Chords of hemithirds

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Below are listed the dyadic chords of 11-limit hemithirds temperament. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering by 441/440 are werckismic, and by 385/384 keenanismic.

Hemithirds has MOS of size 6, 7, 13, 19, 25, 31, 56 and 87. It may be seen that adding essentially tempered chords to the mix allows for a notably richer range of harmonies even for the 13 note MOS.

Triads

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

Tetrads

Number Chord Transversal Type
1 0-2-5-7 1-5/4-7/4-12/11 keenanismic
2 0-3-5-8 1-7/5-7/4-11/9 werckismic
3 0-3-5-20 1-7/5-7/4-7/6 utonal
4 0-15-17-20 1-4/3-5/3-7/6 otonal
5 0-2-5-22 1-5/4-7/4-16/11 keenanismic
6 0-2-7-22 1-5/4-12/11-16/11 keenanismic
7 0-5-7-22 1-7/4-12/11-16/11 keenanismic
8 0-7-15-22 1-12/11-4/3-16/11 ambitonal
9 0-2-17-22 1-5/4-5/3-16/11 keenanismic
10 0-15-17-22 1-4/3-5/3-16/11 keenanismic
11 0-5-20-22 1-7/4-7/6-16/11 keenanismic
12 0-15-20-22 1-4/3-7/6-16/11 keenanismic
13 0-17-20-22 1-5/3-7/6-16/11 keenanismic
14 0-2-7-24 1-5/4-12/11-20/11 keenanismic
15 0-2-17-24 1-5/4-5/3-20/11 utonal
16 0-2-22-24 1-5/4-16/11-20/11 keenanismic
17 0-7-22-24 1-12/11-16/11-20/11 otonal
18 0-17-22-24 1-5/3-16/11-20/11 keenanismic
19 0-3-5-27 1-7/5-7/4-14/11 utonal
20 0-5-7-27 1-7/4-12/11-14/11 keenanismic
21 0-3-20-27 1-7/5-7/6-14/11 utonal
22 0-5-20-27 1-7/4-7/6-14/11 utonal
23 0-5-22-27 1-7/4-16/11-14/11 keenanismic
24 0-7-22-27 1-12/11-16/11-14/11 otonal
25 0-20-22-27 1-7/6-16/11-14/11 keenanismic
26 0-7-24-27 1-12/11-20/11-14/11 otonal
27 0-22-24-27 1-16/11-20/11-14/11 otonal
28 0-3-8-30 1-7/5-11/9-16/9 werckismic
29 0-8-15-30 1-11/9-4/3-16/9 otonal
30 0-15-22-30 1-4/3-16/11-16/9 utonal
31 0-3-27-30 1-7/5-14/11-16/9 werckismic
32 0-22-27-30 1-16/11-14/11-16/9 werckismic
33 0-2-5-32 1-5/4-7/4-10/9 werckismic
34 0-5-8-32 1-7/4-11/9-10/9 werckismic
35 0-8-15-32 1-11/9-4/3-10/9 otonal
36 0-2-17-32 1-5/4-5/3-10/9 utonal
37 0-15-17-32 1-4/3-5/3-10/9 ambitonal
38 0-2-24-32 1-5/4-20/11-10/9 utonal
39 0-17-24-32 1-5/3-20/11-10/9 utonal
40 0-5-27-32 1-7/4-14/11-10/9 werckismic
41 0-24-27-32 1-20/11-14/11-10/9 werckismic
42 0-8-30-32 1-11/9-16/9-10/9 otonal
43 0-15-30-32 1-4/3-16/9-10/9 otonal
44 0-27-30-32 1-14/11-16/9-10/9 werckismic
45 0-3-5-35 1-7/5-7/4-14/9 utonal
46 0-3-8-35 1-7/5-11/9-14/9 werckismic
47 0-5-8-35 1-7/4-11/9-14/9 werckismic
48 0-8-15-35 1-11/9-4/3-14/9 otonal
49 0-3-20-35 1-7/5-7/6-14/9 utonal
50 0-5-20-35 1-7/4-7/6-14/9 utonal
51 0-15-20-35 1-4/3-7/6-14/9 ambitonal
52 0-3-27-35 1-7/5-14/11-14/9 utonal
53 0-5-27-35 1-7/4-14/11-14/9 utonal
54 0-20-27-35 1-7/6-14/11-14/9 utonal
55 0-3-30-35 1-7/5-16/9-14/9 werckismic
56 0-8-30-35 1-11/9-16/9-14/9 otonal
57 0-15-30-35 1-4/3-16/9-14/9 otonal
58 0-27-30-35 1-14/11-16/9-14/9 werckismic
59 0-5-32-35 1-7/4-10/9-14/9 werckismic
60 0-8-32-35 1-11/9-10/9-14/9 otonal
61 0-15-32-35 1-4/3-10/9-14/9 otonal
62 0-27-32-35 1-14/11-10/9-14/9 werckismic
63 0-30-32-35 1-16/9-10/9-14/9 otonal

Pentads

Number Chord Transversal Type
1 0-2-5-7-22 1-5/4-7/4-12/11-16/11 keenanismic
2 0-15-17-20-22 1-4/3-5/3-7/6-16/11 keenanismic
3 0-2-7-22-24 1-5/4-12/11-16/11-20/11 keenanismic
4 0-2-17-22-24 1-5/4-5/3-16/11-20/11 keenanismic
5 0-3-5-20-27 1-7/5-7/4-7/6-14/11 utonal
6 0-5-7-22-27 1-7/4-12/11-16/11-14/11 keenanismic
7 0-5-20-22-27 1-7/4-7/6-16/11-14/11 keenanismic
8 0-7-22-24-27 1-12/11-16/11-20/11-14/11 otonal
9 0-2-17-24-32 1-5/4-5/3-20/11-10/9 utonal
10 0-8-15-30-32 1-11/9-4/3-16/9-10/9 otonal
11 0-3-5-8-35 1-7/5-7/4-11/9-14/9 werckismic
12 0-3-5-20-35 1-7/5-7/4-7/6-14/9 utonal
13 0-3-5-27-35 1-7/5-7/4-14/11-14/9 utonal
14 0-3-20-27-35 1-7/5-7/6-14/11-14/9 utonal
15 0-5-20-27-35 1-7/4-7/6-14/11-14/9 utonal
16 0-3-8-30-35 1-7/5-11/9-16/9-14/9 werckismic
17 0-8-15-30-35 1-11/9-4/3-16/9-14/9 otonal
18 0-3-27-30-35 1-7/5-14/11-16/9-14/9 werckismic
19 0-5-8-32-35 1-7/4-11/9-10/9-14/9 werckismic
20 0-8-15-32-35 1-11/9-4/3-10/9-14/9 otonal
21 0-5-27-32-35 1-7/4-14/11-10/9-14/9 werckismic
22 0-8-30-32-35 1-11/9-16/9-10/9-14/9 otonal
23 0-15-30-32-35 1-4/3-16/9-10/9-14/9 otonal
24 0-27-30-32-35 1-14/11-16/9-10/9-14/9 werckismic

Hexads

Number Chord Transversal Type
1 0-3-5-20-27-35 1-7/5-7/4-7/6-14/11-14/9 utonal
2 0-8-15-30-32-35 1-11/9-4/3-16/9-10/9-14/9 otonal