Chords of magic: Difference between revisions

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autopatrolled, Sysops
4,192 edits
adding chord names -- work in progress
TallKite (talk | contribs)
autopatrolled, Sysops
4,192 edits
added more chord names, added an interval chart
Line 5: Line 5:
Magic has [[mos scale]]s of sizes 7, 10, 13, 16, 19 and 22 notes. It may be seen that even the seven-note mos is not without a few harmonic resources, and the larger ones do much better.
Magic has [[mos scale]]s of sizes 7, 10, 13, 16, 19 and 22 notes. It may be seen that even the seven-note mos is not without a few harmonic resources, and the larger ones do much better.


The chord names use ups and downs as described on the pergens page. The generator is vM3 and the enharmonic interval is ^<sup>5</sup>dd2. To simplify the names, lifts and drops are also used. One lift is 41 generators (41 because 41edo is a near-optimal tuning of magic). Thus /1 = vd-2 = 8.2c - 20¢, i.e. a pyth comma minus an up.
The chord names use ups and downs as described on the pergens page. The generator is vM3 and the enharmonic interval is ^<sup>5</sup>dd2. To simplify the names, lifts and drops are also used. One lift is 41 generators, octave-reduced. (41 because 41edo is a near-optimal tuning of magic.) Thus /1 = ^d2 = 20¢ - 8.2c, i.e. an up minus a tempered pythagorean comma. /C = ^Dbb and \C = vB#. ^C = /B# and vC = \Dbb.
 
{| class="wikitable center-all"
!genspan
|0
|1
|2
|3
|4
|5
|6
|7
|8
|9
|10
|11
|12
|13
|-
!Cents (41edo)
|0
|380
|761
|1141
|322
|702
|1083
|263
|644
|1024
|205
|585
|966
|146
|-
!Ratios
| 1/1
|5/4
|14/9
|27/14
|6/5
|3/2
|15/8
|7/6
|(16/11)
|9/5
|9/8
|7/5
|7/4
|(12/11)
|-
!Interval
|P1
|vM3
|vvA5
v\m6
|^^d8
^/M7
|^m3
|P5
|vM7
|vvA2
v\m3
|^^d5
^/A4
|^m7
|M2
|vA4
\d5
|vvA6
v\m7
|^^m2
^/A1
|}
== Triads ==
== Triads ==


