Miracle/Chords: Difference between revisions

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Jdfreivald (talk | contribs)
autopatrolled, emailconfirmed
64 edits
Changed the main description and the triad description in preparation for adding the table of triads.
Jdfreivald (talk | contribs)
autopatrolled, emailconfirmed
64 edits
→Triads: Added in all of the inversions.
Line 23: Line 23:
| | Type
| | Type
| | Hash
| | Hash
| | As generated
| | First inversion
| | Second inversion
|-
|-
| | 1
| | 1
Line 29: Line 32:
| | werckismic
| | werckismic
| | 5.209453
| | 5.209453
| | 1/1-8/7-7/5 
| | 1/1-11/9-7/4 
| | 1/1-10/7-18/11
|-
|-
| | 2
| | 2
Line 35: Line 41:
| | werckismic
| | werckismic
| | 5.357552
| | 5.357552
| | 1/1-11/9-7/5 
| | 1/1-8/7-18/11
| | 1/1-10/7-7/4 
|-
|-
| | 3
| | 3
Line 41: Line 50:
| | rastmic
| | rastmic
| | 6.189825
| | 6.189825
| | 1/1-11/9-3/2 
| | 1/1-11/9-18/11
| | 1/1-4/3-18/11
|-
|-
| | 4
| | 4
Line 47: Line 59:
| | utonal
| | utonal
| | 7.055282
| | 7.055282
| | 1/1-8/7-8/5 
| | 1/1-7/5-7/4 
| | 1/1-5/4-10/7 
|-
|-
| | 5
| | 5
Line 53: Line 68:
| | otonal
| | otonal
| | 7.330917
| | 7.330917
| | 1/1-7/5-8/5 
| | 1/1-8/7-10/7 
| | 1/1-5/4-7/4 
|-
|-
| | 6
| | 6
Line 59: Line 77:
| | otonal
| | otonal
| | 8.027906
| | 8.027906
| | 1/1-8/7-12/7 
| | 1/1-3/2-7/4 
| | 1/1-7/6-4/3 
|-
|-
| | 7
| | 7
Line 65: Line 86:
| | swetismic
| | swetismic
| | 8.049849
| | 8.049849
| | 1/1-11/9-12/7 
| | 1/1-7/5-18/11
| | 1/1-7/6-10/7 
|-
|-
| | 8
| | 8
Line 71: Line 95:
| | swetismic
| | swetismic
| | 8.174926
| | 8.174926
| | 1/1-7/5-12/7 
| | 1/1-11/9-10/7 
| | 1/1-7/6-18/11
|-
|-
| | 9
| | 9
Line 77: Line 104:
| | utonal
| | utonal
| | 8.326429
| | 8.326429
| | 1/1-3/2-12/7 
| | 1/1-8/7-4/3 
| | 1/1-7/6-7/4 
|-
|-
| | 10
| | 10
Line 83: Line 113:
| | keenanismic
| | keenanismic
| | 9.014020
| | 9.014020
| | 1/1-8/7-11/6 
| | 1/1-8/5-7/4 
| | 1/1-12/11-5/4 
|-
|-
| | 11
| | 11
Line 89: Line 122:
| | utonal
| | utonal
| | 9.025140
| | 9.025140
| | 1/1-11/9-11/6 
| | 1/1-3/2-18/11
| | 1/1-12/11-4/3 
|-
|-
| | 12
| | 12
Line 95: Line 131:
| | otonal
| | otonal
| | 9.172428
| | 9.172428
| | 1/1-3/2-11/6 
| | 1/1-11/9-4/3 
| | 1/1-12/11-18/11
|-
|-
| | 13
| | 13
Line 101: Line 140:
| | keenanismic
| | keenanismic
| | 9.324181
| | 9.324181
| | 1/1-8/5-11/6 
| | 1/1-8/7-5/4 
| | 1/1-12/11-7/4 
|-
|-
| | 14
| | 14
Line 107: Line 149:
| | rastmic
| | rastmic
| | 12.003167
| | 12.003167
| | 1/1-9/8-11/9 
| | 1/1-12/11-16/9 
