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Below are listed the [[dyadic chord]]s of 11-limit [[magic|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.
{{Breadcrumb|Magic}}
Below is a complete list of the [[11-odd-limit]] [[dyadic chord]]s of [[11-limit]] [[magic|magic temperament]]. Note that there are many common chords, for example [[8:10:12:15]], which are not listed; in this case due to [[15/8]] not being in the 11-odd-limit. Every chord listed has multiple [[chord #Inversion|inversions]]; only one is listed, that being the inversion where all notes are a nonnegative number of major third [[generator]]s above the root.


Chords requiring tempering only by [[225/224]] are labeled [[marvel chords|marvel]], by [[245/243]] [[sensamagic chords|sensamagic]], by [[100/99]] [[ptolemismic chords|ptolemismic]], by [[896/891]] [[pentacircle chords|pentacircle]], by [[385/384]] [[keenanismic chords|keenanismic]], and by [[540/539]] [[swetismic chords|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 [[undecimal sensamagic chords|sensamagic11]], any two of 225/224, 385/384 or 540/539 [[undecimal marvel chords|unimarvel]]. Chords requiring both 100/99 and 385/384 are labeled [[supermagic chords|supermagic]]. Finally, anything requiring three independent commas among those discussed above is labeled [[magic chords|magic]].
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 that requires the minimum amount of commas to be tempered out; if there is a tie between multiple transversals, it is analyzed in terms of the transversal which employs 10/9 and 9/5.


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.
Chords requiring tempering only by [[225/224]] are labeled [[marvel chords|marvel]], by [[245/243]] [[sensamagic chords|sensamagic]], by [[100/99]] [[ptolemismic chords|ptolemismic]], by [[896/891]] [[pentacircle chords|pentacircle]], by [[385/384]] [[keenanismic chords|keenanismic]], and by [[540/539]] [[swetismic chords|swetismic]]. Those requiring any two of 100/99, 225/224 or 896/891 are labeled [[apollo chords|apollo]], any two of 100/99, 245/243 or 540/539 [[octarod chords|octarod]], any two of 245/243, 896/891 or 385/384 [[undecimal sensamagic chords|sensamagic11]], any two of 225/224, 385/384, or 540/539 [[undecimal marvel chords|marvel11]]. Chords requiring both 100/99 and 385/384 are labeled [[keemic chords|keemic]]. Finally, anything requiring three independent commas among those discussed above is labeled [[magic chords|magic]].


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


{| class="wikitable center-all"
[[Kite Giedraitis]] has named the chords using arrows (ups and downs), as described in [[Kite's thoughts on pergens]]. The pergen is (P8, P12/5) fifth-of-a-twelfth, #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 {{nowrap| vM3 {{=}} 380{{c}} + ''c''/5 }}, where ''c'' is the amount in cents the tempered fifth exceeds 700{{c}}. The [[Kite's thoughts on enharmonic unisons in ups and downs notation|enharmonic unison]] is ^<sup>5</sup>dd2, thus {{nowrap|^<sup>5</sup>C {{=}} Bx}}. To simplify the chord names, slashes (lifts and drops) are also used. One lift is -22 generators, octave-reduced. Thus {{nowrap|/1 {{=}} −25''G'' + 3''G'' {{=}} m2 + ^^d8 {{=}} ^^d2}}. Thus a lift equals two ups minus a tempered pythagorean comma, so {{nowrap| /C {{=}} ^^Dbb }}, {{nowrap| \C {{=}} vvB# }}, {{nowrap| ^^C {{=}} /B# }}, and {{nowrap| vvC {{=}} \Dbb }}. 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 mw-collapsible mw-collapsed"
|+ style="font-size: 105%; white-space: nowrap;" | Cents values of magic accidentals in various tunings
|-
!
! Sharp
! Up
! Lift
! How to convert the notation to the edo
|-
! 19edo
| 1\19 = 61{{c}}
| 0\19 = 0{{c}}
| 1\19 = 61{{c}}
| Ignore the arrows, treat slashes as sharps/flats
|-
! 22edo
| 3\22 = 164{{c}}
| 1\22 = 55{{c}}
| 0\22 = 0{{c}}
| Ignore the slashes
|-
! 41edo
| 4\41 = 117{{c}}
| 1\41 = 29{{c}}
| 1\41 = 29{{c}}
| Treat slashes as arrows
|-
! 60edo
| 5\60 = 100{{c}}
| 1\60 = 20{{c}}
| 2\60 = 40{{c}}
| Treat slashes as double arrows
|-
! Rank-2
| 100{{c}} + 7''c''
| 20{{c}} + 3.8''c''
| 40{{c}} − 4.4''c''
| N/a
|}
 
In magic, 5/4 = vM3, 7/4 = \m7 and 11/8 = vvA4. Thus an up is ~81/80 and a lift is ~64/63. This may not be true for other (P8, P12/5) temperaments. Therefore, the ratios in the following table are specific to magic, but the chord names apply to any (P8, P12/5) temperament.
 
{| class="wikitable center-all mw-collapsible mw-collapsed"
|+ style="font-size: 105%; white-space: nowrap;" | 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
! …
! 18
! …
! 20
|-
|-
! Cents (41edo)
! Cents (41edo)
Line 40: Line 90:
| 966
| 966
| 146
| 146
| …
| 849
| …
| 410
|-
|-
! Ratios
! Ratio
| 1/1
| 1/1
| 5/4
| 5/4
Line 50: Line 104:
| 15/8
| 15/8
| 7/6
| 7/6
| (16/11)
