There are many conceivable ways to map 82edo 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.
Diatonic
You can use the b val instead, but this is barely distinguishable from a circulating system of 7edo and only covers about 2/3rds of the notes due to the size of the edo.
62
74
73
3
15
27
39
72
2
14
26
38
50
62
74
1
13
25
37
49
61
73
3
15
27
39
0
12
24
36
48
60
72
2
14
26
38
50
62
74
11
23
35
47
59
71
1
13
25
37
49
61
73
3
15
27
39
10
22
34
46
58
70
0
12
24
36
48
60
72
2
14
26
38
50
62
74
21
33
45
57
69
81
11
23
35
47
59
71
1
13
25
37
49
61
73
3
15
27
39
20
32
44
56
68
80
10
22
34
46
58
70
0
12
24
36
48
60
72
2
14
26
38
50
62
74
43
55
67
79
9
21
33
45
57
69
81
11
23
35
47
59
71
1
13
25
37
49
61
73
3
15
27
39
78
8
20
32
44
56
68
80
10
22
34
46
58
70
0
12
24
36
48
60
72
2
14
26
38
50
43
55
67
79
9
21
33
45
57
69
81
11
23
35
47
59
71
1
13
25
37
49
61
78
8
20
32
44
56
68
80
10
22
34
46
58
70
0
12
24
36
48
60
43
55
67
79
9
21
33
45
57
69
81
11
23
35
47
59
71
78
8
20
32
44
56
68
80
10
22
34
46
58
70
43
55
67
79
9
21
33
45
57
69
81
78
8
20
32
44
56
68
80
43
55
67
79
9
78
8
There is an alternate diatonic scale that makes 5-limit chords easy to play, but it has a slight octave stretch. Since that means all notes are available in at least some of the octaves, this may actually be advantageous.
72
3
81
12
25
38
51
77
8
21
34
47
60
73
4
4
17
30
43
56
69
0
13
26
39
52
0
13
26
39
52
65
78
9
22
35
48
61
74
5
9
22
35
48
61
74
5
18
31
44
57
70
1
14
27
40
53
5
18
31
44
57
70
1
14
27
40
53
66
79
10
23
36
49
62
75
6
14
27
40
53
66
79
10
23
36
49
62
75
6
19
32
45
58
71
2
15
28
41
54
10
23
36
49
62
75
6
19
32
45
58
71
2
15
28
41
54
67
80
11
24
37
50
63
76
7
32
45
58
71
2
15
28
41
54
67
80
11
24
37
50
63
76
7
20
33
46
59
72
3
16
29
42
55
67
80
11
24
37
50
63
76
7
20
33
46
59
72
3
16
29
42
55
68
81
12
25
38
51
64
33
46
59
72
3
16
29
42
55
68
81
12
25
38
51
64
77
8
21
34
47
60
73
68
81
12
25
38
51
64
77
8
21
34
47
60
73
4
17
30
43
56
69
34
47
60
73
4
17
30
43
56
69
0
13
26
39
52
65
78
69
0
13
26
39
52
65
78
9
22
35
48
61
74
35
48
61
74
5
18
31
44
57
70
1
70
1
14
27
40
53
66
79
36
49
62
75
6
71
2
Bischismic
The Bischismic mapping can cover the whole gamut, although it needs to be expanded from 2L 8s to 10L 2s to do so.
25
32
38
45
52
59
66
44
51
58
65
72
79
4
11
57
64
71
78
3
10
17
24
31
38
45
63
70
77
2
9
16
23
30
37
44
51
58
65
72
76
1
8
15
22
29
36
43
50
57
64
71
78
3
10
17
24
0
7
14
21
28
35
42
49
56
63
70
77
2
9
16
23
30
37
44
51
13
20
27
34
41
48
55
62
69
76
1
8
15
22
29
36
43
50
57
64
71
78
3
19
26
33
40
47
54
61
68
75
0
7
14
21
28
35
42
49
56
63
70
77
2
9
16
23
30
39
46
53
60
67
74
81
6
13
20
27
34
41
48
55
62
69
76
1
8
15
22
29
36
43
50
57
64
66
73
80
5
12
19
26
33
40
47
54
61
68
75
0
7
14
21
28
35
42
49
56
63
70
77
18
25
32
39
46
53
60
67
74
81
6
13
20
27
34
41
48
55
62
69
76
1
8
45
52
59
66
73
80
5
12
19
26
33
40
47
54
61
68
75
0
7
14
79
4
11
18
25
32
39
46
53
60
67
74
81
6
13
20
27
24
31
38
45
52
59
66
73
80
5
12
19
26
33
58
65
72
79
4
11
18
25
32
39
46
3
10
17
24
31
38
45
52
37
44
51
58
65
64
71
67
74
73
80
5
12
19
72
79
4
11
18
25
32
39
78
3
10
17
24
31
38
45
52
59
66
77
2
9
16
23
30
37
44
51
58
65
72
79
4
1
8
15
22
29
36
43
50
57
64
71
78
3
10
17
24
31
0
7
14
21
28
35
42
49
56
63
70
77
2
9
16
23
30
37
44
51
6
13
20
27
34
41
48
55
62
69
76
1
8
15
22
29
36
43
50
57
64
71
78
5
12
19
26
33
40
47
54
61
68
75
0
7
14
21
28
35
42
49
56
63
70
77
2
9
16
18
25
32
39
46
53
60
67
74
81
6
13
20
27
34
41
48
55
62
69
76
1
8
15
22
29
36
43
38
45
52
59
66
73
80
5
12
19
26
33
40
47
54
61
68
75
0
7
14
21
28
35
42
49
65
72
79
4
11
18
25
32
39
46
53
60
67
74
81
6
13
20
27
34
41
48
55
3
10
17
24
31
38
45
52
59
66
73
80
5
12
19
26
33
40
47
54
30
37
44
51
58
65
72
79
4
11
18
25
32
39
46
53
60
50
57
64
71
78
3
10
17
24
31
38
45
52
59
77
2
9
16
23
30
37
44
51
58
65
15
22
29
36
43
50
57
64
42
49
56
63
70
62
69
Magic (Divination/Soothsaying) related Lumatone mappings
Bryan Deister has demonstrated a 8L 6s mapping of 82edo. Being even 82edo supports a semioctave period, with the diagassormisma (3042/3025) being tempered out in the patent val or the kalisma (9801/9800) being tempered out in the 82e val; this enables it to use the (somewhat sharp) septimal major third ~9/7 (as 30\82) as a generator (which would be contorted down to 41edo with a whole octave period), in a temperament like Soothsaying or Divination, but using the septimal major third as a generator instead of the classic major third ~5/4. (Since 82edo also supports actual Soothsaying in its patent val and actual Divination in its 82e val, it is also possible to use generator 26\82, the somewhat flat ~5/4, although the resulting 6L 4s scale is a bit more tricky to play using this layout.) The range is about 2¾ octaves with no missed notes, and the octaves slant down.
