Chords of ennealimnic

Below are listed the dyadic chords of 11-limit ennealimnic temperament. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering only by 540/539 are labeled swetismic, 441/440 werckismic, and by 243/242 rastmic. Those requiring tempering by any two of 540/539, 441/440 or 243/242 are labeled jove.

The normal mapping for ennealimnic is enn = [<9 1 1 12 -2|, <0 2 3 2 5|]. From this we may derive a val v = enn[1] + 100 enn[2] = <9 201 301 212 498| which we may use to sort and normalize the chords of ennealimmic. Under "Chord" is listed the chord, normalized to start from zero, in the mapping by v, and the nnextw column gives a transversal which tempers to the chord by ennealimmic tempering. Finally, the Graham complexity is listed in the last column.

Ennealimmic has MOS of size 18, 27, 45 and 72. It may be seen that the 18 note MOS has some triads and tetrads, and 27 considerably more.

Triads

Number	Chord	Transversal	Type	Complexity
1	0-7-96	1-12/7-11/9	swetismic	9
2	0-2-98	1-7/6-10/7	swetismic	9
3	0-7-98	1-12/7-10/7	otonal	9
4	0-96-98	1-11/9-10/7	swetismic	9
5	0-2-100	1-7/6-5/3	otonal	9
6	0-98-100	1-10/7-5/3	utonal	9
7	0-7-188	1-12/7-11/10	swetismic	18
8	0-96-188	1-11/9-11/10	utonal	18
9	0-101-188	1-9/5-11/10	otonal	18
10	0-2-190	1-7/6-9/7	swetismic	18
11	0-7-190	1-12/7-9/7	otonal	18
12	0-98-190	1-10/7-9/7	otonal	18
13	0-101-190	1-9/5-9/7	utonal	18
14	0-188-190	1-11/10-9/7	swetismic	18
15	0-2-192	1-7/6-3/2	otonal	18
16	0-7-192	1-12/7-3/2	utonal	18
17	0-96-192	1-11/9-3/2	rastmic	18
18	0-100-192	1-5/3-3/2	otonal	18
19	0-101-192	1-9/5-3/2	utonal	18
20	0-190-192	1-9/7-3/2	utonal	18
21	0-2-194	1-7/6-7/4	utonal	18
22	0-96-194	1-11/9-7/4	werckismic	18
23	0-98-194	1-10/7-7/4	werckismic	18
24	0-192-194	1-3/2-7/4	otonal	18
25	0-98-283	1-10/7-5/4	utonal	27
26	0-100-283	1-5/3-5/4	utonal	27
27	0-192-283	1-3/2-5/4	otonal	27
28	0-194-283	1-7/4-5/4	otonal	27
29	0-7-286	1-12/7-11/7	otonal	27
30	0-96-286	1-11/9-11/7	utonal	27
31	0-98-286	1-10/7-11/7	otonal	27
32	0-101-286	1-9/5-11/7	werckismic	27
33	0-188-286	1-11/10-11/7	utonal	27
34	0-190-286	1-9/7-11/7	otonal	27
35	0-194-286	1-7/4-11/7	werckismic	27
36	0-2-288	1-7/6-11/6	otonal	27
37	0-96-288	1-11/9-11/6	utonal	27
38	0-98-288	1-10/7-11/6	swetismic	27
39	0-100-288	1-5/3-11/6	otonal	27
40	0-188-288	1-11/10-11/6	utonal	27
41	0-190-288	1-9/7-11/6	swetismic	27
42	0-192-288	1-3/2-11/6	otonal	27
43	0-286-288	1-11/7-11/6	utonal	27
44	0-96-375	1-11/9-9/8	rastmic	36
45	0-98-375	1-10/7-9/8	werckismic	36
46	0-101-375	1-9/5-9/8	utonal	36
47	0-190-375	1-9/7-9/8	utonal	36
48	0-192-375	1-3/2-9/8	ambitonal	36
49	0-194-375	1-7/4-9/8	otonal	36
50	0-283-375	1-5/4-9/8	otonal	36
51	0-286-375	1-11/7-9/8	werckismic	36
52	0-288-375	1-11/6-9/8	rastmic	36
53	0-96-471	1-11/9-11/8	utonal	45
54	0-188-471	1-11/10-11/8	utonal	45
55	0-192-471	1-3/2-11/8	otonal	45
56	0-194-471	1-7/4-11/8	otonal	45
57	0-283-471	1-5/4-11/8	otonal	45
58	0-286-471	1-11/7-11/8	utonal	45
59	0-288-471	1-11/6-11/8	utonal	45
60	0-375-471	1-9/8-11/8	otonal	45