| 16/11
| 9/5
| 9/5
| 9/8
| 9/8
| 7/5
| 7/5
| 7/4
| 7/4
| (12/11)
| 12/11
| …
| 18/11
| …
| 14/11
|-
|-
! Interval
! Interval
| P1
| '''P1'''
| vM3
| vM3
| vvA5
| vvA5<br>\m6
v\m6
| ^^d8<br>/M7
| ^^d8
^/M7
| ^m3
| ^m3
| P5
| '''P5'''
| vM7
| vM7
| vvA2
| vvA2<br>\m3
v\m3
| ^^d5<br>/A4
| ^^d5
^/A4
| ^m7
| ^m7
| M2
| '''M2'''
| vA4
| vA4<br>^\d5
\d5
| vvA6<br>\m7
| vvA6
| ^^m2<br>/A1
v\m7
| …
| ^^m2
| ^^m6<br>/A5
^/A1
| …
| '''M3'''
|-
! Note (in C)
| '''C'''
| vE
| vvG#<br>\Ab
| ^^Cb<br>/B
| ^Eb
| '''G'''
| vB
| vvD#<br>\Eb
| ^^Gb<br>/F#
| ^Bb
|'''D'''
| vF#<br>^\Gb
| vvA#<br>\Bb
| ^^Db<br>/C#
| …
| ^^Ab<br>/G#
| …
| '''E'''
|}
|}
'''''TODO: complete the tables'''''
{{Todo|inline=1|complete table}}


== Triads ==
== Triads ==
Line 86: Line 161:
|-
|-
! #
! #
! Chord
! Generators
! Transversal
! Transversal
! Type
! Type
! Name
! Comments
! Comments
! Kite's name
|-
|-
| 1
| 1
| 0-1-2
| 0–1–2
| 1-5/4-14/9
| 1–5/4–14/9
| Marvel
| Marvel
| v(vv#5)
|  
|
| Cv(vv#5)
|-
|-
| 2
| 2
| 0-2-4
| 0–2–4
| 1-14/9-6/5
| 1–6/5–14/9
| Sensamagic
| Sensamagic
| ^m(vv#5)
|  
|
| C^m(vv#5)
|-
|-
| 3
| 3
| 0-1-5
| 0–1–5
| 1-5/4-3/2
| 1–5/4–3/2
| Otonal
| Otonal
| v
| [[4:5:6]]
|
| Cv
|-
|-
| 4
| 4
| 0-4-5
| 0–4–5
| 1-6/5-3/2
| 1–6/5–3/2
| Utonal
| Utonal
| ^m
| [[10:12:15|1/(6:5:4)]]
|
| C^m
|-
|-
| 5
| 5
| 0-2-7
| 0–2–7
| 1-14/9-7/6
| 1–7/6–14/9
| Utonal
| Utonal
| ^/
| [[14:18:21|1/(9:7:6)]]
| 1-9/7-3/2
| C/
|-
|-
| 6
| 6
| 0-5-7
| 0–5–7
| 1-3/2-7/6
| 1–7/6–3/2
| Otonal
| Otonal
| v\m
| [[6:7:9]]
|
| C\m
|-
|-
| 7
| 7
| 0-1-8
| 0–1–8
| 1-5/4-16/11
| 1–5/4–16/11
| Keenanismic
| Keenanismic
| v(^^b5)
|  
|
| Cv(^^b5)
|-
|-
| 8
| 8
| 0-4-8
| 0–4–8
| 1-6/5-16/11
| 1–6/5–16/11
| Ptolemismic
| Ptolemismic
| ^m(^^b5)
|  
|
| C^m(^^b5)
|-
|-
| 9
| 9
| 0-7-8
| 0–7–8
| 1-7/6-16/11
| 1–7/6–16/11
| Keenanismic
| Keenanismic
| v\m(^^b5)
|  
|
| C\m(^^b5)
|-
|-
| 10
| 10
| 0-1-9
| 0–1–9
| 1-5/4-20/11
| 1–5/4–20/11
| Utonal
| Utonal
| v^7no5
|  
|
| Cv^7no5
|-
|-
| 11
| 11
| 0-2-9
| 0–2–9
| 1-14/9-9/5
| 1–14/9–9/5
| Sensamagic
| Sensamagic
| ^m7(vv#5)no3
|  
|
| C^m7(vv#5)no3
|-
|-
| 12
| 12
| 0-4-9
| 0–4–9
| 1-6/5-9/5
| 1–6/5–9/5
| Otonal
| Otonal
| ^m7no5
| [[6:9:10]]
| <u>or</u> 1-3/2-5/3 =  v6no3
| C^m7no5 ''or'' Cv6no3
|-
|-
| 13
| 13
| 0-5-9
| 0–5–9
| 1-3/2-9/5
| 1–3/2–9/5
| Utonal
| Utonal
| ^m7no3
| [[10:15:18|1/(9:6:5)]]
|
| C^m7no3
|-
|-
| 14
| 14
| 0-7-9
| 0–7–9
| 1-7/6-9/5
| 1–7/6–9/5
| Sensamagic
| Sensamagic
| v\m,v7no5
|  
|
| C\mv7no5
|-
|-
| 15
| 15
| 0-8-9
| 0–8–9
| 1-16/11-20/11
| 1–16/11–20/11
| Otonal
| Otonal
| v(^^^bb5)
| 1–5/4–11/8
| 1-5/4-11/8
| Cv(\b5)
|-
|-
| 16
| 16
| 0-1-10
| 0–1–10
| 1-5/4-9/8
| 1–9/8–5/4
| Otonal
| Otonal
| v,9no5
|  
|
| Cv,9no5
|-
|-
| 17
| 17
| 0-2-10
| 0–2–10
| 1-14/9-9/8
| 1–9/8–14/9
| Pentacircle
| Pentacircle
| 2(vv#5)
|  
|
| C2(vv#5)
|-
|-
| 18
| 18
| 0-5-10
| 0–5–10
| 1-3/2-9/8
| 1–9/8–3/2
| Ambitonal
| Ambitonal
| 2
| [[6:8:9]], [[8:9:12]]
|
| C2
|-
|-
| 19
| 19
| 0-8-10
| 0–8–10
| 1-16/11-9/8
| 1–9/8–16/11
| Pentacircle
| Pentacircle
| 2(^^b5)
|  
|
| C2(^^b5)
|-
|-
| 20
| 20
| 0-9-10
| 0–9–10
| 1-9/5-9/8
| 1–9/8–9/5
| Utonal
| Utonal
| ^9no35
|  
| <u>or</u> ^7sus2no5  
| C^9no35 ''or'' C^7sus2no5
|-
|-
| 21
| 21
| 0-1-11
| 0–1–11
| 1-5/4-7/5
| 1–5/4–7/5
| Marvel
| Marvel
| v(\b5)
|  
|
| Cv(^\b5)
|-
|-
| 22
| 22
| 0-2-11
| 0–2–11
| 1-14/9-7/5
| 1–7/5–14/9
| Utonal
| Utonal
| ^/,^7no5
| 1–9/7–9/5
| 1-9/7-9/5
| C/,^7no5
|-
|-
| 23
| 23
| 0-4-11
| 0–4–11
| 1-6/5-7/5
| 1–6/5–7/5
| Otonal
| Otonal
| ^m(\b5)
| [[5:6:7]]
|
| C^m(^\b5)
|-
|-
| 24
| 24
| 0-7-11
| 0–7–11
| 1-7/6-7/5
| 1–7/6–7/5
| Utonal
| Utonal
| v\m(\b5)
| [[30:35:42|1/(7:6:5)]]
|
| C\m(^\b5)
|-
|-
| 25
| 25
| 0-9-11
| 0–9–11
| 1-9/5-7/5
| 1–7/5–9/5
| Otonal
| Otonal
| ^/(^b5)
| 1–9/7–10/7
| 1-9/7-10/7
| C/(^b5)
|-
|-
| 26
| 26
| 0-10-11
| 0–10–11
| 1-9/8-7/5
| 1–9/8–7/5
| Marvel
| Marvel
| v,7no5
| 1–5/4–16/9
| 1-5/4-16/9
| Cv,7no5
|-
|-
| 27
| 27
| 0-1-12
| 0–1–12
| 1-5/4-7/4
| 1–5/4–7/4
| Otonal
| Otonal
| v,v/7
| [[4:5:7]]
|
| Cv,\7no5
|-
|-
| 28
| 28
| 0-2-12
| 0–2–12
| 1-14/9-7/4
| 1–14/9–7/4
| Utonal
| Utonal
| ^/,9no5
| 1–9/8–9/7
| 1-9/8-9/7
| C/,9no5
|-
|-
| 29
| 29
| 0-4-12
| 0–4–12
| 1-6/5-7/4
| 1–6/5–7/4
| Keenanismic
| Keenanismic
| ^m,v\7
|  
|
| C^m\7
|-
|-
| 30
| 30
| 0-5-12
| 0–5–12
| 1-3/2-7/4
| 1–3/2–7/4
| Otonal
| Otonal
| v\m7no3
| [[4:6:7]]
|
| C\7no3
|-
|-
| 31
| 31
| 0-7-12
| 0–7–12
| 1-7/6-7/4
| 1–7/6–7/4
| Utonal
| Utonal
| v\m7no5
| [[14:18:21|1/(12:8:7)]]
|
| C\m7no5
|-
|-
| 32
| 32
| 0-8-12
| 0–8–12
| 1-16/11-7/4
| 1–16/11–7/4
| Keenanismic
| Keenanismic
| ^m(v\b5)
| 1–6/5–11/8
| 1-6/5-11/8
| C^m(\b5)
|-
|-
| 33
| 33
| 0-10-12
| 0–10–12
| 1-9/8-7/4
| 1–9/8–7/4
| Otonal
| Otonal
| v\m7sus2
|  
|
| C\7sus2
|-
|-
| 34
| 34
| 0-11-12
| 0–11–12
| 1-7/5-7/4
| 1–7/5–7/4
| Utonal
| Utonal
| v\7(\b5)no3
| [[28:35:40|1/(10:8:7)]]
|
