Lumatone mapping for 52edo: Difference between revisions

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m Wrong 5-limit extension. Dirt, not ultrapyth.
 
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{{Lumatone mapping intro}} You can use the b val, but it is extremely sharp, to the point where major seconds become 8/7 instead of 9/8.
{{Lumatone mapping intro}}
 
== Diatonic ==
You can use the b val, which produces [[Syntonic–diatonic_equivalence_continuum#Dirt|Dirt]], but the fifth is extremely sharp, to the point where major seconds become [[8/7]] instead of [[9/8]] and the best approximation to [[5/4]] is a doubly augmented 7th.
{{Lumatone EDO mapping|n=52|start=16|xstep=10|ystep=-9}}
{{Lumatone EDO mapping|n=52|start=16|xstep=10|ystep=-9}}


 
== Neutral thirds ==
The [[Lumatone mapping for neutral thirds scales|neutral thirds mapping]] is probably easier to navigate.
The [[Lumatone mapping for neutral thirds scales|neutral thirds mapping]] is probably easier to navigate.
{{Lumatone EDO mapping|n=52|start=43|xstep=7|ystep=1}}
{{Lumatone EDO mapping|n=52|start=43|xstep=7|ystep=1}}
== Pseudo-Pentacircle ==
[[Bryan Deister]] has used a layout for [[52edo]] in which the generator is 9\52, as ~[[9/8]] but mapped by direct approximation rather than as the version mapped by the patent val or by the 52b val, which means that it  has to be constituted as {{nowrap|(3♭ × 3♯) / 8}} to make use of the dual-fifth feature of 52edo. Two of these map to a ~[[14/11]] major third, as in [[Pentacircle clan|Pentacircle]] but for the direct approximation mapping of ~9/8. The upward generator is ~[[16/15]]. Octaves slant down and then wrap around, but the compass is 5 full octaves, with no missed notes, which is competitive with the Diatonic and Neutral Thirds layouts. This layout is demonstrated in [https://www.youtube.com/shorts/lNJCZz7EjL0 ''microtonal improvisation in 52edo''] (2025); in the video, some notes are cut off at the right edge due to the use of only 2 MIDI channels.
{{Lumatone EDO mapping|n=52|start=4|xstep=9|ystep=-5}}


{{Navbox Lumatone}}
{{Navbox Lumatone}}

Latest revision as of 12:43, 14 May 2025

There are many conceivable ways to map 52edo onto the onto the Lumatone keyboard. However, it has 2 mutually-exclusive rings of fifths, so the Standard Lumatone mapping for Pythagorean is not one of them.

Diatonic

You can use the b val, which produces Dirt, but the fifth is extremely sharp, to the point where major seconds become 8/7 instead of 9/8 and the best approximation to 5/4 is a doubly augmented 7th.

16
26
17
27
37
47
5
8
18
28
38
48
6
16
26
9
19
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39
49
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17
27
37
47
5
0
10
20
30
40
50
8
18
28
38
48
6
16
26
1
11
21
31
41
51
9
19
29
39
49
7
17
27
37
47
5
44
2
12
22
32
42
0
10
20
30
40
50
8
18
28
38
48
6
16
26
45
3
13
23
33
43
1
11
21
31
41
51
9
19
29
39
49
7
17
27
37
47
5
36
46
4
14
24
34
44
2
12
22
32
42
0
10
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50
8
18
28
38
48
6
16
26
47
5
15
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35
45
3
13
23
33
43
1
11
21
31
41
51
9
19
29
39
49
7
17
27
37
47
5
16
26
36
46
4
14
24
34
44
2
12
22
32
42
0
10
20
30
40
50
8
18
28
38
48
6
47
5
15
25
35
45
3
13
23
33
43
1
11
21
31
41
51
9
19
29
39
49
7
16
26
36
46
4
14
24
34
44
2
12
22
32
42
0
10
20
30
40
50
47
5
15
25
35
45
3
13
23
33
43
1
11
21
31
41
51
16
26
36
46
4
14
24
34
44
2
12
22
32
42
47
5
15
25
35
45
3
13
23
33
43
16
26
36
46
4
14
24
34
47
5
15
25
35
16
26

Neutral thirds

The neutral thirds mapping is probably easier to navigate.

