Chords of hemithirds

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