Chords of harry

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Below are listed the dyadic chords of 11-limit harry temperament. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering only by 540/539 are swetismic, by 441/440 werckismicmic, 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 harry is har = [<2 4 7 7 9|, <0 -6 -17 -10 -15|]. From this we may derive a val v = har[1] - 100 har[2] = <2 604 1707 1007 1509| which we may use to sort and normalize the chords of harry. 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.

Harry has MOS of size 14, 16, 30, 44, 58 and 72. It may be seen that 14 notes, and even more 16 notes, supply enough chords to be interesting. There is essentially no advantage in accuracy to optimizing for jove temperament rather than harry; in addition to what jove tempers out, harry tempers out 4000/3993. However, POTE tuning, for example, shrinks the three cents of this comma to -0.0827 cents, which is hardly worth worrying about. Hence harry is one way of exploring and organizing the chords of jove, which are therefore also listed below.

Triads

Number Chord Transversal Type Complexity
1 0-201-401 1-9/7-7/6 swetismic 8
2 0-202-401 1-20/11-7/6 swetismic 8
3 0-202-501 1-20/11-10/9 utonal 10
4 0-301-501 1-11/9-10/9 otonal 10
5 0-201-502 1-9/7-11/7 otonal 10
6 0-301-502 1-11/9-11/7 utonal 10
7 0-201-602 1-9/7-3/2 utonal 12
8 0-301-602 1-11/9-3/2 rastmic 12
9 0-401-602 1-7/6-3/2 otonal 12
10 0-201-702 1-9/7-10/7 otonal 14
11 0-202-702 1-20/11-10/7 utonal 14
12 0-301-702 1-11/9-10/7 swetismic 14
13 0-401-702 1-7/6-10/7 swetismic 14
14 0-501-702 1-10/9-10/7 utonal 14
15 0-502-702 1-11/7-10/7 otonal 14
16 0-201-903 1-9/7-11/6 swetismic 18
17 0-301-903 1-11/9-11/6 utonal 18
18 0-401-903 1-7/6-11/6 otonal 18
19 0-502-903 1-11/7-11/6 utonal 18
20 0-602-903 1-3/2-11/6 otonal 18
21 0-702-903 1-10/7-11/6 swetismic 18
22 0-301-1003 1-11/9-7/4 werckismic 20
23 0-401-1003 1-7/6-7/4 utonal 20
24 0-501-1003 1-10/9-7/4 werckismic 20
25 0-502-1003 1-11/7-7/4 werckismic 20
26 0-602-1003 1-3/2-7/4 otonal 20
27 0-702-1003 1-10/7-7/4 werckismic 20
28 0-202-1103 1-20/11-5/3 utonal 22
29 0-401-1103 1-7/6-5/3 otonal 22
30 0-501-1103 1-10/9-5/3 utonal 22
31 0-602-1103 1-3/2-5/3 otonal 22
32 0-702-1103 1-10/7-5/3 utonal 22
33 0-903-1103 1-11/6-5/3 otonal 22
34 0-201-1202 1-9/7-9/8 utonal 24
35 0-301-1202 1-11/9-9/8 rastmic 24
36 0-502-1202 1-11/7-9/8 werckismic 24
37 0-602-1202 1-3/2-9/8 ambitonal 24
38 0-702-1202 1-10/7-9/8 werckismic 24
39 0-903-1202 1-11/6-9/8 rastmic 24
40 0-1003-1202 1-7/4-9/8 otonal 24
41 0-301-1503 1-11/9-11/8 utonal 30
42 0-502-1503 1-11/7-11/8 utonal 30
43 0-602-1503 1-3/2-11/8 otonal 30
44 0-903-1503 1-11/6-11/8 utonal 30
45 0-1003-1503 1-7/4-11/8 otonal 30
46 0-1202-1503 1-9/8-11/8 otonal 30
47 0-202-1703 1-20/11-5/4 utonal 34
48 0-501-1703 1-10/9-5/4 utonal 34
49 0-602-1703 1-3/2-5/4 otonal 34
50 0-702-1703 1-10/7-5/4 utonal 34
51 0-1003-1703 1-7/4-5/4 otonal 34
52 0-1103-1703 1-5/3-5/4 utonal 34
53 0-1202-1703 1-9/8-5/4 otonal 34
54 0-1503-1703 1-11/8-5/4 otonal 34