| | 1/1-18/11-11/6 
|-
|-
| | 15
| | 15
Line 113: Line 158:
| | marvel
| | marvel
| | 12.011577
| | 12.011577
| | 1/1-9/8-7/5 
| | 1/1-56/45-16/9 
| | 1/1-10/7-8/5 
|-
|-
| | 16
| | 16
Line 119: Line 167:
| | ambitonal
| | ambitonal
| | 12.022715
| | 12.022715
| | 1/1-9/8-3/2 
| | 1/1-4/3-16/9 
| | 1/1-4/3-3/2 
|-
|-
| | 17
| | 17
Line 125: Line 176:
| | marvel
| | marvel
| | 12.044736
| | 12.044736
| | 1/1-9/8-8/5 
| | 1/1-10/7-16/9 
| | 1/1-5/4-7/5 
|-
|-
| | 18
| | 18
Line 131: Line 185:
| | rastmic
| | rastmic
| | 12.170238
| | 12.170238
| | 1/1-9/8-11/6 
| | 1/1-18/11-16/9 
| | 1/1-12/11-11/9 
|-
|-
| | 19
| | 19
Line 137: Line 194:
| | otonal
| | otonal
| | 13.005800
| | 13.005800
| | 1/1-6/5-7/5 
| | 1/1-7/6-5/3 
| | 1/1-10/7-12/7 
|-
|-
| | 20
| | 20
Line 143: Line 203:
| | utonal
| | utonal
| | 13.011402
| | 13.011402
| | 1/1-6/5-3/2 
| | 1/1-5/4-5/3 
| | 1/1-4/3-8/5 
|-
|-
| | 21
| | 21
Line 149: Line 212:
| | otonal
| | otonal
| | 13.022541
| | 13.022541
| | 1/1-6/5-8/5 
| | 1/1-4/3-5/3 
| | 1/1-5/4-3/2 
|-
|-
| | 22
| | 22
Line 155: Line 221:
| | utonal
| | utonal
| | 13.044565
| | 13.044565
| | 1/1-6/5-12/7 
| | 1/1-10/7-5/3 
| | 1/1-7/6-7/5 
|-
|-
| | 23
| | 23
Line 161: Line 230:
| | otonal
| | otonal
| | 14.000440
| | 14.000440
| | 1/1-8/7-9/7 
| | 1/1-9/8-7/4 
| | 1/1-14/9-16/9 
|-
|-
| | 24
| | 24
Line 167: Line 239:
| | swetismic
| | swetismic
| | 14.002903
| | 14.002903
| | 1/1-9/7-7/5 
| | 1/1-12/11-14/9 
| | 1/1-10/7-11/6 
|-
|-
| | 25
| | 25
Line 173: Line 248:
| | utonal
| | utonal
| | 14.005712
| | 14.005712
| | 1/1-9/7-3/2 
| | 1/1-7/6-14/9 
| | 1/1-4/3-12/7 
|-
|-
| | 26
| | 26
Line 179: Line 257:
| | marvel
| | marvel
| | 14.011315
| | 14.011315
| | 1/1-9/7-8/5 
| | 1/1-5/4-14/9 
| | 1/1-5/4-8/5 
|-
|-
| | 27
| | 27
Line 185: Line 266:
| | otonal
| | otonal
| | 14.022455
| | 14.022455
| | 1/1-9/7-12/7 
| | 1/1-4/3-14/9 
| | 1/1-7/6-3/2 
|-
|-
| | 28
| | 28
Line 191: Line 275:
| | swetismic
| | swetismic
| | 14.04448
| | 14.04448
| | 1/1-9/7-11/6 
| | 1/1-10/7-14/9 
| | 1/1-12/11-7/5 
|-
|-
| | 29
| | 29
Line 197: Line 284:
| | utonal
| | utonal
| | 14.321999
| | 14.321999
| | 1/1-9/8-9/7 
| | 1/1-8/7-16/9 
| | 1/1-14/9-7/4 
|-
|-
| | 30
| | 30
Line 203: Line 293:
| | keenanismic
| | keenanismic
| | 15.000220
| | 15.000220
| | 1/1-8/7-11/8 
| | 1/1-6/5-7/4 
| | 1/1-16/11-5/3 
|-
|-
| | 31
| | 31
Line 209: Line 302:
| | utonal
| | utonal
| | 15.000396
| | 15.000396
| | 1/1-11/9-11/8 
| | 1/1-9/8-18/11
