There are many conceivable ways to map 63edo onto the onto the Lumatone keyboard. Only one, however, agrees with the Standard Lumatone mapping for Pythagorean.
Diatonic
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
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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
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50
62
7
15
23
31
39
47
55
0
8
16
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32
40
48
56
1
9
17
25
33
41
49
57
2
10
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22
30
38
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62
7
15
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31
39
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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
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59
4
12
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28
36
44
52
60
5
13
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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
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29
35
41
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53
59
2
8
16
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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
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23
29
55
61
4
10
16
22
28
34
21
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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
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61
17
22
27
32
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42
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52
57
62
4
9
14
19
28
33
38
43
48
53
58
0
5
10
15
20
25
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35
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45
34
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59
1
6
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31
36
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61
3
45
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60
2
7
12
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32
37
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62
4
9
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61
3
8
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28
33
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53
58
0
5
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9
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2
7
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4
9
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24
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61
3
8
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38
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58
0
5
10
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30
35
9
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59
1
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60
2
7
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61
3
8
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28
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38
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48
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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
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53
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59
52
55
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61
1
4
7
10
13
16
19
0
3
6
9
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27
30
33
36
39
14
17
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35
38
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53
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25
28
31
34
37
40
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52
55
58
61
1
4
7
10
13
16
19
39
42
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51
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57
60
0
3
6
9
12
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62
2
5
8
11
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32
35
38
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56
59
62
4
7
10
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28
31
34
37
40
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52
55
58
61
1
4
7
10
13
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27
30
33
36
39
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57
60
0
3
6
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50
53
56
59
62
2
5
8
11
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29
32
35
38
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50
4
7
10
13
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19
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25
28
31
34
37
40
43
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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
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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.) 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.
6
16
9
19
29
39
49
2
12
22
32
42
52
62
9
5
15
25
35
45
55
2
12
22
32
42
61
8
18
28
38
48
58
5
15
25
35
45
55
2
1
11
21
31
41
51
61
8
18
28
38
48
58
5
15
25
35
57
4
14
24
34
44
54
1
11
21
31
41
51
61
8
18
28
38
48
58
60
7
17
27
37
47
57
4
14
24
34
44
54
1
11
21
31
41
51
61
8
18
28
53
0
10
20
30
40
50
60
7
17
27
37
47
57
4
14
24
34
44
54
1
11
21
31
41
51
3
13
23
33
43
53
0
10
20
30
40
50
60
7
17
27
37
47
57
4
14
24
34
44
54
1
11
21
26
36
46
56
3
13
23
33
43
53
0
10
20
30
40
50
60
7
17
27
37
47
57
4
14
24
59
6
16
26
36
46
56
3
13
23
33
43
53
0
10
20
30
40
50
60
7
17
27
19
29
39
49
59
6
16
26
36
46
56
3
13
23
33
43
53
0
10
20
52
62
9
19
29
39
49
59
6
16
26
36
46
56
3
13
23
12
22
32
42
52
62
9
19
29
39
49
59
6
16
45
55
2
12
22
32
42
52
62
9
19
5
15
25
35
45
55
2
12
38
48
58
5
15
61
8
