# Chords of miracle

Below are listed the dyadic chords of 11-limit miracle temperament. They are listed in order of increasing Graham complexity, with hash complexity used to break ties.

For any linear temperament, if we chose a generator, we may put any octave-equivalent chord of the temperament in a canonical form by representing it as a set of nonnegative integers, starting with 0, which are the number of generator steps giving an octave-equivalent note class in the chord. If S is such a set, the sum Σ 2s for all s ∊ S provides a unique odd number encoding the chord, and the logarithm base two of this number is the hash complexity, listed under the heading "Hash" below. The floor of hash complexity, that is, the greatest integer less than the hash complexity, is equal to the Graham complexity.

The heading "transversal" shows a JI chord whose intervals temper to the marvel chord. Under "type" it says otonal if it is an essentially just chord best understood in terms of the harmonic series (the overtones) and utonal if it is the inversion of an otonal chord (in other words, fitting the subharmonic series), and ambitonal if it can equally well be seen as otonal or utonal.

The other names denote types of essentially tempered chord, giving the least amount of tempering needed to define the chord. These include:

The generator used below is the standard choice for miracle temperament, the secor, 16/15~15/14. However, it should be noted that the choice of generator does not affect the list of chords, only how those chords are interpreted. Does 0-7-13 denote the major triad or the minor triad? It's on the list of chords either way, but with a secor generator it's the major triad.

The chords are ordered by generator steps. This chord ordering is useful because you can tell how often it will occur in a scale of miracle. For instance, Chord 0-2-5, which is 1/1-8/7-7/5, occurs for the first time on the fifth generation, and will therefore occur five times in miracle[10]. Chord 0-3-9, which is 1/1-11/9-11/6, occurs for the first time on the ninth generation, and therefore appears only once in miracle[10].

Each of the triads generated has three "inversions", i.e., can be written starting on any one of the three tones in the triad.

This ordering does create results that may seem surprising: For example, chord #21, 1/1-6/5-8/5, is the first inversion of 1/1-5/4-3/2; in this list, 1/1-5/4-3/2 is the second inversion of chord #21. Unlike in traditional music theory, there is nothing canonical about these orderings and inversions.

All three inversions for all 63 chords are notated in this PDF and can be heard using a piano, a steel-stringed guitar, a nylon-stringed guitar, and a string ensemble. (All linked files are in MP3 format. They were created in Mus2 using 41 EDO sagittal notation (get Mus2 file), exported to tuned MIDI, and rendered with Timidity++ using soundfonts.) Finally, here is a tuned MIDI file. The sequence is: chord as generated, first inversion, second inversion, quarter-note rest.

Number Chord Transversal Type Hash As generated First inversion Second inversion
1 0-2-5 1-8/7-7/5 werckismic 5.209453 1/1-8/7-7/5 1/1-11/9-7/4 1/1-10/7-18/11
2 0-3-5 1-11/9-7/5 werckismic 5.357552 1/1-11/9-7/5 1/1-8/7-18/11 1/1-10/7-7/4
