Chords of magic: Difference between revisions

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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]] 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 {{nowrap|vM3 {{=}} 380¢ + ''c''/5}}, where ''c'' is the amount in cents the tempered fifth exceeds 700¢. The [[Enharmonic unisons in ups and downs notation|enharmonic unison]] is ^<sup>5</sup>dd2, thus {{nowrap|^<sup>5</sup>C {{=}} B##}}.  
[[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.


To simplify the chord names, slashes (lifts and drops) are also used. One lift is -22 generators, octave-reduced. Thus {{nowrap|/1 {{=}} &minus;25''G'' + 3''G'' {{=}} m2 + ^^d8 {{=}} ^^d2}}. Thus a lift equals two ups minus a tempered pythagorean comma, so {{nowrap|/C {{=}} ^^Dbb|\C {{=}} vvB#|^^C {{=}} /B#|and vvC {{=}} \Dbb}}.
{| class="wikitable mw-collapsible mw-collapsed"
 
|+ style="font-size: 105%; white-space: nowrap;" | Cents values of magic accidentals in various tunings
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"
|+ style="font-size: 105%;" | Cents values of magic accidentals in various tunings
|-
|-
!  
!  
Line 21: Line 17:
|-
|-
! 19edo
! 19edo
| 1\19 = 61¢
| 1\19 = 61{{c}}
| 0\19 = 0¢
| 0\19 = 0{{c}}
| 1\19 = 61¢
| 1\19 = 61{{c}}
| Ignore the arrows, treat slashes as sharps/flats
| Ignore the arrows, treat slashes as sharps/flats
|-
|-
! 22edo
! 22edo
| 3\22 = 164¢
| 3\22 = 164{{c}}
| 1\22 = 55¢
| 1\22 = 55{{c}}
| 0\22 = 0¢
| 0\22 = 0{{c}}
| Ignore the slashes
| Ignore the slashes
|-
|-
! 41edo
! 41edo
| 4\41 = 117¢
| 4\41 = 117{{c}}
| 1\41 = 29¢
| 1\41 = 29{{c}}
| 1\41 = 29¢
| 1\41 = 29{{c}}
| Treat slashes as arrows
| Treat slashes as arrows
|-
|-
! 60edo
! 60edo
| 5\60 = 100¢
| 5\60 = 100{{c}}
| 1\60 = 20¢
| 1\60 = 20{{c}}
| 2\60 = 40¢
| 2\60 = 40{{c}}
| Treat slashes as double arrows
| Treat slashes as double arrows
|-
|-
! Rank-2
! Rank-2
| 100¢ + 7c
| 100{{c}} + 7''c''
| 20¢ + 3.8c
| 20{{c}} + 3.8''c''
| 40¢ &minus; 4.4c
| 40{{c}} − 4.4''c''
| N/a
| 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. So the ratios in the following table are specific to magic. But the chord names apply to any (P8, P12/5) temperament.
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"
 
|+ style="font-size: 105%;" |Magic's genchain
{| class="wikitable center-all mw-collapsible mw-collapsed"
|+ style="font-size: 105%; white-space: nowrap;" | Magic's genchain
|-
|-
! Genspan
! Genspan
Line 161: Line 158:
|-
|-
! #
! #
! Chord
! Generators
! Transversal
! Transversal
! Type
! Type
! Name
! Kite's name
! Comments
! Comments
|-
|-
| 1
| 1
| 0-1-2
| 0–1–2
| 1-5/4-14/9
| 1–5/4–14/9
| Marvel
| Marvel
| Cv(vv#5)
| Cv(vv#5)
|
|  
|-
|-
| 2
| 2
| 0-2-4
| 0–2–4
| 1-14/9-6/5
| 1–14/9–6/5
| Sensamagic
| Sensamagic
| C^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
| Cv
| Cv
|
|  
|-
|-
| 4
| 4
| 0-4-5
| 0–4–5
| 1-6/5-3/2
| 1–6/5–3/2
| Utonal
| Utonal
| C^m
| C^m
|
|  
|-
|-
| 5
| 5
| 0-2-7
| 0–2–7
| 1-14/9-7/6
| 1–14/9–7/6
| Utonal
| Utonal
| C/
| C/
| 1-9/7-3/2
| 1–9/7–3/2
|-
|-
| 6
| 6
| 0-5-7
| 0–5–7
| 1-3/2-7/6
| 1–3/2–7/6
| Otonal
| Otonal
| C\m
| C\m
|
|  
|-
|-
| 7
| 7
| 0-1-8
| 0–1–8
| 1-5/4-16/11
| 1–5/4–16/11
| Keenanismic
| Keenanismic
| Cv(^^b5)
| Cv(^^b5)
|
|  
|-
|-
| 8
| 8
| 0-4-8
| 0–4–8
| 1-6/5-16/11
| 1–6/5–16/11
| Ptolemismic
| Ptolemismic
| C^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
| C\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
| Cv^7no5
| Cv^7no5
|
|  
|-
|-
| 11
| 11
| 0-2-9
| 0–2–9
| 1-14/9-9/5
| 1–14/9–9/5
| Sensamagic
| Sensamagic
| C^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
| C^m7no5
| C^m7no5
| ''or'' 1-3/2-5/3 = Cv6no3
| ''or'' 1–3/2–5/3 = Cv6no3
|-
|-
| 13
| 13
| 0-5-9
| 0–5–9
| 1-3/2-9/5
| 1–3/2–9/5
| Utonal
| Utonal
| C^m7no3
| C^m7no3
|
|  
|-
|-
| 14
| 14
| 0-7-9
| 0–7–9
| 1-7/6-9/5
| 1–7/6–9/5
| Sensamagic
| Sensamagic
| C\mv7no5
| C\mv7no5
|
|  
|-
|-
| 15
| 15
| 0-8-9
| 0–8–9
| 1-16/11-20/11
| 1–16/11–20/11
| Otonal
| Otonal
| Cv(\b5)
| Cv(\b5)
| 1-5/4-11/8
| 1–5/4–11/8
|-
|-
| 16
| 16
| 0-1-10
| 0–1–10
| 1-5/4-9/8
| 1–5/4–9/8
| Otonal
| Otonal
| Cv,9no5
| Cv,9no5
|
|  
|-
|-
| 17
| 17
| 0-2-10
| 0–2–10
| 1-14/9-9/8
| 1–14/9–9/8
| Pentacircle
| Pentacircle
| C2(vv#5)
| C2(vv#5)
|
|  
|-
|-
