While 33edo is poor at approximating harmonics in general, it does manage several composite ratios within fractions of a cent. The terrain mapping is a particularly efficient way to make those easy to play together.
0
6
5
11
17
23
29
4
10
16
22
28
1
7
13
9
15
21
27
0
6
12
18
24
30
3
8
14
20
26
32
5
11
17
23
29
2
8
14
20
13
19
25
31
4
10
16
22
28
1
7
13
19
25
31
4
10
12
18
24
30
3
9
15
21
27
0
6
12
18
24
30
3
9
15
21
27
17
23
29
2
8
14
20
26
32
5
11
17
23
29
2
8
14
20
26
32
5
11
17
16
22
28
1
7
13
19
25
31
4
10
16
22
28
1
7
13
19
25
31
4
10
16
22
28
1
27
0
6
12
18
24
30
3
9
15
21
27
0
6
12
18
24
30
3
9
15
21
27
0
6
12
18
24
11
17
23
29
2
8
14
20
26
32
5
11
17
23
29
2
8
14
20
26
32
5
11
17
23
29
1
7
13
19
25
31
4
10
16
22
28
1
7
13
19
25
31
4
10
16
22
28
1
18
24
30
3
9
15
21
27
0
6
12
18
24
30
3
9
15
21
27
0
8
14
20
26
32
5
11
17
23
29
2
8
14
20
26
32
5
25
31
4
10
16
22
28
1
7
13
19
25
31
4
15
21
27
0
6
12
18
24
30
3
9
32
5
11
17
23
29
2
8
22
28
1
7
13
6
12
Semiquartal
The 4L 1s Semiquartal mapping gives you an even wider range, is a fraction of a cent off the 9-odd limit minmax tuning for beep temperament using the ccd val and is also a significant non patent tuning for godzilla.
24
31
29
3
10
17
24
27
1
8
15
22
29
3
10
32
6
13
20
27
1
8
15
22
29
3
30
4
11
18
25
32
6
13
20
27
1
8
15
22
2
9
16
23
30
4
11
18
25
32
6
13
20
27
1
8
15
0
7
14
21
28
2
9
16
23
30
4
11
18
25
32
6
13
20
27
1
5
12
19
26
0
7
14
21
28
2
9
16
23
30
4
11
18
25
32
6
13
20
27
3
10
17
24
31
5
12
19
26
0
7
14
21
28
2
9
16
23
30
4
11
18
25
32
6
13
15
22
29
3
10
17
24
31
5
12
19
26
0
7
14
21
28
2
9
16
23
30
4
11
18
25
32
6
1
8
15
22
29
3
10
17
24
31
5
12
19
26
0
7
14
21
28
2
9
16
23
30
4
11
27
1
8
15
22
29
3
10
17
24
31
5
12
19
26
0
7
14
21
28
2
9
16
13
20
27
1
8
15
22
29
3
10
17
24
31
5
12
19
26
0
7
14
6
13
20
27
1
8
15
22
29
3
10
17
24
31
5
12
19
25
32
6
13
20
27
1
8
15
22
29
3
10
17
18
25
32
6
13
20
27
1
8
15
22
4
11
18
25
32
6
13
20
30
4
11
18
25
16
23
Sephiroth
To maximise your range while covering all the notes and keeping octaves near horizontal, use the 3L 1s layout.
5
15
8
18
28
5
15
1
11
21
31
8
18
28
5
4
14
24
1
11
21
31
8
18
28
5
30
7
17
27
4
14
24
1
11
21
31
8
18
28
0
10
20
30
7
17
27
4
14
24
1
11
21
31
8
18
28
26
3
13
23
0
10
20
30
7
17
27
4
14
24
1
11
21
31
8
18
29
6
16
26
3
13
23
0
10
20
30
7
17
27
4
14
24
1
11
21
31
8
18
22
32
9
19
29
6
16
26
3
13
23
0
10
20
30
7
17
27
4
14
24
1
11
21
31
8
2
12
22
32
9
19
29
6
16
26
3
13
23
0
10
20
30
7
17
27
4
14
24
1
11
21
31
8
25
2
12
22
32
9
19
29
6
16
26
3
13
23
0
10
20
30
7
17
27
4
14
24
1
11
25
2
12
22
32
9
19
29
6
16
26
3
13
23
0
10
20
30
7
17
27
4
14
15
25
2
12
22
32
9
19
29
6
16
26
3
13
23
0
10
20
30
7
15
25
2
12
22
32
9
19
29
6
16
26
3
13
23
0
10
5
15
25
2
12
22
32
9
19
29
6
16
26
3
5
15
25
2
12
22
32
9
19
29
6
28
5
15
25
2
12
22
32
28
5
15
25
2
18
28
Augmented (triforce) + bohpier Lumatone mappings
Bryan Deister has demonstrated two mappings for 33edo that function for the temperaments augmented (triforce, 33d val, 3L 3s scale with 7:4 step ratio) and bohpier (33cd val, 8L 1s scale with 4:1 step ratio). The down-right (forward chroma version) or rightward (reverse chroma version) generator is a somewhat flat Alpharabian tendoneutral second ~12/11 which can be stacked to get several consonant intervals; however, some of them map inconsistently. Two of these generators make a near-just neogothic minor third ~13/11, mapped consistently. Three of these generators make a near-just septimal major third ~9/7 by sound, but the mapping only works if 9/7 is constituted as (3♭ × 3♯) ÷ 7 or as 9 ÷ 7♭ (33d val). Four of these generators make a near-just lesser septimal tritone ~7/5, mapped consistently (patent val or 33cd val). Six of these generators make a flat classic major sixth ~5/3 by sound, but the mapping only works if 5/3 is constituted as 5♭ ÷ 3 (33c val). Seven of these generators make a near-just classic minor seventh ~9/5 by sound, but the mapping only works if 9/5 is constituted as (3♭ × 3♯) ÷ 5 or as 9 ÷ 5♭ (33c val). The range is a bit over six octaves in the forward chroma version or five octaves in the reverse chroma version; in both cases, the octaves slope moderately downwards resulting in a vertical wraparound.
Bryan Deister has demonstrated a mapping for 33edo that yields both 5L 3s (oneirotonic, 6:1 step ratio) and 3L 2s (antipentic, 7:6 step ratio) scales, in 33edo improv (2025). The underlying temperament is an unidentified temperament that uses the supersharp alternate (33b) fifth, although the patent fifth is about equally accessible. The range is a bit over 4⅔ octaves, with a fair number of repeated notes to mitigate vertical wraparounds and the octaves slope moderately downwards.