Line 16: Line 87:
! Type
! Type
!name
!name
!name with / \
!comments
!comments
|-
|-
Line 24: Line 94:
| marvel
| marvel
|v(vv#5)
|v(vv#5)
|
|
|
|-
|-
Line 32: Line 101:
| sensamagic
| sensamagic
|^m(vv#5)
|^m(vv#5)
|
|
|
|-
|-
Line 40: Line 108:
| otonal
| otonal
|v
|v
|
|
|
|-
|-
Line 48: Line 115:
| utonal
| utonal
|^m
|^m
|
|
|
|-
|-
Line 55: Line 121:
| 1-14/9-7/6
| 1-14/9-7/6
| utonal
| utonal
|vvvA3
|^/
|^/
|1-9/7-3/2, vvvA3 = ^^d4
|1-9/7-3/2
|-
|-
| 6
| 6
Line 63: Line 128:
| 1-3/2-7/6
| 1-3/2-7/6
| otonal
| otonal
|^^^d3
|v\m
|v\m
|^^^d3 = vvA2
|
|-
|-
| 7
| 7
Line 72: Line 136:
| keenanismic
| keenanismic
|v(^^b5)
|v(^^b5)
|
|
|
|-
|-
Line 80: Line 143:
| ptolemismic
| ptolemismic
|^m(^^b5)
|^m(^^b5)
|
|
|
|-
|-
Line 87: Line 149:
| 1-7/6-16/11
| 1-7/6-16/11
| keenanismic
| keenanismic
|^^^d3(^^b5)
|v\m(^^b5)
|v\m(^^b5)
|^^^d3 = vvA2
|
|-
|-
| 10
| 10
Line 96: Line 157:
| utonal
| utonal
|v^7no5
|v^7no5
|
|
|
|-
|-
Line 103: Line 163:
| 1-14/9-9/5
| 1-14/9-9/5
| sensamagic
| sensamagic
|
|^m7(vv#5)no3
|
|
|
|-
|-
Line 112: Line 171:
| otonal
| otonal
|^m7no5
|^m7no5
|
|<u>or</u> 1-3/2-5/3 =  v6no3
|<u>or</u> 1-3/2-5/3 =  v6no3
|-
|-
Line 120: Line 178:
| utonal
| utonal
|^m7no3
|^m7no3
|
|
|
|-
|-
Line 127: Line 184:
| 1-7/6-9/5
| 1-7/6-9/5
| sensamagic
| sensamagic
|^^^d3v7no5
|v\m,v7no5
|
|
|^^^d3 = vvA2
|-
|-
| 15
| 15
Line 136: Line 192:
| otonal
| otonal
|v(^^^bb5)
|v(^^^bb5)
|
|1-5/4-11/8
|1-5/4-11/8
|-
|-
Line 144: Line 199:
| otonal
| otonal
|v,9no5
|v,9no5
|
|
|
|-
|-
Line 152: Line 206:
| pentacircle
| pentacircle
|2(vv#5)
|2(vv#5)
|
|
|
|-
|-
Line 160: Line 213:
| ambitonal
| ambitonal
|2
|2
|
|
|
|-
|-
Line 168: Line 220:
| pentacircle
| pentacircle
|2(^^b5)
|2(^^b5)
|
|
|
|-
|-
Line 175: Line 226:
| 1-9/5-9/8
| 1-9/5-9/8
| utonal
| utonal
|^m9no35
|^9no35
|
|<u>or</u> ^7sus2no5
|<u>or</u> 2^7no5
|-
|-
| 21
| 21
Line 183: Line 233:
| 1-5/4-7/5
| 1-5/4-7/5
| marvel
| marvel
|v(^<sup>4</sup>bb5)
|v(\b5)
|
|
|
|-
|-
Line 191: Line 240:
| 1-14/9-7/5
| 1-14/9-7/5
| utonal
| utonal
|vvvA3v7no5
|^/,^7no5
|
|1-9/7-9/5
|1-9/7-9/5
|-
|-
Line 199: Line 247:
| 1-6/5-7/5
| 1-6/5-7/5
| otonal
| otonal
|^m(vpb5)
|^m(\b5)
|
|
|
|-
|-
Line 207: Line 254:
| 1-7/6-7/5
| 1-7/6-7/5
| utonal
| utonal
|^^^d3(vpb5)
|v\m(\b5)
|
|
|
|-
|-
Line 215: Line 261:
| 1-9/5-7/5
| 1-9/5-7/5
| otonal
| otonal
|
|^/(^b5)
|
|1/1-9/7-10/7
|
|-
|-
| 26
| 26
Line 223: Line 268:
| 1-9/8-7/5
| 1-9/8-7/5
| marvel
| marvel
|
|v,7no5
|
|1/1-5/4-16/9
|
|-
|-
| 27
| 27
Line 231: Line 275:
| 1-5/4-7/4
| 1-5/4-7/4
| otonal
| otonal
|
|v,v/7
|
|
|
|-
|-
Line 239: Line 282:
| 1-14/9-7/4
| 1-14/9-7/4
| utonal
| utonal
|
|^/,9no5
|
|1/1-9/8-9/7
|
|-
|-
| 29
| 29
Line 247: Line 289:
| 1-6/5-7/4
| 1-6/5-7/4
| keenanismic
| keenanismic
|
|^m,v\7
|
|
|
|-
|-
Line 255: Line 296:
| 1-3/2-7/4
| 1-3/2-7/4
| otonal
| otonal
|
|v\m7no3
|
|
|
|-
|-
Line 263: Line 303:
| 1-7/6-7/4
| 1-7/6-7/4
| utonal
| utonal
|
|v\m7no5
|
|
|
|-
|-
Line 271: Line 310:
| 1-16/11-7/4
| 1-16/11-7/4
| keenanismic
| keenanismic
|
|
|
|
|
Line 279: Line 317:
| 1-9/8-7/4
| 1-9/8-7/4