Tetrads

Number	Chord	Transversal	Type	Complexity
1	0-7-96-98	1-12/7-11/9-10/7	swetismic	9
2	0-2-98-100	1-7/6-10/7-5/3	swetismic	9
3	0-7-96-188	1-12/7-11/9-11/10	swetismic	18
4	0-2-98-190	1-7/6-10/7-9/7	swetismic	18
5	0-7-98-190	1-12/7-10/7-9/7	otonal	18
6	0-7-188-190	1-12/7-11/10-9/7	swetismic	18
7	0-101-188-190	1-9/5-11/10-9/7	swetismic	18
8	0-7-96-192	1-12/7-11/9-3/2	jove	18
9	0-2-100-192	1-7/6-5/3-3/2	otonal	18
10	0-2-190-192	1-7/6-9/7-3/2	swetismic	18
11	0-7-190-192	1-12/7-9/7-3/2	ambitonal	18
12	0-101-190-192	1-9/5-9/7-3/2	utonal	18
13	0-2-98-194	1-7/6-10/7-7/4	jove	18
14	0-96-98-194	1-11/9-10/7-7/4	jove	18
15	0-2-192-194	1-7/6-3/2-7/4	ambitonal	18
16	0-96-192-194	1-11/9-3/2-7/4	jove	18
17	0-98-100-283	1-10/7-5/3-5/4	utonal	27
18	0-100-192-283	1-5/3-3/2-5/4	ambitonal	27
19	0-98-194-283	1-10/7-7/4-5/4	werckismic	27
20	0-192-194-283	1-3/2-7/4-5/4	otonal	27
21	0-7-96-286	1-12/7-11/9-11/7	swetismic	27
22	0-7-98-286	1-12/7-10/7-11/7	otonal	27
23	0-96-98-286	1-11/9-10/7-11/7	swetismic	27
24	0-7-188-286	1-12/7-11/10-11/7	swetismic	27
25	0-96-188-286	1-11/9-11/10-11/7	utonal	27
26	0-101-188-286	1-9/5-11/10-11/7	werckismic	27
27	0-7-190-286	1-12/7-9/7-11/7	otonal	27
28	0-98-190-286	1-10/7-9/7-11/7	otonal	27
29	0-101-190-286	1-9/5-9/7-11/7	werckismic	27
30	0-188-190-286	1-11/10-9/7-11/7	swetismic	27
31	0-96-194-286	1-11/9-7/4-11/7	werckismic	27
32	0-98-194-286	1-10/7-7/4-11/7	werckismic	27
33	0-2-98-288	1-7/6-10/7-11/6	swetismic	27
34	0-96-98-288	1-11/9-10/7-11/6	swetismic	27
35	0-2-100-288	1-7/6-5/3-11/6	otonal	27
36	0-98-100-288	1-10/7-5/3-11/6	swetismic	27
37	0-96-188-288	1-11/9-11/10-11/6	utonal	27
38	0-2-190-288	1-7/6-9/7-11/6	swetismic	27
39	0-98-190-288	1-10/7-9/7-11/6	swetismic	27
40	0-188-190-288	1-11/10-9/7-11/6	swetismic	27
41	0-2-192-288	1-7/6-3/2-11/6	otonal	27
42	0-96-192-288	1-11/9-3/2-11/6	rastmic	27
43	0-100-192-288	1-5/3-3/2-11/6	otonal	27
44	0-190-192-288	1-9/7-3/2-11/6	swetismic	27
