Diaschismic/Chords

Below are listed the dyadic chords of 11-limit diaschismic temperament. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering only by 441/440 are labeled werckismic, by 176/175 valinorsmic, by 896/891 pentacircle, and by 126/125 starling. Those requiring tempering by any two of 126/125, 176/175 or 441/440 are labeled thrush, and by both 896/891 and 441/440 pele.

The normal mapping for diaschismic is dia = [<2 0 11 31 45|, <0 1 -2 -8 -12|]. From this we may derive a val v = dia[1] - 100 dia[2] = <2 -100 211 831 1245| which we may use to sort and normalize the chords of diaschismic. Under "Chord" is listed the chord, normalized to start from zero, in the mapping by v. If we look at the highest, rightmost, element of the chord, divide that by 100, round, and multiply by 2, we get the Graham complexity of the chord. Redundantly for the sake of convenience, the Graham complexity is listed in the last column.

Diaschsmic has MOS of size 10, 12, 22, 34, 46 and 58. It may be seen that even ten notes are not without resources, mostly essentially just. By the time we get to 22 notes, we are well-supplied.

Triads

Number	Chord	Transversal	Type	Complexity
1	0-104-208	1-4/3-16/9	ambitonal	4
2	0-104-311	1-4/3-5/3	otonal	6
3	0-207-311	1-5/4-5/3	utonal	6
4	0-104-413	1-4/3-10/9	otonal	8
5	0-207-413	1-5/4-10/9	utonal	8
6	0-208-413	1-16/9-10/9	otonal	8
7	0-311-413	1-5/3-10/9	utonal	8
8	0-207-414	1-5/4-11/7	valinorsmic	8
9	0-208-414	1-16/9-11/7	pentacircle	8
10	0-207-620	1-5/4-7/5	starling	12
11	0-208-620	1-16/9-7/5	werckismic	12
12	0-311-620	1-5/3-7/5	starling	12
13	0-413-620	1-10/9-7/5	starling	12
14	0-414-620	1-11/7-7/5	werckismic	12
15	0-207-827	1-5/4-7/4	otonal	16
16	0-413-827	1-10/9-7/4	werckismic	16
17	0-414-827	1-11/7-7/4	werckismic	16
18	0-620-827	1-7/5-7/4	utonal	16
19	0-104-929	1-4/3-7/6	otonal	18
20	0-311-929	1-5/3-7/6	otonal	18
21	0-620-929	1-7/5-7/6	utonal	18
22	0-827-929	1-7/4-7/6	utonal	18
23	0-207-1032	1-5/4-11/10	valinorsmic	20
24	0-414-1032	1-11/7-11/10	utonal	20
25	0-620-1032	1-7/5-11/10	otonal	20
26	0-827-1032	1-7/4-11/10	valinorsmic	20
27	0-104-1033	1-4/3-14/9	otonal	20
28	0-208-1033	1-16/9-14/9	otonal	20
29	0-413-1033	1-10/9-14/9	otonal	20
30	0-620-1033	1-7/5-14/9	utonal	20
31	0-827-1033	1-7/4-14/9	utonal	20
32	0-929-1033	1-7/6-14/9	utonal	20
33	0-207-1239	1-5/4-11/8	otonal	24
34	0-208-1239	1-16/9-11/8	pentacircle	24
35	0-414-1239	1-11/7-11/8	utonal	24
36	0-827-1239	1-7/4-11/8	otonal	24
37	0-1032-1239	1-11/10-11/8	utonal	24
38	0-1033-1239	1-14/9-11/8	pentacircle	24
39	0-104-1343	1-4/3-11/6	otonal	26
40	0-311-1343	1-5/3-11/6	otonal	26
41	0-414-1343	1-11/7-11/6	utonal	26
42	0-929-1343	1-7/6-11/6	otonal	26
43	0-1032-1343	1-11/10-11/6	utonal	26
44	0-1239-1343	1-11/8-11/6	utonal	26
45	0-104-1445	1-4/3-11/9	otonal	28
46	0-208-1445	1-16/9-11/9	otonal	28
47	0-413-1445	1-10/9-11/9	otonal	28
48	0-414-1445	1-11/7-11/9	utonal	28
49	0-620-1445	1-7/5-11/9	werckismic	28
50	0-827-1445	1-7/4-11/9	werckismic	28
51	0-1032-1445	1-11/10-11/9	utonal	28
52	0-1033-1445	1-14/9-11/9	otonal	28
53	0-1239-1445	1-11/8-11/9	utonal	28
54	0-1343-1445	1-11/6-11/9	utonal	28