3 0-3-6 1-11/9-3/2 rastmic 6.189825 1/1-11/9-3/2 1/1-11/9-18/11 1/1-4/3-18/11
4 0-2-7 1-8/7-8/5 utonal 7.055282 1/1-8/7-8/5 1/1-7/5-7/4 1/1-5/4-10/7
5 0-5-7 1-7/5-8/5 otonal 7.330917 1/1-7/5-8/5 1/1-8/7-10/7 1/1-5/4-7/4
6 0-2-8 1-8/7-12/7 otonal 8.027906 1/1-8/7-12/7 1/1-3/2-7/4 1/1-7/6-4/3
7 0-3-8 1-11/9-12/7 swetismic 8.049849 1/1-11/9-12/7 1/1-7/5-18/11 1/1-7/6-10/7
8 0-5-8 1-7/5-12/7 swetismic 8.174926 1/1-7/5-12/7 1/1-11/9-10/7 1/1-7/6-18/11
9 0-6-8 1-3/2-12/7 utonal 8.326429 1/1-3/2-12/7 1/1-8/7-4/3 1/1-7/6-7/4
10 0-2-9 1-8/7-11/6 keenanismic 9.014020 1/1-8/7-11/6 1/1-8/5-7/4 1/1-12/11-5/4
11 0-3-9 1-11/9-11/6 utonal 9.025140 1/1-11/9-11/6 1/1-3/2-18/11 1/1-12/11-4/3
12 0-6-9 1-3/2-11/6 otonal 9.172428 1/1-3/2-11/6 1/1-11/9-4/3 1/1-12/11-18/11
13 0-7-9 1-8/5-11/6 keenanismic 9.324181 1/1-8/5-11/6 1/1-8/7-5/4 1/1-12/11-7/4
14 0-3-12 1-11/9-9/8 rastmic 12.003167 1/1-9/8-11/9 1/1-12/11-16/9 1/1-18/11-11/6
15 0-5-12 1-7/5-9/8 marvel 12.011577 1/1-9/8-7/5 1/1-56/45-16/9 1/1-10/7-8/5
16 0-6-12 1-3/2-9/8 ambitonal 12.022715 1/1-9/8-3/2 1/1-4/3-16/9 1/1-4/3-3/2
17 0-7-12 1-8/5-9/8 marvel 12.044736 1/1-9/8-8/5 1/1-10/7-16/9 1/1-5/4-7/5
18 0-9-12 1-11/6-9/8 rastmic 12.170238 1/1-9/8-11/6 1/1-18/11-16/9 1/1-12/11-11/9
19 0-5-13 1-7/5-6/5 otonal 13.005800 1/1-6/5-7/5 1/1-7/6-5/3 1/1-10/7-12/7
20 0-6-13 1-3/2-6/5 utonal 13.011402 1/1-6/5-3/2 1/1-5/4-5/3 1/1-4/3-8/5
21 0-7-13 1-8/5-6/5 otonal 13.022541 1/1-6/5-8/5 1/1-4/3-5/3 1/1-5/4-3/2
22 0-8-13 1-12/7-6/5 utonal 13.044565 1/1-6/5-12/7 1/1-10/7-5/3 1/1-7/6-7/5
23 0-2-14 1-8/7-9/7 otonal 14.000440 1/1-8/7-9/7 1/1-9/8-7/4 1/1-14/9-16/9
24 0-5-14 1-7/5-9/7 swetismic 14.002903 1/1-9/7-7/5 1/1-12/11-14/9 1/1-10/7-11/6
25 0-6-14 1-3/2-9/7 utonal 14.005712 1/1-9/7-3/2 1/1-7/6-14/9 1/1-4/3-12/7
26 0-7-14 1-8/5-9/7 marvel 14.011315 1/1-9/7-8/5 1/1-5/4-14/9 1/1-5/4-8/5
27 0-8-14 1-12/7-9/7 otonal 14.022455 1/1-9/7-12/7 1/1-4/3-14/9 1/1-7/6-3/2
28 0-9-14 1-11/6-9/7 swetismic 14.04448 1/1-9/7-11/6 1/1-10/7-14/9 1/1-12/11-7/5
29 0-12-14 1-9/8-9/7 utonal 14.321999 1/1-9/8-9/7 1/1-8/7-16/9 1/1-14/9-7/4
30 0-2-15 1-8/7-11/8 keenanismic 15.000220 1/1-8/7-11/8 1/1-6/5-7/4 1/1-16/11-5/3
31 0-3-15 1-11/9-11/8 utonal 15.000396 1/1-11/9-11/8 1/1-9/8-18/11 1/1-16/11-16/9
32 0-6-15 1-3/2-11/8 otonal 15.002859 1/1-11/8-3/2 1/1-12/11-16/11 1/1-4/3-11/6
33 0-7-15 1-8/5-11/8 keenanismic 15.005660 1/1-11/8-8/5 1/1-7/6-16/11 1/1-5/4-12/7
34 0-8-15 1-12/7-11/8 keenanismic 15.011271 1/1-11/8-12/7 1/1-5/4-16/11 1/1-7/6-8/5
35 0-9-15 1-11/6-11/8 utonal 15.022411 1/1-11/8-11/6 1/1-4/3-16/11 1/1-12/11-3/2
36 0-12-15 1-9/8-11/8 otonal 15.169964 1/1-9/8-11/8 1/1-11/9-16/9 1/1-16/11-18/11
37 0-13-15 1-6/5-11/8 keenanismic 15.321963 1/1-6/5-11/8 1/1-8/7-5/3 1/1-16/11-7/4
38 0-2-17 1-8/7-11/7 otonal 17.000055 1/1-8/7-11/7 1/1-11/8-7/4 1/1-14/11-16/11
39 0-3-17 1-11/9-11/7 utonal 17.000099 1/1-11/9-11/7 1/1-9/7-18/11 1/1-14/11-14/9
40 0-5-17 1-7/5-11/7 werckismic 17.000363 1/1-7/5-11/7 1/1-9/8-10/7 1/1-14/11-16/9
41 0-8-17 1-12/7-11/7 otonal 17.002826 1/1-11/7-12/7 1/1-12/11-14/11 1/1-7/6-11/6
42 0-9-17 1-11/6-11/7 utonal 17.005636 1/1-11/7-11/6 1/1-7/6-14/11 1/1-12/11-12/7
43 0-12-17 1-9/8-11/7 werckismic 17.0444 1/1-9/8-11/7 1/1-7/5-16/9 1/1-14/11-10/7
44 0-14-17 1-9/7-11/7 otonal 17.169935 1/1-9/7-11/7 1/1-11/9-14/9 1/1-14/11-18/11