| 18
| 18
| 0-5-10
| 0–5–10
| 1-3/2-9/8
| 1–3/2–9/8
| Ambitonal
| Ambitonal
| C2
| C2
|
|  
|-
|-
| 19
| 19
| 0-8-10
| 0–8–10
| 1-16/11-9/8
| 1–16/11–9/8
| Pentacircle
| Pentacircle
| C2(^^b5)
| C2(^^b5)
|
|  
|-
|-
| 20
| 20
| 0-9-10
| 0–9–10
| 1-9/5-9/8
| 1–9/5–9/8
| Utonal
| Utonal
| C^9no35
| C^9no35
Line 308: Line 305:
|-
|-
| 21
| 21
| 0-1-11
| 0–1–11
| 1-5/4-7/5
| 1–5/4–7/5
| Marvel
| Marvel
| Cv(^\b5)
| Cv(^\b5)
|
|  
|-
|-
| 22
| 22
| 0-2-11
| 0–2–11
| 1-14/9-7/5
| 1–14/9–7/5
| Utonal
| Utonal
| C/,^7no5
| C/,^7no5
| 1-9/7-9/5
| 1–9/7–9/5
|-
|-
| 23
| 23
| 0-4-11
| 0–4–11
| 1-6/5-7/5
| 1–6/5–7/5
| Otonal
| Otonal
| C^m(^\b5)
| C^m(^\b5)
|
|  
|-
|-
| 24
| 24
| 0-7-11
| 0–7–11
| 1-7/6-7/5
| 1–7/6–7/5
| Utonal
| Utonal
| C\m(^\b5)
| C\m(^\b5)
|
|  
|-
|-
| 25
| 25
| 0-9-11
| 0–9–11
| 1-9/5-7/5
| 1–9/5–7/5
| Otonal
| Otonal
| C/(^b5)
| C/(^b5)
| 1-9/7-10/7
| 1–9/7–10/7
|-
|-
| 26
| 26
| 0-10-11
| 0–10–11
| 1-9/8-7/5
| 1–9/8–7/5
| Marvel
| Marvel
| Cv,7no5
| Cv,7no5
| 1-5/4-16/9
| 1–5/4–16/9
|-
|-
| 27
| 27
| 0-1-12
| 0–1–12
| 1-5/4-7/4
| 1–5/4–7/4
| Otonal
| Otonal
| Cv,\7no5
| Cv,\7no5
|
|  
|-
|-
| 28
| 28
| 0-2-12
| 0–2–12
| 1-14/9-7/4
| 1–14/9–7/4
| Utonal
| Utonal
| C/,9no5
| C/,9no5
| 1-9/8-9/7
| 1–9/8–9/7
|-
|-
| 29
| 29
| 0-4-12
| 0–4–12
| 1-6/5-7/4
| 1–6/5–7/4
| Keenanismic
| Keenanismic
| C^m\7
| C^m\7
|
|  
|-
|-
| 30
| 30
| 0-5-12
| 0–5–12
| 1-3/2-7/4
| 1–3/2–7/4
| Otonal
| Otonal
| C\7no3
| C\7no3
|
|  
|-
|-
| 31
| 31
| 0-7-12
| 0–7–12
| 1-7/6-7/4
| 1–7/6–7/4
| Utonal
| Utonal
| C\m7no5
| C\m7no5
|
|  
|-
|-
| 32
| 32
| 0-8-12
| 0–8–12
| 1-16/11-7/4
| 1–16/11–7/4
| Keenanismic
| Keenanismic
| C^m(\b5)
| C^m(\b5)
| 1-6/5-11/8
| 1–6/5–11/8
|-
|-
| 33
| 33
| 0-10-12
| 0–10–12
| 1-9/8-7/4
| 1–9/8–7/4
| Otonal
| Otonal
| C\7sus2
| C\7sus2
|
|  
|-
|-
| 34
| 34
| 0-11-12
| 0–11–12
| 1-7/5-7/4
| 1–7/5–7/4
| Utonal
| Utonal
| C\7(^\b5)no3
| C\7(^\b5)no3
|
|  
|-
|-
| 35
| 35
| 0-1-13
| 0–1–13
| 1-5/4-12/11
| 1–5/4–12/11
| Keenanismic
| Keenanismic
|
|  
|
|  
|-
|-
| 36
| 36
| 0-2-13
| 0–2–13
| 1-14/9-12/11
| 1–14/9–12/11
| Swetismic
| Swetismic
| C/(^\b5)
| C/(^\b5)
| 1-9/7-7/5
| 1–9/7–7/5
|-
|-
| 37
| 37
| 0-4-13
| 0–4–13
| 1-6/5-12/11
| 1–6/5–12/11
| Utonal
| Utonal
|
|  
|
|  
|-
|-
| 38
| 38
| 0-5-13
| 0–5–13
| 1-3/2-12/11
| 1–3/2–12/11
| Utonal
| Utonal
| C^^b2
| C^^b2
|
|  
|-
|-
| 39
| 39
| 0-8-13
| 0–8–13
| 1-16/11-12/11
| 1–16/11–12/11
| Otonal
| Otonal
| Cvv#4
| Cvv#4
| 1-11/8-3/2
| 1–11/8–3/2
|-
|-
| 40
| 40
| 0-9-13
| 0–9–13
| 1-20/11-12/11
| 1–20/11–12/11
| Otonal
| Otonal
|
|  
|
|  
|-
|-
| 41
| 41
| 0-11-13
| 0–11–13
| 1-7/5-12/11
| 1–7/5–12/11
| Swetismic
| Swetismic
|
|  
|
|  
|-
|-
| 42
| 42
| 0-12-13
| 0–12–13
| 1-7/4-12/11
| 1–7/4–12/11
| 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
| 1–9/5–18/11
| 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
| 1–14/9–14/11
| 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
| 1–16/11–14/11
| Otonal
| Otonal
|
|  
|
|  
|-
|-
| 53
| 53
| 0-9-20
| 0–9–20
| 1-20/11-14/11
| 1–20/11–14/11
| 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
| 1–7/5–14/11
| Utonal
| Utonal
|
|  
|
|  
|-
|-
| 56
| 56
| 0-12-20
| 0–12–20
| 1-7/4-14/11
| 1–7/4–14/11
| 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
| 1–18/11–14/11
| Otonal
| Otonal
|
|  
|
|  
|}
|}


Line 578: Line 575:
|-
|-
! #
! #
! Chord
! Generators
! Transversal
! Transversal
! Type
! Type
! Name
! Kite's name
! Comments
! Comments
|-
|-
| 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
| Cv^7(vv#5)
| Cv^7(vv#5)
Line 592: Line 589:
|-
|-
| 2
| 2
| 0-2-4-9
| 0–2–4–9
| 1-14/9-6/5-9/5
| 1–14/9–6/5–9/5
| Sensamagic
| Sensamagic
| C^m7(vv#5)
| C^m7(vv#5)
Line 599: Line 596:
|-
|-
| 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
| Cv^7
| Cv^7
Line 606: Line 603:
|-
|-
| 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
| C^m7
| C^m7
| ''or'' 1-5/4-3/2-5/3 = Cv6
| ''or'' 1–5/4–3/2–5/3 = Cv6
|-
|-
| 5
| 5
| 0-2-7-9
| 0–2–7–9
| 1-14/9-7/6-9/5
| 1–14/9–7/6–9/5
| Sensamagic
| Sensamagic
| C/,vv#9
| C/,vv#9
| 1-9/7-3/2-7/3
| 1–9/7–3/2–7/3
|-
|-
| 6
| 6
| 0-5-7-9
| 0–5–7–9
| 1-3/2-7/6-9/5
| 1–3/2–7/6–9/5
| Sensamagic
| Sensamagic
| C\m^7
| C\m^7
Line 627: Line 624:
|-
|-
| 7
| 7
| 0-1-8-9
| 0–1–8–9
| 1-5/4-16/11-9/5