45	0-96-286-288	1-11/9-11/7-11/6	utonal	27
46	0-98-286-288	1-10/7-11/7-11/6	swetismic	27
47	0-188-286-288	1-11/10-11/7-11/6	utonal	27
48	0-190-286-288	1-9/7-11/7-11/6	swetismic	27
49	0-96-98-375	1-11/9-10/7-9/8	jove	36
50	0-98-190-375	1-10/7-9/7-9/8	werckismic	36
51	0-101-190-375	1-9/5-9/7-9/8	utonal	36
52	0-96-192-375	1-11/9-3/2-9/8	rastmic	36
53	0-101-192-375	1-9/5-3/2-9/8	utonal	36
54	0-190-192-375	1-9/7-3/2-9/8	utonal	36
55	0-96-194-375	1-11/9-7/4-9/8	jove	36
56	0-98-194-375	1-10/7-7/4-9/8	werckismic	36
57	0-192-194-375	1-3/2-7/4-9/8	otonal	36
58	0-98-283-375	1-10/7-5/4-9/8	werckismic	36
59	0-192-283-375	1-3/2-5/4-9/8	otonal	36
60	0-194-283-375	1-7/4-5/4-9/8	otonal	36
61	0-96-286-375	1-11/9-11/7-9/8	jove	36
62	0-98-286-375	1-10/7-11/7-9/8	werckismic	36
63	0-101-286-375	1-9/5-11/7-9/8	werckismic	36
64	0-190-286-375	1-9/7-11/7-9/8	werckismic	36
65	0-194-286-375	1-7/4-11/7-9/8	werckismic	36
66	0-96-288-375	1-11/9-11/6-9/8	rastmic	36
67	0-98-288-375	1-10/7-11/6-9/8	jove	36
68	0-190-288-375	1-9/7-11/6-9/8	jove	36
69	0-192-288-375	1-3/2-11/6-9/8	rastmic	36
70	0-286-288-375	1-11/7-11/6-9/8	jove	36
71	0-96-188-471	1-11/9-11/10-11/8	utonal	45
72	0-96-192-471	1-11/9-3/2-11/8	rastmic	45
73	0-96-194-471	1-11/9-7/4-11/8	werckismic	45
74	0-192-194-471	1-3/2-7/4-11/8	otonal	45
75	0-192-283-471	1-3/2-5/4-11/8	otonal	45
76	0-194-283-471	1-7/4-5/4-11/8	otonal	45
77	0-96-286-471	1-11/9-11/7-11/8	utonal	45
78	0-188-286-471	1-11/10-11/7-11/8	utonal	45
79	0-194-286-471	1-7/4-11/7-11/8	werckismic	45
80	0-96-288-471	1-11/9-11/6-11/8	utonal	45
81	0-188-288-471	1-11/10-11/6-11/8	utonal	45
82	0-192-288-471	1-3/2-11/6-11/8	ambitonal	45
83	0-286-288-471	1-11/7-11/6-11/8	utonal	45
84	0-96-375-471	1-11/9-9/8-11/8	rastmic	45
85	0-192-375-471	1-3/2-9/8-11/8	otonal	45
86	0-194-375-471	1-7/4-9/8-11/8	otonal	45
87	0-283-375-471	1-5/4-9/8-11/8	otonal	45
88	0-286-375-471	1-11/7-9/8-11/8	werckismic	45
89	0-288-375-471	1-11/6-9/8-11/8	rastmic	45

