There are many conceivable ways to map 84edo onto the onto the Lumatone keyboard. However, it has 7 mutually-exclusive rings of fifths, so the Standard Lumatone mapping for Pythagorean is not one of them. Due to the edos size, it would not cover the whole gamut even if it was. Neither the second, third, nor fourth-best fifths work either, and the maviloid scale generated by 47/84 is even flatter than 25edo.
Instead, the most efficient layout that allows access to all notes is the Sensei mapping, although this does reduce the range to a little over three octaves.
2
11
6
15
24
33
42
1
10
19
28
37
46
55
64
5
14
23
32
41
50
59
68
77
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11
0
9
18
27
36
45
54
63
72
81
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15
24
33
4
13
22
31
40
49
58
67
76
1
10
19
28
37
46
55
64
83
8
17
26
35
44
53
62
71
80
5
14
23
32
41
50
59
68
77
2
3
12
21
30
39
48
57
66
75
0
9
18
27
36
45
54
63
72
81
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15
24
33
82
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16
25
34
43
52
61
70
79
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13
22
31
40
49
58
67
76
1
10
19
28
37
46
55
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20
29
38
47
56
65
74
83
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17
26
35
44
53
62
71
80
5
14
23
32
41
50
59
68
77
2
33
42
51
60
69
78
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12
21
30
39
48
57
66
75
0
9
18
27
36
45
54
63
72
81
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64
73
82
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16
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34
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52
61
70
79
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31
40
49
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67
76
1
10
2
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38
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17
26
35
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71
80
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33
42
51
60
69
78
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30
39
48
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66
75
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9
55
64
73
82
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16
25
34
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61
70
79
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2
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20
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56
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24
33
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51
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78
3
55
64
73
82
7
77
2
Orwell
The Orwell mapping has a smaller range, but is closer to the optimal tuning for the temperament and makes it easier to play harmonics together.
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
1
0
8
16
24
32
40
48
56
64
72
80
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12
20
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11
19
27
35
43
51
59
67
75
83
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15
23
31
39
47
82
6
14
22
30
38
46
54
62
70
78
2
10
18
26
34
42
50
58
66
1
9
17
25
33
41
49
57
65
73
81
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13
21
29
37
45
53
61
69
77
1
9
80
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12
20
28
36
44
52
60
68
76
0
8
16
24
32
40
48
56
64
72
80
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12
20
28
7
15
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31
39
47
55
63
71
79
3
11
19
27
35
43
51
59
67
75
83
7
15
23
31
39
47
55
26
34
42
50
58
66
74
82
6
14
22
30
38
46
54
62
70
78
2
10
18
26
34
42
50
58
53
61
69
77
1
9
17
25
33
41
49
57
65
73
81
5
13
21
29
37
45
53
61
72
80
4
12
20
28
36
44
52
60
68
76
0
8
16
24
32
40
48
56
15
23
31
39
47
55
63
71
79
3
11
19
27
35
43
51
59
34
42
50
58
66
74
82
6
14
22
30
38
46
54
61
69
77
1
9
17
25
33
41
49
57
80
4
12
20
28
36
44
52
23
31
39
47
55
42
50
Diploid Marvel extension
Bryan Deister has demonstrated a 10L 4s (8:1 step ratio) mapping for 84edo in microtonal improvisation in 84edo (2025). The rightward generator 8\84 (shared with the Orwell mapping) functions as both ~15/14 and ~16/15, making this a Marvel temperament; two of these make a slightly flat septimal supermajor second (~8/7); four of these make a slightly flat Barbados third (~13/10). However, by itself this generator would produce a contorted mapping even with the semioctaveperiod implied by 10L 4s, so a second generator is required. The chroma of the scale (7\84, the upwards generator) is not very convenient as a secondary generator, and also produces a contorted mapping if used alone, so it makes sense to use the down-right generator 1\84 (the small step of the scale) as the secondary generator. This functions as a near-just version of the starling chroma (~126/125), but also functions as a narrow version of the syntonic chroma (~81/80), a slightly narrow version of the animist chroma (~105/104), and as a wide version of the buzurgismic/dhanvantarismic chroma (~169/168) or the mycunumic chroma (~196/195); two of these make a near-just septimal chroma (~64/63); and adding three of these to the aforementioned Barbados third (reached with the rightward generator) yields the very accurate fourth (~4/3) at 35\84 (shared with 12edo as 5\12). (Nevertheless, sheer distance may be a problem for people who do not have long fingers — a problem hard to avoid with large EDO sizes, that force octaves to be long to avoid missing notes.) Near-just versions of common intervals are reachable using both generators in combination: three rightward generators minus two down-right generators to get the classic major third ~6/5 at 22\84, and three of each generator to get the classic major third ~5/4 at 27\84. The range would be 2½ octaves with no missed notes if note for a missed note 36 in the highest semioctave; some notes are repeated for ease in vertical transitions; and the octaves are perfectly level.