| otonal
| otonal
|
|v\m7sus2
|
|
|
|-
|-
Line 287: Line 324:
| 1-7/5-7/4
| 1-7/5-7/4
| utonal
| utonal
|
|
|
|
|
Line 295: Line 331:
| 1-5/4-12/11
| 1-5/4-12/11
| keenanismic
| keenanismic
|
|
|
|
|
Line 304: Line 339:
| swetismic
| swetismic
|
|
|
|1/1-9/7-7/5
|
|-
|-
| 37
| 37
Line 311: Line 345:
| 1-6/5-12/11
| 1-6/5-12/11
| utonal
| utonal
|
|
|
|
|
Line 319: Line 352:
| 1-3/2-12/11
| 1-3/2-12/11
| utonal
| utonal
|
|
|
|
|
Line 327: Line 359:
| 1-16/11-12/11
| 1-16/11-12/11
| otonal
| otonal
|
|
|
|
|
Line 335: Line 366:
| 1-20/11-12/11
| 1-20/11-12/11
| otonal
| otonal
|
|
|
|
|
Line 343: Line 373:
| 1-7/5-12/11
| 1-7/5-12/11
| swetismic
| swetismic
|
|
|
|
|
Line 351: Line 380:
| 1-7/4-12/11
| 1-7/4-12/11
| keenanismic
| keenanismic
|
|
|
|
|
Line 359: Line 387:
| 1-3/2-18/11
| 1-3/2-18/11
| utonal
| utonal
|
|
|
|
|
Line 367: Line 394:
| 1-7/6-18/11
| 1-7/6-18/11
| swetismic
| swetismic
|
|
|
|
|
Line 375: Line 401:
| 1-16/11-18/11
| 1-16/11-18/11
| otonal
| otonal
|
|
|
|
|
Line 383: Line 408:
| 1-9/5-18/11
| 1-9/5-18/11
| utonal
| utonal
|
|
|
|
|
Line 391: Line 415:
| 1-9/8-18/11
| 1-9/8-18/11
| utonal
| utonal
|
|
|
|
|
Line 399: Line 422:
| 1-7/5-18/11
| 1-7/5-18/11
| swetismic
| swetismic
|
|
|
|
|
Line 407: Line 429:
| 1-12/11-18/11
| 1-12/11-18/11
| otonal
| otonal
|
|
|
|
|
Line 415: Line 436:
| 1-14/9-14/11
| 1-14/9-14/11
| utonal
| utonal
|
|
|
|
|
Line 423: Line 443:
| 1-7/6-14/11
| 1-7/6-14/11
| utonal
| utonal
|
|
|
|
|
Line 431: Line 450:
| 1-16/11-14/11
| 1-16/11-14/11
| otonal
| otonal
|
|
|
|
|
Line 439: Line 457:
| 1-20/11-14/11
| 1-20/11-14/11
| otonal
| otonal
|
|
|
|
|
Line 447: Line 464:
| 1-9/8-14/11
| 1-9/8-14/11
| pentacircle
| pentacircle
|
|
|
|
|
Line 455: Line 471:
| 1-7/5-14/11
| 1-7/5-14/11
| utonal
| utonal
|
|
|
|
|
Line 463: Line 478:
| 1-7/4-14/11
| 1-7/4-14/11
| utonal
| utonal
|
|
|
|
|
Line 471: Line 485:
| 1-12/11-14/11
| 1-12/11-14/11
| otonal
| otonal
|
|
|
|
|
Line 479: Line 492:
| 1-18/11-14/11
| 1-18/11-14/11
| otonal
| otonal
|
|
|
|
|
Line 506: Line 518:
| 1-14/9-6/5-9/5
| 1-14/9-6/5-9/5
| sensamagic
| sensamagic
|
|^m7(vv#5)
|
|
|-
|-
Line 521: Line 533:
| ambitonal
| ambitonal
|^m7
|^m7
|
|<u>or</u> 1/1-5/4-3/2-5/3 = v6
|-
|-
| 5
| 5
Line 527: Line 539:
| 1-14/9-7/6-9/5
| 1-14/9-7/6-9/5
| sensamagic
| sensamagic
|
|^/,vv#9
|1-7/6-9/7-3/2
|1-9/7-3/2-7/3
|-
|-
| 6
| 6
Line 534: Line 546:
| 1-3/2-7/6-9/5
| 1-3/2-7/6-9/5
| sensamagic
| sensamagic
|^^^d3^7
|v\m^7
|
|
|-
|-
Line 597: Line 609:
| 1-3/2-9/5-9/8
| 1-3/2-9/5-9/8
| utonal
| utonal
|
|^7sus2
|
|<u>or</u> 2,^m7
|-
|-
| 16
| 16
Line 646: Line 658:
| 1-6/5-9/5-7/5
| 1-6/5-9/5-7/5
| otonal
| otonal
|
|^m7(\b5)
|
|
|-
|-
Line 695: Line 707:
| 1-5/4-3/2-7/4
| 1-5/4-3/2-7/4
| otonal
| otonal
|v^^^d7
|v,v\7
|
|
|-
|-
Line 702: Line 714:
| 1-6/5-3/2-7/4
| 1-6/5-3/2-7/4
| keenanismic
| keenanismic
|
|^m,v\7
|
|
|-
|-
Line 716: Line 728:
| 1-3/2-7/6-7/4
| 1-3/2-7/6-7/4
| ambitonal
| ambitonal
|
|v\m7
|
|
|-
|-
Line 758: Line 770:
| 1-3/2-9/8-7/4
| 1-3/2-9/8-7/4
| otonal
| otonal
|
|v\7sus2
|
|<u>or</u> 2,v\7
|-
|-
| 39
| 39