| C\7(^\b5)no3
|-
|-
| 35
| 35
| 0-1-13
| 0–1–13
| 1-5/4-12/11
| 1–12/11–5/4
| Keenanismic
| Keenanismic
|
|  
|
|  
|-
|-
| 36
| 36
| 0-2-13
| 0–2–13
| 1-14/9-12/11
| 1–12/11–14/9
| Swetismic
| Swetismic
|
| 1–9/7–7/5
| 1-9/7-7/5
| C/(^\b5)
|-
|-
| 37
| 37
| 0-4-13
| 0–4–13
| 1-6/5-12/11
| 1–12/11–6/5
| Utonal
| Utonal
|
|  
|
|  
|-
|-
| 38
| 38
| 0-5-13
| 0–5–13
| 1-3/2-12/11
| 1–12/11–3/2
| Utonal
| Utonal
|
|  
|
| C^^b2
|-
|-
| 39
| 39
| 0-8-13
| 0–8–13
| 1-16/11-12/11
| 1–12/11–16/11
| Otonal
| Otonal
|
| 1–11/8–3/2
|
| Cvv#4
|-
|-
| 40
| 40
| 0-9-13
| 0–9–13
| 1-20/11-12/11
| 1–12/11–20/11
| Otonal
| Otonal
|
|  
|
|  
|-
|-
| 41
| 41
| 0-11-13
| 0–11–13
| 1-7/5-12/11
| 1–12/11–7/5
| Swetismic
| Swetismic
|
|  
|
|  
|-
|-
| 42
| 42
| 0-12-13
| 0–12–13
| 1-7/4-12/11
| 1–12/11–7/4
| Keenanismic
| Keenanismic
|
|  
|
|  
|-
|-
| 43
| 43
| 0-5-18
| 0–5–18
| 1-3/2-18/11
| 1–3/2–18/11
| Utonal
| Utonal
|
|  
|
|  
|-
|-
| 44
| 44
| 0-7-18
| 0–7–18
| 1-7/6-18/11
| 1–7/6–18/11
| Swetismic
| Swetismic
|
|  
|
|  
|-
|-
| 45
| 45
| 0-8-18
| 0–8–18
| 1-16/11-18/11
| 1–16/11–18/11
| Otonal
| Otonal
|
|  
|
|  
|-
|-
| 46
| 46
| 0-9-18
| 0–9–18
| 1-9/5-18/11
| 1–18/11–9/5
| Utonal
| Utonal
|
|  
|
|  
|-
|-
| 47
| 47
| 0-10-18
| 0–10–18
| 1-9/8-18/11
| 1–9/8–18/11
| Utonal
| Utonal
|
|  
|
|  
|-
|-
| 48
| 48
| 0-11-18
| 0–11–18
| 1-7/5-18/11
| 1–7/5–18/11
| Swetismic
| Swetismic
|
|  
|
|  
|-
|-
| 49
| 49
| 0-13-18
| 0–13–18
| 1-12/11-18/11
| 1–12/11–18/11
| Otonal
| Otonal
|
|  
|
|  
|-
|-
| 50
| 50
| 0-2-20
| 0–2–20
| 1-14/9-14/11
| 1–14/11–14/9
| Utonal
| Utonal
|
|  
|
|  
|-
|-
| 51
| 51
| 0-7-20
| 0–7–20
| 1-7/6-14/11
| 1–7/6–14/11
| Utonal
| Utonal
|
|  
|
|  
|-
|-
| 52
| 52
| 0-8-20
| 0–8–20
| 1-16/11-14/11
| 1–14/11–16/11
| Otonal
| Otonal
|
|  
|
|  
|-
|-
| 53
| 53
| 0-9-20
| 0–9–20
| 1-20/11-14/11
| 1–14/11–20/11
| Otonal
| Otonal
|
|  
|
|  
|-
|-
| 54
| 54
| 0-10-20
| 0–10–20
| 1-9/8-14/11
| 1–9/8–14/11
| Pentacircle
| Pentacircle
|
|  
|
|  
|-
|-
| 55
| 55
| 0-11-20
| 0–11–20
| 1-7/5-14/11
| 1–14/11–7/5
| Utonal
| Utonal
|
|  
|
|  
|-
|-
| 56
| 56
| 0-12-20
| 0–12–20
| 1-7/4-14/11
| 1–14/11–7/4
| Utonal
| Utonal
|
|  
|
|  
|-
|-
| 57
| 57
| 0-13-20
| 0–13–20
| 1-12/11-14/11
| 1–12/11–14/11
| Otonal
| Otonal
|
|  
|
|  
|-
|-
| 58
| 58
| 0-18-20
| 0–18–20
| 1-18/11-14/11
| 1–14/11–18/11
| Otonal
| Otonal
|
|  
|
|  
|}
|}


Line 503: Line 578:
|-
|-
! #
! #
! Chord
! Generators
! Transversal
! Transversal
! Type
! Type
! Name
! Comments
! Comments
! Kite's name
|-
|-
| 1
| 1
| 0-1-2-9
| 0–1–2–9
| 1-5/4-14/9-9/5
| 1–5/4–14/9–9/5
| Magic
| Magic
| v^7(vv#5)
|  
|  
| Cv^7(vv#5)
|-
|-
| 2
| 2
| 0-2-4-9
| 0–2–4–9
| 1-14/9-6/5-9/5
| 1–6/5–14/9–9/5
| Sensamagic
| Sensamagic
| ^m7(vv#5)
|  
|  
| C^m7(vv#5)
|-
|-
| 3
| 3
| 0-1-5-9
| 0–1–5–9
| 1-5/4-3/2-9/5
| 1–5/4–3/2–9/5
| Ptolemismic
| Ptolemismic
| v^7
|  
|  
| Cv^7
|-
|-
| 4
| 4
| 0-4-5-9
| 0–4–5–9
| 1-6/5-3/2-9/5
| 1–6/5–3/2–9/5
| Ambitonal
| Ambitonal
| ^m7
| [[10:12:15:18]], [[12:15:18:20]]<br>[[9-odd-limit]] [[ASS]]
| <u>or</u> 1-5/4-3/2-5/3 = v6
| C^m7 ''or'' Cv6
|-
|-
| 5
| 5
| 0-2-7-9
| 0–2–7–9
| 1-14/9-7/6-9/5
| 1–7/6–14/9–9/5
| Sensamagic
| Sensamagic
| ^/,vv#9
| 1–9/7–3/2–7/3
| 1-9/7-3/2-7/3
| C/,vv#9
|-
|-
| 6
| 6
| 0-5-7-9
| 0–5–7–9
| 1-3/2-7/6-9/5
| 1–7/6–3/2–9/5
| Sensamagic
| Sensamagic
| v\m^7
|  
|  
| C\m^7
|-
|-
| 7
| 7
| 0-1-8-9
| 0–1–8–9
| 1-5/4-16/11-9/5
| 1–5/4–16/11–9/5
| Supermagic
| Keemic
| v^7(^^b5)
|  
|  
| Cv^7(^^b5)
|-
|-
| 8
| 8
| 0-4-8-9
| 0–4–8–9
| 1-6/5-16/11-9/5
| 1–6/5–16/11–9/5
| Ptolemismic
| Ptolemismic
| ^m7(^^b5)
|  
|  
| C^m7(^^b5)
|-
|-
| 9
| 9
| 0-7-8-9
| 0–7–8–9
| 1-7/6-16/11-9/5
| 1–7/6–16/11–9/5
| Magic
| Magic
| v\m,^7(^^b5)
|  
|  
| C\m^7(^^b5)
|-
|-
| 10
| 10
| 0-1-2-10
| 0–1–2–10
| 1-5/4-14/9-9/8
| 1–9/8–5/4–14/9
| Apollo
| Apollo
| v,9(vv#5)
|  
|  
| Cv,9(vv#5)
|-
|-
| 11
| 11
| 0-1-5-10
| 0–1–5–10
| 1-5/4-3/2-9/8
| 1–9/8–5/4–3/2
| Otonal
| Otonal
| v,9
| [[4:5:6:9]]
|  
| Cv,9
|-
|-
| 12
| 12
| 0-1-8-10
| 0–1–8–10
| 1-5/4-16/11-9/8
| 1–9/8–5/4–16/11
| Sensamagic11
| Sensamagic11
| v,9(^^b5)
|  
|  
| Cv,9(^^b5)
|-
|-
| 13
| 13
| 0-1-9-10
| 0–1–9–10
| 1-5/4-9/5-9/8
| 1–9/8–5/4–9/5
| Ptolemismic
| Ptolemismic
| v^7,9no5
|  
| <u>or</u> v9(^7)no5
| Cv^7,9no5 ''or'' Cv9(^7)no5
|-
|-
| 14
| 14
| 0-2-9-10
| 0–2–9–10
| 1-14/9-9/5-9/8
| 1–9/8–14/9–9/5
| Sensamagic11
| Sensamagic11
| ^9(vv#5)no3
|  
| <u>or</u> ^7(vv#5)sus2
| C^9(vv#5)no3 ''or'' C^7(vv#5)sus2
|-
|-
| 15
| 15
| 0-5-9-10
| 0–5–9–10
| 1-3/2-9/5-9/8
| 1–9/8–3/2–9/5
| Utonal
| Utonal
| ^9no3
| [[20:30:36:45|1/(9:6:5:4)]]
| <u>or</u> ^7sus2 <u>or</u> 2,^7
| C^9no3 ''or'' C^7sus2 ''or'' C2,^7
|-
|-
| 16
| 16
| 0-8-9-10
| 0–8–9–10
| 1-16/11-9/5-9/8
| 1–9/8–16/11–9/5
| Apollo
| Apollo
|  
|  
Line 622: Line 697:
|-
|-
| 17
| 17
| 0-1-2-11
| 0–1–2–11
| 1-5/4-14/9-7/5
