Chords of unidec

Below are listed the dyadic chords of 11-limit unidec temperament. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering by 441/440 are labeled werckismic, and by 385/384 keenanismic.

The normal mapping for unidec is uni = [2 5 8 5 6], 0 -6 -11 2 3]]. From this we may derive a val v = uni[1] + 100 uni[2] = 2 -595 -1092 205 306] which we may use to sort and normalize the chords of unidec. 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.

Unidec has MOS of size 6, 20, 26, 46, and 72. Even the six-note MOS has some werckismic triads, and there are many more chords in the twenty note MOS, including many of the werckismic tetrad of complexity six and the keenanismic tetrad of complexity ten, which are likely to figure large in any composition in unidec. The essentially tempered chords of unidec either temper out 441/440 or 385/384; putting these together produces portent temperament, but there are no essentially portent chords. Adding the small ragisma, 4375/4374, to the commas of portent gives unidec, with very little additional tuning damage. Unidec is, in fact, quite an accurate temperament even compared to such things as miracle, but still has enough give in it to allow for some interesting essential tempering.

Number Chord Transversal Type Complexity
1 0-100-201 1-10/9-7/4 werckismic 4
2 0-101-201 1-11/7-7/4 werckismic 4
3 0-101-300 1-11/7-11/8 utonal 6
4 0-201-300 1-7/4-11/8 otonal 6
5 0-201-499 1-7/4-6/5 keenanismic 10
6 0-300-499 1-11/8-6/5 keenanismic 10
7 0-100-599 1-10/9-4/3 otonal 12
8 0-499-599 1-6/5-4/3 utonal 12
9 0-201-798 1-7/4-7/6 utonal 16
10 0-599-798 1-4/3-7/6 otonal 16
11 0-101-899 1-11/7-11/6 utonal 18
12 0-300-899 1-11/8-11/6 utonal 18
13 0-599-899 1-4/3-11/6 otonal 18
14 0-798-899 1-7/6-11/6 otonal 18
15 0-201-1098 1-7/4-8/5 keenanismic 22
16 0-300-1098 1-11/8-8/5 keenanismic 22
17 0-499-1098 1-6/5-8/5 otonal 22
18 0-599-1098 1-4/3-8/5 utonal 22
19 0-798-1098 1-7/6-8/5 keenanismic 22
20 0-899-1098 1-11/6-8/5 keenanismic 22
21 0-100-1198 1-10/9-16/9 otonal 24
22 0-599-1198 1-4/3-16/9 ambitonal 24
23 0-1098-1198 1-8/5-16/9 utonal 24
24 0-101-1297 1-11/7-7/5 werckismic 26
25 0-201-1297 1-7/4-7/5 utonal 26
26 0-499-1297 1-6/5-7/5 otonal 26
27 0-798-1297 1-7/6-7/5 utonal 26
28 0-1098-1297 1-8/5-7/5 otonal 26
29 0-1198-1297 1-16/9-7/5 werckismic 26
30 0-101-1396 1-11/7-11/10 utonal 28
31 0-300-1396 1-11/8-11/10 utonal 28
32 0-499-1396 1-6/5-11/10 otonal 28
33 0-899-1396 1-11/6-11/10 utonal 28
34 0-1098-1396 1-8/5-11/10 otonal 28
35 0-1297-1396 1-7/5-11/10 otonal 28
36 0-100-1397 1-10/9-14/9 otonal 28
37 0-201-1397 1-7/4-14/9 utonal 28
38 0-599-1397 1-4/3-14/9 otonal 28
39 0-798-1397 1-7/6-14/9 utonal 28
40 0-1198-1397 1-16/9-14/9 otonal 28
41 0-1297-1397 1-7/5-14/9 utonal 28
42 0-100-1496 1-10/9-11/9 otonal 30
43 0-101-1496 1-11/7-11/9 utonal 30
44 0-201-1496 1-7/4-11/9 werckismic 30
45 0-300-1496 1-11/8-11/9 utonal 30
46 0-599-1496 1-4/3-11/9 otonal 30
47 0-899-1496 1-11/6-11/9 utonal 30
48 0-1198-1496 1-16/9-11/9 otonal 30
49 0-1297-1496 1-7/5-11/9 werckismic 30
50 0-1396-1496 1-11/10-11/9 utonal 30
51 0-1397-1496 1-14/9-11/9 otonal 30