Pentads

Number	Chord	Transversal	Type	Complexity
1	0-7-96-98-286	1-12/7-11/9-10/7-11/7	swetismic	27
2	0-7-96-188-286	1-12/7-11/9-11/10-11/7	swetismic	27
3	0-7-98-190-286	1-12/7-10/7-9/7-11/7	otonal	27
4	0-7-188-190-286	1-12/7-11/10-9/7-11/7	swetismic	27
5	0-101-188-190-286	1-9/5-11/10-9/7-11/7	jove	27
6	0-96-98-194-286	1-11/9-10/7-7/4-11/7	jove	27
7	0-2-98-100-288	1-7/6-10/7-5/3-11/6	swetismic	27
8	0-2-98-190-288	1-7/6-10/7-9/7-11/6	swetismic	27
9	0-2-100-192-288	1-7/6-5/3-3/2-11/6	otonal	27
10	0-2-190-192-288	1-7/6-9/7-3/2-11/6	swetismic	27
11	0-96-98-286-288	1-11/9-10/7-11/7-11/6	swetismic	27
12	0-96-188-286-288	1-11/9-11/10-11/7-11/6	utonal	27
13	0-98-190-286-288	1-10/7-9/7-11/7-11/6	swetismic	27
14	0-188-190-286-288	1-11/10-9/7-11/7-11/6	swetismic	27
15	0-101-190-192-375	1-9/5-9/7-3/2-9/8	utonal	36
16	0-96-98-194-375	1-11/9-10/7-7/4-9/8	jove	36
17	0-96-192-194-375	1-11/9-3/2-7/4-9/8	jove	36
18	0-98-194-283-375	1-10/7-7/4-5/4-9/8	werckismic	36
19	0-192-194-283-375	1-3/2-7/4-5/4-9/8	otonal	36
20	0-96-98-286-375	1-11/9-10/7-11/7-9/8	jove	36
21	0-98-190-286-375	1-10/7-9/7-11/7-9/8	werckismic	36
22	0-101-190-286-375	1-9/5-9/7-11/7-9/8	werckismic	36
23	0-96-194-286-375	1-11/9-7/4-11/7-9/8	jove	36
24	0-98-194-286-375	1-10/7-7/4-11/7-9/8	werckismic	36
25	0-96-98-288-375	1-11/9-10/7-11/6-9/8	jove	36
26	0-98-190-288-375	1-10/7-9/7-11/6-9/8	jove	36
27	0-96-192-288-375	1-11/9-3/2-11/6-9/8	rastmic	36
28	0-190-192-288-375	1-9/7-3/2-11/6-9/8	jove	36
29	0-96-286-288-375	1-11/9-11/7-11/6-9/8	jove	36
30	0-98-286-288-375	1-10/7-11/7-11/6-9/8	jove	36
31	0-190-286-288-375	1-9/7-11/7-11/6-9/8	jove	36
32	0-96-192-194-471	1-11/9-3/2-7/4-11/8	jove	45
33	0-192-194-283-471	1-3/2-7/4-5/4-11/8	otonal	45
34	0-96-188-286-471	1-11/9-11/10-11/7-11/8	utonal	45
35	0-96-194-286-471	1-11/9-7/4-11/7-11/8	werckismic	45
36	0-96-188-288-471	1-11/9-11/10-11/6-11/8	utonal	45
37	0-96-192-288-471	1-11/9-3/2-11/6-11/8	rastmic	45
38	0-96-286-288-471	1-11/9-11/7-11/6-11/8	utonal	45
39	0-188-286-288-471	1-11/10-11/7-11/6-11/8	utonal	45
40	0-96-192-375-471	1-11/9-3/2-9/8-11/8	rastmic	45
41	0-96-194-375-471	1-11/9-7/4-9/8-11/8	jove	45
42	0-192-194-375-471	1-3/2-7/4-9/8-11/8	otonal	45
43	0-192-283-375-471	1-3/2-5/4-9/8-11/8	otonal	45
44	0-194-283-375-471	1-7/4-5/4-9/8-11/8	otonal	45
45	0-96-286-375-471	1-11/9-11/7-9/8-11/8	jove	45
46	0-194-286-375-471	1-7/4-11/7-9/8-11/8	werckismic	45
47	0-96-288-375-471	1-11/9-11/6-9/8-11/8	rastmic	45
48	0-192-288-375-471	1-3/2-11/6-9/8-11/8	rastmic	45
49	0-286-288-375-471	1-11/7-11/6-9/8-11/8	jove	45

Hexads

Number	Chord	Transversal	Type	Complexity
1	0-96-98-194-286-375	1-11/9-10/7-7/4-11/7-9/8	jove	36
2	0-96-98-286-288-375	1-11/9-10/7-11/7-11/6-9/8	jove	36
3	0-98-190-286-288-375	1-10/7-9/7-11/7-11/6-9/8	jove	36
4	0-96-188-286-288-471	1-11/9-11/10-11/7-11/6-11/8	utonal	45
5	0-96-192-194-375-471	1-11/9-3/2-7/4-9/8-11/8	jove	45
6	0-192-194-283-375-471	1-3/2-7/4-5/4-9/8-11/8	otonal	45
7	0-96-194-286-375-471	1-11/9-7/4-11/7-9/8-11/8	jove	45
8	0-96-192-288-375-471	1-11/9-3/2-11/6-9/8-11/8	rastmic	45
9	0-96-286-288-375-471	1-11/9-11/7-11/6-9/8-11/8	jove	45