Tetrads

Number Chord Transversal Type Complexity
1 0-201-401-602 1-9/7-7/6-3/2 swetismic 12
2 0-201-401-702 1-9/7-7/6-10/7 swetismic 14
3 0-202-401-702 1-20/11-7/6-10/7 swetismic 14
4 0-202-501-702 1-20/11-10/9-10/7 utonal 14
5 0-301-501-702 1-11/9-10/9-10/7 swetismic 14
6 0-201-502-702 1-9/7-11/7-10/7 otonal 14
7 0-301-502-702 1-11/9-11/7-10/7 swetismic 14
8 0-201-401-903 1-9/7-7/6-11/6 swetismic 18
9 0-201-502-903 1-9/7-11/7-11/6 swetismic 18
10 0-301-502-903 1-11/9-11/7-11/6 utonal 18
11 0-201-602-903 1-9/7-3/2-11/6 swetismic 18
12 0-301-602-903 1-11/9-3/2-11/6 rastmic 18
13 0-401-602-903 1-7/6-3/2-11/6 otonal 18
14 0-201-702-903 1-9/7-10/7-11/6 swetismic 18
15 0-301-702-903 1-11/9-10/7-11/6 swetismic 18
16 0-401-702-903 1-7/6-10/7-11/6 swetismic 18
17 0-502-702-903 1-11/7-10/7-11/6 swetismic 18
18 0-301-501-1003 1-11/9-10/9-7/4 werckismic 20
19 0-301-502-1003 1-11/9-11/7-7/4 werckismic 20
20 0-301-602-1003 1-11/9-3/2-7/4 jove 20
21 0-401-602-1003 1-7/6-3/2-7/4 ambitonal 20
22 0-301-702-1003 1-11/9-10/7-7/4 jove 20
23 0-401-702-1003 1-7/6-10/7-7/4 jove 20
24 0-501-702-1003 1-10/9-10/7-7/4 werckismic 20
25 0-502-702-1003 1-11/7-10/7-7/4 werckismic 20
26 0-202-401-1103 1-20/11-7/6-5/3 swetismic 22
27 0-202-501-1103 1-20/11-10/9-5/3 utonal 22
28 0-401-602-1103 1-7/6-3/2-5/3 otonal 22
29 0-202-702-1103 1-20/11-10/7-5/3 utonal 22
30 0-401-702-1103 1-7/6-10/7-5/3 swetismic 22
31 0-501-702-1103 1-10/9-10/7-5/3 utonal 22
32 0-401-903-1103 1-7/6-11/6-5/3 otonal 22
33 0-602-903-1103 1-3/2-11/6-5/3 otonal 22
34 0-702-903-1103 1-10/7-11/6-5/3 swetismic 22
35 0-201-502-1202 1-9/7-11/7-9/8 werckismic 24
36 0-301-502-1202 1-11/9-11/7-9/8 jove 24
37 0-201-602-1202 1-9/7-3/2-9/8 utonal 24
38 0-301-602-1202 1-11/9-3/2-9/8 rastmic 24
39 0-201-702-1202 1-9/7-10/7-9/8 werckismic 24
