
22
28
34
40
46
52
58
1
7
13
19
25
31
37
43
49
54
60
3
9
15
21
27
33
39
45
51
57
0
6
12
18
24
30
36
42
48
54
60
14
20
26
32
38
44
50
56
62
5
11
17
23
29
35
41
47
53
59
2
43
49
55
61
4
10
16
22
28
34
40
46
52
58
1
7
13
3
9
15
21
27
33
39
45
51
57
0
6
12
18
32
38
44
50
56
62
5
11
17
23
29
55
61
4
10
16
22
28
34
21
27
33
39
45
44
50
However, neither of these makes consonant chords particularly easy to play. The fog and magic mappings have smaller ranges, but are more harmonically effective.
Fog
46
51
57
62
4
9
14
0
5
10
15
20
25
30
35
11
16
21
26
31
36
41
46
51
56
61
17
22
27
32
37
42
47
52
57
62
4
9
14
19
28
33
38
43
48
53
58
0
5
10
15
20
25
30
35
40
45
34
39
44
49
54
59
1
6
11
16
21
26
31
36
41
46
51
56
61
3
45
50
55
60
2
7
12
17
22
27
32
37
42
47
52
57
62
4
9
14
19
24
29
51
56
61
3
8
13
18
23
28
33
38
43
48
53
58
0
5
10
15
20
25
30
35
40
45
50
4
9
14
19
24
29
34
39
44
49
54
59
1
6
11
16
21
26
31
36
41
46
51
56
61
3
8
13
25
30
35
40
45
50
55
60
2
7
12
17
22
27
32
37
42
47
52
57
62
4
9
14
19
24
51
56
61
3
8
13
18
23
28
33
38
43
48
53
58
0
5
10
15
20
25
30
35
9
14
19
24
29
34
39
44
49
54
59
1
6
11
16
21
26
31
36
41
35
40
45
50
55
60
2
7
12
17
22
27
32
37
42
47
52
56
61
3
8
13
18
23
28
33
38
43
48
53
58
19
24
29
34
39
44
49
54
59
1
6
40
45
50
55
60
2
7
12
3
8
13
18
23
24
29
Magic
13
16
27
30
33
36
39
38
41
44
47
50
53
56
59
52
55
58
61
1
4
7
10
13
16
19
0
3
6
9
12
15
18
21
24
27
30
33
36
39
14
17
20
23
26
29
32
35
38
41
44
47
50
53
56
59
62
25
28
31
34
37
40
43
46
49
52
55
58
61
1
4
7
10
13
16
19
39
42
45
48
51
54
57
60
0
3
6
9
12
15
18
21
24
27
30
33
36
39
42
50
53
56
59
62
2
5
8
11
14
17
20
23
26
29
32
35
38
41
44
47
50
53
56
59
62
4
7
10
13
16
19
22
25
28
31
34
37
40
43
46
49
52
55
58
61
1
4
7
10
13
16
19
22
24
27
30
33
36
39
42
45
48
51
54
57
60
0
3
6
9
12
15
18
21
24
27
30
33
36
47
50
53
56
59
62
2
5
8
11
14
17
20
23
26
29
32
35
38
41
44
47
50
4
7
10
13
16
19
22
25
28
31
34
37
40
43
46
49
52
55
58
61
27
30
33
36
39
42
45
48
51
54
57
60
0
3
6
9
12
47
50
53
56
59
62
2
5
8
11
14
17
20
23
7
10
13
16
19
22
25
28
31
34
37
27
30
33
36
39
42
45
48
50
53
56
59
62
7
10
Pseudo-Meantone
Bryan Deister has demonstrated a 6L 1s (10:3 step ratio) mapping for 63edo in microtonal improvisation in 63edo (2025). The generator 10\93 is the quasi-meantone ~19/17, which is composed of highly inaccurate harmonics whose errors nearly cancel out, rendering it just slightly flat; two of them make a somewhat flat classic major third ~5/4. (In contrast to actual meantone temperament, 63edo represents ~19/17, ~10/9, and ~9/8 as distinct intervals — the syntonic comma 81/80 is not tempered out, and instead the aureusma 1445/1444 equates two quasi-meantones to a classic major third.) Although 10\63 can reach all of the notes of 63edo without the need for a second generator, a second generator 7\63 (upward, as a tridecimal supraminor/neutral second that functions as both ~13/12 and ~14/13) is convenient for quick access to additional common intervals — for instance, three rightward generators plus one upward generator reach the just slightly sharp fifth ~3/2; while five rightward generators minus one upwards generator reach a mildly sharp minor sixth ~8/5. The range is somewhat over four octaves (which slant up mildly) with no missed notes and no repeated notes.