45 0-15-17 1-11/8-11/7 utonal 17.321937 1/1-11/8-11/7 1/1-8/7-16/11 1/1-14/11-7/4
46 0-2-19 1-8/7-9/5 werckismic 19.000014 1/1-8/7-9/5 1/1-11/7-7/4 1/1-10/9-14/11
47 0-5-19 1-7/5-9/5 otonal 19.000091 1/1-7/5-9/5 1/1-9/7-10/7 1/1-10/9-14/9
48 0-6-19 1-3/2-9/5 utonal 19.000179 1/1-3/2-9/5 1/1-6/5-4/3 1/1-10/9-5/3
49 0-7-19 1-8/5-9/5 otonal 19.000355 1/1-8/5-9/5 1/1-9/8-5/4 1/1-10/9-16/9
50 0-12-19 1-9/8-9/5 utonal 19.011230 1/1-9/8-9/5 1/1-8/5-16/9 1/1-10/9-5/4
51 0-13-19 1-6/5-9/5 otonal 19.022371 1/1-6/5-9/5 1/1-3/2-5/3 1/1-10/9-4/3
52 0-14-19 1-9/7-9/5 utonal 19.044397 1/1-9/7-9/5 1/1-7/5-14/9 1/1-10/9-10/7
53 0-17-19 1-11/7-9/5 werckismic 19.321930 1/1-11/7-9/5 1/1-8/7-14/11 1/1-10/9-7/4
54 0-3-22 1-11/9-11/10 utonal 22.000003 1/1-11/10-11/9 1/1-10/9-20/11 1/1-18/11-9/5
55 0-5-22 1-7/5-11/10 otonal 22.000011 1/1-11/10-7/5 1/1-14/11-20/11 1/1-10/7-11/7
56 0-7-22 1-8/5-11/10 otonal 22.000044 1/1-11/10-8/5 1/1-16/11-20/11 1/1-5/4-11/8
57 0-8-22 1-12/7-11/10 swetismic 22.000088 1/1-11/10-12/7 1/1-14/9-20/11 1/1-7/6-9/7
58 0-9-22 1-11/6-11/10 utonal 22.000176 1/1-11/10-11/6 1/1-5/3-20/11 1/1-12/11-6/5
59 0-13-22 1-6/5-11/10 otonal 22.002815 1/1-11/10-6/5 1/1-12/11-20/11 1/1-5/3-11/6
60 0-14-22 1-9/7-11/10 swetismic 22.005625 1/1-11/10-9/7 1/1-7/6-20/11 1/1-14/9-12/7
61 0-15-22 1-11/8-11/10 utonal 22.011228 1/1-11/10-11/8 1/1-5/4-20/11 1/1-16/11-8/5
62 0-17-22 1-11/7-11/10 utonal 22.044394 1/1-11/10-11/7 1/1-10/7-20/11 1/1-14/11-7/5
63 0-19-22 1-9/5-11/10 otonal 22.169925 1/1-11/10-9/5 1/1-18/11-20/11 1/1-10/9-11/9

Number Chord Transversal Type Hash As generated First inversion Second inversion Third inversion
1 0-2-5-7 1-8/7-7/5-8/5 werckismic 7.366322 1/1-8/7-7/5-8/5 1/1-11/9-7/5-7/4 1/1-8/7-10/7-18/11 1/1-5/4-10/7-7/4
2 0-2-5-8 1-8/7-7/5-12/7 jove 8.194757 1/1-8/7-7/5-12/7 1/1-11/9-3/2-7/4 1/1-11/9-10/7-18/11 1/1-7/6-4/3-18/11
3 0-3-5-8 1-11/9-7/5-12/7 jove 8.214319 1/1-11/9-7/5-12/7 1/1-8/7-7/5-18/11 1/1-11/9-10/7-7/4 1/1-7/6-10/7-18/11
4 0-3-6-8 1-11/9-3/2-12/7 jove 8.361944 1/1-11/9-3/2-12/7 1/1-11/9-7/5-18/11 1/1-8/7-4/3-18/11 1/1-7/6-10/7-7/4
5 0-3-6-9 1-11/9-3/2-11/6 rastmic 9.192293 1/1-11/9-3/2-11/6 1/1-11/9-3/2-18/11 1/1-11/9-4/3-18/11 1/1-12/11-4/3-18/11
6 0-2-7-9 1-8/7-8/5-11/6 keenanismic 9.333155 1/1-8/7-8/5-11/6 1/1-7/5-8/5-7/4 1/1-8/7-5/4-10/7 1/1-12/11-5/4-7/4
7 0-3-5-12 1-11/9-7/5-9/8 miracle 12.014369 1/1-9/8-11/9-7/5 1/1-12/11-5/4-16/9 1/1-8/7-18/11-11/6 1/1-10/7-8/5-7/4
8 0-3-6-12 1-11/9-3/2-9/8 rastmic 12.025486 1/1-9/8-11/9-3/2 1/1-12/11-4/3-16/9 1/1-11/9-18/11-11/6 1/1-4/3-3/2-18/11
9 0-5-7-12 1-7/5-8/5-9/8 marvel 12.055621 1/1-9/8-7/5-8/5 1/1-5/4-10/7-16/9 1/1-8/7-10/7-8/5 1/1-5/4-7/5-7/4
10 0-3-9-12 1-11/9-11/6-9/8 rastmic 12.172740 1/1-9/8-11/9-11/6 1/1-12/11-18/11-16/9 1/1-3/2-18/11-11/6 1/1-12/11-11/9-4/3
11 0-6-9-12 1-3/2-11/6-9/8 rastmic 12.190133 1/1-9/8-3/2-11/6 1/1-4/3-18/11-16/9 1/1-11/9-4/3-3/2 1/1-12/11-11/9-18/11
12 0-7-9-12 1-8/5-11/6-9/8 miracle 12.209758 1/1-9/8-8/5-11/6 1/1-10/7-18/11-16/9 1/1-8/7-5/4-7/5 1/1-12/11-11/9-7/4
13 0-5-7-13 1-7/5-8/5-6/5 otonal 13.028079 1/1-6/5-7/5-8/5 1/1-7/6-4/3-5/3 1/1-8/7-10/7-12/7 1/1-5/4-3/2-7/4
14 0-5-8-13 1-7/5-12/7-6/5 swetismic 13.050019 1/1-6/5-7/5-12/7 1/1-7/6-10/7-5/3 1/1-11/9-10/7-12/7 1/1-7/6-7/5-18/11
