Chords of magic: Difference between revisions

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TallKite (talk | contribs)
autopatrolled, Sysops
4,199 edits
fixed 2 errors, added a table of cents for all accidentals, added the vM7 and 7;6;5;4 chords
TallKite (talk | contribs)
autopatrolled, Sysops
4,199 edits
major rewrite of chord names: a lift has been redefined from -41 generators to -22 generators. Advantages: makes shorter chord names, also makes a less "tippy" notation, lifts are no longer negative cents for 22edo.
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 arrows (ups and downs) as described on the [[Pergen|pergens]] page. The pergen is (P8, P12/5) fifth-of-a-12th, #37 in the [http://tallkite.com/misc_files/notation%20guide%20for%20rank-2%20pergens.pdf list of pergens]. The generator is vM3 = 380¢ + c/5, where c = the amount in cents the tempered fifth exceeds 700¢. The enharmonic interval is ^<sup>5</sup>dd2, thus ^<sup>5</sup>C = B##. To simplify the chord names, slashes (lifts and drops) are also used. One lift is -41 generators, octave-reduced. (41 because 41edo is a near-optimal tuning of magic.) Thus {{nowrap|/1 {{=}} ^d2 {{=}} 20¢ &minus; 8.2c}}. Thus a lift equals an up minus a tempered pythagorean comma. {{nowrap|/C {{=}} ^Dbb|\C {{=}} vB#|^C {{=}} /B#|and vC {{=}} \Dbb}}. This notation is "tippy" in the sense that if the fifth is wider than 41edo's fifth, a lift will actually be descending. Furthermore if the fifth is narrower than 19edo's, an up will be descending.
The chord names use arrows (ups and downs) as described on the [[Pergen|pergens]] page. The pergen is (P8, P12/5) fifth-of-a-12th, #37 in the [http://tallkite.com/misc_files/notation%20guide%20for%20rank-2%20pergens.pdf list of pergens]. One up is 19 generators, octave-reduced. The generator is vM3 = 380¢ + c/5, where c = the amount in cents the tempered fifth exceeds 700¢. The enharmonic interval is ^<sup>5</sup>dd2, thus ^<sup>5</sup>C = B##.  
 
To simplify the chord names, slashes (lifts and drops) are also used. One lift is -22 generators, octave-reduced. Thus {{nowrap|1=/1 {{=}} -25G + 3G = m2 + ^^d8 = ^^d2}}. Thus a lift equals two ups minus a tempered pythagorean comma. {{nowrap|1=/C {{=}} ^^Dbb|2=\C {{=}} vvB#|3=^^C {{=}} /B#|4=and vvC {{=}} \Dbb}}. When naming 7-limit chords, note that an up is ~81/80 and a lift is ~64/63.
 