| | 1/1-16/11-16/9 
|-
|-
| | 32
| | 32
Line 215: Line 311:
| | otonal
| | otonal
| | 15.002859
| | 15.002859
| | 1/1-11/8-3/2 
| | 1/1-12/11-16/11
| | 1/1-4/3-11/6 
|-
|-
| | 33
| | 33
Line 221: Line 320:
| | keenanismic
| | keenanismic
| | 15.005660
| | 15.005660
| | 1/1-11/8-8/5 
| | 1/1-7/6-16/11
| | 1/1-5/4-12/7 
|-
|-
| | 34
| | 34
Line 227: Line 329:
| | keenanismic
| | keenanismic
| | 15.011271
| | 15.011271
| | 1/1-11/8-12/7 
| | 1/1-5/4-16/11
| | 1/1-7/6-8/5 
|-
|-
| | 35
| | 35
Line 233: Line 338:
| | utonal
| | utonal
| | 15.022411
| | 15.022411
| | 1/1-11/8-11/6 
| | 1/1-4/3-16/11
| | 1/1-12/11-3/2 
|-
|-
| | 36
| | 36
Line 239: Line 347:
| | otonal
| | otonal
| | 15.169964
| | 15.169964
| | 1/1-9/8-11/8 
| | 1/1-11/9-16/9 
| | 1/1-16/11-18/11
|-
|-
| | 37
| | 37
Line 245: Line 356:
| | keenanismic
| | keenanismic
| | 15.321963
| | 15.321963
| | 1/1-6/5-11/8 
| | 1/1-8/7-5/3 
| | 1/1-16/11-7/4 
|-
|-
| | 38
| | 38
Line 251: Line 365:
| | otonal
| | otonal
| | 17.000055
| | 17.000055
| | 1/1-8/7-11/7 
| | 1/1-11/8-7/4 
| | 1/1-14/11-16/11
|-
|-
| | 39
| | 39
Line 257: Line 374:
| | utonal
| | utonal
| | 17.000099
| | 17.000099
| | 1/1-11/9-11/7 
| | 1/1-9/7-18/11
| | 1/1-14/11-14/9 
|-
|-
| | 40
| | 40
Line 263: Line 383:
| | werckismic
| | werckismic
| | 17.000363
| | 17.000363
| | 1/1-7/5-11/7 
| | 1/1-9/8-10/7 
| | 1/1-14/11-16/9 
|-
|-
| | 41
| | 41
Line 269: Line 392:
| | otonal
| | otonal
| | 17.002826
| | 17.002826
| | 1/1-11/7-12/7 
| | 1/1-12/11-14/11
| | 1/1-7/6-11/6 
|-
|-
| | 42
| | 42
Line 275: Line 401:
| | utonal
| | utonal
| | 17.005636
| | 17.005636
| | 1/1-11/7-11/6 
| | 1/1-7/6-14/11
| | 1/1-12/11-12/7 
|-
|-
| | 43
| | 43
Line 281: Line 410:
| | werckismic
| | werckismic
| | 17.0444
| | 17.0444
| | 1/1-9/8-11/7 
| | 1/1-7/5-16/9 
| | 1/1-14/11-10/7 
|-
|-
| | 44
| | 44
Line 287: Line 419:
| | otonal
| | otonal
| | 17.169935
| | 17.169935
| | 1/1-9/7-11/7 
| | 1/1-11/9-14/9 
| | 1/1-14/11-18/11
|-
|-
| | 45
| | 45
Line 293: Line 428:
| | utonal
| | utonal
| | 17.321937
| | 17.321937
| | 1/1-11/8-11/7 
| | 1/1-8/7-16/11
| | 1/1-14/11-7/4 
|-
|-
| | 46
| | 46
Line 299: Line 437:
| | werckismic
| | werckismic
| | 19.000014
| | 19.000014
| | 1/1-8/7-9/5 
| | 1/1-11/7-7/4 
| | 1/1-10/9-14/11
|-
|-
| | 47
| | 47
Line 305: Line 446:
| | otonal
| | otonal
| | 19.000091
| | 19.000091
| | 1/1-7/5-9/5 
| | 1/1-9/7-10/7 
| | 1/1-10/9-14/9 
|-
|-
| | 48
| | 48
Line 311: Line 455:
| | utonal
| | utonal
| | 19.000179