15 0-6-8-13 1-3/2-12/7-6/5 utonal 13.055452 1/1-6/5-3/2-12/7 1/1-5/4-10/7-5/3 1/1-8/7-4/3-8/5 1/1-7/6-7/5-7/4
16 0-2-5-14 1-8/7-7/5-9/7 jove 14.003254 1/1-8/7-9/7-7/5 1/1-9/8-11/9-7/4 1/1-12/11-14/9-16/9 1/1-10/7-18/11-11/6
17 0-2-7-14 1-8/7-8/5-9/7 marvel 14.011664 1/1-8/7-9/7-8/5 1/1-9/8-7/5-7/4 1/1-5/4-14/9-16/9 1/1-5/4-10/7-8/5
18 0-5-7-14 1-7/5-8/5-9/7 unimarvel 14.014108 1/1-9/7-7/5-8/5 1/1-12/11-5/4-14/9 1/1-8/7-10/7-11/6 1/1-5/4-8/5-7/4
19 0-2-8-14 1-8/7-12/7-9/7 otonal 14.022801 1/1-8/7-9/7-12/7 1/1-9/8-3/2-7/4 1/1-4/3-14/9-16/9 1/1-7/6-4/3-3/2
20 0-5-8-14 1-7/5-12/7-9/7 swetismic 14.025226 1/1-9/7-7/5-12/7 1/1-12/11-4/3-14/9 1/1-11/9-10/7-11/6 1/1-7/6-3/2-18/11
21 0-6-8-14 1-3/2-12/7-9/7 ambitonal 14.027992 1/1-9/7-3/2-12/7 1/1-7/6-4/3-14/9 1/1-8/7-4/3-12/7 1/1-7/6-3/2-7/4
22 0-2-9-14 1-8/7-11/6-9/7 unimarvel 14.044821 1/1-8/7-9/7-11/6 1/1-9/8-8/5-7/4 1/1-10/7-14/9-16/9 1/1-12/11-5/4-7/5
23 0-6-9-14 1-3/2-11/6-9/7 swetismic 14.049934 1/1-9/7-3/2-11/6 1/1-7/6-10/7-14/9 1/1-11/9-4/3-12/7 1/1-12/11-7/5-18/11
24 0-7-9-14 1-8/5-11/6-9/7 unimarvel 14.055367 1/1-9/7-8/5-11/6 1/1-5/4-10/7-14/9 1/1-8/7-5/4-8/5 1/1-12/11-7/5-7/4
25 0-5-12-14 1-7/5-9/8-9/7 unimarvel 14.324251 1/1-9/8-9/7-7/5 1/1-8/7-5/4-16/9 1/1-12/11-14/9-7/4 1/1-10/7-8/5-11/6
26 0-6-12-14 1-3/2-9/8-9/7 utonal 14.326500 1/1-9/8-9/7-3/2 1/1-8/7-4/3-16/9 1/1-7/6-14/9-7/4 1/1-4/3-3/2-12/7
27 0-7-12-14 1-8/5-9/8-9/7 marvel 14.330987 1/1-9/8-9/7-8/5 1/1-8/7-10/7-16/9 1/1-5/4-14/9-7/4 1/1-5/4-7/5-8/5
28 0-9-12-14 1-11/6-9/8-9/7 jove 14.357621 1/1-9/8-9/7-11/6 1/1-8/7-18/11-16/9 1/1-10/7-14/9-7/4 1/1-12/11-11/9-7/5
29 0-3-6-15 1-11/9-3/2-11/8 rastmic 15.003210 1/1-11/9-11/8-3/2 1/1-9/8-11/9-18/11 1/1-12/11-16/11-16/9 1/1-4/3-18/11-11/6
30 0-2-7-15 1-8/7-8/5-11/8 keenanismic 15.005844 1/1-8/7-11/8-8/5 1/1-6/5-7/5-7/4 1/1-7/6-16/11-5/3 1/1-5/4-10/7-12/7
31 0-2-8-15 1-8/7-12/7-11/8 keenanismic 15.011446 1/1-8/7-11/8-12/7 1/1-6/5-3/2-7/4 1/1-5/4-16/11-5/3 1/1-7/6-4/3-8/5
32 0-3-8-15 1-11/9-12/7-11/8 unimarvel 15.011620 1/1-11/9-11/8-12/7 1/1-9/8-7/5-18/11 1/1-5/4-16/11-16/9 1/1-7/6-10/7-8/5
33 0-6-8-15 1-3/2-12/7-11/8 keenanismic 15.014064 1/1-11/8-3/2-12/7 1/1-12/11-5/4-16/11 1/1-8/7-4/3-11/6 1/1-7/6-8/5-7/4
34 0-2-9-15 1-8/7-11/6-11/8 keenanismic 15.022585 1/1-8/7-11/8-11/6 1/1-6/5-8/5-7/4 1/1-4/3-16/11-5/3 1/1-12/11-5/4-3/2
35 0-3-9-15 1-11/9-11/6-11/8 utonal 15.022758 1/1-11/9-11/8-11/6 1/1-9/8-3/2-18/11 1/1-4/3-16/11-16/9 1/1-12/11-4/3-3/2
36 0-6-9-15 1-3/2-11/6-11/8 ambitonal 15.025183 1/1-11/8-3/2-11/6 1/1-12/11-4/3-16/11 1/1-11/9-4/3-11/6 1/1-12/11-3/2-18/11
37 0-7-9-15 1-8/5-11/6-11/8 keenanismic 15.027949 1/1-11/8-8/5-11/6 1/1-7/6-4/3-16/11 1/1-8/7-5/4-12/7 1/1-12/11-3/2-7/4
38 0-3-12-15 1-11/9-9/8-11/8 rastmic 15.170277 1/1-9/8-11/9-11/8 1/1-11/10-11/9-16/9 1/1-9/8-18/11-11/6 1/1-16/11-18/11-16/9
39 0-6-12-15 1-3/2-9/8-11/8 otonal 15.172467 1/1-9/8-11/8-3/2 1/1-11/9-4/3-16/9 1/1-12/11-16/11-18/11 1/1-4/3-3/2-11/6
40 0-7-12-15 1-8/5-9/8-11/8 unimarvel 15.174965 1/1-9/8-11/8-8/5 1/1-11/9-10/7-16/9 1/1-7/6-16/11-18/11 1/1-5/4-7/5-12/7
41 0-9-12-15 1-11/6-9/8-11/8 rastmic 15.189863 1/1-9/8-11/8-11/6 1/1-11/9-18/11-16/9 1/1-4/3-16/11-18/11 1/1-12/11-11/9-3/2
42 0-6-13-15 1-3/2-6/5-11/8 keenanismic 15.324216 1/1-6/5-11/8-3/2 1/1-8/7-5/4-5/3 1/1-12/11-16/11-7/4 1/1-4/3-8/5-11/6