The cents values of sharps, ups and lifts vary greatly, as this table shows. Note that if the fifth is wider than 22edo's fifth, a lift will actually be descending. Furthermore if the fifth is narrower than 19edo's, an up will be descending.  
{| class="wikitable"
{| class="wikitable"
|+Cents values of Magic accidentals
|+Cents values of Magic accidentals in various tunings
!
!
!sharp
!sharp
!up
!up
!lift
!lift
!how to convert the score to an edo
!how to convert the notation to an edo
|-
|-
!19edo
!19edo
Line 23: Line 27:
|3\22 = 164¢
|3\22 = 164¢
|1\22 = 55¢
|1\22 = 55¢
| -1\22 = -55¢
|0\22 = 0¢
|treat lifts as downs and drops as ups
|ignore the slashes
|-
|-
!41edo
!41edo
|4\41 = 117¢
|4\41 = 117¢
|1\41 = 29¢
|1\41 = 29¢
|0\41 = 0¢
|1\41 = 29¢
|ignore the slashes
|treat slashes as arrows
|-
|-
!60edo
!60edo
|5\60 = 100¢
|5\60 = 100¢
|1\60 = 20¢
|1\60 = 20¢
|1\60 = 20¢
|2\60 = 40¢
|treat slashes as arrows
|treat slashes as double arrows
|-
|-
!rank-2
!rank-2
|100¢ + 7c
|100¢ + 7c
|20¢ + 3.8c
|20¢ + 3.8c
|20¢ - 8.2c
|40¢ - 4.4c
!
!
|}
|}
{| class="wikitable center-all"
{| class="wikitable center-all"
|+Magic's genchain
|+Magic's genchain
|-
!Genspan
! Genspan
!0
| 0
!1
| 1
!2
| 2
!3
| 3
!4
| 4
!5
| 5
!6
| 6
!7
| 7
!8
| 8
!9
| 9
!10
| 10
!11
| 11
!12
| 12
!13
| 13
|-
|-
! Cents (41edo)
! Cents (41edo)
Line 96: Line 99:
|-
|-
! Interval
! Interval
| '''P1'''
|'''P1'''
| vM3
| vM3
| vvA5
| vvA5
v\m6
\m6
| ^^d8
| ^^d8
^/M7
/M7
| ^m3
| ^m3
| '''P5'''
|'''P5'''
| vM7
| vM7
| vvA2
| vvA2
v\m3
\m3
| ^^d5
| ^^d5
^/A4
/A4
| ^m7
| ^m7
| '''M2'''
|'''M2'''
| vA4
| vA4
\d5
^\d5
| vvA6
| vvA6
v\m7
\m7
| ^^m2
| ^^m2
^/A1
/A1
|-
|-
!Note
!Note
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|vE
|vE
|vvG#
|vvG#
v\Ab
\Ab
|^^Cb
|^^Cb
^/B
/B
|^Eb
|^Eb
|'''G'''
|'''G'''
|vB
|vB
|vvD#
|vvD#
v\Eb
\Eb
|^^Gb
|^^Gb
^/F#
/F#
|^Bb
|^Bb
|'''D'''
|'''D'''
|vF#
|vF#
\Gb
^\Gb
|vvA#
|vvA#
v\Bb
\Bb
|^^Db
|^^Db
^/C#
/C#
|}
|}
'''''TODO: complete the tables'''''
'''''TODO: complete the tables'''''
Line 186: Line 189:
| 1-14/9-7/6
| 1-14/9-7/6
| Utonal
| Utonal
| ^/
| /
| 1-9/7-3/2
| 1-9/7-3/2
|-
|-
Line 193: Line 196:
| 1-3/2-7/6
| 1-3/2-7/6
| Otonal
| Otonal
| v\m
| \m
|
|
|-
|-
Line 214: Line 217:
| 1-7/6-16/11
| 1-7/6-16/11
| Keenanismic
| Keenanismic
| v\m(^^b5)
| \m(^^b5)
|
|
|-
|-
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| 1-7/6-9/5
| 1-7/6-9/5
| Sensamagic
| Sensamagic
| v\m,v7no5
| \m,v7no5
|
|
|-
|-
Line 256: Line 259:
| 1-16/11-20/11
| 1-16/11-20/11
| Otonal
| Otonal
| v(^^^bb5)
| v(\b5)
| 1-5/4-11/8
| 1-5/4-11/8
|-
|-
Line 298: Line 301:
| 1-5/4-7/5
| 1-5/4-7/5
| Marvel
| Marvel
| v(\b5)
| v(^\b5)
|
|
|-
|-
Line 305: Line 308:
| 1-14/9-7/5
| 1-14/9-7/5
| Utonal
| Utonal
| ^/,^7no5
| /,^7no5