Tetrads

Number	Chord	Transversal	Type	Complexity
1	0-104-208-413	1-4/3-16/9-10/9	otonal	8
2	0-104-311-413	1-4/3-5/3-10/9	ambitonal	8
3	0-207-311-413	1-5/4-5/3-10/9	utonal	8
4	0-207-311-620	1-5/4-5/3-7/5	starling	12
5	0-207-413-620	1-5/4-10/9-7/5	starling	12
6	0-208-413-620	1-16/9-10/9-7/5	thrush	12
7	0-311-413-620	1-5/3-10/9-7/5	starling	12
8	0-207-414-620	1-5/4-11/7-7/5	thrush	12
9	0-208-414-620	1-16/9-11/7-7/5	pele	12
10	0-207-413-827	1-5/4-10/9-7/4	werckismic	16
11	0-207-414-827	1-5/4-11/7-7/4	thrush	16
12	0-207-620-827	1-5/4-7/5-7/4	starling	16
13	0-413-620-827	1-10/9-7/5-7/4	thrush	16
14	0-414-620-827	1-11/7-7/5-7/4	werckismic	16
15	0-104-311-929	1-4/3-5/3-7/6	otonal	18
16	0-311-620-929	1-5/3-7/5-7/6	starling	18
17	0-620-827-929	1-7/5-7/4-7/6	utonal	18
18	0-207-414-1032	1-5/4-11/7-11/10	valinorsmic	20
19	0-207-620-1032	1-5/4-7/5-11/10	thrush	20
20	0-414-620-1032	1-11/7-7/5-11/10	werckismic	20
21	0-207-827-1032	1-5/4-7/4-11/10	valinorsmic	20
22	0-414-827-1032	1-11/7-7/4-11/10	thrush	20
23	0-620-827-1032	1-7/5-7/4-11/10	valinorsmic	20
24	0-104-208-1033	1-4/3-16/9-14/9	otonal	20
25	0-104-413-1033	1-4/3-10/9-14/9	otonal	20
26	0-208-413-1033	1-16/9-10/9-14/9	otonal	20
27	0-208-620-1033	1-16/9-7/5-14/9	werckismic	20
28	0-413-620-1033	1-10/9-7/5-14/9	starling	20
29	0-413-827-1033	1-10/9-7/4-14/9	werckismic	20
30	0-620-827-1033	1-7/5-7/4-14/9	utonal	20
31	0-104-929-1033	1-4/3-7/6-14/9	ambitonal	20
32	0-620-929-1033	1-7/5-7/6-14/9	utonal	20
33	0-827-929-1033	1-7/4-7/6-14/9	utonal	20
34	0-207-414-1239	1-5/4-11/7-11/8	valinorsmic	24
35	0-208-414-1239	1-16/9-11/7-11/8	pentacircle	24
36	0-207-827-1239	1-5/4-7/4-11/8	otonal	24
37	0-414-827-1239	1-11/7-7/4-11/8	werckismic	24
38	0-207-1032-1239	1-5/4-11/10-11/8	valinorsmic	24