4
12
7
15
23
31
39
2
10
18
26
34
42
50
58
5
13
21
29
37
45
53
61
69
77
3
0
8
16
24
32
40
48
56
64
72
80
6
14
22
3
11
19
27
35
43
51
59
67
75
1
9
17
25
33
41
49
80
6
14
22
30
38
46
54
62
70
78
4
12
20
28
36
44
52
60
68
1
9
17
25
33
41
49
57
65
73
81
7
15
23
31
39
47
55
63
71
79
5
13
78
4
12
20
28
36
44
52
60
68
76
2
10
18
26
34
42
50
58
66
74
0
8
16
24
32
7
15
23
31
39
47
55
63
71
79
5
13
21
29
37
45
53
61
69
77
3
11
19
27
35
43
51
59
26
34
42
50
58
66
74
0
8
16
24
32
40
48
56
64
72
80
6
14
22
30
38
46
54
62
53
61
69
77
3
11
19
27
35
43
51
59
67
75
1
9
17
25
33
41
49
57
65
72
80
6
14
22
30
38
46
54
62
70
78
4
12
20
28
36
44
52
60
17
25
33
41
49
57
65
73
81
7
15
23
31
39
47
55
63
36
44
52
60
68
76
2
10
18
26
34
42
50
58
63
71
79
5
13
21
29
37
45
53
61
0
8
16
24
32
40
48
56
27
35
43
51
59
46
54
Buzurgic/Dhanvantaric
To maximise your range, you can use the 8L 2s mapping generated by 9/82 and a half octave period (achieving a range slightly over three octaves, with a moderate upwards slant), but this is not particularly efficient at putting the best note combinations close to one-another. Despite not being designed with any temperament in mind, this mapping supports Buzurgic/Dhanvantaric temperament, because the rightward generator is 9\82, and 82edo tempers out the buzurgisma/dhanvantarisma (169/168), which causes this generator to function as both ~14/13 and ~13/12; two of them make a somewhat sharp septimal minor third (~7/6). An article dedicated to this temperament is not currently available, but an article about Buzurgismic chords is available. The choice of whether to use 4\82 (upwards generator) or 5\82 (down-right generator) as the second generator, or to use no second generator and downgrade the temperament to rank-2, depends upon what one wants to do with the 11th harmonic. The patent val of 82edo maps a mildly sharp al-Farabi quarter tone (~33/32) to the upwards generator 4\82; four of these make a slightly sharp ~8/7. Two rightward generators plus one or two upwards generators yield the classic minor and major thirds (~6/5 and ~5/4), respectively; four rightward generators plus three upwards generators yield the near just perfect fifth (~3/2). The 82e val maps a rather flat pentacircle minor second (~22/21) to the down-right generator 5\82; four of them make a slightly flat tridecimal minor third (~13/11, made fairly accurate by cancellation of the errors in the wart-modified 11th harmonic and the patent 13th harmonic, and which would otherwise have to be mapped as ~19/16). However, use of the down-right generator in combination with the rightwards generator to produce common chords tends to require going rightward extra steps and then subtract down-right generators to get the effect of the upwards generator, making this a less attractive choice of secondary generator.
79
6
2
11
20
29
38
80
7
16
25
34
43
52
61
3
12
21
30
39
48
57
66
75
2
11
81
8
17
26
35
44
53
62
71
80
7
16
25
34
4
13
22
31
40
49
58
67
76
3
12
21
30
39
48
57
66
0
9
18
27
36
45
54
63
72
81
8
17
26
35
44
53
62
71
80
7
5
14
23
32
41
50
59
68
77
4
13
22
31
40
49
58
67
76
3
12
21
30
39
1
10
19
28
37
46
55
64
73
0
9
18
27
36
45
54
63
72
81
8
17
26
35
44
53
62
15
24
33
42
51
60
69
78
5
14
23
32
41
50
59
68
77
4
13
22
31
40
49
58
67
76
3
12
38
47
56
65
74
1
10
19
28
37
46
55
64
73
0
9
18
27
36
45
54
63
72
81
8
17
70
79
6
15
24
33
42
51
60
69
78
5
14
23
32
41
50
59
68
77
4
13
22
11
20
29
38
47
56
65
74
1
10
19
28
37
46
55
64
73
0
9
18
43
52
61
70
79
6
15
24
33
42
51
60
69
78
5
14
23
66
75
2
11
20
29
38
47
56
65
74
1
10
19
16
25
34
43
52
61
70
79
6
15
24
39
48
57
66
75
2
11
20
71
80
7
16
25
12
21
