Chords of valentine

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Below are listed the dyadic chords of 11-limit valentine temperament. Typing the chords requires consideration of the fact that valentine conflates 12/11 and 11/10 and so also 11/6 and 20/11. If a transversal can be found which shows the chord to be essentially just, that transversal is listed along with a typing as otonal, utonal, or ambitonal. If the chord is essentially tempered, it is analyzed in terms of the transversal which employs 11/10 and 20/11.

If only 126/125 needs to be tempered out, the chord is labeled starling, if 121/120, biyatismic, if 176/175, valinorsmic, if 385/384, keenanismic, and if 441/440, werckismic. Chords which require any two of 121/120, 176/175 or 385/384 are labeled zeus, if they require any two of 126/125, 176/175 or 441/440, they are labeled thrush. Finally, if they require any three independent commas among those discussed above, it is labeled valentine.

Valentine has MOS of size 15, 16, 31 and 46. It is readily observed from the list below that even the smallest of these is well-supplied with chords. Because Carlos Alpha is the generator chain of valentine in the tuning with pure 3/2's, the list below is also a list of chords of Carlos Alpha, so long as the transversals are adjusted so that the notes are in the correct octave. This means that a number in a chord listed under "chord" less than 16 corresponds to a note in the transversal which should be left unaltered, whereas the notes from 16 to 21 correspond to transversal notes which should be adjusted up an octave. Hence, tetrad 8, the 0-2-5-9 chord with transversal 1-6/5-11/8-3/2, is an essentially zeus chord of Carlos Alpha as well as valentine. On the other hand, tetrad 76, 0-10-13-18 with transversal 1-11/7-9/5-9/8, corresponds to the werckismic 1-11/7-9/5-9/4 chord of Carlos Alpha.

In other words, each chord here has an unlimited number of "voicings" in valentine temperament, but exactly one voicing in Carlos Alpha, because there are no octaves.

Triads

Number Chord Transversal Type
1 0-2-4 1-11/10-6/5 otonal
2 0-2-5 1-11/10-5/4 valinorsmic
3 0-3-5 1-8/7-5/4 valinorsmic
4 0-2-7 1-11/10-11/8 utonal
5 0-3-7 1-8/7-11/8 keenanismic
6 0-4-7 1-6/5-11/8 keenanismic
7 0-5-7 1-5/4-11/8 otonal
8 0-3-8 1-8/7-10/7 otonal
9 0-4-8 1-6/5-10/7 starling
10 0-5-8 1-5/4-10/7 utonal
11 0-2-9 1-12/11-3/2 utonal
12 0-4-9 1-6/5-3/2 utonal
13 0-5-9 1-5/4-3/2 otonal
14 0-7-9 1-11/8-3/2 otonal
15 0-2-10 1-11/10-11/7 utonal
16 0-3-10 1-8/7-11/7 otonal
17 0-5-10 1-5/4-11/7 valinorsmic
18 0-7-10 1-11/8-11/7 utonal
19 0-8-10 1-10/7-11/7 otonal
20 0-2-11 1-12/11-18/11 otonal
21 0-3-11 1-8/7-18/11 werckismic
22 0-4-11 1-6/5-18/11 biyatismic
23 0-7-11 1-11/8-18/11 biyatismic
24 0-8-11 1-10/7-18/11 werckismic
25 0-9-11 1-3/2-18/11 utonal
26 0-2-12 1-12/11-12/7 utonal
27 0-3-12 1-8/7-12/7 otonal
28 0-4-12 1-6/5-12/7 utonal
29 0-5-12 1-5/4-12/7 keenanismic
30 0-7-12 1-11/8-12/7 keenanismic
31 0-8-12 1-10/7-12/7 otonal
32 0-9-12 1-3/2-12/7 utonal
33 0-10-12 1-11/7-12/7 otonal
34 0-2-13 1-11/10-9/5 otonal
35 0-3-13 1-8/7-9/5 werckismic
36 0-4-13 1-6/5-9/5 otonal
37 0-5-13 1-5/4-9/5 starling
38 0-8-13 1-10/7-9/5 starling
39 0-9-13 1-3/2-9/5 utonal
40 0-10-13 1-11/7-9/5 werckismic
41 0-11-13 1-18/11-9/5 utonal
42 0-5-18 1-5/4-9/8 otonal
43 0-7-18 1-11/8-9/8 otonal
44 0-8-18 1-10/7-9/8 werckismic
45 0-9-18 1-3/2-9/8 ambitonal
46 0-10-18 1-11/7-9/8 werckismic
47 0-11-18 1-18/11-9/8 utonal
48 0-13-18 1-9/5-9/8 utonal
49 0-3-21 1-8/7-9/7 otonal
50 0-8-21 1-10/7-9/7 otonal
51 0-9-21 1-3/2-9/7 utonal
52 0-10-21 1-11/7-9/7 otonal
53 0-11-21 1-18/11-9/7 utonal
54 0-12-21 1-12/7-9/7 otonal
55 0-13-21 1-9/5-9/7 utonal
56 0-18-21 1-9/8-9/7 utonal