| 1–5/4–7/5–14/9
| Marvel
| Marvel
|  
|  
Line 629: Line 704:
|-
|-
| 18
| 18
| 0-2-4-11
| 0–2–4–11
| 1-14/9-6/5-7/5
| 1–6/5–7/5–14/9
| Sensamagic
| Sensamagic
|  
|  
Line 636: Line 711:
|-
|-
| 19
| 19
| 0-2-7-11
| 0–2–7–11
| 1-14/9-7/6-7/5
| 1–7/6–7/5–14/9
| Utonal
| Utonal
|  
| [[70:90:105:126|1/(9:7:6:5)]]
|  
|  
|-
|-
| 20
| 20
| 0-1-9-11
| 0–1–9–11
| 1-5/4-9/5-7/5
| 1–5/4–7/5–9/5
| Apollo
| Apollo
|  
|  
Line 650: Line 725:
|-
|-
| 21
| 21
| 0-2-9-11
| 0–2–9–11
| 1-14/9-9/5-7/5
| 1–7/5–14/9–9/5
| Sensamagic
| Sensamagic
|  
|  
Line 657: Line 732:
|-
|-
| 22
| 22
| 0-4-9-11
| 0–4–9–11
| 1-6/5-9/5-7/5
| 1–6/5–7/5–9/5
| Otonal
| Otonal
| ^m7(\b5)
| [[6:7:9:10]]
|
| C^m7(^\b5) ''or'' C\mv6
|-
|-
| 23
| 23
| 0-7-9-11
| 0–7–9–11
| 1-7/6-9/5-7/5
| 1–7/6–7/5–9/5
| Sensamagic
| Sensamagic
|  
|  
Line 671: Line 746:
|-
|-
| 24
| 24
| 0-1-10-11
| 0–1–10–11
| 1-5/4-9/8-7/5
| 1–9/8–5/4–7/5
| Marvel
| Marvel
|  
|  
Line 678: Line 753:
|-
|-
| 25
| 25
| 0-2-10-11
| 0–2–10–11
| 1-14/9-9/8-7/5
| 1–9/8–7/5–14/9
| Apollo
| Apollo
|  
|  
Line 685: Line 760:
|-
|-
| 26
| 26
| 0-9-10-11
| 0–9–10–11
| 1-9/5-9/8-7/5
| 1–9/8–7/5–9/5
| Marvel
| Marvel
|  
|  
Line 692: Line 767:
|-
|-
| 27
| 27
| 0-1-2-12
| 0–1–2–12
| 1-5/4-14/9-7/4
| 1–5/4–14/9–7/4
| Marvel
| Marvel
|  
|  
Line 699: Line 774:
|-
|-
| 28
| 28
| 0-2-4-12
| 0–2–4–12
| 1-14/9-6/5-7/4
| 1–6/5–14/9–7/4
| Sensamagic11
| Sensamagic11
|  
|  
Line 706: Line 781:
|-
|-
| 29
| 29
| 0-1-5-12
| 0–1–5–12
| 1-5/4-3/2-7/4
| 1–5/4–3/2–7/4
| Otonal
| Otonal
| v,v\7
| [[4:5:6:7]]
|
| Cv,\7
|-
|-
| 30
| 30
| 0-4-5-12
| 0–4–5–12
| 1-6/5-3/2-7/4
| 1–6/5–3/2–7/4
| Keenanismic
| Keenanismic
| ^mv\7
|
|
| C^m\7
|-
|-
| 31
| 31
| 0-2-7-12
| 0–2–7–12
| 1-14/9-7/6-7/4
| 1–7/6–14/9–7/4
| Utonal
| Utonal
| v\m7(vv#5)
|  
|  
| C\m7(vv#5)
|-
|-
| 32
| 32
| 0-5-7-12
| 0–5–7–12
| 1-3/2-7/6-7/4
| 1–7/6–3/2–7/4
| Ambitonal
| Ambitonal
| v\m7
| [[12:14:18:21]], [[14:18:21:24]]<br>9-odd-limit ASS
|
| C\m7
|-
|-
| 33
| 33
| 0-1-8-12
| 0–1–8–12
| 1-5/4-16/11-7/4
| 1–5/4–16/11–7/4
| Keenanismic
| Keenanismic
|  
|  
Line 741: Line 816:
|-
|-
| 34
| 34
| 0-4-8-12
| 0–4–8–12
| 1-6/5-16/11-7/4
| 1–6/5–16/11–7/4
| Supermagic
| Keemic
|  
|  
|  
|  
|-
|-
| 35
| 35
| 0-7-8-12
| 0–7–8–12
| 1-7/6-16/11-7/4
| 1–7/6–16/11–7/4
| Keenanismic
| Keenanismic
| v\m7(^^b5)
|  
|  
| C\m7(^^b5)
|-
|-
| 36
| 36
| 0-1-10-12
| 0–1–10–12
| 1-5/4-9/8-7/4
| 1–9/8–5/4–7/4
| Otonal
| Otonal
|  
| [[4:5:7:9]]
|  
|  
|-
|-
| 37
| 37
| 0-2-10-12
| 0–2–10–12
| 1-14/9-9/8-7/4
| 1–9/8–14/9–7/4
| Pentacircle
| Pentacircle
|  
|  
Line 769: Line 844:
|-
|-
| 38
| 38
| 0-5-10-12
| 0–5–10–12
| 1-3/2-9/8-7/4
| 1–9/8–3/2–7/4
| Otonal
| Otonal
| v\7sus2
| [[4:6:7:9]]
| <u>or</u> 2,v\7 <u>or</u> v\9no3
| C2\7 ''or'' C\7sus2 ''or'' C\9no3
|-
|-
| 39
| 39
| 0-8-10-12
| 0–8–10–12
| 1-16/11-9/8-7/4
| 1–9/8–16/11–7/4
| Sensamagic11
| Sensamagic11
|  
|  
Line 783: Line 858:
|-
|-
| 40
| 40
| 0-1-11-12
| 0–1–11–12
| 1-5/4-7/5-7/4
| 1–5/4–7/5–7/4
| Marvel
| Marvel
|  
|  
Line 790: Line 865:
|-
|-
| 41
| 41
| 0-2-11-12
| 0–2–11–12
| 1-14/9-7/5-7/4
| 1–7/5–14/9–7/4
| Utonal
| Utonal
|  
| [[140:180:252:315|1/(9:7:5:4)]]
|  
|  
|-
|-
| 42
| 42
| 0-4-11-12
| 0–4–11–12
| 1-6/5-7/5-7/4
| 1–6/5–7/5–7/4
| Keenanismic
| Keenanismic
|  
|  
Line 804: Line 879:
|-
|-
| 43
| 43
| 0-7-11-12
| 0–7–11–12
| 1-7/6-7/5-7/4
| 1–7/6–7/5–7/4
| Utonal
| Utonal
|  
| [[70:84:105:120|1/(12:10:8:7)]]
|  
| C\m7(^\b5) ''or'' C^m/6
|-
|-
| 44
| 44
| 0-10-11-12
| 0–10–11–12
| 1-9/8-7/5-7/4
| 1–9/8–7/5–7/4
| Marvel
| Marvel
|  
|  
Line 818: Line 893:
|-
|-
| 45
| 45
| 0-1-2-13
| 0–1–2–13
| 1-5/4-14/9-12/11
| 1–12/11–5/4–14/9
| Unimarvel
| Marvel11
|  
|  
|  
|  
|-
|-
| 46
| 46
| 0-2-4-13
| 0–2–4–13
| 1-14/9-6/5-12/11
| 1–12/11–6/5–14/9
| Octarod
| Octarod
|  
|  
Line 832: Line 907:
|-
|-
| 47
| 47
| 0-1-5-13
| 0–1–5–13
| 1-5/4-3/2-12/11
| 1–12/11–5/4–3/2
| Keenanismic
| Keenanismic
|  
|  
Line 839: Line 914:
|-
|-
| 48
| 48
| 0-4-5-13
| 0–4–5–13
| 1-6/5-3/2-12/11
| 1–12/11–6/5–3/2
| Utonal
| Utonal
|  
|  
Line 846: Line 921:
|-
|-
| 49
| 49
| 0-1-8-13
| 0–1–8–13
| 1-5/4-16/11-12/11
| 1–12/11–5/4–16/11
| Keenanismic
| Keenanismic
|  
|  
Line 853: Line 928:
|-
|-
| 50
| 50
| 0-4-8-13
| 0–4–8–13
| 1-6/5-16/11-12/11
| 1–12/11–6/5–16/11
| Ptolemismic
| Ptolemismic
|  
|  
Line 860: Line 935:
|-
|-
| 51
| 51
| 0-1-9-13
| 0–1–9–13
| 1-5/4-9/5-12/11
| 1–12/11–5/4–9/5
| Supermagic
| Keemic
|  
|  
|  
|  
|-
|-
| 52
| 52
| 0-2-9-13
| 0–2–9–13
| 1-14/9-9/5-12/11
| 1–12/11–14/9–9/5
| Octarod
| Octarod
|  
|  
Line 874: Line 949:
|-
|-
| 53
| 53
| 0-4-9-13
| 0–4–9–13
| 1-6/5-9/5-12/11
| 1–12/11–6/5–9/5
| Ptolemismic
| Ptolemismic
|  
|  
Line 881: Line 956:
|-
|-
| 54
| 54
| 0-5-9-13
| 0–5–9–13
| 1-3/2-9/5-12/11
| 1–12/11–3/2–9/5
| Ptolemismic
| Ptolemismic
|  
|  
Line 888: Line 963:
|-
|-
| 55