Number Chord Transversal Type Complexity
1 0-101-201-300 1-11/7-7/4-11/8 werckismic 6
2 0-201-300-499 1-7/4-11/8-6/5 keenanismic 10
3 0-101-300-899 1-11/7-11/8-11/6 utonal 18
4 0-599-798-899 1-4/3-7/6-11/6 otonal 18
5 0-201-300-1098 1-7/4-11/8-8/5 keenanismic 22
6 0-201-499-1098 1-7/4-6/5-8/5 keenanismic 22
7 0-300-499-1098 1-11/8-6/5-8/5 keenanismic 22
8 0-499-599-1098 1-6/5-4/3-8/5 ambitonal 22
9 0-201-798-1098 1-7/4-7/6-8/5 keenanismic 22
10 0-599-798-1098 1-4/3-7/6-8/5 keenanismic 22
11 0-300-899-1098 1-11/8-11/6-8/5 keenanismic 22
12 0-599-899-1098 1-4/3-11/6-8/5 keenanismic 22
13 0-798-899-1098 1-7/6-11/6-8/5 keenanismic 22
14 0-100-599-1198 1-10/9-4/3-16/9 otonal 24
15 0-599-1098-1198 1-4/3-8/5-16/9 utonal 24
16 0-101-201-1297 1-11/7-7/4-7/5 werckismic 26
17 0-201-499-1297 1-7/4-6/5-7/5 keenanismic 26
18 0-201-798-1297 1-7/4-7/6-7/5 utonal 26
19 0-201-1098-1297 1-7/4-8/5-7/5 keenanismic 26
20 0-499-1098-1297 1-6/5-8/5-7/5 otonal 26
21 0-798-1098-1297 1-7/6-8/5-7/5 keenanismic 26
22 0-1098-1198-1297 1-8/5-16/9-7/5 werckismic 26
23 0-101-300-1396 1-11/7-11/8-11/10 utonal 28
24 0-300-499-1396 1-11/8-6/5-11/10 keenanismic 28
25 0-101-899-1396 1-11/7-11/6-11/10 utonal 28
26 0-300-899-1396 1-11/8-11/6-11/10 utonal 28
27 0-300-1098-1396 1-11/8-8/5-11/10 keenanismic 28
28 0-499-1098-1396 1-6/5-8/5-11/10 otonal 28
29 0-899-1098-1396 1-11/6-8/5-11/10 keenanismic 28
30 0-101-1297-1396 1-11/7-7/5-11/10 werckismic 28
31 0-499-1297-1396 1-6/5-7/5-11/10 otonal 28
32 0-1098-1297-1396 1-8/5-7/5-11/10 otonal 28
33 0-100-201-1397 1-10/9-7/4-14/9 werckismic 28
34 0-100-599-1397 1-10/9-4/3-14/9 otonal 28
35 0-201-798-1397 1-7/4-7/6-14/9 utonal 28
36 0-599-798-1397 1-4/3-7/6-14/9 ambitonal 28
37 0-100-1198-1397 1-10/9-16/9-14/9 otonal 28
38 0-599-1198-1397 1-4/3-16/9-14/9 otonal 28
39 0-201-1297-1397 1-7/4-7/5-14/9 utonal 28
40 0-798-1297-1397 1-7/6-7/5-14/9 utonal 28
41 0-1198-1297-1397 1-16/9-7/5-14/9 werckismic 28
42 0-100-201-1496 1-10/9-7/4-11/9 werckismic 30
43 0-101-201-1496 1-11/7-7/4-11/9 werckismic 30
44 0-101-300-1496 1-11/7-11/8-11/9 utonal 30
45 0-201-300-1496 1-7/4-11/8-11/9 werckismic 30
46 0-100-599-1496 1-10/9-4/3-11/9 otonal 30
47 0-101-899-1496 1-11/7-11/6-11/9 utonal 30
48 0-300-899-1496 1-11/8-11/6-11/9 utonal 30
49 0-599-899-1496 1-4/3-11/6-11/9 ambitonal 30
50 0-100-1198-1496 1-10/9-16/9-11/9 otonal 30
51 0-599-1198-1496 1-4/3-16/9-11/9 otonal 30
52 0-101-1297-1496 1-11/7-7/5-11/9 werckismic 30
53 0-201-1297-1496 1-7/4-7/5-11/9 werckismic 30
54 0-1198-1297-1496 1-16/9-7/5-11/9 werckismic 30
55 0-101-1396-1496 1-11/7-11/10-11/9 utonal 30
56 0-300-1396-1496 1-11/8-11/10-11/9 utonal 30
57 0-899-1396-1496 1-11/6-11/10-11/9 utonal 30
58 0-1297-1396-1496 1-7/5-11/10-11/9 werckismic 30
59 0-100-1397-1496 1-10/9-14/9-11/9 otonal 30
60 0-201-1397-1496 1-7/4-14/9-11/9 werckismic 30
61 0-599-1397-1496 1-4/3-14/9-11/9 otonal 30
62 0-1198-1397-1496 1-16/9-14/9-11/9 otonal 30
63 0-1297-1397-1496 1-7/5-14/9-11/9 werckismic 30