Tetrads

Number Chord Transversal Type
1 0-2-4-7 1-11/10-6/5-11/8 zeus
2 0-2-5-7 1-11/10-5/4-11/8 valinorsmic
3 0-3-5-7 1-8/7-5/4-11/8 zeus
4 0-3-5-8 1-8/7-5/4-10/7 valinorsmic
5 0-2-4-9 1-12/11-6/5-3/2 utonal
6 0-2-5-9 1-11/10-5/4-3/2 zeus
7 0-2-7-9 1-11/10-11/8-3/2 biyatismic
8 0-4-7-9 1-6/5-11/8-3/2 zeus
9 0-5-7-9 1-5/4-11/8-3/2 otonal
10 0-2-5-10 1-11/10-5/4-11/7 valinorsmic
11 0-3-5-10 1-8/7-5/4-11/7 valinorsmic
12 0-2-7-10 1-11/10-11/8-11/7 utonal
13 0-3-7-10 1-8/7-11/8-11/7 keenanismic
14 0-5-7-10 1-5/4-11/8-11/7 valinorsmic
15 0-3-8-10 1-8/7-10/7-11/7 otonal
16 0-5-8-10 1-5/4-10/7-11/7 valinorsmic
17 0-2-4-11 1-11/10-6/5-18/11 biyatismic
18 0-2-7-11 1-11/10-11/8-18/11 biyatismic
19 0-3-7-11 1-8/7-11/8-18/11 valentine
20 0-4-7-11 1-6/5-11/8-18/11 zeus
21 0-3-8-11 1-8/7-10/7-18/11 werckismic
22 0-4-8-11 1-6/5-10/7-18/11 valentine
23 0-2-9-11 1-12/11-3/2-18/11 ambitonal
24 0-4-9-11 1-6/5-3/2-18/11 biyatismic
25 0-7-9-11 1-11/8-3/2-18/11 biyatismic
26 0-2-4-12 1-12/11-6/5-12/7 utonal
27 0-2-5-12 1-11/10-5/4-12/7 zeus
28 0-3-5-12 1-8/7-5/4-12/7 zeus
29 0-2-7-12 1-11/10-11/8-12/7 zeus
30 0-3-7-12 1-8/7-11/8-12/7 keenanismic
31 0-4-7-12 1-6/5-11/8-12/7 keenanismic
32 0-5-7-12 1-5/4-11/8-12/7 keenanismic
33 0-3-8-12 1-8/7-10/7-12/7 otonal
34 0-4-8-12 1-6/5-10/7-12/7 starling
35 0-5-8-12 1-5/4-10/7-12/7 keenanismic
36 0-2-9-12 1-12/11-3/2-12/7 utonal
37 0-4-9-12 1-6/5-3/2-12/7 utonal
38 0-5-9-12 1-5/4-3/2-12/7 keenanismic
39 0-7-9-12 1-11/8-3/2-12/7 zeus
40 0-2-10-12 1-11/10-11/7-12/7 biyatismic
41 0-3-10-12 1-8/7-11/7-12/7 otonal
42 0-5-10-12 1-5/4-11/7-12/7 zeus
43 0-7-10-12 1-11/8-11/7-12/7 zeus
44 0-8-10-12 1-10/7-11/7-12/7 otonal
45 0-2-4-13 1-11/10-6/5-9/5 otonal
46 0-2-5-13 1-11/10-5/4-9/5 thrush
47 0-3-5-13 1-8/7-5/4-9/5 thrush
48 0-3-8-13 1-8/7-10/7-9/5 thrush