43 0-7-13-15 1-8/5-6/5-11/8 keenanismic 15.326465 1/1-6/5-11/8-8/5 1/1-8/7-4/3-5/3 1/1-7/6-16/11-7/4 1/1-5/4-3/2-12/7
44 0-8-13-15 1-12/7-6/5-11/8 keenanismic 15.330952 1/1-6/5-11/8-12/7 1/1-8/7-10/7-5/3 1/1-5/4-16/11-7/4 1/1-7/6-7/5-8/5
45 0-2-5-17 1-8/7-7/5-11/7 werckismic 17.000407 1/1-8/7-7/5-11/7 1/1-11/9-11/8-7/4 1/1-9/8-10/7-18/11 1/1-14/11-16/11-16/9
46 0-3-5-17 1-11/9-7/5-11/7 werckismic 17.000451 1/1-11/9-7/5-11/7 1/1-8/7-9/7-18/11 1/1-9/8-10/7-7/4 1/1-14/11-14/9-16/9
47 0-2-8-17 1-8/7-12/7-11/7 otonal 17.002870 1/1-8/7-11/7-12/7 1/1-11/8-3/2-7/4 1/1-12/11-14/11-16/11 1/1-7/6-4/3-11/6
48 0-3-8-17 1-11/9-12/7-11/7 swetismic 17.002914 1/1-11/9-11/7-12/7 1/1-9/7-7/5-18/11 1/1-12/11-14/11-14/9 1/1-7/6-10/7-11/6
49 0-5-8-17 1-7/5-12/7-11/7 jove 17.003177 1/1-7/5-11/7-12/7 1/1-9/8-11/9-10/7 1/1-12/11-14/11-16/9 1/1-7/6-18/11-11/6
50 0-2-9-17 1-8/7-11/6-11/7 keenanismic 17.005679 1/1-8/7-11/7-11/6 1/1-11/8-8/5-7/4 1/1-7/6-14/11-16/11 1/1-12/11-5/4-12/7
51 0-3-9-17 1-11/9-11/6-11/7 utonal 17.005723 1/1-11/9-11/7-11/6 1/1-9/7-3/2-18/11 1/1-7/6-14/11-14/9 1/1-12/11-4/3-12/7
52 0-3-12-17 1-11/9-9/8-11/7 jove 17.044490 1/1-9/8-11/9-11/7 1/1-12/11-7/5-16/9 1/1-9/7-18/11-11/6 1/1-14/11-10/7-14/9
53 0-5-12-17 1-7/5-9/8-11/7 prodigy 17.044746 1/1-9/8-7/5-11/7 1/1-5/4-7/5-16/9 1/1-9/8-10/7-8/5 1/1-14/11-10/7-16/9
54 0-9-12-17 1-11/6-9/8-11/7 jove 17.049859 1/1-9/8-11/7-11/6 1/1-7/5-18/11-16/9 1/1-7/6-14/11-10/7 1/1-12/11-11/9-12/7
55 0-2-14-17 1-8/7-9/7-11/7 otonal 17.169974 1/1-8/7-9/7-11/7 1/1-9/8-11/8-7/4 1/1-11/9-14/9-16/9 1/1-14/11-16/11-18/11
56 0-5-14-17 1-7/5-9/7-11/7 jove 17.170248 1/1-9/7-7/5-11/7 1/1-12/11-11/9-14/9 1/1-9/8-10/7-11/6 1/1-14/11-18/11-16/9
57 0-8-14-17 1-12/7-9/7-11/7 otonal 17.172437 1/1-9/7-11/7-12/7 1/1-11/9-4/3-14/9 1/1-12/11-14/11-18/11 1/1-7/6-3/2-11/6
58 0-9-14-17 1-11/6-9/7-11/7 swetismic 17.174935 1/1-9/7-11/7-11/6 1/1-11/9-10/7-14/9 1/1-7/6-14/11-18/11 1/1-12/11-7/5-12/7
59 0-12-14-17 1-9/8-9/7-11/7 werckismic 17.209463 1/1-9/8-9/7-11/7 1/1-8/7-7/5-16/9 1/1-11/9-14/9-7/4 1/1-14/11-10/7-18/11
60 0-2-15-17 1-8/7-11/8-11/7 keenanismic 17.321972 1/1-8/7-11/8-11/7 1/1-6/5-11/8-7/4 1/1-8/7-16/11-5/3 1/1-14/11-16/11-7/4
61 0-3-15-17 1-11/9-11/8-11/7 utonal 17.322007 1/1-11/9-11/8-11/7 1/1-9/8-9/7-18/11 1/1-8/7-16/11-16/9 1/1-14/11-14/9-7/4
62 0-8-15-17 1-12/7-11/8-11/7 keenanismic 17.324189 1/1-11/8-11/7-12/7 1/1-8/7-5/4-16/11 1/1-12/11-14/11-7/4 1/1-7/6-8/5-11/6
63 0-9-15-17 1-11/6-11/8-11/7 utonal 17.326438 1/1-11/8-11/7-11/6 1/1-8/7-4/3-16/11 1/1-7/6-14/11-7/4 1/1-12/11-3/2-12/7
64 0-12-15-17 1-9/8-11/8-11/7 werckismic 17.357561 1/1-9/8-11/8-11/7 1/1-11/9-7/5-16/9 1/1-8/7-16/11-18/11 1/1-14/11-10/7-7/4
65 0-2-5-19 1-8/7-7/5-9/5 werckismic 19.000102 1/1-8/7-7/5-9/5 1/1-11/9-11/7-7/4 1/1-9/7-10/7-18/11 1/1-10/9-14/11-14/9
66 0-2-7-19 1-8/7-8/5-9/5 werckismic 19.000366 1/1-8/7-8/5-9/5 1/1-7/5-11/7-7/4 1/1-9/8-5/4-10/7 1/1-10/9-14/11-16/9
67 0-5-7-19 1-7/5-8/5-9/5 otonal 19.000443 1/1-7/5-8/5-9/5 1/1-8/7-9/7-10/7 1/1-9/8-5/4-7/4 1/1-10/9-14/9-16/9
68 0-5-12-19 1-7/5-9/8-9/5 marvel 19.011317 1/1-9/8-7/5-9/5 1/1-5/4-8/5-16/9 1/1-9/7-10/7-8/5 1/1-10/9-5/4-14/9
69 0-6-12-19 1-3/2-9/8-9/5 utonal 19.011405 1/1-9/8-3/2-9/5 1/1-4/3-8/5-16/9 1/1-6/5-4/3-3/2 1/1-10/9-5/4-5/3
70 0-7-12-19 1-8/5-9/8-9/5 marvel 19.011579 1/1-9/8-8/5-9/5 1/1-10/7-8/5-16/9 1/1-9/8-5/4-7/5 1/1-10/9-5/4-16/9