| 1-9/7-9/5
| 1-9/7-9/5
|-
|-
Line 312: Line 315:
| 1-6/5-7/5
| 1-6/5-7/5
| Otonal
| Otonal
| ^m(\b5)
| ^m(^\b5)
|
|
|-
|-
Line 319: Line 322:
| 1-7/6-7/5
| 1-7/6-7/5
| Utonal
| Utonal
| v\m(\b5)
| \m(^\b5)
|
|
|-
|-
Line 326: Line 329:
| 1-9/5-7/5
| 1-9/5-7/5
| Otonal
| Otonal
| ^/(^b5)
| /(^b5)
| 1-9/7-10/7
| 1-9/7-10/7
|-
|-
Line 340: Line 343:
| 1-5/4-7/4
| 1-5/4-7/4
| Otonal
| Otonal
| v,v/7
| v,\7no5
|
|
|-
|-
Line 347: Line 350:
| 1-14/9-7/4
| 1-14/9-7/4
| Utonal
| Utonal
| ^/,9no5
| /,9no5
| 1-9/8-9/7
| 1-9/8-9/7
|-
|-
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| 1-6/5-7/4
| 1-6/5-7/4
| Keenanismic
| Keenanismic
| ^m,v\7
| ^m\7
|
|
|-
|-
Line 361: Line 364:
| 1-3/2-7/4
| 1-3/2-7/4
| Otonal
| Otonal
| v\m7no3
| \7no3
|
|
|-
|-
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| 1-7/6-7/4
| 1-7/6-7/4
| Utonal
| Utonal
| v\m7no5
| \m7no5
|
|
|-
|-
Line 375: Line 378:
| 1-16/11-7/4
| 1-16/11-7/4
| Keenanismic
| Keenanismic
| ^m(v\b5)
| ^m(\b5)
| 1-6/5-11/8
| 1-6/5-11/8
|-
|-
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| 1-9/8-7/4
| 1-9/8-7/4
| Otonal
| Otonal
| v\m7sus2
| \7sus2
|
|
|-
|-
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| 1-7/5-7/4
| 1-7/5-7/4
| Utonal
| Utonal
| v\7(\b5)no3
| \7(^\b5)no3
|
|
|-
|-
Line 403: Line 406:
| 1-14/9-12/11
| 1-14/9-12/11
| Swetismic
| Swetismic
|
|/(^\b5)
| 1-9/7-7/5
| 1-9/7-7/5
|-
|-
Line 610: Line 613:
| 1-14/9-7/6-9/5
| 1-14/9-7/6-9/5
| Sensamagic
| Sensamagic
| ^/,vv#9
| /,vv#9
| 1-9/7-3/2-7/3
| 1-9/7-3/2-7/3
|-
|-
Line 617: Line 620:
| 1-3/2-7/6-9/5
| 1-3/2-7/6-9/5
| Sensamagic
| Sensamagic
| v\m^7
| \m^7
|  
|  
|-
|-
Line 638: Line 641:
| 1-7/6-16/11-9/5
| 1-7/6-16/11-9/5
| Magic
| Magic
| v\m,^7(^^b5)
| \m,^7(^^b5)
|  
|  
|-
|-
Line 729: Line 732:
| 1-6/5-9/5-7/5
| 1-6/5-9/5-7/5
| Otonal
| Otonal
| ^m7(\b5)
| ^m7(^\b5)
|  
|  
|-
|-
Line 778: Line 781:
| 1-5/4-3/2-7/4
| 1-5/4-3/2-7/4
| Otonal
| Otonal
| v,v\7
| v,\7
|  
|  
|-
|-
Line 785: Line 788:
| 1-6/5-3/2-7/4
| 1-6/5-3/2-7/4
| Keenanismic
| Keenanismic
| ^mv\7
| ^m\7
|  
|  
|-
|-
Line 792: Line 795:
| 1-14/9-7/6-7/4
| 1-14/9-7/6-7/4
| Utonal
| Utonal
| v\m7(vv#5)
| \m7(vv#5)
|  
|  
|-
|-
Line 799: Line 802:
| 1-3/2-7/6-7/4
| 1-3/2-7/6-7/4
| Ambitonal
| Ambitonal
| v\m7
| \m7
|  
|  
|-
|-
Line 820: Line 823:
| 1-7/6-16/11-7/4
| 1-7/6-16/11-7/4
| Keenanismic
| Keenanismic
| v\m7(^^b5)
| \m7(^^b5)
|  
|  
|-
|-
Line 827: Line 830:
|1-7/6-7/5-7/4
|1-7/6-7/5-7/4
|Otonal
|Otonal
|v\m7(\b5)
|\m7(^\b5)
|<u>or</u> 1-6/5-3/2-12/7 = ^m^/6
|<u>or</u> 1-6/5-3/2-12/7 = ^m/6
|-
|-
| 38
| 38
Line 848: Line 851:
| 1-3/2-9/8-7/4
| 1-3/2-9/8-7/4
| Otonal
| Otonal
| v\7sus2
| \7sus2
|<u>or</u> 2,v\7 <u>or</u> v\9no3
|<u>or</u> 2,\7 <u>or</u> \9no3
|-
|-
| 41
| 41

