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<span style="line-height: 1.5;">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.</span> | <span style="line-height: 1.5;">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.</span> | ||
All three inversions for all 63 chords are notated in this [ | All three inversions for all 63 chords are notated in this [https://en.xen.wiki/images/4/41/41-EDO-Miracle-scale-and-triads.pdf PDF] and can be heard using a [https://en.xen.wiki/images/5/5c/41_EDO_Miracle_-_scale_and_triads_-_piano.mp3 piano], a [https://en.xen.wiki/images/8/88/41_EDO_Miracle_-_scale_and_triads_-_steel_gtr.mp3 steel-stringed guitar], a [https://en.xen.wiki/images/e/e8/41_EDO_Miracle_-_scale_and_triads_-_nylon_guitar.mp3 nylon-stringed guitar], and a [media:41_EDO_Miracle_-_scale_and_triads_-_strings.mp3 | string ensemble]. (All linked files are in MP3 format. They were created in [http://www.mus2.com.tr/en/ Mus2] using 41 EDO sagittal notation, exported to tuned MIDI, and rendered with Timidity++ using soundfonts.) Finally, here is a [http://soonlabel.com/xenharmonic/wp-content/uploads/2014/11/41-EDO-Miracle-scale-and-triads.mid tuned MIDI file]. The sequence is: chord as outlined in the list below, first inversion, second inversion, quarter-note rest. | ||
{| class="wikitable" | {| class="wikitable" | ||
Revision as of 20:22, 15 January 2020
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 2^s 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 overtone series, utonal if it is the inversion of an otonal chord, 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, so that if for example it says "werckismic" only 441/440 needs to be tempered out. Also, "marvel" denotes 9 odd limit (7-limit) marvel, whereas "unimarvel" means 11-limit marvel.
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.
Triads
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 [media:41_EDO_Miracle_-_scale_and_triads_-_strings.mp3 | string ensemble]. (All linked files are in MP3 format. They were created in Mus2 using 41 EDO sagittal notation, exported to tuned MIDI, and rendered with Timidity++ using soundfonts.) Finally, here is a tuned MIDI file. The sequence is: chord as outlined in the list below, 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 |
Tetrads
| 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 |
Pentads
| 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 |
Hexads
| 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 |