You can use either the second- best alternate fifth, but it is extremely sharp, so much so that "major seconds" become 8/7 instead of 9/8.
24
38
25
39
53
67
9
12
26
40
54
68
10
24
38
13
27
41
55
69
11
25
39
53
67
9
0
14
28
42
56
70
12
26
40
54
68
10
24
38
1
15
29
43
57
71
13
27
41
55
69
11
25
39
53
67
9
60
2
16
30
44
58
0
14
28
42
56
70
12
26
40
54
68
10
24
38
61
3
17
31
45
59
1
15
29
43
57
71
13
27
41
55
69
11
25
39
53
67
9
48
62
4
18
32
46
60
2
16
30
44
58
0
14
28
42
56
70
12
26
40
54
68
10
24
38
63
5
19
33
47
61
3
17
31
45
59
1
15
29
43
57
71
13
27
41
55
69
11
25
39
53
67
9
20
34
48
62
4
18
32
46
60
2
16
30
44
58
0
14
28
42
56
70
12
26
40
54
68
10
63
5
19
33
47
61
3
17
31
45
59
1
15
29
43
57
71
13
27
41
55
69
11
20
34
48
62
4
18
32
46
60
2
16
30
44
58
0
14
28
42
56
70
63
5
19
33
47
61
3
17
31
45
59
1
15
29
43
57
71
20
34
48
62
4
18
32
46
60
2
16
30
44
58
63
5
19
33
47
61
3
17
31
45
59
20
34
48
62
4
18
32
46
63
5
19
33
47
20
34
or the third-best:
48
58
59
69
7
17
27
60
70
8
18
28
38
48
58
71
9
19
29
39
49
59
69
7
17
27
0
10
20
30
40
50
60
70
8
18
28
38
48
58
11
21
31
41
51
61
71
9
19
29
39
49
59
69
7
17
27
12
22
32
42
52
62
0
10
20
30
40
50
60
70
8
18
28
38
48
58
23
33
43
53
63
1
11
21
31
41
51
61
71
9
19
29
39
49
59
69
7
17
27
24
34
44
54
64
2
12
22
32
42
52
62
0
10
20
30
40
50
60
70
8
18
28
38
48
58
45
55
65
3
13
23
33
43
53
63
1
11
21
31
41
51
61
71
9
19
29
39
49
59
69
7
17
27
4
14
24
34
44
54
64
2
12
22
32
42
52
62
0
10
20
30
40
50
60
70
8
18
28
38
45
55
65
3
13
23
33
43
53
63
1
11
21
31
41
51
61
71
9
19
29
39
49
4
14
24
34
44
54
64
2
12
22
32
42
52
62
0
10
20
30
40
50
45
55
65
3
13
23
33
43
53
63
1
11
21
31
41
51
61
4
14
24
34
44
54
64
2
12
22
32
42
52
62
45
55
65
3
13
23
33
43
53
63
1
4
14
24
34
44
54
64
2
45
55
65
3
13
4
14
but these do not cover the full gamut or make the best-tuned intervals easily accessible.
Miracle
Instead, the most efficient way to put the best-tuned intervals near each other while allowing access to all of them is the Miracle mapping, although this does reduce the range to a little over three octaves.
30
37
39
46
53
60
67
41
48
55
62
69
4
11
18
50
57
64
71
6
13
20
27
34
41
48
52
59
66
1
8
15
22
29
36
43
50
57
64
71
61
68
3
10
17
24
31
38
45
52
59
66
1
8
15
22
29
63
70
5
12
19
26
33
40
47
54
61
68
3
10
17
24
31
38
45
52
0
7
14
21
28
35
42
49
56
63
70
5
12
19
26
33
40
47
54
61
68
3
10
2
9
16
23
30
37
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51
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65
0
7
14
21
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35
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49
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63
70
5
12
19
26
33
18
25
32
39
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2
9
16
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0
7
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41
48
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4
11
18
25
32
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53
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67
2
9
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30
37
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0
71
6
13
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41
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69
4
11
18
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60
67
2
9
22
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36
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57
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71
6
13
20
27
34
41
48
55
62
69
4
11
52
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66
1
8
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36
43
50
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71
6
13
20
3
10
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1
8
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40
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54
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68
3
10
17
24
31
56
63
70
5
12
19
26
33
14
21
28
35
42
37
44
Semimiracle
Slicing the period in half to produce semimiracle makes ratios of 13 and 17 just as easy to play as the 11-limit ones and also keeps octaves closer to horizontal.