40 0-301-702-1202 1-11/9-10/7-9/8 jove 24
41 0-502-702-1202 1-11/7-10/7-9/8 werckismic 24
42 0-201-903-1202 1-9/7-11/6-9/8 jove 24
43 0-301-903-1202 1-11/9-11/6-9/8 rastmic 24
44 0-502-903-1202 1-11/7-11/6-9/8 jove 24
45 0-602-903-1202 1-3/2-11/6-9/8 rastmic 24
46 0-702-903-1202 1-10/7-11/6-9/8 jove 24
47 0-301-1003-1202 1-11/9-7/4-9/8 jove 24
48 0-502-1003-1202 1-11/7-7/4-9/8 werckismic 24
49 0-602-1003-1202 1-3/2-7/4-9/8 otonal 24
50 0-702-1003-1202 1-10/7-7/4-9/8 werckismic 24
51 0-301-502-1503 1-11/9-11/7-11/8 utonal 30
52 0-301-602-1503 1-11/9-3/2-11/8 rastmic 30
53 0-301-903-1503 1-11/9-11/6-11/8 utonal 30
54 0-502-903-1503 1-11/7-11/6-11/8 utonal 30
55 0-602-903-1503 1-3/2-11/6-11/8 ambitonal 30
56 0-301-1003-1503 1-11/9-7/4-11/8 werckismic 30
57 0-502-1003-1503 1-11/7-7/4-11/8 werckismic 30
58 0-602-1003-1503 1-3/2-7/4-11/8 otonal 30
59 0-301-1202-1503 1-11/9-9/8-11/8 rastmic 30
60 0-502-1202-1503 1-11/7-9/8-11/8 werckismic 30
61 0-602-1202-1503 1-3/2-9/8-11/8 otonal 30
62 0-903-1202-1503 1-11/6-9/8-11/8 rastmic 30
63 0-1003-1202-1503 1-7/4-9/8-11/8 otonal 30
64 0-202-501-1703 1-20/11-10/9-5/4 utonal 34
65 0-202-702-1703 1-20/11-10/7-5/4 utonal 34
66 0-501-702-1703 1-10/9-10/7-5/4 utonal 34
67 0-501-1003-1703 1-10/9-7/4-5/4 werckismic 34
68 0-602-1003-1703 1-3/2-7/4-5/4 otonal 34
69 0-702-1003-1703 1-10/7-7/4-5/4 werckismic 34
70 0-202-1103-1703 1-20/11-5/3-5/4 utonal 34
71 0-501-1103-1703 1-10/9-5/3-5/4 utonal 34
72 0-602-1103-1703 1-3/2-5/3-5/4 ambitonal 34
73 0-702-1103-1703 1-10/7-5/3-5/4 utonal 34
74 0-602-1202-1703 1-3/2-9/8-5/4 otonal 34
75 0-702-1202-1703 1-10/7-9/8-5/4 werckismic 34
76 0-1003-1202-1703 1-7/4-9/8-5/4 otonal 34
77 0-602-1503-1703 1-3/2-11/8-5/4 otonal 34
78 0-1003-1503-1703 1-7/4-11/8-5/4 otonal 34
79 0-1202-1503-1703 1-9/8-11/8-5/4 otonal 34