71 0-5-13-19 1-7/5-6/5-9/5 otonal 19.022457 1/1-6/5-7/5-9/5 1/1-7/6-3/2-5/3 1/1-9/7-10/7-12/7 1/1-10/9-4/3-14/9
72 0-6-13-19 1-3/2-6/5-9/5 ambitonal 19.022544 1/1-6/5-3/2-9/5 1/1-5/4-3/2-5/3 1/1-6/5-4/3-8/5 1/1-10/9-4/3-5/3
73 0-7-13-19 1-8/5-6/5-9/5 otonal 19.022717 1/1-6/5-8/5-9/5 1/1-4/3-3/2-5/3 1/1-9/8-5/4-3/2 1/1-10/9-4/3-16/9
74 0-2-14-19 1-8/7-9/7-9/5 werckismic 19.044407 1/1-8/7-9/7-9/5 1/1-9/8-11/7-7/4 1/1-7/5-14/9-16/9 1/1-10/9-14/11-10/7
75 0-5-14-19 1-7/5-9/7-9/5 swetismic 19.044482 1/1-9/7-7/5-9/5 1/1-12/11-7/5-14/9 1/1-9/7-10/7-11/6 1/1-10/9-10/7-14/9
76 0-6-14-19 1-3/2-9/7-9/5 utonal 19.044568 1/1-9/7-3/2-9/5 1/1-7/6-7/5-14/9 1/1-6/5-4/3-12/7 1/1-10/9-10/7-5/3
77 0-7-14-19 1-8/5-9/7-9/5 marvel 19.044738 1/1-9/7-8/5-9/5 1/1-5/4-7/5-14/9 1/1-9/8-5/4-8/5 1/1-10/9-10/7-16/9
78 0-12-14-19 1-9/8-9/7-9/5 utonal 19.055285 1/1-9/8-9/7-9/5 1/1-8/7-8/5-16/9 1/1-7/5-14/9-7/4 1/1-10/9-5/4-10/7
79 0-2-17-19 1-8/7-11/7-9/5 werckismic 19.321939 1/1-8/7-11/7-9/5 1/1-11/8-11/7-7/4 1/1-8/7-14/11-16/11 1/1-10/9-14/11-7/4
80 0-5-17-19 1-7/5-11/7-9/5 werckismic 19.322001 1/1-7/5-11/7-9/5 1/1-9/8-9/7-10/7 1/1-8/7-14/11-16/9 1/1-10/9-14/9-7/4
81 0-12-17-19 1-9/8-11/7-9/5 werckismic 19.330919 1/1-9/8-11/7-9/5 1/1-7/5-8/5-16/9 1/1-8/7-14/11-10/7 1/1-10/9-5/4-7/4
82 0-14-17-19 1-9/7-11/7-9/5 werckismic 19.357554 1/1-9/7-11/7-9/5 1/1-11/9-7/5-14/9 1/1-8/7-14/11-18/11 1/1-10/9-10/7-7/4
83 0-3-5-22 1-11/9-7/5-11/10 werckismic 22.000014 1/1-11/10-11/9-7/5 1/1-10/9-14/11-20/11 1/1-8/7-18/11-9/5 1/1-10/7-11/7-7/4
84 0-5-7-22 1-7/5-8/5-11/10 otonal 22.000055 1/1-11/10-7/5-8/5 1/1-14/11-16/11-20/11 1/1-8/7-10/7-11/7 1/1-5/4-11/8-7/4
85 0-3-8-22 1-11/9-12/7-11/10 swetismic 22.000091 1/1-11/10-11/9-12/7 1/1-10/9-14/9-20/11 1/1-7/5-18/11-9/5 1/1-7/6-9/7-10/7
86 0-5-8-22 1-7/5-12/7-11/10 swetismic 22.000099 1/1-11/10-7/5-12/7 1/1-14/11-14/9-20/11 1/1-11/9-10/7-11/7 1/1-7/6-9/7-18/11
87 0-3-9-22 1-11/9-11/6-11/10 utonal 22.000179 1/1-11/10-11/9-11/6 1/1-10/9-5/3-20/11 1/1-3/2-18/11-9/5 1/1-12/11-6/5-4/3
88 0-7-9-22 1-8/5-11/6-11/10 keenanismic 22.000220 1/1-11/10-8/5-11/6 1/1-16/11-5/3-20/11 1/1-8/7-5/4-11/8 1/1-12/11-6/5-7/4
89 0-5-13-22 1-7/5-6/5-11/10 otonal 22.002826 1/1-11/10-6/5-7/5 1/1-12/11-14/11-20/11 1/1-7/6-5/3-11/6 1/1-10/7-11/7-12/7
90 0-7-13-22 1-8/5-6/5-11/10 otonal 22.002859 1/1-11/10-6/5-8/5 1/1-12/11-16/11-20/11 1/1-4/3-5/3-11/6 1/1-5/4-11/8-3/2
91 0-8-13-22 1-12/7-6/5-11/10 swetismic 22.002903 1/1-11/10-6/5-12/7 1/1-12/11-14/9-20/11 1/1-10/7-5/3-11/6 1/1-7/6-9/7-7/5
92 0-5-14-22 1-7/5-9/7-11/10 swetismic 22.005636 1/1-11/10-9/7-7/5 1/1-7/6-14/11-20/11 1/1-12/11-14/9-12/7 1/1-10/7-11/7-11/6
93 0-7-14-22 1-8/5-9/7-11/10 unimarvel 22.005669 1/1-11/10-9/7-8/5 1/1-7/6-16/11-20/11 1/1-5/4-14/9-12/7 1/1-5/4-11/8-8/5
94 0-8-14-22 1-12/7-9/7-11/10 swetismic 22.005713 1/1-11/10-9/7-12/7 1/1-7/6-14/9-20/11 1/1-4/3-14/9-12/7 1/1-7/6-9/7-3/2
95 0-9-14-22 1-11/6-9/7-11/10 swetismic 22.005800 1/1-11/10-9/7-11/6 1/1-7/6-5/3-20/11 1/1-10/7-14/9-12/7 1/1-12/11-6/5-7/5
96 0-3-15-22 1-11/9-11/8-11/10 utonal 22.011230 1/1-11/10-11/9-11/8 1/1-10/9-5/4-20/11 1/1-9/8-18/11-9/5 1/1-16/11-8/5-16/9
97 0-7-15-22 1-8/5-11/8-11/10 keenanismic 22.011271 1/1-11/10-11/8-8/5 1/1-5/4-16/11-20/11 1/1-7/6-16/11-8/5 1/1-5/4-11/8-12/7