| 55
| 0-8-9-13
| 0–8–9–13
| 1-16/11-20/11-12/11
| 1–12/11–16/11–20/11
| Otonal
| Otonal
|  
|  
Line 895: Line 970:
|-
|-
| 56
| 56
| 0-1-11-13
| 0–1–11–13
| 1-5/4-7/5-12/11
| 1–12/11–5/4–7/5
| Unimarvel
| Marvel11
|  
|  
|  
|  
|-
|-
| 57
| 57
| 0-2-11-13
| 0–2–11–13
| 1-14/9-7/5-12/11
| 1–12/11–7/5–14/9
| Swetismic
| Swetismic
|  
|  
Line 909: Line 984:
|-
|-
| 58
| 58
| 0-4-11-13
| 0–4–11–13
| 1-6/5-7/5-12/11
| 1–12/11–6/5–7/5
| Octarod
| Octarod
|  
|  
Line 916: Line 991:
|-
|-
| 59
| 59
| 0-9-11-13
| 0–9–11–13
| 1-9/5-7/5-12/11
| 1–12/11–7/5–9/5
| Octarod
| Octarod
|  
|  
Line 923: Line 998:
|-
|-
| 60
| 60
| 0-1-12-13
| 0–1–12–13
| 1-5/4-7/4-12/11
| 1–12/11–5/4–7/4
| Keenanismic
| Keenanismic
|  
|  
Line 930: Line 1,005:
|-
|-
| 61
| 61
| 0-2-12-13
| 0–2–12–13
| 1-14/9-7/4-12/11
| 1–12/11–14/9–7/4
| Unimarvel
| Marvel11
|  
|  
|  
|  
|-
|-
| 62
| 62
| 0-4-12-13
| 0–4–12–13
| 1-6/5-7/4-12/11
| 1–12/11–6/5–7/4
| Supermagic
| Keemic
|  
|  
|  
|  
|-
|-
| 63
| 63
| 0-5-12-13
| 0–5–12–13
| 1-3/2-7/4-12/11
| 1–12/11–3/2–7/4
| Keenanismic
| Keenanismic
|  
|  
Line 951: Line 1,026:
|-
|-
| 64
| 64
| 0-8-12-13
| 0–8–12–13
| 1-16/11-7/4-12/11
| 1–12/11–16/11–7/4
| Keenanismic
| Keenanismic
|  
|  
Line 958: Line 1,033:
|-
|-
| 65
| 65
| 0-11-12-13
| 0–11–12–13
| 1-7/5-7/4-12/11
| 1–12/11–7/5–7/4
| Unimarvel
| Marvel11
|  
|  
|  
|  
|-
|-
| 66
| 66
| 0-5-7-18
| 0–5–7–18
| 1-3/2-7/6-18/11
| 1–7/6–3/2–18/11
| Swetismic
| Swetismic
|  
|  
Line 972: Line 1,047:
|-
|-
| 67
| 67
| 0-7-8-18
| 0–7–8–18
| 1-7/6-16/11-18/11
| 1–7/6–16/11–18/11
| Unimarvel
| Marvel11
|  
|  
|  
|  
|-
|-
| 68
| 68
| 0-5-9-18
| 0–5–9–18
| 1-3/2-9/5-18/11
| 1–3/2–18/11–9/5
| Utonal
| Utonal
|  
|  
Line 986: Line 1,061:
|-
|-
| 69
| 69
| 0-7-9-18
| 0–7–9–18
| 1-7/6-9/5-18/11
| 1–7/6–18/11–9/5
| Octarod
| Octarod
|  
|  
Line 993: Line 1,068:
|-
|-
| 70
| 70
| 0-8-9-18
| 0–8–9–18
| 1-16/11-20/11-18/11
| 1–16/11–18/11–20/11
| Otonal
| Otonal
|  
|  
Line 1,000: Line 1,075:
|-
|-
| 71
| 71
| 0-5-10-18
| 0–5–10–18
| 1-3/2-9/8-18/11
| 1–9/8–3/2–18/11
| Utonal
| Utonal
|  
|  
Line 1,007: Line 1,082:
|-
|-
| 72
| 72
| 0-8-10-18
| 0–8–10–18
| 1-16/11-9/8-18/11
| 1–9/8–16/11–18/11
| Pentacircle
| Pentacircle
|  
|  
Line 1,014: Line 1,089:
|-
|-
| 73
| 73
| 0-9-10-18
| 0–9–10–18
| 1-9/5-9/8-18/11
| 1–9/8–18/11–9/5
| Utonal
| Utonal
|  
|  
Line 1,021: Line 1,096:
|-
|-
| 74
| 74
| 0-7-11-18
| 0–7–11–18
| 1-7/6-7/5-18/11
| 1–7/6–7/5–18/11
| Swetismic
| Swetismic
|  
|  
Line 1,028: Line 1,103:
|-
|-
| 75
| 75
| 0-9-11-18
| 0–9–11–18
| 1-9/5-7/5-18/11
| 1–7/5–18/11–9/5
| Octarod
| Octarod
|  
|  
Line 1,035: Line 1,110:
|-
|-
| 76
| 76
| 0-10-11-18
| 0–10–11–18
| 1-9/8-7/5-18/11
| 1–9/8–7/5–18/11
| Unimarvel
| Marvel11
|  
|  
|  
|  
|-
|-
| 77
| 77
| 0-5-13-18
| 0–5–13–18
| 1-3/2-12/11-18/11
| 1–12/11–3/2–18/11
| Ambitonal
| Ambitonal
|  
|  
Line 1,049: Line 1,124:
|-
|-
| 78
| 78
| 0-8-13-18
| 0–8–13–18
| 1-16/11-12/11-18/11
| 1–12/11–16/11–18/11
| Otonal
| Otonal
|  
|  
Line 1,056: Line 1,131:
|-
|-
| 79
| 79
| 0-9-13-18
| 0–9–13–18
| 1-20/11-12/11-18/11
| 1–12/11–18/11–20/11
| Otonal
| Otonal
|  
|  
Line 1,063: Line 1,138:
|-
|-
| 80
| 80
| 0-11-13-18
| 0–11–13–18
| 1-7/5-12/11-18/11
| 1–12/11–7/5–18/11
| Swetismic
| Swetismic
|  
|  
Line 1,070: Line 1,145:
|-
|-
| 81
| 81
| 0-2-7-20
| 0–2–7–20
| 1-14/9-7/6-14/11
| 1–7/6–14/11–14/9
| Utonal
| Utonal
|  
|  
Line 1,077: Line 1,152:
|-
|-
| 82
| 82
| 0-7-8-20
| 0–7–8–20
| 1-7/6-16/11-14/11
| 1–7/6–14/11–16/11
| Keenanismic
| Keenanismic
|  
|  
Line 1,084: Line 1,159:
|-
|-
| 83
| 83
| 0-2-9-20
| 0–2–9–20
| 1-14/9-9/5-14/11
| 1–14/11–14/9–9/5
| Octarod
| Octarod
|  
|  
Line 1,091: Line 1,166:
|-
|-
| 84
| 84
| 0-7-9-20
| 0–7–9–20
| 1-7/6-9/5-14/11
| 1–7/6–14/11–9/5
| Octarod
| Octarod
|  
|  
Line 1,098: Line 1,173:
|-
|-
| 85
| 85
| 0-8-9-20
| 0–8–9–20
| 1-16/11-20/11-14/11
| 1–14/11–16/11–20/11
| Otonal
| Otonal
|  
|  
Line 1,105: Line 1,180:
|-
|-
| 86
| 86
| 0-2-10-20
| 0–2–10–20
| 1-14/9-9/8-14/11
| 1–9/8–14/11–14/9
| Pentacircle
| Pentacircle
|  
|  
Line 1,112: Line 1,187:
|-
|-
| 87
| 87
| 0-8-10-20
| 0–8–10–20
| 1-16/11-9/8-14/11
| 1–9/8–14/11–16/11
| Pentacircle
| Pentacircle
|  
|  
Line 1,119: Line 1,194:
|-
|-
| 88
| 88
| 0-9-10-20
| 0–9–10–20
| 1-9/5-9/8-14/11
| 1–9/8–14/11–9/5
| Apollo
| Apollo
|  
|  
Line 1,126: Line 1,201:
|-
|-
| 89
| 89
| 0-2-11-20
| 0–2–11–20
| 1-14/9-7/5-14/11
| 1–7/5–14/11–14/9
| Utonal
| Utonal
|  
|  
Line 1,133: Line 1,208:
|-
|-
| 90
| 90
| 0-7-11-20
| 0–7–11–20
| 1-7/6-7/5-14/11
| 1–7/6–14/11–7/5
| Utonal
| Utonal
|  
|  
Line 1,140: Line 1,215:
|-
|-
| 91
| 91
| 0-9-11-20
| 0–9–11–20
| 1-9/5-7/5-14/11
| 1–7/5–14/11–9/5
| Ptolemismic
| Ptolemismic
|  
|  
Line 1,147: Line 1,222:
|-
|-
| 92
| 92
| 0-10-11-20
| 0–10–11–20
| 1-9/8-7/5-14/11
| 1–9/8–14/11–7/5
| Apollo