Pentads

Number Chord Transversal Type Complexity
1 0-201-401-602-903 1-9/7-7/6-3/2-11/6 swetismic 18
2 0-201-401-702-903 1-9/7-7/6-10/7-11/6 swetismic 18
3 0-201-502-702-903 1-9/7-11/7-10/7-11/6 swetismic 18
4 0-301-502-702-903 1-11/9-11/7-10/7-11/6 swetismic 18
5 0-301-501-702-1003 1-11/9-10/9-10/7-7/4 jove 20
6 0-301-502-702-1003 1-11/9-11/7-10/7-7/4 jove 20
7 0-202-401-702-1103 1-20/11-7/6-10/7-5/3 swetismic 22
8 0-202-501-702-1103 1-20/11-10/9-10/7-5/3 utonal 22
9 0-401-602-903-1103 1-7/6-3/2-11/6-5/3 otonal 22
10 0-401-702-903-1103 1-7/6-10/7-11/6-5/3 swetismic 22
11 0-201-502-702-1202 1-9/7-11/7-10/7-9/8 werckismic 24
12 0-301-502-702-1202 1-11/9-11/7-10/7-9/8 jove 24
13 0-201-502-903-1202 1-9/7-11/7-11/6-9/8 jove 24
14 0-301-502-903-1202 1-11/9-11/7-11/6-9/8 jove 24
15 0-201-602-903-1202 1-9/7-3/2-11/6-9/8 jove 24
16 0-301-602-903-1202 1-11/9-3/2-11/6-9/8 rastmic 24
17 0-201-702-903-1202 1-9/7-10/7-11/6-9/8 jove 24
18 0-301-702-903-1202 1-11/9-10/7-11/6-9/8 jove 24
19 0-502-702-903-1202 1-11/7-10/7-11/6-9/8 jove 24
20 0-301-502-1003-1202 1-11/9-11/7-7/4-9/8 jove 24
21 0-301-602-1003-1202 1-11/9-3/2-7/4-9/8 jove 24
22 0-301-702-1003-1202 1-11/9-10/7-7/4-9/8 jove 24
23 0-502-702-1003-1202 1-11/7-10/7-7/4-9/8 werckismic 24
24 0-301-502-903-1503 1-11/9-11/7-11/6-11/8 utonal 30
25 0-301-602-903-1503 1-11/9-3/2-11/6-11/8 rastmic 30
26 0-301-502-1003-1503 1-11/9-11/7-7/4-11/8 werckismic 30
27 0-301-602-1003-1503 1-11/9-3/2-7/4-11/8 jove 30
28 0-301-502-1202-1503 1-11/9-11/7-9/8-11/8 jove 30
29 0-301-602-1202-1503 1-11/9-3/2-9/8-11/8 rastmic 30
30 0-301-903-1202-1503 1-11/9-11/6-9/8-11/8 rastmic 30
31 0-502-903-1202-1503 1-11/7-11/6-9/8-11/8 jove 30
32 0-602-903-1202-1503 1-3/2-11/6-9/8-11/8 rastmic 30
33 0-301-1003-1202-1503 1-11/9-7/4-9/8-11/8 jove 30
34 0-502-1003-1202-1503 1-11/7-7/4-9/8-11/8 werckismic 30
35 0-602-1003-1202-1503 1-3/2-7/4-9/8-11/8 otonal 30
36 0-202-501-702-1703 1-20/11-10/9-10/7-5/4 utonal 34
37 0-501-702-1003-1703 1-10/9-10/7-7/4-5/4 werckismic 34
38 0-202-501-1103-1703 1-20/11-10/9-5/3-5/4 utonal 34
39 0-202-702-1103-1703 1-20/11-10/7-5/3-5/4 utonal 34
40 0-501-702-1103-1703 1-10/9-10/7-5/3-5/4 utonal 34
41 0-602-1003-1202-1703 1-3/2-7/4-9/8-5/4 otonal 34
42 0-702-1003-1202-1703 1-10/7-7/4-9/8-5/4 werckismic 34
43 0-602-1003-1503-1703 1-3/2-7/4-11/8-5/4 otonal 34
44 0-602-1202-1503-1703 1-3/2-9/8-11/8-5/4 otonal 34
45 0-1003-1202-1503-1703 1-7/4-9/8-11/8-5/4 otonal 34

Hexads

Number Chord Transversal Type Complexity
1 0-201-502-702-903-1202 1-9/7-11/7-10/7-11/6-9/8 jove 24
2 0-301-502-702-903-1202 1-11/9-11/7-10/7-11/6-9/8 jove 24
3 0-301-502-702-1003-1202 1-11/9-11/7-10/7-7/4-9/8 jove 24
4 0-301-502-903-1202-1503 1-11/9-11/7-11/6-9/8-11/8 jove 30
5 0-301-602-903-1202-1503 1-11/9-3/2-11/6-9/8-11/8 rastmic 30
6 0-301-502-1003-1202-1503 1-11/9-11/7-7/4-9/8-11/8 jove 30
7 0-301-602-1003-1202-1503 1-11/9-3/2-7/4-9/8-11/8 jove 30
8 0-202-501-702-1103-1703 1-20/11-10/9-10/7-5/3-5/4 utonal 34
9 0-602-1003-1202-1503-1703 1-3/2-7/4-9/8-11/8-5/4 otonal 34