Lumatone mapping for magic

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Note the following equivalences in magic, meaning that a key labeled with one of the ratios also represents others:

  • 16/15 ~ 15/14 ~ 14/13
  • 13/12 ~ 12/11
  • 11/10 ~ 10/9
  • 8/7 ~ 15/13
  • 11/9 ~ 16/13
  • 11/8 ~ 18/13
  • 13/9 ~ 16/11
  • 13/8 ~ 18/11
  • 26/15 ~ 7/4
  • 9/5 ~ 20/11
  • 11/6 ~ 24/13
  • 13/7 ~ 28/15 ~ 15/8

And the letter c refers to the chroma, representing 25/24 ~ 27/26 ~ 28/27 ~ 33/32 ~ 36/35 ~ 128/125, but not 26/25.

Compressed

This mapping covers 10 complete octaves. The magic[4] MOS has a zigzag pattern with 60 degree angles.

Lumatone.svg
13/9
9/5
13/7
7/6
13/9
9/5
9/8
-c
6/5
3/2
13/7
7/6
13/9
9/5
9/8
5/4
14/9
-c
6/5
3/2
13/7
7/6
13/9
9/5
9/8
7/5
9/7
8/5
1/1
5/4
14/9
-c
6/5
3/2
13/7
7/6
13/9
9/5
9/8
7/5
5/3
c
9/7
8/5
1/1
5/4
14/9
-c
6/5
3/2
13/7
7/6
13/9
9/5
9/8
7/5
7/4
12/7
14/13
4/3
5/3
c
9/7
8/5
1/1
5/4
14/9
-c
6/5
3/2
13/7
7/6
13/9
9/5
9/8
7/5
7/4
10/9
11/8
12/7
14/13
4/3
5/3
c
9/7
8/5
1/1
5/4
14/9
-c
6/5
3/2
13/7
7/6
13/9
9/5
9/8
7/5
7/4
12/11
8/7
10/7
16/9
10/9
11/8
12/7
14/13
4/3
5/3
c
9/7
8/5
1/1
5/4
14/9
-c
6/5
3/2
13/7
7/6
13/9
9/5
9/8
7/5
7/4
12/11
11/6
8/7
10/7
16/9
10/9
11/8
12/7
14/13
4/3
5/3
c
9/7
8/5
1/1
5/4
14/9
-c
6/5
3/2
13/7
7/6
13/9
9/5
9/8
7/5
7/4
12/11
15/11
11/6
8/7
10/7
16/9
10/9
11/8
12/7
14/13
4/3
5/3
c
9/7
8/5
1/1
5/4
14/9
-c
6/5
3/2
13/7
7/6
13/9
9/5
9/8
7/5
7/4
8/7
10/7
16/9
10/9
11/8
12/7
14/13
4/3
5/3
c
9/7
8/5
1/1
5/4
14/9
-c
6/5
3/2
13/7
7/6
13/9
9/5
9/8
8/7
10/7
16/9
10/9
11/8
12/7
14/13
4/3
5/3
c
9/7
8/5
1/1
5/4
14/9
-c
6/5
3/2
13/7
7/6
10/7
16/9
10/9
11/8
12/7
14/13
4/3
5/3
c
9/7
8/5
1/1
5/4
14/9
-c
6/5
3/2
10/7
16/9
10/9
11/8
12/7
14/13
4/3
5/3
c
9/7
8/5
1/1
5/4
14/9
16/9
10/9
11/8
12/7
14/13
4/3
5/3
c
9/7
8/5
1/1
16/9
10/9
11/8
12/7
14/13
4/3
5/3
c
10/9
11/8
12/7
14/13
4/3
10/9
11/8

Semi-compressed

This mapping covers 8 complete octaves. The magic[7] MOS has a zigzag pattern with 60 degree angles.

Lumatone.svg
13/10
13/8
15/11
27/16
21/20
13/10
13/8
9/8
7/5
7/4
12/11
15/11
27/16
21/20
13/10
7/6
13/9
9/5
9/8
7/5
7/4
12/11
15/11
27/16
21/20
13/10
-c
6/5
3/2
13/7
7/6
13/9
9/5
9/8
7/5
7/4
12/11
15/11
27/16
21/20
1/1
5/4
14/9
-c
6/5
3/2
13/7
7/6
13/9
9/5
9/8
7/5
7/4
12/11
15/11
27/16
21/20
5/3
c
9/7
8/5
1/1
5/4
14/9
-c
6/5
3/2
13/7
7/6
13/9
9/5
9/8
7/5
7/4
12/11
15/11
27/16
12/7
14/13
4/3
5/3
c
9/7
8/5
1/1
5/4
14/9
-c
6/5
3/2
13/7
7/6
13/9
9/5
9/8
7/5
7/4
12/11
15/11
27/16
10/7
16/9
10/9
11/8
12/7
14/13
4/3
5/3
c
9/7
8/5
1/1
5/4
14/9
-c
6/5
3/2
13/7
7/6
13/9
9/5
9/8
7/5
7/4
12/11
15/11
11/6
8/7
10/7
16/9
10/9
11/8
12/7
14/13
4/3
5/3
c
9/7
8/5
1/1
5/4
14/9
-c
6/5
3/2
13/7
7/6
13/9
9/5
9/8
7/5
7/4
12/11
15/11
22/15
11/6
8/7
10/7
16/9
10/9
11/8
12/7
14/13
4/3
5/3
c
9/7
8/5
1/1
5/4
14/9
-c
6/5
3/2
13/7
7/6
13/9
9/5
9/8
7/5
22/15
11/6
8/7
10/7
16/9
10/9
11/8
12/7
14/13
4/3
5/3
c
9/7
8/5
1/1
5/4
14/9
-c
6/5
3/2
13/7
7/6
13/9
32/27
22/15
11/6
8/7
10/7
16/9
10/9
11/8
12/7
14/13
4/3
5/3
c
9/7
8/5
1/1
5/4
14/9
-c
6/5
32/27
22/15
11/6
8/7
10/7
16/9
10/9
11/8
12/7
14/13
4/3
5/3
c
9/7
8/5
1/1
5/4
40/21
32/27
22/15
11/6
8/7
10/7
16/9
10/9
11/8
12/7
14/13
4/3
5/3
c
40/21
32/27
22/15
11/6
8/7
10/7
16/9
10/9
11/8
12/7
14/13
20/13
40/21
32/27
22/15
11/6
8/7
10/7
16/9
20/13
40/21
32/27
22/15
11/6
11/9
20/13