| 1–5/4–16/11–9/5
| Keemic
| Keemic
| Cv^7(^^b5)
| Cv^7(^^b5)
Line 634: Line 631:
|-
|-
| 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
| C^m7(^^b5)
| C^m7(^^b5)
Line 641: Line 638:
|-
|-
| 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
| C\m^7(^^b5)
| C\m^7(^^b5)
Line 648: Line 645:
|-
|-
| 10
| 10
| 0-1-2-10
| 0–1–2–10
| 1-5/4-14/9-9/8
| 1–5/4–14/9–9/8
| Apollo
| Apollo
| Cv,9(vv#5)
| Cv,9(vv#5)
Line 655: Line 652:
|-
|-
| 11
| 11
| 0-1-5-10
| 0–1–5–10
| 1-5/4-3/2-9/8
| 1–5/4–3/2–9/8
| Otonal
| Otonal
| Cv,9
| Cv,9
Line 662: Line 659:
|-
|-
| 12
| 12
| 0-1-8-10
| 0–1–8–10
| 1-5/4-16/11-9/8
| 1–5/4–16/11–9/8
| Sensamagic11
| Sensamagic11
| Cv,9(^^b5)
| Cv,9(^^b5)
Line 669: Line 666:
|-
|-
| 13
| 13
| 0-1-9-10
| 0–1–9–10
| 1-5/4-9/5-9/8
| 1–5/4–9/5–9/8
| Ptolemismic
| Ptolemismic
| Cv^7,9no5
| Cv^7,9no5
Line 676: Line 673:
|-
|-
| 14
| 14
| 0-2-9-10
| 0–2–9–10
| 1-14/9-9/5-9/8
| 1–14/9–9/5–9/8
| Sensamagic11
| Sensamagic11
| C^9(vv#5)no3
| C^9(vv#5)no3
Line 683: Line 680:
|-
|-
| 15
| 15
| 0-5-9-10
| 0–5–9–10
| 1-3/2-9/5-9/8
| 1–3/2–9/5–9/8
| Utonal
| Utonal
| C^9no3
| C^9no3
Line 690: Line 687:
|-
|-
| 16
| 16
| 0-8-9-10
| 0–8–9–10
| 1-16/11-9/5-9/8
| 1–16/11–9/5–9/8
| Apollo
| Apollo
|
|  
|  
|  
|-
|-
| 17
| 17
| 0-1-2-11
| 0–1–2–11
| 1-5/4-14/9-7/5
| 1–5/4–14/9–7/5
| Marvel
| Marvel
|
|  
|  
|  
|-
|-
| 18
| 18
| 0-2-4-11
| 0–2–4–11
| 1-14/9-6/5-7/5
| 1–14/9–6/5–7/5
| Sensamagic
| Sensamagic
|
|  
|  
|  
|-
|-
| 19
| 19
| 0-2-7-11
| 0–2–7–11
| 1-14/9-7/6-7/5
| 1–14/9–7/6–7/5
| Utonal
| Utonal
|
|  
|  
|  
|-
|-
| 20
| 20
| 0-1-9-11
| 0–1–9–11
| 1-5/4-9/5-7/5
| 1–5/4–9/5–7/5
| Apollo
| Apollo
|
|  
|  
|  
|-
|-
| 21
| 21
| 0-2-9-11
| 0–2–9–11
| 1-14/9-9/5-7/5
| 1–14/9–9/5–7/5
| Sensamagic
| Sensamagic
|
|  
|  
|  
|-
|-
| 22
| 22
| 0-4-9-11
| 0–4–9–11
| 1-6/5-9/5-7/5
| 1–6/5–9/5–7/5
| Otonal
| Otonal
| C^m7(^\b5)
| C^m7(^\b5)
| ''or'' 1-7/6-3/2-5/3 = C\mv6
| ''or'' 1–7/6–3/2–5/3 = C\mv6
|-
|-
| 23
| 23
| 0-7-9-11
| 0–7–9–11
| 1-7/6-9/5-7/5
| 1–7/6–9/5–7/5
| Sensamagic
| Sensamagic
|
|  
|  
|  
|-
|-
| 24
| 24
| 0-1-10-11
| 0–1–10–11
| 1-5/4-9/8-7/5
| 1–5/4–9/8–7/5
| Marvel
| Marvel
|
|  
|  
|  
|-
|-
| 25
| 25
| 0-2-10-11
| 0–2–10–11
| 1-14/9-9/8-7/5
| 1–14/9–9/8–7/5
| Apollo
| Apollo
|
|  
|  
|  
|-
|-
| 26
| 26
| 0-9-10-11
| 0–9–10–11
| 1-9/5-9/8-7/5
| 1–9/5–9/8–7/5
| Marvel
| Marvel
|
|  
|  
|  
|-
|-
| 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
|
|  
|  
|  
|-
|-
| 28
| 28
| 0-2-4-12
| 0–2–4–12
| 1-14/9-6/5-7/4
| 1–14/9–6/5–7/4
| Sensamagic11
| Sensamagic11
|
|  
|  
|  
|-
|-
| 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
| Cv,\7
| Cv,\7
Line 788: Line 785:
|-
|-
| 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
| C^m\7
| C^m\7
Line 795: Line 792:
|-
|-
| 31
| 31
| 0-2-7-12
| 0–2–7–12
| 1-14/9-7/6-7/4
| 1–14/9–7/6–7/4
| Utonal
| Utonal
| C\m7(vv#5)
| C\m7(vv#5)
Line 802: Line 799:
|-
|-
| 32
| 32
| 0-5-7-12
| 0–5–7–12
| 1-3/2-7/6-7/4
| 1–3/2–7/6–7/4
| Ambitonal
| Ambitonal
| C\m7
| C\m7
Line 809: Line 806:
|-
|-
| 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
|
|  
|  
|  
|-
|-
| 34
| 34
| 0-4-8-12
| 0–4–8–12
| 1-6/5-16/11-7/4
| 1–6/5–16/11–7/4
| Keemic
| 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
| C\m7(^^b5)
| C\m7(^^b5)
Line 830: Line 827:
|-
|-
| 36
| 36
| 0-1-10-12
| 0–1–10–12
| 1-5/4-9/8-7/4
| 1–5/4–9/8–7/4
| Otonal
| Otonal
|
|  
|  
|  
|-
|-
| 37
| 37
| 0-2-10-12
| 0–2–10–12
| 1-14/9-9/8-7/4
| 1–14/9–9/8–7/4
| Pentacircle
| Pentacircle
|
|  
|  
|  
|-
|-
| 38
| 38
| 0-5-10-12
| 0–5–10–12
| 1-3/2-9/8-7/4
| 1–3/2–9/8–7/4
| Otonal
| Otonal
| C2\7
| C2\7
Line 851: Line 848:
|-
|-
| 39
| 39
| 0-8-10-12
| 0–8–10–12
| 1-16/11-9/8-7/4
| 1–16/11–9/8–7/4
| Sensamagic11
| Sensamagic11
|
|  
|  
|  
|-
|-
| 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
|
|  
|  
|  
|-
|-
| 41
| 41
| 0-2-11-12
| 0–2–11–12
| 1-14/9-7/5-7/4
| 1–14/9–7/5–7/4
| Utonal
| Utonal
|
|  
|  
|  
|-
|-
| 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
|
|  
|  
|  
|-
|-
| 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
| C\m7(^\b5)
| C\m7(^\b5)
| ''or'' 1-6/5-3/2-12/7 = C^m/6
| ''or'' 1–6/5–3/2–12/7 = 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
|
|  
|  
|  
|-
|-
| 45
| 45
| 0-1-2-13
| 0–1–2–13