Revision as of 11:15, 14 November 2024

Below are listed the dyadic chords of 11-limit magic temperament. Typing the chords requires consideration of the fact that magic conflates 10/9 and 11/10 and so also 9/5 and 20/11. If a transversal can be found which shows the chord to be essentially just, that transversal is listed along with a typing as otonal, utonal, or ambitonal. If the chord is essentially tempered, it is analyzed in terms of the transversal which employs 10/9 and 9/5.

Chords requiring tempering only by 225/224 are labeled marvel, by 245/243 sensamagic, by 100/99 ptolemismic, by 896/891 pentacircle, by 385/384 keenanismic, and by 540/539 swetismic. Those requiring any two of 225/224, 100/99 or 896/891 are labeled apollo, any two of 100/99, 245/243 or 540/539 octarod, any two of 245/243, 896/891 or 385/384 sensamagic11, any two of 225/224, 385/384 or 540/539 unimarvel. Chords requiring both 100/99 and 385/384 are labeled supermagic. Finally, anything requiring three independent commas among those discussed above is labeled magic.

Magic has mos scales of sizes 7, 10, 13, 16, 19 and 22 notes. It may be seen that even the seven-note mos is not without a few harmonic resources, and the larger ones do much better.

The chord names use ups and downs as described on the pergens page. The generator is vM3 and the enharmonic interval is ^5dd2. To simplify the names, lifts and drops are also used. One lift is 41 generators, octave-reduced. (41 because 41edo is a near-optimal tuning of magic.) Thus /1 = ^d2 = 20¢ - 8.2c, i.e. an up minus a tempered pythagorean comma. /C = ^Dbb and \C = vB#. ^C = /B# and vC = \Dbb.

genspan 0 1 2 3 4 5 6 7 8 9 10 11 12 13
Cents (41edo) 0 380 761 1141 322 702 1083 263 644 1024 205 585 966 146
Ratios 1/1 5/4 14/9 27/14 6/5 3/2 15/8 7/6 (16/11) 9/5 9/8 7/5 7/4 (12/11)
Interval P1 vM3 vvA5

v\m6

^^d8

^/M7

^m3 P5 vM7 vvA2

v\m3

^^d5

^/A4

^m7 M2 vA4

\d5

vvA6

v\m7

^^m2

^/A1

Triads

# Chord Transversal Type name comments
1 0-1-2 1-5/4-14/9 marvel v(vv#5)
2 0-2-4 1-14/9-6/5 sensamagic ^m(vv#5)
3 0-1-5 1-5/4-3/2 otonal v
4 0-4-5 1-6/5-3/2 utonal ^m
5 0-2-7 1-14/9-7/6 utonal ^/ 1-9/7-3/2
6 0-5-7 1-3/2-7/6 otonal v\m
7 0-1-8 1-5/4-16/11 keenanismic v(^^b5)
8 0-4-8 1-6/5-16/11 ptolemismic ^m(^^b5)
9 0-7-8 1-7/6-16/11 keenanismic v\m(^^b5)
10 0-1-9 1-5/4-20/11 utonal v^7no5
11 0-2-9 1-14/9-9/5 sensamagic ^m7(vv#5)no3
12 0-4-9 1-6/5-9/5 otonal ^m7no5 or 1-3/2-5/3 = v6no3
13 0-5-9 1-3/2-9/5 utonal ^m7no3
14 0-7-9 1-7/6-9/5 sensamagic v\m,v7no5
15 0-8-9 1-16/11-20/11 otonal v(^^^bb5) 1-5/4-11/8
16 0-1-10 1-5/4-9/8 otonal v,9no5
17 0-2-10 1-14/9-9/8 pentacircle 2(vv#5)
18 0-5-10 1-3/2-9/8 ambitonal 2
19 0-8-10 1-16/11-9/8 pentacircle 2(^^b5)
20 0-9-10 1-9/5-9/8 utonal ^9no35 or ^7sus2no5
21 0-1-11 1-5/4-7/5 marvel v(\b5)
22 0-2-11 1-14/9-7/5 utonal ^/,^7no5 1-9/7-9/5
23 0-4-11 1-6/5-7/5 otonal ^m(\b5)
24 0-7-11 1-7/6-7/5 utonal v\m(\b5)
25 0-9-11 1-9/5-7/5 otonal ^/(^b5) 1/1-9/7-10/7
26 0-10-11 1-9/8-7/5 marvel v,7no5 1/1-5/4-16/9
27 0-1-12 1-5/4-7/4 otonal v,v/7
28 0-2-12 1-14/9-7/4 utonal ^/,9no5 1/1-9/8-9/7
29 0-4-12 1-6/5-7/4 keenanismic ^m,v\7
30 0-5-12 1-3/2-7/4 otonal v\m7no3
31 0-7-12 1-7/6-7/4 utonal v\m7no5
32 0-8-12 1-16/11-7/4 keenanismic
33 0-10-12 1-9/8-7/4 otonal v\m7sus2
34 0-11-12 1-7/5-7/4 utonal
35 0-1-13 1-5/4-12/11 keenanismic
36 0-2-13 1-14/9-12/11 swetismic 1/1-9/7-7/5
37 0-4-13 1-6/5-12/11 utonal
38 0-5-13 1-3/2-12/11 utonal
39 0-8-13 1-16/11-12/11 otonal
40 0-9-13 1-20/11-12/11 otonal
41 0-11-13 1-7/5-12/11 swetismic
42 0-12-13 1-7/4-12/11 keenanismic
43 0-5-18 1-3/2-18/11 utonal
44 0-7-18 1-7/6-18/11 swetismic
45 0-8-18 1-16/11-18/11 otonal
46 0-9-18 1-9/5-18/11 utonal
47 0-10-18 1-9/8-18/11 utonal
48 0-11-18 1-7/5-18/11 swetismic
49 0-13-18 1-12/11-18/11 otonal
50 0-2-20 1-14/9-14/11 utonal
51 0-7-20 1-7/6-14/11 utonal
52 0-8-20 1-16/11-14/11 otonal
53 0-9-20 1-20/11-14/11 otonal
54 0-10-20 1-9/8-14/11 pentacircle
55 0-11-20 1-7/5-14/11 utonal
56 0-12-20 1-7/4-14/11 utonal
57 0-13-20 1-12/11-14/11 otonal
58 0-18-20 1-18/11-14/11 otonal