| Apollo
|  
|  
Line 1,154: Line 1,229:
|-
|-
| 93
| 93
| 0-2-12-20
| 0–2–12–20
| 1-14/9-7/4-14/11
| 1–14/11–14/9–7/4
| Utonal
| Utonal
|  
|  
Line 1,161: Line 1,236:
|-
|-
| 94
| 94
| 0-7-12-20
| 0–7–12–20
| 1-7/6-7/4-14/11
| 1–7/6–14/11–7/4
| Utonal
| Utonal
|  
|  
Line 1,168: Line 1,243:
|-
|-
| 95
| 95
| 0-8-12-20
| 0–8–12–20
| 1-16/11-7/4-14/11
| 1–14/11–16/11–7/4
| Keenanismic
| Keenanismic
|  
|  
Line 1,175: Line 1,250:
|-
|-
| 96
| 96
| 0-10-12-20
| 0–10–12–20
| 1-9/8-7/4-14/11
| 1–9/8–14/11–7/4
| Pentacircle
| Pentacircle
|  
|  
Line 1,182: Line 1,257:
|-
|-
| 97
| 97
| 0-11-12-20
| 0–11–12–20
| 1-7/5-7/4-14/11
| 1–14/11–7/5–7/4
| Utonal
| Utonal
|  
|  
Line 1,189: Line 1,264:
|-
|-
| 98
| 98
| 0-2-13-20
| 0–2–13–20
| 1-14/9-12/11-14/11
| 1–12/11–14/11–14/9
| Swetismic
| Swetismic
|  
|  
Line 1,196: Line 1,271:
|-
|-
| 99
| 99
| 0-8-13-20
| 0–8–13–20
| 1-16/11-12/11-14/11
| 1–12/11–14/11–16/11
| Otonal
| Otonal
|  
|  
Line 1,203: Line 1,278:
|-
|-
| 100
| 100
| 0-9-13-20
| 0–9–13–20
| 1-20/11-12/11-14/11
| 1–12/11–14/11–20/11
| Otonal
| Otonal
|  
|  
Line 1,210: Line 1,285:
|-
|-
| 101
| 101
| 0-11-13-20
| 0–11–13–20
| 1-7/5-12/11-14/11
| 1–12/11–14/11–7/5
| Octarod
| Octarod
|  
|  
Line 1,217: Line 1,292:
|-
|-
| 102
| 102
| 0-12-13-20
| 0–12–13–20
| 1-7/4-12/11-14/11
| 1–12/11–14/11–7/4
| Keenanismic
| Keenanismic
|  
|  
Line 1,224: Line 1,299:
|-
|-
| 103
| 103
| 0-7-18-20
| 0–7–18–20
| 1-7/6-18/11-14/11
| 1–7/6–14/11–18/11
| Swetismic
| Swetismic
|  
|  
Line 1,231: Line 1,306:
|-
|-
| 104
| 104
| 0-8-18-20
| 0–8–18–20
| 1-16/11-18/11-14/11
| 1–14/11–16/11–18/11
| Otonal
| Otonal
|  
|  
Line 1,238: Line 1,313:
|-
|-
| 105
| 105
| 0-9-18-20
| 0–9–18–20
| 1-20/11-18/11-14/11
| 1–14/11–18/11–20/11
| Otonal
| Otonal
|  
|  
Line 1,245: Line 1,320:
|-
|-
| 106
| 106
| 0-10-18-20
| 0–10–18–20
| 1-9/8-18/11-14/11
| 1–9/8–14/11–18/11
| Pentacircle
| Pentacircle
|  
|  
Line 1,252: Line 1,327:
|-
|-
| 107
| 107
| 0-11-18-20
| 0–11–18–20
| 1-7/5-18/11-14/11
| 1–14/11–7/5–18/11
| Octarod
| Octarod
|  
|  
Line 1,259: Line 1,334:
|-
|-
| 108
| 108
| 0-13-18-20
| 0–13–18–20
| 1-12/11-18/11-14/11
| 1–12/11–14/11–18/11
| Otonal
| Otonal
|  
|  
Line 1,270: Line 1,345:
|-
|-
! #
! #
! Chord
! Generators
! Transversal
! Transversal
! Type
! Type
! Comments
! Kite's name
|-
|-
| 1
| 1
| 0-1-2-9-10
| 0–1–2–9–10
| 1-5/4-14/9-9/5-9/8
| 1–9/8–5/4–14/9–9/5
| Magic
| Magic
|
|
|-
|-
| 2
| 2
| 0-1-5-9-10
| 0–1–5–9–10
| 1-5/4-3/2-9/5-9/8
| 1–9/8–5/4–3/2–9/5
| Ptolemismic
| Ptolemismic
|
| Cv9(^7)
|-
|-
| 3
| 3
| 0-1-8-9-10
| 0–1–8–9–10
| 1-5/4-16/11-9/5-9/8
| 1–9/8–5/4–16/11–9/5
| Magic
| Magic
|
|
|-
|-
| 4
| 4
| 0-1-2-9-11
| 0–1–2–9–11
| 1-5/4-14/9-9/5-7/5
| 1–5/4–7/5–14/9–9/5
| Magic
| Magic
|
|
|-
|-
| 5
| 5
| 0-2-4-9-11
| 0–2–4–9–11
| 1-14/9-6/5-9/5-7/5
| 1–6/5–7/5–14/9–9/5
| Sensamagic
| Sensamagic
|
|
|-
|-
| 6
| 6
| 0-2-7-9-11
| 0–2–7–9–11
| 1-14/9-7/6-9/5-7/5
| 1–7/6–7/5–14/9–9/5
| Sensamagic
| Sensamagic
|
|
|-
|-
| 7
| 7
| 0-1-2-10-11
| 0–1–2–10–11
| 1-5/4-14/9-9/8-7/5
| 1–9/8–5/4–7/5–14/9
| Apollo
| Apollo
|
|
|-
|-
| 8
| 8
| 0-1-9-10-11
| 0–1–9–10–11
| 1-5/4-9/5-9/8-7/5
| 1–9/8–5/4–7/5–9/5
| Apollo
| Apollo
|
|
|-
|-
| 9
| 9
| 0-2-9-10-11
| 0–2–9–10–11
| 1-14/9-9/5-9/8-7/5
| 1–9/8–7/5–14/9–9/5
| Magic
| Magic
|
|
|-
|-
| 10
| 10
| 0-1-2-10-12
| 0–1–2–10–12
| 1-5/4-14/9-9/8-7/4
| 1–9/8–5/4–14/9–7/4
| Apollo
| Apollo
|
|
|-
|-
| 11
| 11
| 0-1-5-10-12
| 0–1–5–10–12
| 1-5/4-3/2-9/8-7/4
| 1–9/8–5/4–3/2–7/4
| Otonal
| Otonal
| [[4:5:6:7:9]]
| Cv9(\7)
|-
|-
| 12
| 12
| 0-1-8-10-12
| 0–1–8–10–12
| 1-5/4-16/11-9/8-7/4
| 1–9/8–5/4–16/11–7/4
| Sensamagic11
| Sensamagic11
|
|
|-
|-
| 13
| 13
| 0-1-2-11-12
| 0–1–2–11–12
| 1-5/4-14/9-7/5-7/4
| 1–5/4–7/5–14/9–7/4
| Marvel
| Marvel
|
|
|-
|-
| 14
| 14
| 0-2-4-11-12
| 0–2–4–11–12
| 1-14/9-6/5-7/5-7/4
| 1–6/5–7/5–14/9–7/4
| Sensamagic11
| Sensamagic11
|
|
|-
|-
| 15
| 15
| 0-2-7-11-12
| 0–2–7–11–12
| 1-14/9-7/6-7/5-7/4
| 1–7/6–7/5–14/9–7/4
| Utonal
| Utonal
| [[210:252:315:360:560|1/(24:20:16:14:9)]]
| C/9(^7)
|-
|-
| 16
| 16
| 0-1-10-11-12
| 0–1–10–11–12
| 1-5/4-9/8-7/5-7/4
| 1–9/8–5/4–7/5–7/4
| Marvel
| Marvel
|
|
|-
|-
| 17
| 17
| 0-2-10-11-12
| 0–2–10–11–12
| 1-14/9-9/8-7/5-7/4
| 1–9/8–7/5–14/9–7/4
| Apollo
| Apollo
|
|
|-
|-
| 18
| 18
| 0-1-2-9-13
| 0–1–2–9–13
| 1-5/4-14/9-9/5-12/11
| 1–12/11–5/4–14/9–9/5
| Magic
| Magic
|
|
|-
|-
| 19
| 19
| 0-2-4-9-13
| 0–2–4–9–13
| 1-14/9-6/5-9/5-12/11
| 1–12/11–6/5–14/9–9/5
| Octarod
| Octarod
|
|
|-
|-
| 20
| 20
| 0-1-5-9-13
| 0–1–5–9–13
| 1-5/4-3/2-9/5-12/11
| 1–12/11–5/4–3/2–9/5
| Supermagic
| Keemic
|
|
|-
|-
| 21
| 21
| 0-4-5-9-13
| 0–4–5–9–13
| 1-6/5-3/2-9/5-12/11
| 1–12/11–6/5–3/2–9/5
| Ptolemismic
| Ptolemismic
|
|
|-
|-
| 22
| 22
| 0-1-8-9-13
| 0–1–8–9–13
| 1-5/4-16/11-9/5-12/11
| 1–12/11–5/4–16/11–9/5
| supermagic
| Keemic
|
|
|-
|-
| 23
