There are many conceivable ways to map 81edo onto the onto the Lumatone keyboard. Only one, however, agrees with the Standard Lumatone mapping for Pythagorean. (Note that the 81b sharp fifth is shared with 27edo, thereby making three mutually exclusive rings of fifths.)
Diatonic
The patent val diatonic mapping would be a perfectly respectable Meantone mapping on a hypothetical XL-sized Lumatone having at least 405 keys in the space of five octaves.
75
7
2
15
28
41
54
78
10
23
36
49
62
75
7
5
18
31
44
57
70
2
15
28
41
54
0
13
26
39
52
65
78
10
23
36
49
62
75
7
8
21
34
47
60
73
5
18
31
44
57
70
2
15
28
41
54
3
16
29
42
55
68
0
13
26
39
52
65
78
10
23
36
49
62
75
7
11
24
37
50
63
76
8
21
34
47
60
73
5
18
31
44
57
70
2
15
28
41
54
6
19
32
45
58
71
3
16
29
42
55
68
0
13
26
39
52
65
78
10
23
36
49
62
75
7
27
40
53
66
79
11
24
37
50
63
76
8
21
34
47
60
73
5
18
31
44
57
70
2
15
28
41
54
61
74
6
19
32
45
58
71
3
16
29
42
55
68
0
13
26
39
52
65
78
10
23
36
49
62
27
40
53
66
79
11
24
37
50
63
76
8
21
34
47
60
73
5
18
31
44
57
70
61
74
6
19
32
45
58
71
3
16
29
42
55
68
0
13
26
39
52
65
27
40
53
66
79
11
24
37
50
63
76
8
21
34
47
60
73
61
74
6
19
32
45
58
71
3
16
29
42
55
68
27
40
53
66
79
11
24
37
50
63
76
61
74
6
19
32
45
58
71
27
40
53
66
79
61
74
Meantone-related rank-3 mapping
Bryan Deister has demonstrated the m-chromatic (7L 5s with 8:5 step ratio) mapping for 81edo in ''microtonal improvisation in 81edo (2025). The rightward generator 8\81 functions as ~15/14 and ~16/15; six of them make the alternate sharp fifth. The down-right generator 5\81 functions as ~23/22 and ~24/23; two of them make an Alpharabian tendoneutral second (~12/11); four of them make the near-just octave-reduced 19th harmonic ~19/16; eleven of them make a near-just classic minor sixth ~8/5. The patent fifth 47\81 is four rightward generators plus three down-right generators. The range is just over three octaves, with no missed notes, and the octaves slant down moderately.
76
3
0
8
16
24
32
78
5
13
21
29
37
45
53
2
10
18
26
34
42
50
58
66
74
1
80
7
15
23
31
39
47
55
63
71
79
6
14
22
4
12
20
28
36
44
52
60
68
76
3
11
19
27
35
43
51
1
9
17
25
33
41
49
57
65
73
0
8
16
24
32
40
48
56
64
72
6
14
22
30
38
46
54
62
70
78
5
13
21
29
37
45
53
61
69
77
4
12
20
3
11
19
27
35
43
51
59
67
75
2
10
18
26
34
42
50
58
66
74
1
9
17
25
33
41
16
24
32
40
48
56
64
72
80
7
15
23
31
39
47
55
63
71
79
6
14
22
30
38
46
54
62
70
37
45
53
61
69
77
4
12
20
28
36
44
52
60
68
76
3
11
19
27
35
43
51
59
67
75
66
74
1
9
17
25
33
41
49
57
65
73
0
8
16
24
32
40
48
56
64
72
80
6
14
22
30
38
46
54
62
70
78
5
13
21
29
37
45
53
61
69
77
35
43
51
59
67
75
2
10
18
26
34
42
50
58
66
74
1
56
64
72
80
7
15
23
31
39
47
55
63
71
79
4
12
20
28
36
44
52
60
68
76
3
25
33
41
49
57
65
73
0
54
62
70
78
5
75
2