Revision as of 03:17, 15 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 arrows (ups and downs) as described on the pergens page. The pergen is (P8, P12/5) fifth-of-a-12th, #37 in the list of pergens. One up is 19 generators, octave-reduced. The generator is vM3 = 380¢ + c/5, where c = the amount in cents the tempered fifth exceeds 700¢. The enharmonic interval is ^5dd2, thus ^5C = B##.

To simplify the chord names, slashes (lifts and drops) are also used. One lift is -22 generators, octave-reduced. Thus /1 = -25G + 3G = m2 + ^^d8 = ^^d2. Thus a lift equals two ups minus a tempered pythagorean comma. /C = ^^Dbb, \C = vvB#, ^^C = /B#, and vvC = \Dbb. When naming 7-limit chords, note that an up is ~81/80 and a lift is ~64/63.

The cents values of sharps, ups and lifts vary greatly, as this table shows. Note that if the fifth is wider than 22edo's fifth, a lift will actually be descending. Furthermore if the fifth is narrower than 19edo's, an up will be descending.

Cents values of Magic accidentals in various tunings
sharp up lift how to convert the notation to an edo
19edo 1\19 = 61¢ 0\19 = 0¢ 1\19 = 61¢ ignore the arrows, treat slashes as sharps/flats
22edo 3\22 = 164¢ 1\22 = 55¢ 0\22 = 0¢ ignore the slashes
41edo 4\41 = 117¢ 1\41 = 29¢ 1\41 = 29¢ treat slashes as arrows
60edo 5\60 = 100¢ 1\60 = 20¢ 2\60 = 40¢ treat slashes as double arrows
rank-2 100¢ + 7c 20¢ + 3.8c 40¢ - 4.4c
Magic's genchain
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
Ratio 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

\m6

^^d8

/M7

^m3 P5 vM7 vvA2

\m3

^^d5

/A4

^m7 M2 vA4

^\d5

vvA6

\m7

^^m2

/A1

Note

(in C)