Tetrads

# Chord Transversal Type name comments
1 0-1-2-9 1-5/4-14/9-9/5 magic
2 0-2-4-9 1-14/9-6/5-9/5 sensamagic ^m7(vv#5)
3 0-1-5-9 1-5/4-3/2-9/5 ptolemismic v^7
4 0-4-5-9 1-6/5-3/2-9/5 ambitonal ^m7 or 1/1-5/4-3/2-5/3 = v6
5 0-2-7-9 1-14/9-7/6-9/5 sensamagic ^/,vv#9 1-9/7-3/2-7/3
6 0-5-7-9 1-3/2-7/6-9/5 sensamagic v\m^7
7 0-1-8-9 1-5/4-16/11-9/5 supermagic
8 0-4-8-9 1-6/5-16/11-9/5 ptolemismic
9 0-7-8-9 1-7/6-16/11-9/5 magic
10 0-1-2-10 1-5/4-14/9-9/8 apollo
11 0-1-5-10 1-5/4-3/2-9/8 otonal v,9
12 0-1-8-10 1-5/4-16/11-9/8 sensamagic11
13 0-1-9-10 1-5/4-9/5-9/8 ptolemismic
14 0-2-9-10 1-14/9-9/5-9/8 sensamagic11
15 0-5-9-10 1-3/2-9/5-9/8 utonal ^7sus2 or 2,^m7
16 0-8-9-10 1-16/11-9/5-9/8 apollo
17 0-1-2-11 1-5/4-14/9-7/5 marvel
18 0-2-4-11 1-14/9-6/5-7/5 sensamagic
19 0-2-7-11 1-14/9-7/6-7/5 utonal
20 0-1-9-11 1-5/4-9/5-7/5 apollo
21 0-2-9-11 1-14/9-9/5-7/5 sensamagic
22 0-4-9-11 1-6/5-9/5-7/5 otonal ^m7(\b5)
23 0-7-9-11 1-7/6-9/5-7/5 sensamagic
24 0-1-10-11 1-5/4-9/8-7/5 marvel
25 0-2-10-11 1-14/9-9/8-7/5 apollo
26 0-9-10-11 1-9/5-9/8-7/5 marvel
27 0-1-2-12 1-5/4-14/9-7/4 marvel
28 0-2-4-12 1-14/9-6/5-7/4 sensamagic11
29 0-1-5-12 1-5/4-3/2-7/4 otonal v,v\7
30 0-4-5-12 1-6/5-3/2-7/4 keenanismic ^m,v\7
31 0-2-7-12 1-14/9-7/6-7/4 utonal
32 0-5-7-12 1-3/2-7/6-7/4 ambitonal v\m7
33 0-1-8-12 1-5/4-16/11-7/4 keenanismic
34 0-4-8-12 1-6/5-16/11-7/4 supermagic
35 0-7-8-12 1-7/6-16/11-7/4 keenanismic
36 0-1-10-12 1-5/4-9/8-7/4 otonal
37 0-2-10-12 1-14/9-9/8-7/4 pentacircle
38 0-5-10-12 1-3/2-9/8-7/4 otonal v\7sus2 or 2,v\7
39 0-8-10-12 1-16/11-9/8-7/4 sensamagic11
40 0-1-11-12 1-5/4-7/5-7/4 marvel
41 0-2-11-12 1-14/9-7/5-7/4 utonal
42 0-4-11-12 1-6/5-7/5-7/4 keenanismic
43 0-7-11-12 1-7/6-7/5-7/4 utonal
44 0-10-11-12 1-9/8-7/5-7/4 marvel
45 0-1-2-13 1-5/4-14/9-12/11 unimarvel
46 0-2-4-13 1-14/9-6/5-12/11 octarod
47 0-1-5-13 1-5/4-3/2-12/11 keenanismic
48 0-4-5-13 1-6/5-3/2-12/11 utonal
49 0-1-8-13 1-5/4-16/11-12/11 keenanismic
50 0-4-8-13 1-6/5-16/11-12/11 ptolemismic
51 0-1-9-13 1-5/4-9/5-12/11 supermagic
52 0-2-9-13 1-14/9-9/5-12/11 octarod
53 0-4-9-13 1-6/5-9/5-12/11 ptolemismic
54 0-5-9-13 1-3/2-9/5-12/11 ptolemismic