Number Chord Transversal Type Complexity
1 0-201-300-499-1098 1-7/4-11/8-6/5-8/5 keenanismic 22
2 0-599-798-899-1098 1-4/3-7/6-11/6-8/5 keenanismic 22
3 0-201-499-1098-1297 1-7/4-6/5-8/5-7/5 keenanismic 26
4 0-201-798-1098-1297 1-7/4-7/6-8/5-7/5 keenanismic 26
5 0-101-300-899-1396 1-11/7-11/8-11/6-11/10 utonal 28
6 0-300-499-1098-1396 1-11/8-6/5-8/5-11/10 keenanismic 28
7 0-300-899-1098-1396 1-11/8-11/6-8/5-11/10 keenanismic 28
8 0-499-1098-1297-1396 1-6/5-8/5-7/5-11/10 otonal 28
9 0-100-599-1198-1397 1-10/9-4/3-16/9-14/9 otonal 28
10 0-201-798-1297-1397 1-7/4-7/6-7/5-14/9 utonal 28
11 0-101-201-300-1496 1-11/7-7/4-11/8-11/9 werckismic 30
12 0-101-300-899-1496 1-11/7-11/8-11/6-11/9 utonal 30
13 0-100-599-1198-1496 1-10/9-4/3-16/9-11/9 otonal 30
14 0-101-201-1297-1496 1-11/7-7/4-7/5-11/9 werckismic 30
15 0-101-300-1396-1496 1-11/7-11/8-11/10-11/9 utonal 30
16 0-101-899-1396-1496 1-11/7-11/6-11/10-11/9 utonal 30
17 0-300-899-1396-1496 1-11/8-11/6-11/10-11/9 utonal 30
18 0-101-1297-1396-1496 1-11/7-7/5-11/10-11/9 werckismic 30
19 0-100-201-1397-1496 1-10/9-7/4-14/9-11/9 werckismic 30
20 0-100-599-1397-1496 1-10/9-4/3-14/9-11/9 otonal 30
21 0-100-1198-1397-1496 1-10/9-16/9-14/9-11/9 otonal 30
22 0-599-1198-1397-1496 1-4/3-16/9-14/9-11/9 otonal 30
23 0-201-1297-1397-1496 1-7/4-7/5-14/9-11/9 werckismic 30
24 0-1198-1297-1397-1496 1-16/9-7/5-14/9-11/9 werckismic 30