| | 19.000179
| | 1/1-3/2-9/5 
| | 1/1-6/5-4/3 
| | 1/1-10/9-5/3 
|-
|-
| | 49
| | 49
Line 317: Line 464:
| | otonal
| | otonal
| | 19.000355
| | 19.000355
| | 1/1-8/5-9/5 
| | 1/1-9/8-5/4 
| | 1/1-10/9-16/9 
|-
|-
| | 50
| | 50
Line 323: Line 473:
| | utonal
| | utonal
| | 19.011230
| | 19.011230
| | 1/1-9/8-9/5 
| | 1/1-8/5-16/9 
| | 1/1-10/9-5/4 
|-
|-
| | 51
| | 51
Line 329: Line 482:
| | otonal
| | otonal
| | 19.022371
| | 19.022371
| | 1/1-6/5-9/5 
| | 1/1-3/2-5/3 
| | 1/1-10/9-4/3 
|-
|-
| | 52
| | 52
Line 335: Line 491:
| | utonal
| | utonal
| | 19.044397
| | 19.044397
| | 1/1-9/7-9/5 
| | 1/1-7/5-14/9 
| | 1/1-10/9-10/7 
|-
|-
| | 53
| | 53
Line 341: Line 500:
| | werckismic
| | werckismic
| | 19.321930
| | 19.321930
| | 1/1-11/7-9/5 
| | 1/1-8/7-14/11
| | 1/1-10/9-7/4 
|-
|-
| | 54
| | 54
Line 347: Line 509:
| | utonal
| | utonal
| | 22.000003
| | 22.000003
| | 1/1-11/10-11/9 
| | 1/1-10/9-20/11
| | 1/1-18/11-9/5 
|-
|-
| | 55
| | 55
Line 353: Line 518:
| | otonal
| | otonal
| | 22.000011
| | 22.000011
| | 1/1-11/10-7/5 
| | 1/1-14/11-20/11
| | 1/1-10/7-11/7 
|-
|-
| | 56
| | 56
Line 359: Line 527:
| | otonal
| | otonal
| | 22.000044
| | 22.000044
| | 1/1-11/10-8/5 
| | 1/1-16/11-20/11
| | 1/1-5/4-11/8 
|-
|-
| | 57
| | 57
Line 365: Line 536:
| | swetismic
| | swetismic
| | 22.000088
| | 22.000088
| | 1/1-11/10-12/7 
| | 1/1-14/9-20/11
| | 1/1-7/6-9/7 
|-
|-
| | 58
| | 58
Line 371: Line 545:
| | utonal
| | utonal
| | 22.000176
| | 22.000176
| | 1/1-11/10-11/6 
| | 1/1-5/3-20/11
| | 1/1-12/11-6/5 
|-
|-
| | 59
| | 59
Line 377: Line 554:
| | otonal
| | otonal
| | 22.002815
| | 22.002815
| | 1/1-11/10-6/5 
| | 1/1-12/11-20/11
| | 1/1-5/3-11/6 
|-
|-
| | 60
| | 60
Line 383: Line 563:
| | swetismic
| | swetismic
| | 22.005625
| | 22.005625
| | 1/1-11/10-9/7 
| | 1/1-7/6-20/11
| | 1/1-14/9-12/7 
|-
|-
| | 61
| | 61
Line 389: Line 572:
| | utonal
| | utonal
| | 22.011228
| | 22.011228
| | 1/1-11/10-11/8 
| | 1/1-5/4-20/11
| | 1/1-16/11-8/5 
|-
|-
| | 62
| | 62
Line 395: Line 581:
| | utonal
| | utonal
| | 22.044394
| | 22.044394
| | 1/1-11/10-11/7 
| | 1/1-10/7-20/11
| | 1/1-14/11-7/5 
|-
|-
| | 63
| | 63
Line 401: Line 590:
| | otonal
| | otonal
| | 22.169925
| | 22.169925
| | 1/1-11/10-9/5 
| | 1/1-18/11-20/11
| | 1/1-10/9-11/9 
|}
|}


Revision as of 01:07, 1 May 2019

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

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

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].