49 0-4-8-13 1-6/5-10/7-9/5 starling
50 0-5-8-13 1-5/4-10/7-9/5 starling
51 0-2-9-13 1-11/10-3/2-9/5 biyatismic
52 0-4-9-13 1-6/5-3/2-9/5 ambitonal
53 0-5-9-13 1-5/4-3/2-9/5 starling
54 0-2-10-13 1-11/10-11/7-9/5 werckismic
55 0-3-10-13 1-8/7-11/7-9/5 werckismic
56 0-5-10-13 1-5/4-11/7-9/5 thrush
57 0-8-10-13 1-10/7-11/7-9/5 thrush
58 0-2-11-13 1-11/10-18/11-9/5 biyatismic
59 0-3-11-13 1-8/7-18/11-9/5 werckismic
60 0-4-11-13 1-6/5-18/11-9/5 biyatismic
61 0-8-11-13 1-10/7-18/11-9/5 thrush
62 0-9-11-13 1-3/2-18/11-9/5 utonal
63 0-5-7-18 1-5/4-11/8-9/8 otonal
64 0-5-8-18 1-5/4-10/7-9/8 werckismic
65 0-5-9-18 1-5/4-3/2-9/8 otonal
66 0-7-9-18 1-11/8-3/2-9/8 otonal
67 0-5-10-18 1-5/4-11/7-9/8 thrush
68 0-7-10-18 1-11/8-11/7-9/8 werckismic
69 0-8-10-18 1-10/7-11/7-9/8 werckismic
70 0-7-11-18 1-11/8-18/11-9/8 biyatismic
71 0-8-11-18 1-10/7-18/11-9/8 werckismic
72 0-9-11-18 1-3/2-18/11-9/8 utonal
73 0-5-13-18 1-5/4-9/5-9/8 starling
74 0-8-13-18 1-10/7-9/5-9/8 thrush
75 0-9-13-18 1-3/2-9/5-9/8 utonal
76 0-10-13-18 1-11/7-9/5-9/8 werckismic
77 0-11-13-18 1-18/11-9/5-9/8 utonal
78 0-3-8-21 1-8/7-10/7-9/7 otonal
79 0-3-10-21 1-8/7-11/7-9/7 otonal
80 0-8-10-21 1-10/7-11/7-9/7 otonal
81 0-3-11-21 1-8/7-18/11-9/7 werckismic
82 0-8-11-21 1-10/7-18/11-9/7 werckismic
83 0-9-11-21 1-3/2-18/11-9/7 utonal
84 0-3-12-21 1-8/7-12/7-9/7 otonal
85 0-8-12-21 1-10/7-12/7-9/7 otonal
86 0-9-12-21 1-3/2-12/7-9/7 ambitonal
87 0-10-12-21 1-11/7-12/7-9/7 otonal
88 0-3-13-21 1-8/7-9/5-9/7 werckismic
89 0-8-13-21 1-10/7-9/5-9/7 starling
90 0-9-13-21 1-3/2-9/5-9/7 utonal
91 0-10-13-21 1-11/7-9/5-9/7 werckismic
92 0-11-13-21 1-18/11-9/5-9/7 utonal
93 0-8-18-21 1-10/7-9/8-9/7 werckismic
94 0-9-18-21 1-3/2-9/8-9/7 utonal
95 0-10-18-21 1-11/7-9/8-9/7 werckismic
96 0-11-18-21 1-18/11-9/8-9/7 utonal
97 0-13-18-21 1-9/5-9/8-9/7 utonal