| 1-5/4-14/9-12/11
| 1–5/4–14/9–12/11
| Unimarvel
| Unimarvel
|
|  
|  
|  
|-
|-
| 46
| 46
| 0-2-4-13
| 0–2–4–13
| 1-14/9-6/5-12/11
| 1–14/9–6/5–12/11
| Octarod
| Octarod
|
|  
|  
|  
|-
|-
| 47
| 47
| 0-1-5-13
| 0–1–5–13
| 1-5/4-3/2-12/11
| 1–5/4–3/2–12/11
| Keenanismic
| Keenanismic
|
|  
|  
|  
|-
|-
| 48
| 48
| 0-4-5-13
| 0–4–5–13
| 1-6/5-3/2-12/11
| 1–6/5–3/2–12/11
| Utonal
| Utonal
|
|  
|  
|  
|-
|-
| 49
| 49
| 0-1-8-13
| 0–1–8–13
| 1-5/4-16/11-12/11
| 1–5/4–16/11–12/11
| Keenanismic
| Keenanismic
|
|  
|  
|  
|-
|-
| 50
| 50
| 0-4-8-13
| 0–4–8–13
| 1-6/5-16/11-12/11
| 1–6/5–16/11–12/11
| Ptolemismic
| Ptolemismic
|
|  
|  
|  
|-
|-
| 51
| 51
| 0-1-9-13
| 0–1–9–13
| 1-5/4-9/5-12/11
| 1–5/4–9/5–12/11
| Keemic
| Keemic
|
|  
|  
|  
|-
|-
| 52
| 52
| 0-2-9-13
| 0–2–9–13
| 1-14/9-9/5-12/11
| 1–14/9–9/5–12/11
| Octarod
| Octarod
|
|  
|  
|  
|-
|-
| 53
| 53
| 0-4-9-13
| 0–4–9–13
| 1-6/5-9/5-12/11
| 1–6/5–9/5–12/11
| Ptolemismic
| Ptolemismic
|
|  
|  
|  
|-
|-
| 54
| 54
| 0-5-9-13
| 0–5–9–13
| 1-3/2-9/5-12/11
| 1–3/2–9/5–12/11
| Ptolemismic
| Ptolemismic
|
|  
|  
|  
|-
|-
| 55
| 55
| 0-8-9-13
| 0–8–9–13
| 1-16/11-20/11-12/11
| 1–16/11–20/11–12/11
| Otonal
| Otonal
|
|  
|  
|  
|-
|-
| 56
| 56
| 0-1-11-13
| 0–1–11–13
| 1-5/4-7/5-12/11
| 1–5/4–7/5–12/11
| Unimarvel
| Unimarvel
|
|  
|  
|  
|-
|-
| 57
| 57
| 0-2-11-13
| 0–2–11–13
| 1-14/9-7/5-12/11
| 1–14/9–7/5–12/11
| Swetismic
| Swetismic
|
|  
|  
|  
|-
|-
| 58
| 58
| 0-4-11-13
| 0–4–11–13
| 1-6/5-7/5-12/11
| 1–6/5–7/5–12/11
| Octarod
| Octarod
|
|  
|  
|  
|-
|-
| 59
| 59
| 0-9-11-13
| 0–9–11–13
| 1-9/5-7/5-12/11
| 1–9/5–7/5–12/11
| Octarod
| Octarod
|
|  
|  
|  
|-
|-
| 60
| 60
| 0-1-12-13
| 0–1–12–13
| 1-5/4-7/4-12/11
| 1–5/4–7/4–12/11
| Keenanismic
| Keenanismic
|
|  
|  
|  
|-
|-
| 61
| 61
| 0-2-12-13
| 0–2–12–13
| 1-14/9-7/4-12/11
| 1–14/9–7/4–12/11
| Unimarvel
| Unimarvel
|
|  
|  
|  
|-
|-
| 62
| 62
| 0-4-12-13
| 0–4–12–13
| 1-6/5-7/4-12/11
| 1–6/5–7/4–12/11
| Keemic
| Keemic
|
|  
|  
|  
|-
|-
| 63
| 63
| 0-5-12-13
| 0–5–12–13
| 1-3/2-7/4-12/11
| 1–3/2–7/4–12/11
| Keenanismic
| Keenanismic
|
|  
|  
|  
|-
|-
| 64
| 64
| 0-8-12-13
| 0–8–12–13
| 1-16/11-7/4-12/11
| 1–16/11–7/4–12/11
| Keenanismic
| Keenanismic
|
|  
|  
|  
|-
|-
| 65
| 65
| 0-11-12-13
| 0–11–12–13
| 1-7/5-7/4-12/11
| 1–7/5–7/4–12/11
| Unimarvel
| Unimarvel
|
|  
|  
|  
|-
|-
| 66
| 66
| 0-5-7-18
| 0–5–7–18
| 1-3/2-7/6-18/11
| 1–3/2–7/6–18/11
| Swetismic
| Swetismic
|
|  
|  
|  
|-
|-
| 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
| Unimarvel
|
|  
|  
|  
|-
|-
| 68
| 68
| 0-5-9-18
| 0–5–9–18
| 1-3/2-9/5-18/11
| 1–3/2–9/5–18/11
| Utonal
| Utonal
|
|  
|  
|  
|-
|-
| 69
| 69
| 0-7-9-18
| 0–7–9–18
| 1-7/6-9/5-18/11
| 1–7/6–9/5–18/11
| Octarod
| Octarod
|
|  
|  
|  
|-
|-
| 70
| 70
| 0-8-9-18
| 0–8–9–18
| 1-16/11-20/11-18/11
| 1–16/11–20/11–18/11
| Otonal
| Otonal
|
|  
|  
|  
|-
|-
| 71
| 71
| 0-5-10-18
| 0–5–10–18
| 1-3/2-9/8-18/11
| 1–3/2–9/8–18/11
| Utonal
| Utonal
|
|  
|  
|  
|-
|-
| 72
| 72
| 0-8-10-18
| 0–8–10–18
| 1-16/11-9/8-18/11
| 1–16/11–9/8–18/11
| Pentacircle
| Pentacircle
|
|  
|  
|  
|-
|-
| 73
| 73
| 0-9-10-18
| 0–9–10–18
| 1-9/5-9/8-18/11
| 1–9/5–9/8–18/11
| Utonal
| Utonal
|
|  
|  
|  
|-
|-
| 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
|
|  
|  
|  
|-
|-
| 75
| 75
| 0-9-11-18
| 0–9–11–18
| 1-9/5-7/5-18/11
| 1–9/5–7/5–18/11
| Octarod
| Octarod
|
|  
|  
|  
|-
|-
| 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
| Unimarvel
|
|  
|  
|  
|-
|-
| 77
| 77
| 0-5-13-18
| 0–5–13–18
| 1-3/2-12/11-18/11
| 1–3/2–12/11–18/11
| Ambitonal
| Ambitonal
|
|  
|  
|  
|-
|-
| 78
| 78
| 0-8-13-18
| 0–8–13–18
| 1-16/11-12/11-18/11
| 1–16/11–12/11–18/11
| Otonal
| Otonal
|
|  
|  
|  
|-
|-
| 79
| 79
| 0-9-13-18
| 0–9–13–18
| 1-20/11-12/11-18/11
| 1–20/11–12/11–18/11
| Otonal
| Otonal
|
|  
|  
|  
|-
|-
| 80
| 80
| 0-11-13-18
| 0–11–13–18
| 1-7/5-12/11-18/11
| 1–7/5–12/11–18/11
| Swetismic
| Swetismic
|
|  
|  
|  
|-
|-
| 81
| 81
| 0-2-7-20
| 0–2–7–20
| 1-14/9-7/6-14/11
| 1–14/9–7/6–14/11
| Utonal
| Utonal
|
|  
|  
|  
|-
|-
| 82
| 82
| 0-7-8-20
| 0–7–8–20
| 1-7/6-16/11-14/11
| 1–7/6–16/11–14/11
| Keenanismic
| Keenanismic
|
|  
|  
|  
|-
|-
| 83
| 83
| 0-2-9-20
| 0–2–9–20
| 1-14/9-9/5-14/11