C vE vvG#

\Ab

^^Cb

/B

^Eb G vB vvD#

\Eb

^^Gb

/F#

^Bb D vF#

^\Gb

vvA#

\Bb

^^Db

/C#

TODO: complete the tables

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 \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 \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 \m,v7no5
15 0-8-9 1-16/11-20/11 Otonal v(\b5) 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 \m(^\b5)
25 0-9-11 1-9/5-7/5 Otonal /(^b5) 1-9/7-10/7
26 0-10-11 1-9/8-7/5 Marvel v,7no5 1-5/4-16/9
27 0-1-12 1-5/4-7/4 Otonal v,\7no5
28 0-2-12 1-14/9-7/4 Utonal /,9no5 1-9/8-9/7
29 0-4-12 1-6/5-7/4 Keenanismic ^m\7
30 0-5-12 1-3/2-7/4 Otonal \7no3
31 0-7-12 1-7/6-7/4 Utonal \m7no5
32 0-8-12 1-16/11-7/4 Keenanismic ^m(\b5) 1-6/5-11/8
33 0-10-12 1-9/8-7/4 Otonal \7sus2
34 0-11-12 1-7/5-7/4 Utonal \7(^\b5)no3
35 0-1-13 1-5/4-12/11 Keenanismic
36 0-2-13 1-14/9-12/11 Swetismic /(^\b5) 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 0-1-5-6 1-5/4-3/2-15/8 Ambitonal vM7
2 0-1-2-9 1-5/4-14/9-9/5 Magic v^7(vv#5)
3 0-2-4-9 1-14/9-6/5-9/5 Sensamagic ^m7(vv#5)
4 0-1-5-9 1-5/4-3/2-9/5 Ptolemismic v^7
5 0-4-5-9 1-6/5-3/2-9/5 Ambitonal ^m7 or 1-5/4-3/2-5/3 = v6
6 0-2-7-9 1-14/9-7/6-9/5 Sensamagic /,vv#9 1-9/7-3/2-7/3
7 0-5-7-9 1-3/2-7/6-9/5 Sensamagic \m^7
8 0-1-8-9 1-5/4-16/11-9/5 Supermagic v^7(^^b5)
9 0-4-8-9 1-6/5-16/11-9/5 Ptolemismic ^m7(^^b5)
10 0-7-8-9 1-7/6-16/11-9/5 Magic \m,^7(^^b5)
11 0-1-2-10 1-5/4-14/9-9/8 Apollo v,9(vv#5)
12 0-1-5-10 1-5/4-3/2-9/8 Otonal v,9
13 0-1-8-10 1-5/4-16/11-9/8 Sensamagic11 v,9(^^b5)
14 0-1-9-10 1-5/4-9/5-9/8 Ptolemismic v^7,9no5 or v9(^7)no5
15 0-2-9-10 1-14/9-9/5-9/8 Sensamagic11 ^9(vv#5)no3 or ^7(vv#5)sus2
16 0-5-9-10 1-3/2-9/5-9/8 Utonal ^9no3 or ^7sus2 or 2,^7
17 0-8-9-10 1-16/11-9/5-9/8 Apollo
18 0-1-2-11 1-5/4-14/9-7/5 Marvel
19 0-2-4-11 1-14/9-6/5-7/5 Sensamagic
20 0-2-7-11 1-14/9-7/6-7/5 Utonal
21 0-1-9-11 1-5/4-9/5-7/5 Apollo
22 0-2-9-11 1-14/9-9/5-7/5 Sensamagic
23 0-4-9-11 1-6/5-9/5-7/5 Otonal ^m7(^\b5)
24 0-7-9-11 1-7/6-9/5-7/5 Sensamagic
25 0-1-10-11 1-5/4-9/8-7/5 Marvel
26 0-2-10-11 1-14/9-9/8-7/5 Apollo
27 0-9-10-11 1-9/5-9/8-7/5 Marvel
28 0-1-2-12 1-5/4-14/9-7/4 Marvel
29 0-2-4-12 1-14/9-6/5-7/4 Sensamagic11
30 0-1-5-12 1-5/4-3/2-7/4 Otonal v,\7
31 0-4-5-12 1-6/5-3/2-7/4 Keenanismic ^m\7
32 0-2-7-12 1-14/9-7/6-7/4 Utonal \m7(vv#5)
33 0-5-7-12 1-3/2-7/6-7/4 Ambitonal \m7
34 0-1-8-12 1-5/4-16/11-7/4 Keenanismic
35 0-4-8-12 1-6/5-16/11-7/4 Supermagic
36 0-7-8-12 1-7/6-16/11-7/4 Keenanismic \m7(^^b5)
37 0-7-11-12 1-7/6-7/5-7/4 Otonal \m7(^\b5) or 1-6/5-3/2-12/7 = ^m/6
38 0-1-10-12 1-5/4-9/8-7/4 Otonal
39 0-2-10-12 1-14/9-9/8-7/4 Pentacircle
40 0-5-10-12 1-3/2-9/8-7/4 Otonal \7sus2 or 2,\7 or \9no3
41 0-8-10-12 1-16/11-9/8-7/4 Sensamagic11
42 0-1-11-12 1-5/4-7/5-7/4 Marvel