55 0-8-9-13 1-16/11-20/11-12/11 otonal
56 0-1-11-13 1-5/4-7/5-12/11 unimarvel
57 0-2-11-13 1-14/9-7/5-12/11 swetismic
58 0-4-11-13 1-6/5-7/5-12/11 octarod
59 0-9-11-13 1-9/5-7/5-12/11 octarod
60 0-1-12-13 1-5/4-7/4-12/11 keenanismic
61 0-2-12-13 1-14/9-7/4-12/11 unimarvel
62 0-4-12-13 1-6/5-7/4-12/11 supermagic
63 0-5-12-13 1-3/2-7/4-12/11 keenanismic
64 0-8-12-13 1-16/11-7/4-12/11 keenanismic
65 0-11-12-13 1-7/5-7/4-12/11 unimarvel
66 0-5-7-18 1-3/2-7/6-18/11 swetismic
67 0-7-8-18 1-7/6-16/11-18/11 unimarvel
68 0-5-9-18 1-3/2-9/5-18/11 utonal
69 0-7-9-18 1-7/6-9/5-18/11 octarod
70 0-8-9-18 1-16/11-20/11-18/11 otonal
71 0-5-10-18 1-3/2-9/8-18/11 utonal
72 0-8-10-18 1-16/11-9/8-18/11 pentacircle
73 0-9-10-18 1-9/5-9/8-18/11 utonal
74 0-7-11-18 1-7/6-7/5-18/11 swetismic
75 0-9-11-18 1-9/5-7/5-18/11 octarod
76 0-10-11-18 1-9/8-7/5-18/11 unimarvel
77 0-5-13-18 1-3/2-12/11-18/11 ambitonal
78 0-8-13-18 1-16/11-12/11-18/11 otonal
79 0-9-13-18 1-20/11-12/11-18/11 otonal
80 0-11-13-18 1-7/5-12/11-18/11 swetismic
81 0-2-7-20 1-14/9-7/6-14/11 utonal
82 0-7-8-20 1-7/6-16/11-14/11 keenanismic
83 0-2-9-20 1-14/9-9/5-14/11 octarod
84 0-7-9-20 1-7/6-9/5-14/11 octarod
85 0-8-9-20 1-16/11-20/11-14/11 otonal
86 0-2-10-20 1-14/9-9/8-14/11 pentacircle
87 0-8-10-20 1-16/11-9/8-14/11 pentacircle
88 0-9-10-20 1-9/5-9/8-14/11 apollo
89 0-2-11-20 1-14/9-7/5-14/11 utonal
90 0-7-11-20 1-7/6-7/5-14/11 utonal
91 0-9-11-20 1-9/5-7/5-14/11 ptolemismic
92 0-10-11-20 1-9/8-7/5-14/11 apollo
93 0-2-12-20 1-14/9-7/4-14/11 utonal
94 0-7-12-20 1-7/6-7/4-14/11 utonal
95 0-8-12-20 1-16/11-7/4-14/11 keenanismic
96 0-10-12-20 1-9/8-7/4-14/11 pentacircle
97 0-11-12-20 1-7/5-7/4-14/11 utonal
98 0-2-13-20 1-14/9-12/11-14/11 swetismic
99 0-8-13-20 1-16/11-12/11-14/11 otonal
100 0-9-13-20 1-20/11-12/11-14/11 otonal
101 0-11-13-20 1-7/5-12/11-14/11 octarod
102 0-12-13-20 1-7/4-12/11-14/11 keenanismic
103 0-7-18-20 1-7/6-18/11-14/11 swetismic
104 0-8-18-20 1-16/11-18/11-14/11 otonal
105 0-9-18-20 1-20/11-18/11-14/11 otonal
106 0-10-18-20 1-9/8-18/11-14/11 pentacircle
107 0-11-18-20 1-7/5-18/11-14/11 octarod
108 0-13-18-20 1-12/11-18/11-14/11 otonal