| 1–14/9–9/5–14/11
| Octarod
| Octarod
|
|  
|  
|  
|-
|-
| 84
| 84
| 0-7-9-20
| 0–7–9–20
| 1-7/6-9/5-14/11
| 1–7/6–9/5–14/11
| Octarod
| Octarod
|
|  
|  
|  
|-
|-
| 85
| 85
| 0-8-9-20
| 0–8–9–20
| 1-16/11-20/11-14/11
| 1–16/11–20/11–14/11
| Otonal
| Otonal
|
|  
|  
|  
|-
|-
| 86
| 86
| 0-2-10-20
| 0–2–10–20
| 1-14/9-9/8-14/11
| 1–14/9–9/8–14/11
| Pentacircle
| Pentacircle
|
|  
|  
|  
|-
|-
| 87
| 87
| 0-8-10-20
| 0–8–10–20
| 1-16/11-9/8-14/11
| 1–16/11–9/8–14/11
| Pentacircle
| Pentacircle
|
|  
|  
|  
|-
|-
| 88
| 88
| 0-9-10-20
| 0–9–10–20
| 1-9/5-9/8-14/11
| 1–9/5–9/8–14/11
| Apollo
| Apollo
|
|  
|  
|  
|-
|-
| 89
| 89
| 0-2-11-20
| 0–2–11–20
| 1-14/9-7/5-14/11
| 1–14/9–7/5–14/11
| Utonal
| Utonal
|
|  
|  
|  
|-
|-
| 90
| 90
| 0-7-11-20
| 0–7–11–20
| 1-7/6-7/5-14/11
| 1–7/6–7/5–14/11
| Utonal
| Utonal
|
|  
|  
|  
|-
|-
| 91
| 91
| 0-9-11-20
| 0–9–11–20
| 1-9/5-7/5-14/11
| 1–9/5–7/5–14/11
| Ptolemismic
| Ptolemismic
|
|  
|  
|  
|-
|-
| 92
| 92
| 0-10-11-20
| 0–10–11–20
| 1-9/8-7/5-14/11
| 1–9/8–7/5–14/11
| Apollo
| Apollo
|
|  
|  
|  
|-
|-
| 93
| 93
| 0-2-12-20
| 0–2–12–20
| 1-14/9-7/4-14/11
| 1–14/9–7/4–14/11
| Utonal
| Utonal
|
|  
|  
|  
|-
|-
| 94
| 94
| 0-7-12-20
| 0–7–12–20
| 1-7/6-7/4-14/11
| 1–7/6–7/4–14/11
| Utonal
| Utonal
|
|  
|  
|  
|-
|-
| 95
| 95
| 0-8-12-20
| 0–8–12–20
| 1-16/11-7/4-14/11
| 1–16/11–7/4–14/11
| Keenanismic
| Keenanismic
|
|  
|  
|  
|-
|-
| 96
| 96
| 0-10-12-20
| 0–10–12–20
| 1-9/8-7/4-14/11
| 1–9/8–7/4–14/11
| Pentacircle
| Pentacircle
|
|  
|  
|  
|-
|-
| 97
| 97
| 0-11-12-20
| 0–11–12–20
| 1-7/5-7/4-14/11
| 1–7/5–7/4–14/11
| Utonal
| Utonal
|
|  
|  
|  
|-
|-
| 98
| 98
| 0-2-13-20
| 0–2–13–20
| 1-14/9-12/11-14/11
| 1–14/9–12/11–14/11
| Swetismic
| Swetismic
|
|  
|  
|  
|-
|-
| 99
| 99
| 0-8-13-20
| 0–8–13–20
| 1-16/11-12/11-14/11
| 1–16/11–12/11–14/11
| Otonal
| Otonal
|
|  
|  
|  
|-
|-
| 100
| 100
| 0-9-13-20
| 0–9–13–20
| 1-20/11-12/11-14/11
| 1–20/11–12/11–14/11
| Otonal
| Otonal
|
|  
|  
|  
|-
|-
| 101
| 101
| 0-11-13-20
| 0–11–13–20
| 1-7/5-12/11-14/11
| 1–7/5–12/11–14/11
| Octarod
| Octarod
|
|  
|  
|  
|-
|-
| 102
| 102
| 0-12-13-20
| 0–12–13–20
| 1-7/4-12/11-14/11
| 1–7/4–12/11–14/11
| Keenanismic
| Keenanismic
|
|  
|  
|  
|-
|-
| 103
| 103
| 0-7-18-20
| 0–7–18–20
| 1-7/6-18/11-14/11
| 1–7/6–18/11–14/11
| Swetismic
| Swetismic
|
|  
|  
|  
|-
|-
| 104
| 104
| 0-8-18-20
| 0–8–18–20
| 1-16/11-18/11-14/11
| 1–16/11–18/11–14/11
| Otonal
| Otonal
|
|  
|  
|  
|-
|-
| 105
| 105
| 0-9-18-20
| 0–9–18–20
| 1-20/11-18/11-14/11
| 1–20/11–18/11–14/11
| Otonal
| Otonal
|
|  
|  
|  
|-
|-
| 106
| 106
| 0-10-18-20
| 0–10–18–20
| 1-9/8-18/11-14/11
| 1–9/8–18/11–14/11
| Pentacircle
| Pentacircle
|
|  
|  
|  
|-
|-
| 107
| 107
| 0-11-18-20
| 0–11–18–20
| 1-7/5-18/11-14/11
| 1–7/5–18/11–14/11
| Octarod
| Octarod
|
|  
|  
|  
|-
|-
| 108
| 108
| 0-13-18-20
| 0–13–18–20
| 1-12/11-18/11-14/11
| 1–12/11–18/11–14/11
| Otonal
| Otonal
|
|  
|  
|  
|}
|}
Line 1,345: Line 1,342:
|-
|-
! #
! #
! Chord
! Generators
! Transversal
! Transversal
! Type
! Type
! Name
! Kite's name
! Comments
! Comments
|-
|-
| 1
| 1
| 0-1-2-9-10
| 0–1–2–9–10
| 1-5/4-14/9-9/5-9/8
| 1–5/4–14/9–9/5–9/8
| Magic
| Magic
|
|  
|
|  
|-
|-
| 2
| 2
| 0-1-5-9-10
| 0–1–5–9–10
| 1-5/4-3/2-9/5-9/8
| 1–5/4–3/2–9/5–9/8
| Ptolemismic
| Ptolemismic
| Cv9(^7)
| Cv9(^7)
|
|  
|-
|-
| 3
| 3
| 0-1-8-9-10
| 0–1–8–9–10
| 1-5/4-16/11-9/5-9/8
| 1–5/4–16/11–9/5–9/8
| Magic
| Magic
|
|  
|
|  
|-
|-
| 4
| 4
| 0-1-2-9-11
| 0–1–2–9–11
| 1-5/4-14/9-9/5-7/5
| 1–5/4–14/9–9/5–7/5
| Magic
| Magic
|
|  
|
|  
|-
|-
| 5
| 5
| 0-2-4-9-11
| 0–2–4–9–11
| 1-14/9-6/5-9/5-7/5
| 1–14/9–6/5–9/5–7/5
| Sensamagic
| Sensamagic
|
|  
|
|  
|-
|-
| 6
| 6
| 0-2-7-9-11
| 0–2–7–9–11
| 1-14/9-7/6-9/5-7/5
| 1–14/9–7/6–9/5–7/5
| Sensamagic
| Sensamagic
|
|  
|
|  
|-
|-
| 7
| 7
| 0-1-2-10-11
| 0–1–2–10–11
| 1-5/4-14/9-9/8-7/5
| 1–5/4–14/9–9/8–7/5
| Apollo
| Apollo
|
|  
|
|  
|-
|-
| 8
| 8
| 0-1-9-10-11
| 0–1–9–10–11
| 1-5/4-9/5-9/8-7/5
| 1–5/4–9/5–9/8–7/5
| Apollo
| Apollo
|
|  
|
|  
|-
|-
| 9
| 9
| 0-2-9-10-11
| 0–2–9–10–11
| 1-14/9-9/5-9/8-7/5
| 1–14/9–9/5–9/8–7/5
| Magic
| Magic
|
|  
|
|  
|-
|-
| 10
| 10
| 0-1-2-10-12
| 0–1–2–10–12
| 1-5/4-14/9-9/8-7/4
| 1–5/4–14/9–9/8–7/4
| Apollo
| Apollo