| 23
| 0-4-8-9-13
| 0–4–8–9–13
| 1-6/5-16/11-9/5-12/11
| 1–12/11–6/5–16/11–9/5
| Ptolemismic
| Ptolemismic
|
|
|-
|-
| 24
| 24
| 0-1-2-11-13
| 0–1–2–11–13
| 1-5/4-14/9-7/5-12/11
| 1–12/11–5/4–7/5–14/9
| Unimarvel
| Marvel11
|
|  
|-
|-
| 25
| 25
| 0-2-4-11-13
| 0–2–4–11–13
| 1-14/9-6/5-7/5-12/11
| 1–12/11–6/5–7/5–14/9
| Octarod
| Octarod
|
|
|-
|-
| 26
| 26
| 0-1-9-11-13
| 0–1–9–11–13
| 1-5/4-9/5-7/5-12/11
| 1–12/11–5/4–7/5–9/5
| Magic
| Magic
|
|
|-
|-
| 27
| 27
| 0-2-9-11-13
| 0–2–9–11–13
| 1-14/9-9/5-7/5-12/11
| 1–12/11–7/5–14/9–9/5
| Octarod
| Octarod
|
|
|-
|-
| 28
| 28
| 0-4-9-11-13
| 0–4–9–11–13
| 1-6/5-9/5-7/5-12/11
| 1–12/11–6/5–7/5–9/5
| Octarod
| Octarod
|
|
|-
|-
| 29
| 29
| 0-1-2-12-13
| 0–1–2–12–13
| 1-5/4-14/9-7/4-12/11
| 1–12/11–5/4–14/9–7/4
| Unimarvel
| Marvel11
|
|
|-
|-
| 30
| 30
| 0-2-4-12-13
| 0–2–4–12–13
| 1-14/9-6/5-7/4-12/11
| 1–12/11–6/5–14/9–7/4
| Magic
| Magic
|
|
|-
|-
| 31
| 31
| 0-1-5-12-13
| 0–1–5–12–13
| 1-5/4-3/2-7/4-12/11
| 1–12/11–5/4–3/2–7/4
| Keenanismic
| Keenanismic
|
|
|-
|-
| 32
| 32
| 0-4-5-12-13
| 0–4–5–12–13
| 1-6/5-3/2-7/4-12/11
| 1–12/11–6/5–3/2–7/4
| Supermagic
| Keemic
|
|
|-
|-
| 33
| 33
| 0-1-8-12-13
| 0–1–8–12–13
| 1-5/4-16/11-7/4-12/11
| 1–12/11–5/4–16/11–7/4
| Keenanismic
| Keenanismic
|
|
|-
|-
| 34
| 34
| 0-4-8-12-13
| 0–4–8–12–13
| 1-6/5-16/11-7/4-12/11
| 1–12/11–6/5–16/11–7/4
| Supermagic
| Keemic
|
|
|-
|-
| 35
| 35
| 0-1-11-12-13
| 0–1–11–12–13
| 1-5/4-7/5-7/4-12/11
| 1–12/11–5/4–7/5–7/4
| Unimarvel
| Marvel11
|
|
|-
|-
| 36
| 36
| 0-2-11-12-13
| 0–2–11–12–13
| 1-14/9-7/5-7/4-12/11
| 1–12/11–7/5–14/9–7/4
| Unimarvel
| Marvel11
|
|
|-
|-
| 37
| 37
| 0-4-11-12-13
| 0–4–11–12–13
| 1-6/5-7/5-7/4-12/11
| 1–12/11–6/5–7/5–7/4
| Magic
| Magic
|
|
|-
|-
| 38
| 38
| 0-5-7-9-18
| 0–5–7–9–18
| 1-3/2-7/6-9/5-18/11
| 1–7/6–3/2–18/11–9/5
| Octarod
| Octarod
|
|
|-
|-
| 39
| 39
| 0-7-8-9-18
| 0–7–8–9–18
| 1-7/6-16/11-9/5-18/11
| 1–7/6–16/11–18/11–9/5
| Magic
| Magic
|
|
|-
|-
| 40
| 40
| 0-5-9-10-18
| 0–5–9–10–18
| 1-3/2-9/5-9/8-18/11
| 1–9/8–3/2–18/11–9/5
| Utonal
| Utonal
| [[330:396:495:720:880|1/(24:20:16:11:9)]]
|
|-
|-
| 41
| 41
| 0-8-9-10-18
| 0–8–9–10–18
| 1-16/11-9/5-9/8-18/11
| 1–9/8–16/11–18/11–9/5
| Apollo
| Apollo
|
|
|-
|-
| 42
| 42
| 0-7-9-11-18
| 0–7–9–11–18
| 1-7/6-9/5-7/5-18/11
| 1–7/6–7/5–18/11–9/5
| Octarod
| Octarod
|
|
|-
|-
| 43
| 43
| 0-9-10-11-18
| 0–9–10–11–18
| 1-9/5-9/8-7/5-18/11
| 1–9/8–7/5–18/11–9/5
| Magic
| Magic
|
|
|-
|-
| 44
| 44
| 0-5-9-13-18
| 0–5–9–13–18
| 1-3/2-9/5-12/11-18/11
| 1–3/2–12/11–18/11–9/5
| Ptolemismic
| Ptolemismic
|
|
|-
|-
| 45
| 45
| 0-8-9-13-18
| 0–8–9–13–18
| 1-16/11-20/11-12/11-18/11
| 1–12/11–16/11–18/11–20/11
| Otonal
| Otonal
| [[4:5:6:9:11]]
|
|-
|-
| 46
| 46
| 0-9-11-13-18
| 0–9–11–13–18
| 1-9/5-7/5-12/11-18/11
| 1–7/5–12/11–18/11–9/5
| Octarod
| Octarod
|
|
|-
|-
| 47
| 47
| 0-2-7-9-20
| 0–2–7–9–20
| 1-14/9-7/6-9/5-14/11
| 1–7/6–14/11–14/9–9/5
| Octarod
| Octarod
|
|
|-
|-
| 48
| 48
| 0-7-8-9-20
| 0–7–8–9–20
| 1-7/6-16/11-9/5-14/11
| 1–7/6–14/11–16/11–9/5
| Magic
| Magic
|
|
|-
|-
| 49
| 49
| 0-2-9-10-20
| 0–2–9–10–20
| 1-14/9-9/5-9/8-14/11
| 1–9/8–14/11–14/9–9/5
| Magic
| Magic
|
|
|-
|-
| 50
| 50
| 0-8-9-10-20
| 0–8–9–10–20
| 1-16/11-9/5-9/8-14/11
| 1–9/8–14/11–16/11–9/5
| Apollo
| Apollo
|
|
|-
|-
| 51
| 51
| 0-2-7-11-20
| 0–2–7–11–20
| 1-14/9-7/6-7/5-14/11
| 1–7/6–7/5–14/11–14/9
| Utonal
| Utonal
| [[1155:1386:1980:2520:3080|1/(24:20:14:11:9)]]
|
|-
|-
| 52
| 52
| 0-2-9-11-20
| 0–2–9–11–20
| 1-14/9-9/5-7/5-14/11
| 1–14/11–7/5–14/9–9/5
| Octarod
| Octarod
|
|
|-
|-
| 53
| 53
| 0-7-9-11-20
| 0–7–9–11–20
| 1-7/6-9/5-7/5-14/11
| 1–7/6–14/11–7/5–9/5
| Octarod
| Octarod
|
|
|-
|-
| 54
| 54
| 0-2-10-11-20
| 0–2–10–11–20
| 1-14/9-9/8-7/5-14/11
| 1–9/8–14/11–7/5–14/9
| Apollo
| Apollo
|
|
|-
|-
| 55
| 55
| 0-9-10-11-20
| 0–9–10–11–20
| 1-9/5-9/8-7/5-14/11
| 1–9/8–14/11–7/5–9/5
| Apollo
| Apollo
|
|
|-
|-
| 56
| 56
| 0-2-7-12-20
| 0–2–7–12–20
| 1-14/9-7/6-7/4-14/11
| 1–7/6–14/11–14/9–7/4
| Utonal
| Utonal
| [[462:693:792:1008:1232|1/(24:16:14:11:9)]]
|
|-
|-
| 57
| 57
| 0-7-8-12-20
| 0–7–8–12–20
| 1-7/6-16/11-7/4-14/11
| 1–7/6–14/11–16/11–7/4
| Keenanismic
| Keenanismic
|
|
|-
|-
| 58
| 58
| 0-2-10-12-20
| 0–2–10–12–20
| 1-14/9-9/8-7/4-14/11
| 1–9/8–14/11–14/9–7/4
| Pentacircle
| Pentacircle
|
|
|-
|-
| 59
| 59
| 0-8-10-12-20
| 0–8–10–12–20
| 1-16/11-9/8-7/4-14/11
| 1–9/8–14/11–16/11–7/4
| Sensamagic11
| Sensamagic11
|
|
|-
|-
| 60
| 60
| 0-2-11-12-20
| 0–2–11–12–20
| 1-14/9-7/5-7/4-14/11
| 1–14/11–7/5–14/9–7/4
| Utonal
| Utonal
| [[924:1155:1320:2016:2464|1/(20:16:14:11:9)]]
|
|-
|-
| 61
| 61
| 0-7-11-12-20
| 0–7–11–12–20
| 1-7/6-7/5-7/4-14/11
| 1–7/6–14/11–7/5–7/4
| Utonal
| Utonal
| [[770:924:1155:1320:1680|1/(24:20:16:14:11)]]
|
|-
|-
| 62
| 62
| 0-10-11-12-20
| 0–10–11–12–20
| 1-9/8-7/5-7/4-14/11
| 1–9/8–14/11–7/5–7/4
| Apollo
