Chords of miracle
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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:
- marvel, for the tempering of 225/224
- keenanismic, for the tempering of 385/384
- swetismic, for the tempering of 540/539
- rastmic, for the tempering of 243/242
- werckismic, for the tempering of 441/440
- unimarvel, for the tempering of any two of 225/224, 385/384 or 540/539
- prodigy, for the tempering of both 225/224 and 441/440
- jove, for the tempering of any two of 243/242, 441/440 or 540/539
- miracle, for the tempering of any three independent commas mentioned above
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 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 |
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 |