Pentads

Number Chord Transversal Type
1 0-2-4-7-9 1-11/10-6/5-11/8-3/2 zeus
2 0-2-5-7-9 1-11/10-5/4-11/8-3/2 zeus
3 0-2-5-7-10 1-11/10-5/4-11/8-11/7 valinorsmic
4 0-3-5-7-10 1-8/7-5/4-11/8-11/7 zeus
5 0-3-5-8-10 1-8/7-5/4-10/7-11/7 valinorsmic
6 0-2-4-7-11 1-11/10-6/5-11/8-18/11 zeus
7 0-2-4-9-11 1-11/10-6/5-3/2-18/11 biyatismic
8 0-2-7-9-11 1-11/10-11/8-3/2-18/11 biyatismic
9 0-4-7-9-11 1-6/5-11/8-3/2-18/11 zeus
10 0-2-4-7-12 1-11/10-6/5-11/8-12/7 zeus
11 0-2-5-7-12 1-11/10-5/4-11/8-12/7 zeus
12 0-3-5-7-12 1-8/7-5/4-11/8-12/7 zeus
13 0-3-5-8-12 1-8/7-5/4-10/7-12/7 zeus
14 0-2-4-9-12 1-12/11-6/5-3/2-12/7 utonal
15 0-2-5-9-12 1-11/10-5/4-3/2-12/7 zeus
16 0-2-7-9-12 1-11/10-11/8-3/2-12/7 zeus
17 0-4-7-9-12 1-6/5-11/8-3/2-12/7 zeus
18 0-5-7-9-12 1-5/4-11/8-3/2-12/7 zeus
19 0-2-5-10-12 1-11/10-5/4-11/7-12/7 zeus
20 0-3-5-10-12 1-8/7-5/4-11/7-12/7 zeus
21 0-2-7-10-12 1-11/10-11/8-11/7-12/7 zeus
22 0-3-7-10-12 1-8/7-11/8-11/7-12/7 zeus
23 0-5-7-10-12 1-5/4-11/8-11/7-12/7 zeus
24 0-3-8-10-12 1-8/7-10/7-11/7-12/7 otonal
25 0-5-8-10-12 1-5/4-10/7-11/7-12/7 zeus
26 0-3-5-8-13 1-8/7-5/4-10/7-9/5 thrush
27 0-2-4-9-13 1-11/10-6/5-3/2-9/5 biyatismic
28 0-2-5-9-13 1-11/10-5/4-3/2-9/5 valentine
29 0-2-5-10-13 1-11/10-5/4-11/7-9/5 thrush
30 0-3-5-10-13 1-8/7-5/4-11/7-9/5 thrush
31 0-3-8-10-13 1-8/7-10/7-11/7-9/5 thrush
32 0-5-8-10-13 1-5/4-10/7-11/7-9/5 thrush
33 0-2-4-11-13 1-11/10-6/5-18/11-9/5 biyatismic
34 0-3-8-11-13 1-8/7-10/7-18/11-9/5 thrush
35 0-4-8-11-13 1-6/5-10/7-18/11-9/5 valentine
36 0-2-9-11-13 1-11/10-3/2-18/11-9/5 biyatismic
37 0-4-9-11-13 1-6/5-3/2-18/11-9/5 biyatismic
38 0-5-7-9-18 1-5/4-11/8-3/2-9/8 otonal
39 0-5-7-10-18 1-5/4-11/8-11/7-9/8 thrush
40 0-5-8-10-18 1-5/4-10/7-11/7-9/8 thrush
41 0-7-9-11-18 1-11/8-3/2-18/11-9/8 biyatismic
42 0-5-8-13-18 1-5/4-10/7-9/5-9/8 thrush
43 0-5-9-13-18 1-5/4-3/2-9/5-9/8 starling
44 0-5-10-13-18 1-5/4-11/7-9/5-9/8 thrush
45 0-8-10-13-18 1-10/7-11/7-9/5-9/8 thrush
46 0-8-11-13-18 1-10/7-18/11-9/5-9/8 thrush
47 0-9-11-13-18 1-3/2-18/11-9/5-9/8 utonal
48 0-3-8-10-21 1-8/7-10/7-11/7-9/7 otonal
49 0-3-8-11-21 1-8/7-10/7-18/11-9/7 werckismic
50 0-3-8-12-21 1-8/7-10/7-12/7-9/7 otonal
51 0-3-10-12-21 1-8/7-11/7-12/7-9/7 otonal
52 0-8-10-12-21 1-10/7-11/7-12/7-9/7 otonal
53 0-3-8-13-21 1-8/7-10/7-9/5-9/7 thrush
54 0-3-10-13-21 1-8/7-11/7-9/5-9/7 werckismic
55 0-8-10-13-21 1-10/7-11/7-9/5-9/7 thrush
56 0-3-11-13-21 1-8/7-18/11-9/5-9/7 werckismic
57 0-8-11-13-21 1-10/7-18/11-9/5-9/7 thrush
58 0-9-11-13-21 1-3/2-18/11-9/5-9/7 utonal
59 0-8-10-18-21 1-10/7-11/7-9/8-9/7 werckismic
60 0-8-11-18-21 1-10/7-18/11-9/8-9/7 werckismic
61 0-9-11-18-21 1-3/2-18/11-9/8-9/7 utonal
62 0-8-13-18-21 1-10/7-9/5-9/8-9/7 thrush
63 0-9-13-18-21 1-3/2-9/5-9/8-9/7 utonal
64 0-10-13-18-21 1-11/7-9/5-9/8-9/7 werckismic
65 0-11-13-18-21 1-18/11-9/5-9/8-9/7 utonal