43 0-2-11-12 1-14/9-7/5-7/4 Utonal
44 0-4-11-12 1-6/5-7/5-7/4 Keenanismic
45 0-7-11-12 1-7/6-7/5-7/4 Utonal
46 0-10-11-12 1-9/8-7/5-7/4 Marvel
47 0-1-2-13 1-5/4-14/9-12/11 Unimarvel
48 0-2-4-13 1-14/9-6/5-12/11 Octarod
49 0-1-5-13 1-5/4-3/2-12/11 Keenanismic
50 0-4-5-13 1-6/5-3/2-12/11 Utonal
51 0-1-8-13 1-5/4-16/11-12/11 Keenanismic
52 0-4-8-13 1-6/5-16/11-12/11 Ptolemismic
53 0-1-9-13 1-5/4-9/5-12/11 Supermagic
54 0-2-9-13 1-14/9-9/5-12/11 Octarod
55 0-4-9-13 1-6/5-9/5-12/11 Ptolemismic
56 0-5-9-13 1-3/2-9/5-12/11 Ptolemismic
57 0-8-9-13 1-16/11-20/11-12/11 Otonal
58 0-1-11-13 1-5/4-7/5-12/11 Unimarvel
59 0-2-11-13 1-14/9-7/5-12/11 Swetismic
60 0-4-11-13 1-6/5-7/5-12/11 Octarod
61 0-9-11-13 1-9/5-7/5-12/11 Octarod
62 0-1-12-13 1-5/4-7/4-12/11 Keenanismic
63 0-2-12-13 1-14/9-7/4-12/11 Unimarvel
64 0-4-12-13 1-6/5-7/4-12/11 Supermagic
65 0-5-12-13 1-3/2-7/4-12/11 Keenanismic
66 0-8-12-13 1-16/11-7/4-12/11 Keenanismic
67 0-11-12-13 1-7/5-7/4-12/11 Unimarvel
68 0-5-7-18 1-3/2-7/6-18/11 Swetismic
69 0-7-8-18 1-7/6-16/11-18/11 Unimarvel
70 0-5-9-18 1-3/2-9/5-18/11 Utonal
71 0-7-9-18 1-7/6-9/5-18/11 Octarod
72 0-8-9-18 1-16/11-20/11-18/11 Otonal
73 0-5-10-18 1-3/2-9/8-18/11 Utonal
74 0-8-10-18 1-16/11-9/8-18/11 Pentacircle
75 0-9-10-18 1-9/5-9/8-18/11 Utonal
76 0-7-11-18 1-7/6-7/5-18/11 Swetismic
77 0-9-11-18 1-9/5-7/5-18/11 Octarod
78 0-10-11-18 1-9/8-7/5-18/11 Unimarvel
79 0-5-13-18 1-3/2-12/11-18/11 Ambitonal
80 0-8-13-18 1-16/11-12/11-18/11 Otonal
81 0-9-13-18 1-20/11-12/11-18/11 Otonal
82 0-11-13-18 1-7/5-12/11-18/11 Swetismic
83 0-2-7-20 1-14/9-7/6-14/11 Utonal
84 0-7-8-20 1-7/6-16/11-14/11 Keenanismic
85 0-2-9-20 1-14/9-9/5-14/11 Octarod
86 0-7-9-20 1-7/6-9/5-14/11 Octarod
87 0-8-9-20 1-16/11-20/11-14/11 Otonal
88 0-2-10-20 1-14/9-9/8-14/11 Pentacircle
89 0-8-10-20 1-16/11-9/8-14/11 Pentacircle
90 0-9-10-20 1-9/5-9/8-14/11 Apollo
91 0-2-11-20 1-14/9-7/5-14/11 Utonal
92 0-7-11-20 1-7/6-7/5-14/11 Utonal
93 0-9-11-20 1-9/5-7/5-14/11 Ptolemismic
94 0-10-11-20 1-9/8-7/5-14/11 Apollo
95 0-2-12-20 1-14/9-7/4-14/11 Utonal
96 0-7-12-20 1-7/6-7/4-14/11 Utonal
97 0-8-12-20 1-16/11-7/4-14/11 Keenanismic
98 0-10-12-20 1-9/8-7/4-14/11 Pentacircle
99 0-11-12-20 1-7/5-7/4-14/11 Utonal
100 0-2-13-20 1-14/9-12/11-14/11 Swetismic
101 0-8-13-20 1-16/11-12/11-14/11 Otonal
102 0-9-13-20 1-20/11-12/11-14/11 Otonal
103 0-11-13-20 1-7/5-12/11-14/11 Octarod
104 0-12-13-20 1-7/4-12/11-14/11 Keenanismic
105 0-7-18-20 1-7/6-18/11-14/11 Swetismic
106 0-8-18-20 1-16/11-18/11-14/11 Otonal
107 0-9-18-20 1-20/11-18/11-14/11 Otonal
108 0-10-18-20 1-9/8-18/11-14/11 Pentacircle
109 0-11-18-20 1-7/5-18/11-14/11 Octarod
110 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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