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.
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
A version of the above that duplicates note 0 (as note 52, as if making a layout for 53edo) keeps the octaves level. This is demonstrated in Bryan Deister's 52edo improv (2025).