39	0-414-1032-1239	1-11/7-11/10-11/8	utonal	24
40	0-827-1032-1239	1-7/4-11/10-11/8	valinorsmic	24
41	0-208-1033-1239	1-16/9-14/9-11/8	pentacircle	24
42	0-827-1033-1239	1-7/4-14/9-11/8	pentacircle	24
43	0-104-311-1343	1-4/3-5/3-11/6	otonal	26
44	0-104-929-1343	1-4/3-7/6-11/6	otonal	26
45	0-311-929-1343	1-5/3-7/6-11/6	otonal	26
46	0-414-1032-1343	1-11/7-11/10-11/6	utonal	26
47	0-414-1239-1343	1-11/7-11/8-11/6	utonal	26
48	0-1032-1239-1343	1-11/10-11/8-11/6	utonal	26
49	0-104-208-1445	1-4/3-16/9-11/9	otonal	28
50	0-104-413-1445	1-4/3-10/9-11/9	otonal	28
51	0-208-413-1445	1-16/9-10/9-11/9	otonal	28
52	0-208-414-1445	1-16/9-11/7-11/9	pentacircle	28
53	0-208-620-1445	1-16/9-7/5-11/9	werckismic	28
54	0-413-620-1445	1-10/9-7/5-11/9	thrush	28
55	0-414-620-1445	1-11/7-7/5-11/9	werckismic	28
56	0-413-827-1445	1-10/9-7/4-11/9	werckismic	28
57	0-414-827-1445	1-11/7-7/4-11/9	werckismic	28
58	0-620-827-1445	1-7/5-7/4-11/9	werckismic	28
59	0-414-1032-1445	1-11/7-11/10-11/9	utonal	28
60	0-620-1032-1445	1-7/5-11/10-11/9	werckismic	28
61	0-827-1032-1445	1-7/4-11/10-11/9	thrush	28
62	0-104-1033-1445	1-4/3-14/9-11/9	otonal	28
63	0-208-1033-1445	1-16/9-14/9-11/9	otonal	28
64	0-413-1033-1445	1-10/9-14/9-11/9	otonal	28
65	0-620-1033-1445	1-7/5-14/9-11/9	werckismic	28
66	0-827-1033-1445	1-7/4-14/9-11/9	werckismic	28
67	0-208-1239-1445	1-16/9-11/8-11/9	pentacircle	28
68	0-414-1239-1445	1-11/7-11/8-11/9	utonal	28
69	0-827-1239-1445	1-7/4-11/8-11/9	werckismic	28
70	0-1032-1239-1445	1-11/10-11/8-11/9	utonal	28
71	0-1033-1239-1445	1-14/9-11/8-11/9	pentacircle	28
72	0-104-1343-1445	1-4/3-11/6-11/9	ambitonal	28
73	0-414-1343-1445	1-11/7-11/6-11/9	utonal	28
74	0-1032-1343-1445	1-11/10-11/6-11/9	utonal	28
75	0-1239-1343-1445	1-11/8-11/6-11/9	utonal	28