|
|  
|
|  
|-
|-
| 11
| 11
| 0-1-5-10-12
| 0–1–5–10–12
| 1-5/4-3/2-9/8-7/4
| 1–5/4–3/2–9/8–7/4
| Otonal
| Otonal
| Cv9(\7)
| Cv9(\7)
|
|  
|-
|-
| 12
| 12
| 0-1-8-10-12
| 0–1–8–10–12
| 1-5/4-16/11-9/8-7/4
| 1–5/4–16/11–9/8–7/4
| Sensamagic11
| Sensamagic11
|
|  
|
|  
|-
|-
| 13
| 13
| 0-1-2-11-12
| 0–1–2–11–12
| 1-5/4-14/9-7/5-7/4
| 1–5/4–14/9–7/5–7/4
| Marvel
| Marvel
|
|  
|
|  
|-
|-
| 14
| 14
| 0-2-4-11-12
| 0–2–4–11–12
| 1-14/9-6/5-7/5-7/4
| 1–14/9–6/5–7/5–7/4
| Sensamagic11
| Sensamagic11
|
|  
|
|  
|-
|-
| 15
| 15
| 0-2-7-11-12
| 0–2–7–11–12
| 1-14/9-7/6-7/5-7/4
| 1–14/9–7/6–7/5–7/4
| Utonal
| Utonal
| C/9(^7)
| C/9(^7)
| 1-9/7-3/2-9/5-9/4
| 1–9/7–3/2–9/5–9/4
|-
|-
| 16
| 16
| 0-1-10-11-12
| 0–1–10–11–12
| 1-5/4-9/8-7/5-7/4
| 1–5/4–9/8–7/5–7/4
| Marvel
| Marvel
|
|  
|
|  
|-
|-
| 17
| 17
| 0-2-10-11-12
| 0–2–10–11–12
| 1-14/9-9/8-7/5-7/4
| 1–14/9–9/8–7/5–7/4
| Apollo
| Apollo
|
|  
|
|  
|-
|-
| 18
| 18
| 0-1-2-9-13
| 0–1–2–9–13
| 1-5/4-14/9-9/5-12/11
| 1–5/4–14/9–9/5–12/11
| Magic
| Magic
|
|  
|
|  
|-
|-
| 19
| 19
| 0-2-4-9-13
| 0–2–4–9–13
| 1-14/9-6/5-9/5-12/11
| 1–14/9–6/5–9/5–12/11
| Octarod
| Octarod
|
|  
|
|  
|-
|-
| 20
| 20
| 0-1-5-9-13
| 0–1–5–9–13
| 1-5/4-3/2-9/5-12/11
| 1–5/4–3/2–9/5–12/11
| Keemic
| Keemic
|
|  
|
|  
|-
|-
| 21
| 21
| 0-4-5-9-13
| 0–4–5–9–13
| 1-6/5-3/2-9/5-12/11
| 1–6/5–3/2–9/5–12/11
| Ptolemismic
| Ptolemismic
|
|  
|
|  
|-
|-
| 22
| 22
| 0-1-8-9-13
| 0–1–8–9–13
| 1-5/4-16/11-9/5-12/11
| 1–5/4–16/11–9/5–12/11
| Keemic
| Keemic
|
|  
|
|  
|-
|-
| 23
| 23
| 0-4-8-9-13
| 0–4–8–9–13
| 1-6/5-16/11-9/5-12/11
| 1–6/5–16/11–9/5–12/11
| Ptolemismic
| Ptolemismic
|
|  
|
|  
|-
|-
| 24
| 24
| 0-1-2-11-13
| 0–1–2–11–13
| 1-5/4-14/9-7/5-12/11
| 1–5/4–14/9–7/5–12/11
| Unimarvel
| Unimarvel
|
|  
|
|  
|-
|-
| 25
| 25
| 0-2-4-11-13
| 0–2–4–11–13
| 1-14/9-6/5-7/5-12/11
| 1–14/9–6/5–7/5–12/11
| Octarod
| Octarod
|
|  
|
|  
|-
|-
| 26
| 26
| 0-1-9-11-13
| 0–1–9–11–13
| 1-5/4-9/5-7/5-12/11
| 1–5/4–9/5–7/5–12/11
| Magic
| Magic
|
|  
|
|  
|-
|-
| 27
| 27
| 0-2-9-11-13
| 0–2–9–11–13
| 1-14/9-9/5-7/5-12/11
| 1–14/9–9/5–7/5–12/11
| Octarod
| Octarod
|
|  
|
|  
|-
|-
| 28
| 28
| 0-4-9-11-13
| 0–4–9–11–13
| 1-6/5-9/5-7/5-12/11
| 1–6/5–9/5–7/5–12/11
| Octarod
| Octarod
|
|  
|
|  
|-
|-
| 29
| 29
| 0-1-2-12-13
| 0–1–2–12–13
| 1-5/4-14/9-7/4-12/11
| 1–5/4–14/9–7/4–12/11
| Unimarvel
| Unimarvel
|
|  
|
|  
|-
|-
| 30
| 30
| 0-2-4-12-13
| 0–2–4–12–13
| 1-14/9-6/5-7/4-12/11
| 1–14/9–6/5–7/4–12/11
| Magic
| Magic
|
|  
|
|  
|-
|-
| 31
| 31
| 0-1-5-12-13
| 0–1–5–12–13
| 1-5/4-3/2-7/4-12/11
| 1–5/4–3/2–7/4–12/11
| Keenanismic
| Keenanismic
|
|  
|
|  
|-
|-
| 32
| 32
| 0-4-5-12-13
| 0–4–5–12–13
| 1-6/5-3/2-7/4-12/11
| 1–6/5–3/2–7/4–12/11
| Keemic
| Keemic
|
|  
|
|  
|-
|-
| 33
| 33
| 0-1-8-12-13
| 0–1–8–12–13
| 1-5/4-16/11-7/4-12/11
| 1–5/4–16/11–7/4–12/11
| Keenanismic
| Keenanismic
|
|  
|
|  
|-
|-
| 34
| 34
| 0-4-8-12-13
| 0–4–8–12–13
| 1-6/5-16/11-7/4-12/11
| 1–6/5–16/11–7/4–12/11
| Keemic
| Keemic
|
|  
|
|  
|-
|-
| 35
| 35
| 0-1-11-12-13
| 0–1–11–12–13
| 1-5/4-7/5-7/4-12/11
| 1–5/4–7/5–7/4–12/11
| Unimarvel
| Unimarvel
|
|  
|
|  
|-
|-
| 36
| 36
| 0-2-11-12-13
| 0–2–11–12–13
| 1-14/9-7/5-7/4-12/11
| 1–14/9–7/5–7/4–12/11
| Unimarvel
| Unimarvel
|
|  
|
|  
|-
|-
| 37
| 37
| 0-4-11-12-13
| 0–4–11–12–13
| 1-6/5-7/5-7/4-12/11
| 1–6/5–7/5–7/4–12/11
| Magic
| Magic
|
|  
|
|  
|-
|-
| 38
| 38
| 0-5-7-9-18
| 0–5–7–9–18
| 1-3/2-7/6-9/5-18/11
| 1–3/2–7/6–9/5–18/11
| Octarod
| Octarod
|
|  
|
|  
|-
|-
| 39
| 39
| 0-7-8-9-18
| 0–7–8–9–18
| 1-7/6-16/11-9/5-18/11
| 1–7/6–16/11–9/5–18/11
| Magic
| Magic
|
|  
|
|  
|-
|-
| 40
| 40
| 0-5-9-10-18
| 0–5–9–10–18
| 1-3/2-9/5-9/8-18/11
| 1–3/2–9/5–9/8–18/11
| Utonal
| Utonal
|
|  
|
|  
|-
|-
| 41
| 41
| 0-8-9-10-18
| 0–8–9–10–18
| 1-16/11-9/5-9/8-18/11
| 1–16/11–9/5–9/8–18/11
| Apollo
| Apollo
|
|  
|
|  
|-
|-
| 42
| 42
| 0-7-9-11-18
| 0–7–9–11–18
| 1-7/6-9/5-7/5-18/11
| 1–7/6–9/5–7/5–18/11
| Octarod
| Octarod
|
|  
|
|  
|-
|-
| 43
| 43
| 0-9-10-11-18
| 0–9–10–11–18
| 1-9/5-9/8-7/5-18/11
| 1–9/5–9/8–7/5–18/11
| Magic
| Magic
|
|  
|
|  
|-
|-
| 44
| 44
| 0-5-9-13-18
| 0–5–9–13–18
| 1-3/2-9/5-12/11-18/11
| 1–3/2–9/5–12/11–18/11
| Ptolemismic
| Ptolemismic
|
|  
|
|  
|-
|-
| 45
| 45
| 0-8-9-13-18
| 0–8–9–13–18