Pentads

# Chord Transversal Type
1 0-1-2-9-10 1-5/4-14/9-9/5-9/8 magic
2 0-1-5-9-10 1-5/4-3/2-9/5-9/8 ptolemismic
3 0-1-8-9-10 1-5/4-16/11-9/5-9/8 magic
4 0-1-2-9-11 1-5/4-14/9-9/5-7/5 magic
5 0-2-4-9-11 1-14/9-6/5-9/5-7/5 sensamagic
6 0-2-7-9-11 1-14/9-7/6-9/5-7/5 sensamagic
7 0-1-2-10-11 1-5/4-14/9-9/8-7/5 apollo
8 0-1-9-10-11 1-5/4-9/5-9/8-7/5 apollo
9 0-2-9-10-11 1-14/9-9/5-9/8-7/5 magic
10 0-1-2-10-12 1-5/4-14/9-9/8-7/4 apollo
11 0-1-5-10-12 1-5/4-3/2-9/8-7/4 otonal
12 0-1-8-10-12 1-5/4-16/11-9/8-7/4 sensamagic11
13 0-1-2-11-12 1-5/4-14/9-7/5-7/4 marvel
14 0-2-4-11-12 1-14/9-6/5-7/5-7/4 sensamagic11
15 0-2-7-11-12 1-14/9-7/6-7/5-7/4 utonal
16 0-1-10-11-12 1-5/4-9/8-7/5-7/4 marvel
17 0-2-10-11-12 1-14/9-9/8-7/5-7/4 apollo
18 0-1-2-9-13 1-5/4-14/9-9/5-12/11 magic
19 0-2-4-9-13 1-14/9-6/5-9/5-12/11 octarod
20 0-1-5-9-13 1-5/4-3/2-9/5-12/11 supermagic
21 0-4-5-9-13 1-6/5-3/2-9/5-12/11 ptolemismic
22 0-1-8-9-13 1-5/4-16/11-9/5-12/11 supermagic
23 0-4-8-9-13 1-6/5-16/11-9/5-12/11 ptolemismic
24 0-1-2-11-13 1-5/4-14/9-7/5-12/11 unimarvel
25 0-2-4-11-13 1-14/9-6/5-7/5-12/11 octarod
26 0-1-9-11-13 1-5/4-9/5-7/5-12/11 magic
27 0-2-9-11-13 1-14/9-9/5-7/5-12/11 octarod
28 0-4-9-11-13 1-6/5-9/5-7/5-12/11 octarod
29 0-1-2-12-13 1-5/4-14/9-7/4-12/11 unimarvel
30 0-2-4-12-13 1-14/9-6/5-7/4-12/11 magic
31 0-1-5-12-13 1-5/4-3/2-7/4-12/11 keenanismic
32 0-4-5-12-13 1-6/5-3/2-7/4-12/11 supermagic
33 0-1-8-12-13 1-5/4-16/11-7/4-12/11 keenanismic
34 0-4-8-12-13 1-6/5-16/11-7/4-12/11 supermagic
35 0-1-11-12-13 1-5/4-7/5-7/4-12/11 unimarvel
36 0-2-11-12-13 1-14/9-7/5-7/4-12/11 unimarvel
37 0-4-11-12-13 1-6/5-7/5-7/4-12/11 magic
38 0-5-7-9-18 1-3/2-7/6-9/5-18/11 octarod
39 0-7-8-9-18 1-7/6-16/11-9/5-18/11 magic
40 0-5-9-10-18 1-3/2-9/5-9/8-18/11 utonal
41 0-8-9-10-18 1-16/11-9/5-9/8-18/11 apollo
42 0-7-9-11-18 1-7/6-9/5-7/5-18/11 octarod
43 0-9-10-11-18 1-9/5-9/8-7/5-18/11 magic
44 0-5-9-13-18 1-3/2-9/5-12/11-18/11 ptolemismic
45 0-8-9-13-18 1-16/11-20/11-12/11-18/11 otonal
46 0-9-11-13-18 1-9/5-7/5-12/11-18/11 octarod
47 0-2-7-9-20 1-14/9-7/6-9/5-14/11 octarod
48 0-7-8-9-20 1-7/6-16/11-9/5-14/11 magic
49 0-2-9-10-20 1-14/9-9/5-9/8-14/11 magic
50 0-8-9-10-20 1-16/11-9/5-9/8-14/11 apollo
51 0-2-7-11-20 1-14/9-7/6-7/5-14/11 utonal
52 0-2-9-11-20 1-14/9-9/5-7/5-14/11 octarod
53 0-7-9-11-20 1-7/6-9/5-7/5-14/11 octarod
54 0-2-10-11-20 1-14/9-9/8-7/5-14/11 apollo
55 0-9-10-11-20 1-9/5-9/8-7/5-14/11 apollo
56 0-2-7-12-20 1-14/9-7/6-7/4-14/11 utonal
57 0-7-8-12-20 1-7/6-16/11-7/4-14/11 keenanismic
58 0-2-10-12-20 1-14/9-9/8-7/4-14/11 pentacircle
59 0-8-10-12-20 1-16/11-9/8-7/4-14/11 sensamagic11
60 0-2-11-12-20 1-14/9-7/5-7/4-14/11 utonal
61 0-7-11-12-20 1-7/6-7/5-7/4-14/11 utonal
62 0-10-11-12-20 1-9/8-7/5-7/4-14/11 apollo
63 0-2-9-13-20 1-14/9-9/5-12/11-14/11 octarod
64 0-8-9-13-20 1-16/11-20/11-12/11-14/11 otonal
65 0-2-11-13-20 1-14/9-7/5-12/11-14/11 octarod
66 0-9-11-13-20 1-9/5-7/5-12/11-14/11 octarod
67 0-2-12-13-20 1-14/9-7/4-12/11-14/11 unimarvel
68 0-8-12-13-20 1-16/11-7/4-12/11-14/11 keenanismic
69 0-11-12-13-20 1-7/5-7/4-12/11-14/11 magic
70 0-7-8-18-20 1-7/6-16/11-18/11-14/11 unimarvel
71 0-7-9-18-20 1-7/6-9/5-18/11-14/11 octarod
72 0-8-9-18-20 1-16/11-20/11-18/11-14/11 otonal
73 0-8-10-18-20 1-16/11-9/8-18/11-14/11 pentacircle
74 0-9-10-18-20 1-9/5-9/8-18/11-14/11 apollo
75 0-7-11-18-20 1-7/6-7/5-18/11-14/11 octarod
76 0-9-11-18-20 1-9/5-7/5-18/11-14/11 octarod
77 0-10-11-18-20 1-9/8-7/5-18/11-14/11 magic
78 0-8-13-18-20 1-16/11-12/11-18/11-14/11 otonal
79 0-9-13-18-20 1-20/11-12/11-18/11-14/11 otonal
80 0-11-13-18-20 1-7/5-12/11-18/11-14/11 octarod