Pentads

Number	Chord	Transversal	Type	Complexity
1	0-207-311-413-620	1-5/4-5/3-10/9-7/5	starling	12
2	0-207-413-620-827	1-5/4-10/9-7/5-7/4	thrush	16
3	0-207-414-620-827	1-5/4-11/7-7/5-7/4	thrush	16
4	0-207-414-620-1032	1-5/4-11/7-7/5-11/10	thrush	20
5	0-207-414-827-1032	1-5/4-11/7-7/4-11/10	thrush	20
6	0-207-620-827-1032	1-5/4-7/5-7/4-11/10	thrush	20
7	0-414-620-827-1032	1-11/7-7/5-7/4-11/10	thrush	20
8	0-104-208-413-1033	1-4/3-16/9-10/9-14/9	otonal	20
9	0-208-413-620-1033	1-16/9-10/9-7/5-14/9	thrush	20
10	0-413-620-827-1033	1-10/9-7/5-7/4-14/9	thrush	20
11	0-620-827-929-1033	1-7/5-7/4-7/6-14/9	utonal	20
12	0-207-414-827-1239	1-5/4-11/7-7/4-11/8	thrush	24
13	0-207-414-1032-1239	1-5/4-11/7-11/10-11/8	valinorsmic	24
14	0-207-827-1032-1239	1-5/4-7/4-11/10-11/8	valinorsmic	24
15	0-414-827-1032-1239	1-11/7-7/4-11/10-11/8	thrush	24
16	0-104-311-929-1343	1-4/3-5/3-7/6-11/6	otonal	26
17	0-414-1032-1239-1343	1-11/7-11/10-11/8-11/6	utonal	26
18	0-104-208-413-1445	1-4/3-16/9-10/9-11/9	otonal	28
19	0-208-413-620-1445	1-16/9-10/9-7/5-11/9	thrush	28
20	0-208-414-620-1445	1-16/9-11/7-7/5-11/9	pele	28
21	0-413-620-827-1445	1-10/9-7/5-7/4-11/9	thrush	28
22	0-414-620-827-1445	1-11/7-7/5-7/4-11/9	werckismic	28
23	0-414-620-1032-1445	1-11/7-7/5-11/10-11/9	werckismic	28
24	0-414-827-1032-1445	1-11/7-7/4-11/10-11/9	thrush	28
25	0-620-827-1032-1445	1-7/5-7/4-11/10-11/9	thrush	28
26	0-104-208-1033-1445	1-4/3-16/9-14/9-11/9	otonal	28
27	0-104-413-1033-1445	1-4/3-10/9-14/9-11/9	otonal	28
28	0-208-413-1033-1445	1-16/9-10/9-14/9-11/9	otonal	28
29	0-208-620-1033-1445	1-16/9-7/5-14/9-11/9	werckismic	28
30	0-413-620-1033-1445	1-10/9-7/5-14/9-11/9	thrush	28
31	0-413-827-1033-1445	1-10/9-7/4-14/9-11/9	werckismic	28
32	0-620-827-1033-1445	1-7/5-7/4-14/9-11/9	werckismic	28
33	0-208-414-1239-1445	1-16/9-11/7-11/8-11/9	pentacircle	28
34	0-414-827-1239-1445	1-11/7-7/4-11/8-11/9	werckismic	28
35	0-414-1032-1239-1445	1-11/7-11/10-11/8-11/9	utonal	28
36	0-827-1032-1239-1445	1-7/4-11/10-11/8-11/9	thrush	28
37	0-208-1033-1239-1445	1-16/9-14/9-11/8-11/9	pentacircle	28
38	0-827-1033-1239-1445	1-7/4-14/9-11/8-11/9	pele	28
39	0-414-1032-1343-1445	1-11/7-11/10-11/6-11/9	utonal	28
40	0-414-1239-1343-1445	1-11/7-11/8-11/6-11/9	utonal	28
41	0-1032-1239-1343-1445	1-11/10-11/8-11/6-11/9	utonal	28

Hexads

Number	Chord	Transversal	Type	Complexity
1	0-207-414-620-827-1032	1-5/4-11/7-7/5-7/4-11/10	thrush	20
2	0-207-414-827-1032-1239	1-5/4-11/7-7/4-11/10-11/8	thrush	24
3	0-414-620-827-1032-1445	1-11/7-7/5-7/4-11/10-11/9	thrush	28
4	0-104-208-413-1033-1445	1-4/3-16/9-10/9-14/9-11/9	otonal	28
5	0-208-413-620-1033-1445	1-16/9-10/9-7/5-14/9-11/9	thrush	28
6	0-413-620-827-1033-1445	1-10/9-7/5-7/4-14/9-11/9	thrush	28
7	0-414-827-1032-1239-1445	1-11/7-7/4-11/10-11/8-11/9	thrush	28
8	0-414-1032-1239-1343-1445	1-11/7-11/10-11/8-11/6-11/9	utonal	28