Intermediate

This mapping covers 5 complete octaves. The magic[10] MOS has a zigzag pattern with 60 degree angles.

Lumatone.svg
11/8
10/7
5/3
12/7
16/9
11/6
40/21
-c
1/1
c
14/13
10/9
8/7
32/27
11/9
7/6
6/5
5/4
9/7
4/3
11/8
10/7
22/15
20/13
11/7
15/11
7/5
13/9
3/2
14/9
8/5
5/3
12/7
16/9
11/6
40/21
13/8
27/16
7/4
9/5
13/7
-c
1/1
c
14/13
10/9
8/7
32/27
11/9
21/20
12/11
9/8
7/6
6/5
5/4
9/7
4/3
11/8
10/7
22/15
20/13
11/7
14/11
13/10
15/11
7/5
13/9
3/2
14/9
8/5
5/3
12/7
16/9
11/6
40/21
13/8
27/16
7/4
9/5
13/7
-c
1/1
c
14/13
10/9
8/7
32/27
11/9
21/20
12/11
9/8
7/6
6/5
5/4
9/7
4/3
11/8
10/7
22/15
20/13
11/7
14/11
13/10
15/11
7/5
13/9
3/2
14/9
8/5
5/3
12/7
16/9
11/6
40/21
13/8
27/16
7/4
9/5
13/7
-c
1/1
c
14/13
10/9
8/7
32/27
11/9
21/20
12/11
9/8
7/6
6/5
5/4
9/7
4/3
11/8
10/7
22/15
20/13
11/7
14/11
13/10
15/11
7/5
13/9
3/2
14/9
8/5
5/3
12/7
16/9
11/6
40/21
13/8
27/16
7/4
9/5
13/7
-c
1/1
c
14/13
10/9
8/7
32/27
11/9
21/20
12/11
9/8
7/6
6/5
5/4
9/7
4/3
11/8
10/7
22/15
15/11
7/5
13/9
3/2
14/9
8/5
5/3
12/7
9/5
13/7
-c
1/1
c
7/6
6/5

Semi-expanded

There are only 3 complete octaves. The magic[13] MOS has a zigzag pattern with 60 degree angles.

Lumatone.svg
10/7
22/15
20/13
11/7
5/3
12/7
16/9
11/6
40/21
13/7
-c
1/1
c
14/13
10/9
8/7
32/27
11/9
12/11
9/8
7/6
6/5
5/4
9/7
4/3
11/8
10/7
22/15
20/13
11/7
14/11
13/10
15/11
7/5
13/9
3/2
14/9
8/5
5/3
12/7
16/9
11/6
40/21
13/8
27/16
7/4
9/5
13/7
-c
1/1
c
14/13
10/9
8/7
32/27
11/9
21/20
12/11
9/8
7/6
6/5
5/4
9/7
4/3
11/8
10/7
22/15
20/13
11/7
14/11
13/10
15/11
7/5
13/9
3/2
14/9
8/5
5/3
12/7
16/9
11/6
40/21
13/8
27/16
7/4
9/5
13/7
-c
1/1
c
14/13
10/9
8/7
32/27
11/9
21/20
12/11
9/8
7/6
6/5
5/4
9/7
4/3
11/8
10/7
22/15
20/13
11/7
14/11
13/10
15/11
7/5
13/9
3/2
14/9
8/5
5/3
12/7
16/9
11/6
13/8
27/16
7/4
9/5
13/7
-c
1/1
c
14/13
21/20
12/11
9/8
7/6
6/5
14/11
13/10
15/11
7/5

Expanded

There are only 2 complete octaves. The magic[16] MOS has a zigzag pattern with 60 degree angles.

Lumatone.svg
22/15
20/13
11/7
5/3
12/7
16/9
11/6
40/21
9/5
13/7
-c
1/1
c
14/13
10/9
8/7
32/27
11/9
21/20
12/11
9/8
7/6
6/5
5/4
9/7
4/3
11/8
10/7
22/15
20/13
11/7
14/11
13/10
15/11
7/5
13/9
3/2
14/9
8/5
5/3
12/7
16/9
11/6
40/21
13/8
27/16
7/4
9/5
13/7
-c
1/1
c
14/13
10/9
8/7
32/27
11/9
21/20
12/11
9/8
7/6
6/5
5/4
9/7
4/3
11/8
10/7
22/15
20/13
11/7
14/11
13/10
15/11
7/5
13/9
3/2
14/9
8/5
5/3
12/7
16/9
11/6
40/21
13/8
27/16
7/4
9/5
13/7
-c
1/1
c
14/13
10/9
21/20
12/11
9/8
7/6
6/5
5/4
14/11
13/10
15/11
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