43
50
51
6
13
20
27
0
7
14
21
28
35
42
49
8
15
22
29
36
43
50
5
12
19
26
9
16
23
30
37
44
51
6
13
20
27
34
41
48
17
24
31
38
45
0
7
14
21
28
35
42
49
4
11
18
25
18
25
32
39
46
1
8
15
22
29
36
43
50
5
12
19
26
33
40
47
26
33
40
47
2
9
16
23
30
37
44
51
6
13
20
27
34
41
48
3
10
17
24
27
34
41
48
3
10
17
24
31
38
45
0
7
14
21
28
35
42
49
4
11
18
25
32
39
46
42
49
4
11
18
25
32
39
46
1
8
15
22
29
36
43
50
5
12
19
26
33
40
47
2
9
16
23
12
19
26
33
40
47
2
9
16
23
30
37
44
51
6
13
20
27
34
41
48
3
10
17
24
31
41
48
3
10
17
24
31
38
45
0
7
14
21
28
35
42
49
4
11
18
25
32
39
11
18
25
32
39
46
1
8
15
22
29
36
43
50
5
12
19
26
33
40
40
47
2
9
16
23
30
37
44
51
6
13
20
27
34
41
48
10
17
24
31
38
45
0
7
14
21
28
35
42
49
39
46
1
8
15
22
29
36
43
50
5
9
16
23
30
37
44
51
6
38
45
0
7
14
8
15

Pseudo-Pentacircle

Bryan Deister has used a layout for 52edo in which the generator is 9\52, as ~9/8 but mapped by direct approximation rather than as the version mapped by the patent val or by the 52b val, which means that it has to be constituted as (3♭ × 3♯) / 8 to make use of the dual-fifth feature of 52edo. Two of these map to a ~14/11 major third, as in Pentacircle but for the direct approximation mapping of ~9/8. The upward generator is ~16/15. Octaves slant down and then wrap around, but the compass is 5 full octaves, with no missed notes, which is competitive with the Diatonic and Neutral Thirds layouts. This layout is demonstrated in microtonal improvisation in 52edo (2025); in the video, some notes are cut off at the right edge due to the use of only 2 MIDI channels.

4
13
8
17
26
35
44
3
12
21
30
39
48
5
14
7
16
25
34
43
0
9
18
27
36
45
2
11
20
29
38
47
4
13
22
31
40
49
6
15
6
15
24
33
42
51
8
17
26
35
44
1
10
19
28
37
46
1
10
19
28
37
46
3
12
21
30
39
48
5
14
23
32
41
50
7
16
5
14
23
32
41
50
7
16
25
34
43
0
9
18
27
36
45
2
11
20
29
38
47
0
9
18
27
36
45
2
11
20
29
38
47
4
13
22
31
40
49
6
15
24
33
42
51
8
17
13
22
31
40
49
6
15
24
33
42
51
8
17
26
35
44
1
10
19
28
37
46
3
12
21
30
39
48
35
44
1
10
19
28
37
46
3
12
21
30
39
48
5
14
23
32
41
50
7
16
25
34
43
0
14
23
32
41
50
7
16
25
34
43
0
9
18
27
36
45
2
11
20
29
38
47
4
36
45
2
11
20
29
38
47
4
13
22
31
40
49
6
15
24
33
42
51
15
24
33
42
51
8
17
26
35
44
1
10
19
28
37
46
3
37
46
3
12
21
30
39
48
5
14
23
32
41
50
16
25
34
43
0
9
18
27
36
45
2
38
47
4
13
22
31
40
49
17
26
35
44
1
39
48


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