| 1-16/11-20/11-12/11-18/11
| 1–16/11–20/11–12/11–18/11
| Otonal
| Otonal
|
|  
|
|  
|-
|-
| 46
| 46
| 0-9-11-13-18
| 0–9–11–13–18
| 1-9/5-7/5-12/11-18/11
| 1–9/5–7/5–12/11–18/11
| Octarod
| Octarod
|
|  
|
|  
|-
|-
| 47
| 47
| 0-2-7-9-20
| 0–2–7–9–20
| 1-14/9-7/6-9/5-14/11
| 1–14/9–7/6–9/5–14/11
| Octarod
| Octarod
|
|  
|
|  
|-
|-
| 48
| 48
| 0-7-8-9-20
| 0–7–8–9–20
| 1-7/6-16/11-9/5-14/11
| 1–7/6–16/11–9/5–14/11
| Magic
| Magic
|
|  
|
|  
|-
|-
| 49
| 49
| 0-2-9-10-20
| 0–2–9–10–20
| 1-14/9-9/5-9/8-14/11
| 1–14/9–9/5–9/8–14/11
| Magic
| Magic
|
|  
|
|  
|-
|-
| 50
| 50
| 0-8-9-10-20
| 0–8–9–10–20
| 1-16/11-9/5-9/8-14/11
| 1–16/11–9/5–9/8–14/11
| Apollo
| Apollo
|
|  
|
|  
|-
|-
| 51
| 51
| 0-2-7-11-20
| 0–2–7–11–20
| 1-14/9-7/6-7/5-14/11
| 1–14/9–7/6–7/5–14/11
| Utonal
| Utonal
|
|  
|
|  
|-
|-
| 52
| 52
| 0-2-9-11-20
| 0–2–9–11–20
| 1-14/9-9/5-7/5-14/11
| 1–14/9–9/5–7/5–14/11
| Octarod
| Octarod
|
|  
|
|  
|-
|-
| 53
| 53
| 0-7-9-11-20
| 0–7–9–11–20
| 1-7/6-9/5-7/5-14/11
| 1–7/6–9/5–7/5–14/11
| Octarod
| Octarod
|
|  
|
|  
|-
|-
| 54
| 54
| 0-2-10-11-20
| 0–2–10–11–20
| 1-14/9-9/8-7/5-14/11
| 1–14/9–9/8–7/5–14/11
| Apollo
| Apollo
|
|  
|
|  
|-
|-
| 55
| 55
| 0-9-10-11-20
| 0–9–10–11–20
| 1-9/5-9/8-7/5-14/11
| 1–9/5–9/8–7/5–14/11
| Apollo
| Apollo
|
|  
|
|  
|-
|-
| 56
| 56
| 0-2-7-12-20
| 0–2–7–12–20
| 1-14/9-7/6-7/4-14/11
| 1–14/9–7/6–7/4–14/11
| Utonal
| Utonal
|
|  
|
|  
|-
|-
| 57
| 57
| 0-7-8-12-20
| 0–7–8–12–20
| 1-7/6-16/11-7/4-14/11
| 1–7/6–16/11–7/4–14/11
| Keenanismic
| Keenanismic
|
|  
|
|  
|-
|-
| 58
| 58
| 0-2-10-12-20
| 0–2–10–12–20
| 1-14/9-9/8-7/4-14/11
| 1–14/9–9/8–7/4–14/11
| Pentacircle
| Pentacircle
|
|  
|
|  
|-
|-
| 59
| 59
| 0-8-10-12-20
| 0–8–10–12–20
| 1-16/11-9/8-7/4-14/11
| 1–16/11–9/8–7/4–14/11
| Sensamagic11
| Sensamagic11
|
|  
|
|  
|-
|-
| 60
| 60
| 0-2-11-12-20
| 0–2–11–12–20
| 1-14/9-7/5-7/4-14/11
| 1–14/9–7/5–7/4–14/11
| Utonal
| Utonal
|
|  
|
|  
|-
|-
| 61
| 61
| 0-7-11-12-20
| 0–7–11–12–20
| 1-7/6-7/5-7/4-14/11
| 1–7/6–7/5–7/4–14/11
| Utonal
| Utonal
|
|  
|
|  
|-
|-
| 62
| 62
| 0-10-11-12-20
| 0–10–11–12–20
| 1-9/8-7/5-7/4-14/11
| 1–9/8–7/5–7/4–14/11
| Apollo
| Apollo
|
|  
|
|  
|-
|-
| 63
| 63
| 0-2-9-13-20
| 0–2–9–13–20
| 1-14/9-9/5-12/11-14/11
| 1–14/9–9/5–12/11–14/11
| Octarod
| Octarod
|
|  
|
|  
|-
|-
| 64
| 64
| 0-8-9-13-20
| 0–8–9–13–20
| 1-16/11-20/11-12/11-14/11
| 1–16/11–20/11–12/11–14/11
| Otonal
| Otonal
|
|  
|
|  
|-
|-
| 65
| 65
| 0-2-11-13-20
| 0–2–11–13–20
| 1-14/9-7/5-12/11-14/11
| 1–14/9–7/5–12/11–14/11
| Octarod
| Octarod
|
|  
|
|  
|-
|-
| 66
| 66
| 0-9-11-13-20
| 0–9–11–13–20
| 1-9/5-7/5-12/11-14/11
| 1–9/5–7/5–12/11–14/11
| Octarod
| Octarod
|
|  
|
|  
|-
|-
| 67
| 67
| 0-2-12-13-20
| 0–2–12–13–20
| 1-14/9-7/4-12/11-14/11
| 1–14/9–7/4–12/11–14/11
| Unimarvel
| Unimarvel
|
|  
|
|  
|-
|-
| 68
| 68
| 0-8-12-13-20
| 0–8–12–13–20
| 1-16/11-7/4-12/11-14/11
| 1–16/11–7/4–12/11–14/11
| Keenanismic
| Keenanismic
|
|  
|
|  
|-
|-
| 69
| 69
| 0-11-12-13-20
| 0–11–12–13–20
| 1-7/5-7/4-12/11-14/11
| 1–7/5–7/4–12/11–14/11
| Magic
| Magic
|
|  
|
|  
|-
|-
| 70
| 70
| 0-7-8-18-20
| 0–7–8–18–20
| 1-7/6-16/11-18/11-14/11
| 1–7/6–16/11–18/11–14/11
| Unimarvel
| Unimarvel
|
|  
|
|  
|-
|-
| 71
| 71
| 0-7-9-18-20
| 0–7–9–18–20
| 1-7/6-9/5-18/11-14/11
| 1–7/6–9/5–18/11–14/11
| Octarod
| Octarod
|
|  
|
|  
|-
|-
| 72
| 72
| 0-8-9-18-20
| 0–8–9–18–20
| 1-16/11-20/11-18/11-14/11
| 1–16/11–20/11–18/11–14/11
| Otonal
| Otonal
|
|  
|
|  
|-
|-
| 73
| 73
| 0-8-10-18-20
| 0–8–10–18–20
| 1-16/11-9/8-18/11-14/11
| 1–16/11–9/8–18/11–14/11
| Pentacircle
| Pentacircle
|
|  
|
|  
|-
|-
| 74
| 74
| 0-9-10-18-20
| 0–9–10–18–20
| 1-9/5-9/8-18/11-14/11
| 1–9/5–9/8–18/11–14/11
| Apollo
| Apollo
|
|  
|
|  
|-
|-
| 75
| 75
| 0-7-11-18-20
| 0–7–11–18–20
| 1-7/6-7/5-18/11-14/11
| 1–7/6–7/5–18/11–14/11
| Octarod
| Octarod
|
|  
|
|  
|-
|-
| 76
| 76
| 0-9-11-18-20
| 0–9–11–18–20
| 1-9/5-7/5-18/11-14/11
| 1–9/5–7/5–18/11–14/11
| Octarod
| Octarod
|
|  
|
|  
|-
|-
| 77
| 77
| 0-10-11-18-20
| 0–10–11–18–20
| 1-9/8-7/5-18/11-14/11
| 1–9/8–7/5–18/11–14/11
| Magic
| Magic
|
|  
|
|  
|-
|-
| 78
| 78
| 0-8-13-18-20
| 0–8–13–18–20
| 1-16/11-12/11-18/11-14/11
| 1–16/11–12/11–18/11–14/11
| Otonal
| Otonal
|
|  
|
|  
|-
|-
| 79
| 79