98 0-8-15-22 1-12/7-11/8-11/10 unimarvel 22.011315 1/1-11/10-11/8-12/7 1/1-5/4-14/9-20/11 1/1-5/4-16/11-8/5 1/1-7/6-9/7-8/5
99 0-9-15-22 1-11/6-11/8-11/10 utonal 22.011402 1/1-11/10-11/8-11/6 1/1-5/4-5/3-20/11 1/1-4/3-16/11-8/5 1/1-12/11-6/5-3/2
100 0-13-15-22 1-6/5-11/8-11/10 keenanismic 22.014021 1/1-11/10-6/5-11/8 1/1-12/11-5/4-20/11 1/1-8/7-5/3-11/6 1/1-16/11-8/5-7/4
101 0-3-17-22 1-11/9-11/7-11/10 utonal 22.044397 1/1-11/10-11/9-11/7 1/1-10/9-10/7-20/11 1/1-9/7-18/11-9/5 1/1-14/11-7/5-14/9
102 0-5-17-22 1-7/5-11/7-11/10 werckismic 22.044405 1/1-11/10-7/5-11/7 1/1-14/11-10/7-20/11 1/1-9/8-10/7-11/7 1/1-14/11-7/5-16/9
103 0-8-17-22 1-12/7-11/7-11/10 swetismic 22.044480 1/1-11/10-11/7-12/7 1/1-10/7-14/9-20/11 1/1-12/11-14/11-7/5 1/1-7/6-9/7-11/6
104 0-9-17-22 1-11/6-11/7-11/10 utonal 22.044565 1/1-11/10-11/7-11/6 1/1-10/7-5/3-20/11 1/1-7/6-14/11-7/5 1/1-12/11-6/5-12/7
105 0-14-17-22 1-9/7-11/7-11/10 swetismic 22.049849 1/1-11/10-9/7-11/7 1/1-7/6-10/7-20/11 1/1-11/9-14/9-12/7 1/1-14/11-7/5-18/11
106 0-15-17-22 1-11/8-11/7-11/10 utonal 22.055283 1/1-11/10-11/8-11/7 1/1-5/4-10/7-20/11 1/1-8/7-16/11-8/5 1/1-14/11-7/5-7/4
107 0-5-19-22 1-7/5-9/5-11/10 otonal 22.169935 1/1-11/10-7/5-9/5 1/1-14/11-18/11-20/11 1/1-9/7-10/7-11/7 1/1-10/9-11/9-14/9
108 0-7-19-22 1-8/5-9/5-11/10 otonal 22.169964 1/1-11/10-8/5-9/5 1/1-16/11-18/11-20/11 1/1-9/8-5/4-11/8 1/1-10/9-11/9-16/9
109 0-13-19-22 1-6/5-9/5-11/10 otonal 22.172428 1/1-11/10-6/5-9/5 1/1-12/11-18/11-20/11 1/1-3/2-5/3-11/6 1/1-10/9-11/9-4/3
110 0-14-19-22 1-9/7-9/5-11/10 swetismic 22.174926 1/1-11/10-9/7-9/5 1/1-7/6-18/11-20/11 1/1-7/5-14/9-12/7 1/1-10/9-11/9-10/7
111 0-17-19-22 1-11/7-9/5-11/10 werckismic 22.209454 1/1-11/10-11/7-9/5 1/1-10/7-18/11-20/11 1/1-8/7-14/11-7/5 1/1-10/9-11/9-7/4

Number Chord Transversal Type Hash
1 0-3-6-9-12 1-11/9-3/2-11/6-9/8 rastmic 12.192601
2 0-2-5-7-14 1-8/7-7/5-8/5-9/7 miracle 14.014456
3 0-2-5-8-14 1-8/7-7/5-12/7-9/7 jove 14.025572
4 0-2-7-9-14 1-8/7-8/5-11/6-9/7 unimarvel 14.055706
5 0-5-7-12-14 1-7/5-8/5-9/8-9/7 unimarvel 14.333225
6 0-6-9-12-14 1-3/2-11/6-9/8-9/7 jove 14.362012
7 0-7-9-12-14 1-8/5-11/6-9/8-9/7 miracle 14.366391
8 0-3-6-8-15 1-11/9-3/2-12/7-11/8 miracle 15.014413
9 0-3-6-9-15 1-11/9-3/2-11/6-11/8 rastmic 15.025529
10 0-2-7-9-15 1-8/7-8/5-11/6-11/8 keenanismic 15.028122
11 0-3-6-12-15 1-11/9-3/2-9/8-11/8 rastmic 15.172779
12 0-3-9-12-15 1-11/9-11/6-9/8-11/8 rastmic 15.190172
13 0-6-9-12-15 1-3/2-11/6-9/8-11/8 rastmic 15.192331
14 0-7-9-12-15 1-8/5-11/6-9/8-11/8 miracle 15.194795
15 0-6-8-13-15 1-3/2-12/7-6/5-11/8 keenanismic 15.333190
16 0-2-5-8-17 1-8/7-7/5-12/7-11/7 jove 17.003221
17 0-3-5-8-17 1-11/9-7/5-12/7-11/7 jove 17.003265
18 0-3-5-12-17 1-11/9-7/5-9/8-11/7 miracle 17.044832
19 0-3-9-12-17 1-11/9-11/6-9/8-11/7 jove 17.049944
20 0-2-5-14-17 1-8/7-7/5-9/7-11/7 jove 17.170287
21 0-2-8-14-17 1-8/7-12/7-9/7-11/7 otonal 17.172476
22 0-5-8-14-17 1-7/5-12/7-9/7-11/7 jove 17.172750
23 0-2-9-14-17 1-8/7-11/6-9/7-11/7 unimarvel 17.174974
24 0-5-12-14-17 1-7/5-9/8-9/7-11/7 miracle 17.209767
25 0-9-12-14-17 1-11/6-9/8-9/7-11/7 jove 17.214329
26 0-2-8-15-17 1-8/7-12/7-11/8-11/7 keenanismic 17.324225
27 0-3-8-15-17 1-11/9-12/7-11/8-11/7 unimarvel 17.324260
28 0-2-9-15-17 1-8/7-11/6-11/8-11/7 keenanismic 17.326473
