Chords of semisept

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Below are listed the dyadic chords of 11-limit semisept temperament. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering by 540/539 are swetismic, and by 176/175 valinorsmic.

Semisept has MOS of size 5, 8, 13, 18, 31, 49 and 80. Some amount triadic and tetradic harmony shows itself by the 13-note MOS and much more with 18 notes. The swetismic tetrad with complexity 11 is worthy of particular note.

Triads

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

Tetrads

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

Pentads

Number Chord Transversal Type
1 0-2-9-11-21 1-12/7-7/5-6/5-11/10 swetismic
2 0-2-9-19-21 1-12/7-7/5-9/7-11/10 swetismic
3 0-2-12-19-21 1-12/7-11/7-9/7-11/10 swetismic
4 0-10-12-19-21 1-11/6-11/7-9/7-11/10 swetismic
5 0-6-15-17-27 1-5/4-7/4-3/2-11/8 otonal
6 0-6-12-21-27 1-5/4-11/7-11/10-11/8 valinorsmic
7 0-10-12-21-27 1-11/6-11/7-11/10-11/8 utonal
8 0-6-15-21-27 1-5/4-7/4-11/10-11/8 valinorsmic
9 0-7-9-19-28 1-18/11-7/5-9/7-9/5 swetismic
10 0-7-17-19-28 1-18/11-3/2-9/7-9/5 utonal
11 0-9-11-21-28 1-7/5-6/5-11/10-9/5 otonal
12 0-9-19-21-28 1-7/5-9/7-11/10-9/5 swetismic
13 0-6-15-17-34 1-5/4-7/4-3/2-9/8 otonal
14 0-7-17-19-34 1-18/11-3/2-9/7-9/8 utonal
15 0-6-15-27-34 1-5/4-7/4-11/8-9/8 otonal
16 0-6-17-27-34 1-5/4-3/2-11/8-9/8 otonal
17 0-15-17-27-34 1-7/4-3/2-11/8-9/8 otonal
18 0-7-17-28-34 1-18/11-3/2-9/5-9/8 utonal
19 0-7-19-28-34 1-18/11-9/7-9/5-9/8 utonal
20 0-17-19-28-34 1-3/2-9/7-9/5-9/8 utonal

Hexads

Number Chord Transversal Type
1 0-6-15-17-27-34 1-5/4-7/4-3/2-11/8-9/8 otonal
2 0-7-17-19-28-34 1-18/11-3/2-9/7-9/5-9/8 utonal