Chords of ennealimnic

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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