Lumatone mapping for 86edo

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There are many conceivable ways to map 86edo onto the onto the Lumatone keyboard. However, it has 2 mutually-exclusive rings of fifths, so the Standard Lumatone mapping for Pythagorean is not one of them. You can use the b val, but it is very sharp and will not cover all the notes due to the size of the edo.

Diatonic

20
36
23
39
55
71
1
10
26
42
58
74
4
20
36
13
29
45
61
77
7
23
39
55
71
1
0
16
32
48
64
80
10
26
42
58
74
4
20
36
3
19
35
51
67
83
13
29
45
61
77
7
23
39
55
71
1
76
6
22
38
54
70
0
16
32
48
64
80
10
26
42
58
74
4
20
36
79
9
25
41
57
73
3
19
35
51
67
83
13
29
45
61
77
7
23
39
55
71
1
66
82
12
28
44
60
76
6
22
38
54
70
0
16
32
48
64
80
10
26
42
58
74
4
20
36
85
15
31
47
63
79
9
25
41
57
73
3
19
35
51
67
83
13
29
45
61
77
7
23
39
55
71
1
34
50
66
82
12
28
44
60
76
6
22
38
54
70
0
16
32
48
64
80
10
26
42
58
74
4
85
15
31
47
63
79
9
25
41
57
73
3
19
35
51
67
83
13
29
45
61
77
7
34
50
66
82
12
28
44
60
76
6
22
38
54
70
0
16
32
48
64
80
85
15
31
47
63
79
9
25
41
57
73
3
19
35
51
67
83
34
50
66
82
12
28
44
60
76
6
22
38
54
70
85
15
31
47
63
79
9
25
41
57
73
34
50
66
82
12
28
44
60
85
15
31
47
63
34
50

Tesseract + Negri

Bryan Deister has demonstrated a 9L 1s mapping for 86edo in microtonal improvisation in 86edo (2025). The rightwards generator 9\86 is a slightly flat tridecimal supraminor second (~14\13), which is a quarter of the somewhat sharp perfect fourth (~4/3), as befits Tesseract temperament (28812/28561 is tempered out); unfortunately, the infill extension of Tesseract to include the 5th harmonic (as three of these generators) reaches the second-best approximation of it for 86 (86c val); this also puts this mapping on the spectrum for Negri temperament in the 5-limit, although not in the 7-limit, since 86edo does not temper ~8/7, ~7/6, and ~15/13 to the same interval (instead, it represents them all as distinct intervals). It is possible to reach all of the notes in each octave with sufficient stacking of only the rightward generator; but for convenience, it may be preferable to add as a second generator the upwards generator 4\86, a chromatic quarter-tone that functions primarily as the al-Farabi quarter tone ~33/32, but also ~30/29, ~31/30, and ~32/31. The range is just a bit over three octaves with no missed notes, and the octaves slope up substantially, hence the placement of the first note 0 in the lower left corner.

82
5
1
10
19
28
37
83
6
15
24
33
42
51
60
2
11
20
29
38
47
56
65
74
83
6
84
7
16
25
34
43
52
61
70
79
2
11
20
29
3
12
21
30
39
48
57
66
75
84
7
16
25
34
43
52
61
85
8
17
26
35
44
53
62
71
80
3
12
21
30
39
48
57
66
75
84
4
13
22
31
40
49
58
67
76
85
8
17
26
35
44
53
62
71
80
3
12
21
30
0
9
18
27
36
45
54
63
72
81
4
13
22
31
40
49
58
67
76
85
8
17
26
35
44
53
14
23
32
41
50
59
68
77
0
9
18
27
36
45
54
63
72
81
4
13
22
31
40
49
58
67
76
85
37
46
55
64
73
82
5
14
23
32
41
50
59
68
77
0
9
18
27
36
45
54
63
72
81
4
69
78
1
10
19
28
37
46
55
64
73
82
5
14
23
32
41
50
59
68
77
0
9
6
15
24
33
42
51
60
69
78
1
10
19
28
37
46
55
64
73
82
5
38
47
56
65
74
83
6
15
24
33
42
51
60
69
78
1
10
61
70
79
2
11
20
29
38
47
56
65
74
83
6
7
16
25
34
43
52
61
70
79
2
11
30
39
48
57
66
75
84
7
62
71
80
3
12
85
8


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