45
52
53
60
67
2
9
54
61
68
3
10
17
24
31
62
69
4
11
18
25
32
39
46
53
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63
70
5
12
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40
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54
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68
3
10
71
6
13
20
27
34
41
48
55
62
69
4
11
18
25
32
39
0
7
14
21
28
35
42
49
56
63
70
5
12
19
26
33
40
47
54
61
8
15
22
29
36
43
50
57
64
71
6
13
20
27
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41
48
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69
4
11
18
9
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65
0
7
14
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63
70
5
12
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40
24
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1
8
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6
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46
53
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2
9
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0
7
14
21
28
35
42
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63
70
5
3
10
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31
38
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66
1
8
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36
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50
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64
71
6
13
25
32
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60
67
2
9
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0
7
14
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68
3
10
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66
1
8
15
22
4
11
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25
32
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60
67
2
9
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3
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32
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40
34
41
Harry + Marvolo (Marvel) + Miracle
Bryan Deister has demonstrated a mapping of 72edo as nine rings of 8edo going right, offset so as to also produce the scale 11L 9s (4/1-equivalent), in microtonal improvisation in 72edo (2025). While this mapping works to get as many notes as possible of 72edo into 280 keys (yielding a range of over 3⅔ octaves, it was designed to work to support specific temperaments. The close approximations of ~6/5 as 19\72 and ~5/4 as 23\72 (if using note 0 as the root) are next to each other and not far from the root right and somewhat down. From note 0, moving right and somewhat down between the note 1 and note 6 keys to reach 14\72 yields a highly accurate ~8/7, which corresponds to two generators (~15/14) of Miracle. (It is also the generator of Guiron, Mothra, and Slendric, but 72edo is contorted in those temperaments). Repeating this move twice more yields the highly accurate ~3/2 as 42\72; repeating it once more after that to reach 56\72 yields an almost-just ~12/7; from there, moving one key to the right yields the primary generator of Marvel temperament, ~15/8, as 65\72. The down-right generator 5\72 (20/19 ~ 21/20 ~ 22/21) matches Harry and Marvolo.
0
9
5
14
23
32
41
1
10
19
28
37
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55
64
6
15
24
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69
6
15
24
2
11
20
29
38
47
56
65
2
11
20
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38
47
7
16
25
34
43
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70
7
16
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34
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52
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70
7
3
12
21
30
39
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66
3
12
21
30
39
48
57
66
3
12
21
30
8
17
26
35
44
53
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71
8
17
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53
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8
17
26
35
44
53
62
4
13
22
31
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49
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67
4
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4
13
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4
13
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0
9
18
27
36
45
54
63
0
9
18
27
36
45
54
63
0
9
18
27
36
45
41
50
59
68
5
14
23
32
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50
59
68
5
14
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68
5
14
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41
50
1
10
19
28
37
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55
64
1
10
19
28
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55
64
1
10
19
28
37
46
55
24
33
42
51
60
69
6
15
24
33
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51
60
69
6
15
24
33
42
51
56
65
2
11
20
29
38
47
56
65
2
11
20
29
38
47
56
7
16
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61
70
7
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66
3
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21
30
39
48
57
62
71
8
17
26
35
44
53
22
31
40
49
58
45
54
Ennealimmal (currently untested)
This mapping uses ennealimmal temperament; it maps one axis to 1\9 and one axis to ~21/20, an ennealimmal generator.
0
8
3
11
19
27
35
70
6
14
22
30
38
46
54
1
9
17
25
33
41
49
57
65
1
9
68
4
12
20
28
36
44
52
60
68
4
12
20
28
71
7
15
23
31
39
47
55
63
71
7
15
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31
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55
66
2
10
18
26
34
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50
58
66
2
10
18
26
34
42
50
58
66
2
69
5
13
21
29
37
45
53
61
69
5
13
21
29
37
45
53
61
69
5
13
21
29
64
0
8
16
24
32
40
48
56
64
0
8
16
24
32
40
48
56
64
0
8
16
24
32
40
48
3
11
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27
35
43
51
59
67
3
11
19
27
35
43
51
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67
3
11
19
27
35
43
51
59
67
3
22
30
38
46
54
62
70
6
14
22
30
38
46
54
62
70
6
14
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30
38
46
54
62
70
6
49
57
65
1
9
17
25
33
41
49
57
65
1
9
17
25
33
41
49
57
65
1
9
68
4
12
20
28
36
44
52
60
68
4
12
20
28
36
44
52
60
68
4
23
31
39
47
55
63
71
7
15
23
31
39
47
55
63
71
7
42
50
58
66
2
10
18
26
34
42
50
58
66
2
69
5
13
21
29
37
45
53
61
69
5
16
24
32
40
48
56
64
0
43
51
59
67
3
62
70
Catakleismic-related rank-3 (Harmonic table)
Bryan Deister has demonstrated an ultra-compressed mapping for 72edo in 72edo groove (2026). The rightward generator 42\72 is the near-just perfect fifth ~3/2; the upward generator 19\72 is the near-just classic minor third ~6/5 (as in catakleismic temperament); this makes the down-right generator 23/72 the near-just classic major third ~5/4 (being derived from the other generators, this does not expand the temperament beyond rank-3). That makes this mapping sort of a harmonic table mapping, although different from that for 12edo since neither the classic major third nor the classic minor third divide 72edo evenly, thus causing comma pumping if either of these is stacked with itself. With such a compressed layout, most notes are not present in any one octave, but all notes are present in some octave, even within the limited part of the Lumatone that was actually mapped in the demonstration video; the synthesized sound used in the demonstration video also ensures that all of the notes are audible, even pushing the brain to do automatic octave-reduction.