Hexads

Number Chord Transversal Type
1 0-2-4-7-9-11 1-11/10-6/5-11/8-3/2-18/11 zeus
2 0-2-4-7-9-12 1-11/10-6/5-11/8-3/2-12/7 zeus
3 0-2-5-7-9-12 1-11/10-5/4-11/8-3/2-12/7 zeus
4 0-2-5-7-10-12 1-11/10-5/4-11/8-11/7-12/7 zeus
5 0-3-5-7-10-12 1-8/7-5/4-11/8-11/7-12/7 zeus
6 0-3-5-8-10-12 1-8/7-5/4-10/7-11/7-12/7 zeus
7 0-3-5-8-10-13 1-8/7-5/4-10/7-11/7-9/5 thrush
8 0-2-4-9-11-13 1-11/10-6/5-3/2-18/11-9/5 biyatismic
9 0-5-8-10-13-18 1-5/4-10/7-11/7-9/5-9/8 thrush
10 0-3-8-10-12-21 1-8/7-10/7-11/7-12/7-9/7 otonal
11 0-3-8-10-13-21 1-8/7-10/7-11/7-9/5-9/7 thrush
12 0-3-8-11-13-21 1-8/7-10/7-18/11-9/5-9/7 thrush
13 0-8-10-13-18-21 1-10/7-11/7-9/5-9/8-9/7 thrush
14 0-8-11-13-18-21 1-10/7-18/11-9/5-9/8-9/7 thrush
15 0-9-11-13-18-21 1-3/2-18/11-9/5-9/8-9/7 utonal