29 0-3-9-15-17 1-11/9-11/6-11/8-11/7 utonal 17.326508
30 0-3-12-15-17 1-11/9-9/8-11/8-11/7 jove 17.357629
31 0-9-12-15-17 1-11/6-9/8-11/8-11/7 jove 17.361952
32 0-2-5-7-19 1-8/7-7/5-8/5-9/5 werckismic 19.000454
33 0-5-7-12-19 1-7/5-8/5-9/8-9/5 marvel 19.011667
34 0-5-7-13-19 1-7/5-8/5-6/5-9/5 otonal 19.022804
35 0-2-5-14-19 1-8/7-7/5-9/7-9/5 jove 19.044493
36 0-2-7-14-19 1-8/7-8/5-9/7-9/5 prodigy 19.044749
37 0-5-7-14-19 1-7/5-8/5-9/7-9/5 unimarvel 19.044824
38 0-5-12-14-19 1-7/5-9/8-9/7-9/5 unimarvel 19.055370
39 0-6-12-14-19 1-3/2-9/8-9/7-9/5 utonal 19.055455
40 0-7-12-14-19 1-8/5-9/8-9/7-9/5 marvel 19.055624
41 0-2-5-17-19 1-8/7-7/5-11/7-9/5 werckismic 19.322010
42 0-5-12-17-19 1-7/5-9/8-11/7-9/5 prodigy 19.330989
43 0-2-14-17-19 1-8/7-9/7-11/7-9/5 werckismic 19.357563
44 0-5-14-17-19 1-7/5-9/7-11/7-9/5 jove 19.357623
45 0-12-14-17-19 1-9/8-9/7-11/7-9/5 werckismic 19.366324
46 0-3-5-8-22 1-11/9-7/5-12/7-11/10 jove 22.000102
47 0-5-7-13-22 1-7/5-8/5-6/5-11/10 otonal 22.002870
48 0-5-8-13-22 1-7/5-12/7-6/5-11/10 swetismic 22.002914
49 0-5-7-14-22 1-7/5-8/5-9/7-11/10 unimarvel 22.005680
50 0-5-8-14-22 1-7/5-12/7-9/7-11/10 swetismic 22.005724
51 0-7-9-14-22 1-8/5-11/6-9/7-11/10 unimarvel 22.005844
52 0-3-8-15-22 1-11/9-12/7-11/8-11/10 unimarvel 22.011318
53 0-3-9-15-22 1-11/9-11/6-11/8-11/10 utonal 22.011405
54 0-7-9-15-22 1-8/5-11/6-11/8-11/10 keenanismic 22.011446
55 0-7-13-15-22 1-8/5-6/5-11/8-11/10 keenanismic 22.014064
56 0-8-13-15-22 1-12/7-6/5-11/8-11/10 unimarvel 22.014108
57 0-3-5-17-22 1-11/9-7/5-11/7-11/10 werckismic 22.044408
58 0-3-8-17-22 1-11/9-12/7-11/7-11/10 swetismic 22.044483
59 0-5-8-17-22 1-7/5-12/7-11/7-11/10 jove 22.044491
60 0-3-9-17-22 1-11/9-11/6-11/7-11/10 utonal 22.044568
61 0-5-14-17-22 1-7/5-9/7-11/7-11/10 jove 22.049860
62 0-8-14-17-22 1-12/7-9/7-11/7-11/10 swetismic 22.049934
63 0-9-14-17-22 1-11/6-9/7-11/7-11/10 swetismic 22.050019
64 0-3-15-17-22 1-11/9-11/8-11/7-11/10 utonal 22.055285
65 0-8-15-17-22 1-12/7-11/8-11/7-11/10 unimarvel 22.055368
66 0-9-15-17-22 1-11/6-11/8-11/7-11/10 utonal 22.055452
67 0-5-7-19-22 1-7/5-8/5-9/5-11/10 otonal 22.169974
68 0-5-13-19-22 1-7/5-6/5-9/5-11/10 otonal 22.172438
69 0-7-13-19-22 1-8/5-6/5-9/5-11/10 otonal 22.172467
70 0-5-14-19-22 1-7/5-9/7-9/5-11/10 swetismic 22.174936
71 0-7-14-19-22 1-8/5-9/7-9/5-11/10 unimarvel 22.174965
72 0-5-17-19-22 1-7/5-11/7-9/5-11/10 werckismic 22.209463
73 0-14-17-19-22 1-9/7-11/7-9/5-11/10 jove 22.214319

Number Chord Transversal Type Hash
1 0-3-6-9-12-15 1-11/9-3/2-11/6-9/8-11/8 rastmic 15.192640
2 0-2-5-8-14-17 1-8/7-7/5-12/7-9/7-11/7 jove 17.172789
3 0-3-9-12-15-17 1-11/9-11/6-9/8-11/8-11/7 jove 17.362021
4 0-2-5-7-14-19 1-8/7-7/5-8/5-9/7-9/5 miracle 19.044834
5 0-5-7-12-14-19 1-7/5-8/5-9/8-9/7-9/5 unimarvel 19.055709
6 0-2-5-14-17-19 1-8/7-7/5-9/7-11/7-9/5 jove 19.357631
7 0-5-12-14-17-19 1-7/5-9/8-9/7-11/7-9/5 miracle 19.366393
8 0-3-5-8-17-22 1-11/9-7/5-12/7-11/7-11/10 jove 22.044493
9 0-5-8-14-17-22 1-7/5-12/7-9/7-11/7-11/10 jove 22.049945
10 0-3-8-15-17-22 1-11/9-12/7-11/8-11/7-11/10 unimarvel 22.055370
11 0-3-9-15-17-22 1-11/9-11/6-11/8-11/7-11/10 utonal 22.055455
12 0-5-7-13-19-22 1-7/5-8/5-6/5-9/5-11/10 otonal 22.172477
13 0-5-7-14-19-22 1-7/5-8/5-9/7-9/5-11/10 unimarvel 22.174975
14 0-5-14-17-19-22 1-7/5-9/7-11/7-9/5-11/10 jove 22.214329