Revision as of 04:43, 6 July 2026 by Lucius Chiaraviglio(talk | contribs)(→Supermajor: Add Bryan Deister's Aureus Pseudo-Meantone + Orwell-related rank-3 temperament + Semisept mapping)
Due to the size of the edo, this mapping does not cover all the notes. In addition, the best approximation to 5/4 is a pentuply-augmented sixth or hextuply-diminished unison, which is impossible to play with the root note of the scale.
8
22
13
27
41
55
69
4
18
32
46
60
74
8
22
9
23
37
51
65
79
13
27
41
55
69
0
14
28
42
56
70
4
18
32
46
60
74
8
22
5
19
33
47
61
75
9
23
37
51
65
79
13
27
41
55
69
76
10
24
38
52
66
0
14
28
42
56
70
4
18
32
46
60
74
8
22
1
15
29
43
57
71
5
19
33
47
61
75
9
23
37
51
65
79
13
27
41
55
69
72
6
20
34
48
62
76
10
24
38
52
66
0
14
28
42
56
70
4
18
32
46
60
74
8
22
11
25
39
53
67
1
15
29
43
57
71
5
19
33
47
61
75
9
23
37
51
65
79
13
27
41
55
69
44
58
72
6
20
34
48
62
76
10
24
38
52
66
0
14
28
42
56
70
4
18
32
46
60
74
11
25
39
53
67
1
15
29
43
57
71
5
19
33
47
61
75
9
23
37
51
65
79
44
58
72
6
20
34
48
62
76
10
24
38
52
66
0
14
28
42
56
70
11
25
39
53
67
1
15
29
43
57
71
5
19
33
47
61
75
44
58
72
6
20
34
48
62
76
10
24
38
52
66
11
25
39
53
67
1
15
29
43
57
71
44
58
72
6
20
34
48
62
11
25
39
53
67
44
58
Diaschismic
On the other hand, the diaschismic mapping can cover the whole gamut and make harmonics easy to play together, although it needs to be expanded from 2L 8s to 10L 2s to hit every single note.
29
36
41
48
55
62
69
46
53
60
67
74
1
8
15
58
65
72
79
6
13
20
27
34
41
48
63
70
77
4
11
18
25
32
39
46
53
60
67
74
75
2
9
16
23
30
37
44
51
58
65
72
79
6
13
20
27
0
7
14
21
28
35
42
49
56
63
70
77
4
11
18
25
32
39
46
53
12
19
26
33
40
47
54
61
68
75
2
9
16
23
30
37
44
51
58
65
72
79
6
17
24
31
38
45
52
59
66
73
0
7
14
21
28
35
42
49
56
63
70
77
4
11
18
25
32
36
43
50
57
64
71
78
5
12
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26
33
40
47
54
61
68
75
2
9
16
23
30
37
44
51
58
65
62
69
76
3
10
17
24
31
38
45
52
59
66
73
0
7
14
21
28
35
42
49
56
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70
77
15
22
29
36
43
50
57
64
71
78
5
12
19
26
33
40
47
54
61
68
75
2
9
41
48
55
62
69
76
3
10
17
24
31
38
45
52
59
66
73
0
7
14
74
1
8
15
22
29
36
43
50
57
64
71
78
5
12
19
26
20
27
34
41
48
55
62
69
76
3
10
17
24
31
53
60
67
74
1
8
15
22
29
36
43
79
6
13
20
27
34
41
48
32
39
46
53
60
58
65
71
78
76
3
10
17
24
74
1
8
15
22
29
36
43
79
6
13
20
27
34
41
48
55
62
69
77
4
11
18
25
32
39
46
53
60
67
74
1
8
2
9
16
23
30
37
44
51
58
65
72
79
6
13
20
27
34
0
7
14
21
28
35
42
49
56
63
70
77
4
11
18
25
32
39
46
53
5
12
19
26
33
40
47
54
61
68
75
2
9
16
23
30
37
44
51
58
65
72
79
3
10
17
24
31
38
45
52
59
66
73
0
7
14
21
28
35
42
49
56
63
70
77
4
11
18
15
22
29
36
43
50
57
64
71
78
5
12
19
26
33
40
47
54
61
68
75
2
9
16
23
30
37
44
34
41
48
55
62
69
76
3
10
17
24
31
38
45
52
59
66
73
0
7
14
21
28
35
42
49
60
67
74
1
8
15
22
29
36
43
50
57
64
71
78
5
12
19
26
33
40
47
54
79
6
13
20
27
34
41
48
55
62
69
76
3
10
17
24
31
38
45
52
25
32
39
46
53
60
67
74
1
8
15
22
29
36
43
50
57
44
51
58
65
72
79
6
13
20
27
34
41
48
55
70
77
4
11
18
25
32
39
46
53
60
9
16
23
30
37
44
51
58
35
42
49
56
63
54
61
Bidia
Slicing the period into quarters produces the Bidia mapping, which keeps octaves closer to horizontal and makes the well-tuned 19th harmonic easily accessible. The (rightward) generator 7\80 is the Bidia generator which functions as ~16/15, ~17/16, and ~18/17; two of these make a somewhat sharp ~9/8; if allowed to pass the quarter-octave, three of these make a near-just classic minor third ~6/5; and four of them make a slightly sharp undecimal major third ~14/11.
Bryan Deister has demonstrated this mapping (except shifted to put the first note 0 where the first note 6 is shown here, to avoid a missed first note 3) in microtonal improvisation in 80edo (2025). The range is about 2¾ octaves, and the octaves slope down very gently.
The 3L 8sSupermajor mapping covers the gamut with slightly greater range while keeping octaves near horizontal, but many of the other harmonics involve awkward vertical stretches.
The slightly sharp quasi-meantone ~19/17 as 13\80 (one key down-right) stacks to a mildly sharp classic major third ~5/4 (the aureusma 1445/1444 is tempered out), although by itself this generator does not make very well-space MOS scales. At the same time, as seen in Orwell temperament, a mildly sharp septimal minor third ~7/6 is an attractive generator for producing well-spaced MOS scales, but being 18\80 (one key right + one key down-right), it is not co-prime, thereby suffering contorsion. One way to get around the contorsion problem to use both generators to make a rank-3 temperament. Bryan Deister has used this mapping in 80edo improv (2026), with the Lumatone rotated so as to make progression by 13\80 approximately horizontal. Another way to get MOS scales with reasonable spacing is to take the octave complement of ~7/6 as ~12/7, which is 62\80, and then split it in half to get 31\80 (one key right + two keys down-right), which is the septendecimal subfourth ~17/13, which is the bright generator for an oneirotonic 5L 3s scale having a 13:5 step ratio; the downside of this rank-2 temperament is that many generator steps are needed to reach some common consonant intervals. Either way, the range is somewhat under 2½ complete octaves (which slope downwards rather severely, and have only a few repeated notes), with considerable partial octaves in the base and treble chopped off by the upper left and lower right corners, respectively.
