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
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6
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24
30
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8
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26
32
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11
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23
29
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8
14
20
13
19
25
31
4
10
16
22
28
1
7
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19
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31
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10
12
18
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30
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9
15
21
27
0
6
12
18
24
30
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9
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21
27
17
23
29
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8
14
20
26
32
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11
17
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29
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8
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20
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32
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11
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22
28
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7
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25
31
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10
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7
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31
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10
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1
27
0
6
12
18
24
30
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9
15
21
27
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6
12
18
24
30
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9
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0
6
12
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24
11
17
23
29
2
8
14
20
26
32
5
11
17
23
29
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8
14
20
26
32
5
11
17
23
29
1
7
13
19
25
31
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10
16
22
28
1
7
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25
31
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10
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1
18
24
30
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9
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21
27
0
6
12
18
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30
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9
15
21
27
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8
14
20
26
32
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11
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23
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8
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26
32
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25
31
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10
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28
1
7
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19
25
31
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15
21
27
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6
12
18
24
30
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9
32
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11
17
23
29
2
8
22
28
1
7
13
6
12
Semiquartal
To maximise your range while keeping octaves near horizontal, use the 4L 1s layout.
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
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22
29
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10
17
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31
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12
19
26
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7
14
21
28
2
9
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23
30
4
11
27
1
8
15
22
29
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10
17
24
31
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12
19
26
0
7
14
21
28
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9
16
13
20
27
1
8
15
22
29
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10
17
24
31
5
12
19
26
0
7
14
6
13
20
27
1
8
15
22
29
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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
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.