Hexads

# Chord Transversal Type
1 0-1-2-9-10-11 1-5/4-14/9-9/5-9/8-7/5 magic
2 0-1-2-10-11-12 1-5/4-14/9-9/8-7/5-7/4 apollo
3 0-1-2-9-11-13 1-5/4-14/9-9/5-7/5-12/11 magic
4 0-2-4-9-11-13 1-14/9-6/5-9/5-7/5-12/11 octarod
5 0-1-2-11-12-13 1-5/4-14/9-7/5-7/4-12/11 unimarvel
6 0-2-4-11-12-13 1-14/9-6/5-7/5-7/4-12/11 magic
7 0-2-7-9-11-20 1-14/9-7/6-9/5-7/5-14/11 octarod
8 0-2-9-10-11-20 1-14/9-9/5-9/8-7/5-14/11 magic
9 0-2-7-11-12-20 1-14/9-7/6-7/5-7/4-14/11 utonal
10 0-2-10-11-12-20 1-14/9-9/8-7/5-7/4-14/11 apollo
11 0-2-9-11-13-20 1-14/9-9/5-7/5-12/11-14/11 octarod
12 0-2-11-12-13-20 1-14/9-7/5-7/4-12/11-14/11 magic
13 0-7-8-9-18-20 1-7/6-16/11-9/5-18/11-14/11 magic
14 0-8-9-10-18-20 1-16/11-9/5-9/8-18/11-14/11 apollo
15 0-7-9-11-18-20 1-7/6-9/5-7/5-18/11-14/11 octarod
16 0-9-10-11-18-20 1-9/5-9/8-7/5-18/11-14/11 magic
17 0-8-9-13-18-20 1-16/11-20/11-12/11-18/11-14/11 otonal
18 0-9-11-13-18-20 1-9/5-7/5-12/11-18/11-14/11 octarod
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