| Apollo
|
|
|-
|-
| 63
| 63
| 0-2-9-13-20
| 0–2–9–13–20
| 1-14/9-9/5-12/11-14/11
| 1–12/11–14/11–14/9–9/5
| Octarod
| Octarod
|
|
|-
|-
| 64
| 64
| 0-8-9-13-20
| 0–8–9–13–20
| 1-16/11-20/11-12/11-14/11
| 1–12/11–14/11–16/11–20/11
| Otonal
| Otonal
| [[4:5:6:7:11]]
|
|-
|-
| 65
| 65
| 0-2-11-13-20
| 0–2–11–13–20
| 1-14/9-7/5-12/11-14/11
| 1–12/11–14/11–7/5–14/9
| Octarod
| Octarod
|
|
|-
|-
| 66
| 66
| 0-9-11-13-20
| 0–9–11–13–20
| 1-9/5-7/5-12/11-14/11
| 1–12/11–14/11–7/5–9/5
| Octarod
| Octarod
|
|
|-
|-
| 67
| 67
| 0-2-12-13-20
| 0–2–12–13–20
| 1-14/9-7/4-12/11-14/11
| 1–12/11–14/11–14/9–7/4
| Unimarvel
| Marvel11
|
|  
|-
|-
| 68
| 68
| 0-8-12-13-20
| 0–8–12–13–20
| 1-16/11-7/4-12/11-14/11
| 1–12/11–14/11–16/11–7/4
| Keenanismic
| Keenanismic
|
|
|-
|-
| 69
| 69
| 0-11-12-13-20
| 0–11–12–13–20
| 1-7/5-7/4-12/11-14/11
| 1–12/11–14/11–7/5–7/4
| Magic
| Magic
|
|
|-
|-
| 70
| 70
| 0-7-8-18-20
| 0–7–8–18–20
| 1-7/6-16/11-18/11-14/11
| 1–7/6–14/11–16/11–18/11
| Unimarvel
| Marvel11
|
|
|-
|-
| 71
| 71
| 0-7-9-18-20
| 0–7–9–18–20
| 1-7/6-9/5-18/11-14/11
| 1–7/6–14/11–18/11–9/5
| Octarod
| Octarod
|
|
|-
|-
| 72
| 72
| 0-8-9-18-20
| 0–8–9–18–20
| 1-16/11-20/11-18/11-14/11
| 1–14/11–16/11–18/11–20/11
| Otonal
| Otonal
| [[4:5:7:9:11]]
|
|-
|-
| 73
| 73
| 0-8-10-18-20
| 0–8–10–18–20
| 1-16/11-9/8-18/11-14/11
| 1–9/8–14/11–16/11–18/11
| Pentacircle
| Pentacircle
|
|
|-
|-
| 74
| 74
| 0-9-10-18-20
| 0–9–10–18–20
| 1-9/5-9/8-18/11-14/11
| 1–9/8–14/11–18/11–9/5
| Apollo
| Apollo
|
|
|-
|-
| 75
| 75
| 0-7-11-18-20
| 0–7–11–18–20
| 1-7/6-7/5-18/11-14/11
| 1–7/6–14/11–7/5–18/11
| Octarod
| Octarod
|
|
|-
|-
| 76
| 76
| 0-9-11-18-20
| 0–9–11–18–20
| 1-9/5-7/5-18/11-14/11
| 1–14/11–7/5–18/11–9/5
| Octarod
| Octarod
|
|
|-
|-
| 77
| 77
| 0-10-11-18-20
| 0–10–11–18–20
| 1-9/8-7/5-18/11-14/11
| 1–9/8–14/11–7/5–18/11
| Magic
| Magic
|
|
|-
|-
| 78
| 78
| 0-8-13-18-20
| 0–8–13–18–20
| 1-16/11-12/11-18/11-14/11
| 1–12/11–14/11–16/11–18/11
| Otonal
| Otonal
| [[4:6:7:9:11]]
|
|-
|-
| 79
| 79
| 0-9-13-18-20
| 0–9–13–18–20
| 1-20/11-12/11-18/11-14/11
| 1–12/11–14/11–18/11–20/11
| Otonal
| Otonal
| [[5:6:7:9:11]]
|
|-
|-
| 80
| 80
| 0-11-13-18-20
| 0–11–13–18–20
| 1-7/5-12/11-18/11-14/11
| 1–12/11–14/11–7/5–18/11
| Octarod
| Octarod
|
|
|}
|}


== Hexads ==
== Hexads ==
{| class="wikitable center-1"
{| class="wikitable center-1"
|-
|-
! #
! #
! Chord
! Generators
! Transversal
! Transversal
! Type
! Type
! Comment
|-
|-
| 1
| 1
| 0-1-2-9-10-11
| 0–1–2–9–10–11
| 1-5/4-14/9-9/5-9/8-7/5
| 1–9/8–5/4–7/5–14/9–9/5
| magic
| Magic
|
|-
|-
| 2
| 2
| 0-1-2-10-11-12
| 0–1–2–10–11–12
| 1-5/4-14/9-9/8-7/5-7/4
| 1–9/8–5/4–7/5–14/9–7/4
| apollo
| Apollo
|
|-
|-
| 3
| 3
| 0-1-2-9-11-13
| 0–1–2–9–11–13
| 1-5/4-14/9-9/5-7/5-12/11
| 1–12/11–5/4–7/5–14/9–9/5
| magic
| Magic
|
|-
|-
| 4
| 4
| 0-2-4-9-11-13
| 0–2–4–9–11–13
| 1-14/9-6/5-9/5-7/5-12/11
| 1–12/11–6/5–7/5–14/9–9/5
| octarod
| Octarod
|
|-
|-
| 5
| 5
| 0-1-2-11-12-13
| 0–1–2–11–12–13
| 1-5/4-14/9-7/5-7/4-12/11
| 1–12/11–5/4–7/5–14/9–7/4
| unimarvel
| Marvel11
|
|-
|-
| 6
| 6
| 0-2-4-11-12-13
| 0–2–4–11–12–13
| 1-14/9-6/5-7/5-7/4-12/11
| 1–12/11–6/5–7/5–14/9–7/4
| magic
| Magic
|
|-
|-
| 7
| 7
| 0-2-7-9-11-20
| 0–2–7–9–11–20
| 1-14/9-7/6-9/5-7/5-14/11
| 1–7/6–14/11–7/5–14/9–9/5
| octarod
| Octarod
|
|-
|-
| 8
| 8
| 0-2-9-10-11-20
| 0–2–9–10–11–20
| 1-14/9-9/5-9/8-7/5-14/11
| 1–9/8–14/11–7/5–14/9–9/5
| magic
| Magic
|
|-
|-
| 9
| 9
| 0-2-7-11-12-20
| 0–2–7–11–12–20
| 1-14/9-7/6-7/5-7/4-14/11
| 1–14/11–7/6–7/5–14/9–7/4
| utonal
| Utonal
| [[2310:2772:3465:3960:5040:6160|1/(24:20:16:14:11:9)]]
|-
|-
| 10
| 10
| 0-2-10-11-12-20
| 0–2–10–11–12–20
| 1-14/9-9/8-7/5-7/4-14/11
| 1–9/8–14/11–7/5–14/9–7/4
| apollo
| Apollo
|
|-
|-
| 11
| 11
| 0-2-9-11-13-20
| 0–2–9–11–13–20
| 1-14/9-9/5-7/5-12/11-14/11
| 1–12/11–14/11–7/5–14/9–9/5
| octarod
| Octarod
|  
|-
|-
| 12
| 12
| 0-2-11-12-13-20
| 0–2–11–12–13–20
| 1-14/9-7/5-7/4-12/11-14/11
| 1–12/11–14/11–7/5–14/9–7/4
| magic
| Magic
|  
|-
|-
| 13
| 13
| 0-7-8-9-18-20
| 0–7–8–9–18–20
| 1-7/6-16/11-9/5-18/11-14/11
| 1–7/6–14/11–16/11–18/11–9/5
| magic
| Magic
|  
|-
|-
| 14
| 14
| 0-8-9-10-18-20
| 0–8–9–10–18–20
| 1-16/11-9/5-9/8-18/11-14/11
| 1–9/8–14/11–16/11–18/11–9/5
| apollo
| Apollo
|  
|-
|-
| 15
| 15
| 0-7-9-11-18-20
| 0–7–9–11–18–20
| 1-7/6-9/5-7/5-18/11-14/11
| 1–7/6–14/11–7/5–18/11–9/5
| octarod
| Octarod
|  
|-
|-
| 16
| 16
| 0-9-10-11-18-20
| 0–9–10–11–18–20
| 1-9/5-9/8-7/5-18/11-14/11
| 1–9/8–14/11–7/5–18/11–9/5
| magic
| Magic
|  
|-
|-
| 17
| 17
| 0-8-9-13-18-20
| 0–8–9–13–18–20
| 1-16/11-20/11-12/11-18/11-14/11
| 1–12/11–14/11–16/11–18/11–20/11
| otonal
| Otonal
| [[4:5:6:7:9:11]]
|-
|-
| 18
| 18
| 0-9-11-13-18-20
| 0–9–11–13–18–20
| 1-9/5-7/5-12/11-18/11-14/11
| 1–12/11–14/11–7/5–18/11–9/5
| octarod
| Octarod
|  
|}
|}


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