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 (uses 41 EDO sagittal notation) and can be heard using piano, oud, or sine wave timbres (all links in MP3 format and tuned to 41 EDO). 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
1 0-2-5-7 1-8/7-7/5-8/5 werckismic 7.366322
2 0-2-5-8 1-8/7-7/5-12/7 jove 8.194757
3 0-3-5-8 1-11/9-7/5-12/7 jove 8.214319
4 0-3-6-8 1-11/9-3/2-12/7 jove 8.361944
5 0-3-6-9 1-11/9-3/2-11/6 rastmic 9.192293
6 0-2-7-9 1-8/7-8/5-11/6 keenanismic 9.333155
7 0-3-5-12 1-11/9-7/5-9/8 miracle 12.014369
8 0-3-6-12 1-11/9-3/2-9/8 rastmic 12.025486
9 0-5-7-12 1-7/5-8/5-9/8 marvel 12.055621
10 0-3-9-12 1-11/9-11/6-9/8 rastmic 12.172740
11 0-6-9-12 1-3/2-11/6-9/8 rastmic 12.190133
12 0-7-9-12 1-8/5-11/6-9/8 miracle 12.209758
13 0-5-7-13 1-7/5-8/5-6/5 otonal 13.028079
14 0-5-8-13 1-7/5-12/7-6/5 swetismic 13.050019
15 0-6-8-13 1-3/2-12/7-6/5 utonal 13.055452
16 0-2-5-14 1-8/7-7/5-9/7 jove 14.003254
17 0-2-7-14 1-8/7-8/5-9/7 marvel 14.011664
18 0-5-7-14 1-7/5-8/5-9/7 unimarvel 14.014108
19 0-2-8-14 1-8/7-12/7-9/7 otonal 14.022801
20 0-5-8-14 1-7/5-12/7-9/7 swetismic 14.025226
21 0-6-8-14 1-3/2-12/7-9/7 ambitonal 14.027992
22 0-2-9-14 1-8/7-11/6-9/7 unimarvel 14.044821
23 0-6-9-14 1-3/2-11/6-9/7 swetismic 14.049934
24 0-7-9-14 1-8/5-11/6-9/7 unimarvel 14.055367
25 0-5-12-14 1-7/5-9/8-9/7 unimarvel 14.324251
26 0-6-12-14 1-3/2-9/8-9/7 utonal 14.326500
27 0-7-12-14 1-8/5-9/8-9/7 marvel 14.330987
28 0-9-12-14 1-11/6-9/8-9/7 jove 14.357621
29 0-3-6-15 1-11/9-3/2-11/8 rastmic 15.003210
30 0-2-7-15 1-8/7-8/5-11/8 keenanismic 15.005844
31 0-2-8-15 1-8/7-12/7-11/8 keenanismic 15.011446
32 0-3-8-15 1-11/9-12/7-11/8 unimarvel 15.011620
33 0-6-8-15 1-3/2-12/7-11/8 keenanismic 15.014064
34 0-2-9-15 1-8/7-11/6-11/8 keenanismic 15.022585
35 0-3-9-15 1-11/9-11/6-11/8 utonal 15.022758
36 0-6-9-15 1-3/2-11/6-11/8 ambitonal 15.025183
37 0-7-9-15 1-8/5-11/6-11/8 keenanismic 15.027949
38 0-3-12-15 1-11/9-9/8-11/8 rastmic 15.170277
39 0-6-12-15 1-3/2-9/8-11/8 otonal 15.172467
40 0-7-12-15 1-8/5-9/8-11/8 unimarvel 15.174965
41 0-9-12-15 1-11/6-9/8-11/8 rastmic 15.189863
42 0-6-13-15 1-3/2-6/5-11/8 keenanismic 15.324216
43 0-7-13-15 1-8/5-6/5-11/8 keenanismic 15.326465
44 0-8-13-15 1-12/7-6/5-11/8 keenanismic 15.330952
45 0-2-5-17 1-8/7-7/5-11/7 werckismic 17.000407
46 0-3-5-17 1-11/9-7/5-11/7 werckismic 17.000451
47 0-2-8-17 1-8/7-12/7-11/7 otonal 17.002870
48 0-3-8-17 1-11/9-12/7-11/7 swetismic 17.002914
49 0-5-8-17 1-7/5-12/7-11/7 jove 17.003177
50 0-2-9-17 1-8/7-11/6-11/7 keenanismic 17.005679
51 0-3-9-17 1-11/9-11/6-11/7 utonal 17.005723
52 0-3-12-17 1-11/9-9/8-11/7 jove 17.044490
53 0-5-12-17 1-7/5-9/8-11/7 prodigy 17.044746
54 0-9-12-17 1-11/6-9/8-11/7 jove 17.049859
55 0-2-14-17 1-8/7-9/7-11/7 otonal 17.169974
