Lumatone mapping for 72edo: Difference between revisions
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{{Lumatone mapping intro}} You can use either the second | {{Lumatone mapping intro}} | ||
== Diatonic == | |||
You can use either the second- best alternate fifth: | |||
{{Lumatone EDO mapping|n=72|start=24|xstep=14|ystep=-13}} | {{Lumatone EDO mapping|n=72|start=24|xstep=14|ystep=-13}} | ||
or the third-best: | |||
{{Lumatone EDO mapping|n=72|start=48|xstep=10|ystep=1}} | {{Lumatone EDO mapping|n=72|start=48|xstep=10|ystep=1}} | ||
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. | |||
{{Lumatone EDO mapping|n=72|start=30|xstep=7|ystep=2}} | {{Lumatone EDO mapping|n=72|start=30|xstep=7|ystep=2}} | ||
=== 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. | 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. | ||
{{Lumatone EDO mapping|n=72|start=45|xstep=7|ystep=1}} | {{Lumatone EDO mapping|n=72|start=45|xstep=7|ystep=1}} | ||
{{Navbox Lumatone}} | {{Navbox Lumatone}} | ||
Revision as of 15:30, 23 March 2025
There are many conceivable ways to map 72edo onto the onto the Lumatone keyboard. However, it has 6 mutually-exclusive rings of fifths, so the Standard Lumatone mapping for Pythagorean is not one of them.
Diatonic
You can use either the second- best alternate fifth:
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
44
51
58
65
0
7
14
21
28
35
42
49
56
63
70
5
12
19
26
33
18
25
32
39
46
53
60
67
2
9
16
23
30
37
44
51
58
65
0
7
14
21
28
35
42
49
56
63
41
48
55
62
69
4
11
18
25
32
39
46
53
60
67
2
9
16
23
30
37
44
51
58
65
0
71
6
13
20
27
34
41
48
55
62
69
4
11
18
25
32
39
46
53
60
67
2
9
22
29
36
43
50
57
64
71
6
13
20
27
34
41
48
55
62
69
4
11
52
59
66
1
8
15
22
29
36
43
50
57
64
71
6
13
20
3
10
17
24
31
38
45
52
59
66
1
8
15
22
33
40
47
54
61
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
60
63
70
5
12
19
26
33
40
47
54
61
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
34
41
48
55
62
69
4
11
18
9
16
23
30
37
44
51
58
65
0
7
14
21
28
35
42
49
56
63
70
5
12
19
26
33
40
24
31
38
45
52
59
66
1
8
15
22
29
36
43
50
57
64
71
6
13
20
27
34
41
48
55
62
69
46
53
60
67
2
9
16
23
30
37
44
51
58
65
0
7
14
21
28
35
42
49
56
63
70
5
3
10
17
24
31
38
45
52
59
66
1
8
15
22
29
36
43
50
57
64
71
6
13
25
32
39
46
53
60
67
2
9
16
23
30
37
44
51
58
65
0
7
14
54
61
68
3
10
17
24
31
38
45
52
59
66
1
8
15
22
4
11
18
25
32
39
46
53
60
67
2
9
16
23
33
40
47
54
61
68
3
10
17
24
31
55
62
69
4
11
18
25
32
12
19
26
33
40
34
41