56 0-5-14-17 1-7/5-9/7-11/7 jove 17.170248
57 0-8-14-17 1-12/7-9/7-11/7 otonal 17.172437
58 0-9-14-17 1-11/6-9/7-11/7 swetismic 17.174935
59 0-12-14-17 1-9/8-9/7-11/7 werckismic 17.209463
60 0-2-15-17 1-8/7-11/8-11/7 keenanismic 17.321972
61 0-3-15-17 1-11/9-11/8-11/7 utonal 17.322007
62 0-8-15-17 1-12/7-11/8-11/7 keenanismic 17.324189
63 0-9-15-17 1-11/6-11/8-11/7 utonal 17.326438
64 0-12-15-17 1-9/8-11/8-11/7 werckismic 17.357561
65 0-2-5-19 1-8/7-7/5-9/5 werckismic 19.000102
66 0-2-7-19 1-8/7-8/5-9/5 werckismic 19.000366
67 0-5-7-19 1-7/5-8/5-9/5 otonal 19.000443
68 0-5-12-19 1-7/5-9/8-9/5 marvel 19.011317
69 0-6-12-19 1-3/2-9/8-9/5 utonal 19.011405
70 0-7-12-19 1-8/5-9/8-9/5 marvel 19.011579
71 0-5-13-19 1-7/5-6/5-9/5 otonal 19.022457
72 0-6-13-19 1-3/2-6/5-9/5 ambitonal 19.022544
73 0-7-13-19 1-8/5-6/5-9/5 otonal 19.022717
74 0-2-14-19 1-8/7-9/7-9/5 werckismic 19.044407
75 0-5-14-19 1-7/5-9/7-9/5 swetismic 19.044482
76 0-6-14-19 1-3/2-9/7-9/5 utonal 19.044568
77 0-7-14-19 1-8/5-9/7-9/5 marvel 19.044738
78 0-12-14-19 1-9/8-9/7-9/5 utonal 19.055285
79 0-2-17-19 1-8/7-11/7-9/5 werckismic 19.321939
80 0-5-17-19 1-7/5-11/7-9/5 werckismic 19.322001
81 0-12-17-19 1-9/8-11/7-9/5 werckismic 19.330919
82 0-14-17-19 1-9/7-11/7-9/5 werckismic 19.357554
83 0-3-5-22 1-11/9-7/5-11/10 werckismic 22.000014
84 0-5-7-22 1-7/5-8/5-11/10 otonal 22.000055
85 0-3-8-22 1-11/9-12/7-11/10 swetismic 22.000091
86 0-5-8-22 1-7/5-12/7-11/10 swetismic 22.000099
87 0-3-9-22 1-11/9-11/6-11/10 utonal 22.000179
88 0-7-9-22 1-8/5-11/6-11/10 keenanismic 22.000220
89 0-5-13-22 1-7/5-6/5-11/10 otonal 22.002826
90 0-7-13-22 1-8/5-6/5-11/10 otonal 22.002859
91 0-8-13-22 1-12/7-6/5-11/10 swetismic 22.002903
92 0-5-14-22 1-7/5-9/7-11/10 swetismic 22.005636
93 0-7-14-22 1-8/5-9/7-11/10 unimarvel 22.005669
94 0-8-14-22 1-12/7-9/7-11/10 swetismic 22.005713
95 0-9-14-22 1-11/6-9/7-11/10 swetismic 22.005800
96 0-3-15-22 1-11/9-11/8-11/10 utonal 22.011230
97 0-7-15-22 1-8/5-11/8-11/10 keenanismic 22.011271
98 0-8-15-22 1-12/7-11/8-11/10 unimarvel 22.011315
99 0-9-15-22 1-11/6-11/8-11/10 utonal 22.011402
100 0-13-15-22 1-6/5-11/8-11/10 keenanismic 22.014021
101 0-3-17-22 1-11/9-11/7-11/10 utonal 22.044397
102 0-5-17-22 1-7/5-11/7-11/10 werckismic 22.044405
103 0-8-17-22 1-12/7-11/7-11/10 swetismic 22.044480
104 0-9-17-22 1-11/6-11/7-11/10 utonal 22.044565
105 0-14-17-22 1-9/7-11/7-11/10 swetismic 22.049849
106 0-15-17-22 1-11/8-11/7-11/10 utonal 22.055283
107 0-5-19-22 1-7/5-9/5-11/10 otonal 22.169935
108 0-7-19-22 1-8/5-9/5-11/10 otonal 22.169964
109 0-13-19-22 1-6/5-9/5-11/10 otonal 22.172428
110 0-14-19-22 1-9/7-9/5-11/10 swetismic 22.174926
111 0-17-19-22 1-11/7-9/5-11/10 werckismic 22.209454

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
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