| 0-9-13-18-20
| 0–9–13–18–20
| 1-20/11-12/11-18/11-14/11
| 1–20/11–12/11–18/11–14/11
| Otonal
| Otonal
|
|  
|
|  
|-
|-
| 80
| 80
| 0-11-13-18-20
| 0–11–13–18–20
| 1-7/5-12/11-18/11-14/11
| 1–7/5–12/11–18/11–14/11
| 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
| 1–5/4–14/9–9/5–9/8–7/5
| 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
| 1–5/4–14/9–9/8–7/5–7/4
| 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
| 1–5/4–14/9–9/5–7/5–12/11
| 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
| 1–14/9–6/5–9/5–7/5–12/11
| 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
| 1–5/4–14/9–7/5–7/4–12/11
| Unimarvel
| Unimarvel
|
|-
|-
| 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
| 1–14/9–6/5–7/5–7/4–12/11
| 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
| 1–14/9–7/6–9/5–7/5–14/11
| 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
| 1–14/9–9/5–9/8–7/5–14/11
| 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
| 1–14/9–7/6–7/5–7/4–14/11
| Utonal
| Utonal
|
|-
|-
| 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
| 1–14/9–9/8–7/5–7/4–14/11
| 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
| 1–14/9–9/5–7/5–12/11–14/11
| 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
| 1–14/9–7/5–7/4–12/11–14/11
| 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
| 1–7/6–16/11–9/5–18/11–14/11
| 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
| 1–16/11–9/5–9/8–18/11–14/11
| 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
| 1–7/6–9/5–7/5–18/11–14/11
| 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
| 1–9/5–9/8–7/5–18/11–14/11
| 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
| 1–16/11–20/11–12/11–18/11–14/11
| Otonal
| Otonal
|
|-
|-
| 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
| 1–9/5–7/5–12/11–18/11–14/11
| Octarod
| Octarod
|
|}
|}


Revision as of 11:41, 3 February 2026

Below are listed the 11-odd-limit 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 keemic. 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.

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 list of pergens. One up is 19 generators, octave-reduced. The generator is vM3 = 380 ¢ + c/5, where c is the amount in cents the tempered fifth exceeds 700 ¢. The enharmonic unison is ^5dd2, thus ^5C = Bx. 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, so /C = ^^Dbb, \C = vvB#, ^^C = /B#, and 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.

Cents values of magic accidentals in various tunings
Sharp Up Lift How to convert the notation to the 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 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.

Magic's genchain
Genspan 0 1 2 3 4 5 6 7 8 9 10 11 12 13 … 18 … 20
Cents (41edo) 0 380 761 1141 322 702 1083 263 644 1024 205 585 966 146 … 849 … 410
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 … 18/11 … 14/11
Interval P1 vM3 vvA5
\m6 		^^d8
/M7 		^m3 P5 vM7 vvA2
\m3 		^^d5
/A4 		^m7 M2 vA4
^\d5 		vvA6
\m7 		^^m2
/A1 		… ^^m6
/A5 		… M3
Note (in C) C vE vvG#
\Ab 		^^Cb
/B 		^Eb G vB vvD#
\Eb 		^^Gb
/F# 		^Bb D vF#
^\Gb 		vvA#
\Bb 		^^Db
/C# 		… ^^Ab
/G# 		… E
Todo: complete table

Triads

# Generators Transversal Type Kite's name Comments
1 0–1–2 1–5/4–14/9 Marvel Cv(vv#5)
2 0–2–4 1–14/9–6/5 Sensamagic C^m(vv#5)
3 0–1–5 1–5/4–3/2 Otonal Cv
4 0–4–5 1–6/5–3/2 Utonal C^m
5 0–2–7 1–14/9–7/6 Utonal C/ 1–9/7–3/2
6 0–5–7 1–3/2–7/6 Otonal C\m
7 0–1–8 1–5/4–16/11 Keenanismic Cv(^^b5)
8 0–4–8 1–6/5–16/11 Ptolemismic C^m(^^b5)
9 0–7–8 1–7/6–16/11 Keenanismic C\m(^^b5)
10 0–1–9 1–5/4–20/11 Utonal Cv^7no5
11 0–2–9 1–14/9–9/5 Sensamagic C^m7(vv#5)no3
12 0–4–9 1–6/5–9/5 Otonal C^m7no5 or 1–3/2–5/3 = Cv6no3
13 0–5–9 1–3/2–9/5 Utonal C^m7no3
14 0–7–9 1–7/6–9/5 Sensamagic C\mv7no5
15 0–8–9 1–16/11–20/11 Otonal Cv(\b5) 1–5/4–11/8
16 0–1–10 1–5/4–9/8 Otonal Cv,9no5
17 0–2–10 1–14/9–9/8 Pentacircle C2(vv#5)
18 0–5–10 1–3/2–9/8 Ambitonal C2
19 0–8–10 1–16/11–9/8 Pentacircle C2(^^b5)
20 0–9–10 1–9/5–9/8 Utonal C^9no35 or C^7sus2no5
21 0–1–11 1–5/4–7/5 Marvel Cv(^\b5)
22 0–2–11 1–14/9–7/5 Utonal C/,^7no5 1–9/7–9/5
23 0–4–11 1–6/5–7/5 Otonal C^m(^\b5)
24 0–7–11 1–7/6–7/5 Utonal C\m(^\b5)
25 0–9–11 1–9/5–7/5 Otonal C/(^b5) 1–9/7–10/7
26 0–10–11 1–9/8–7/5 Marvel Cv,7no5 1–5/4–16/9
27 0–1–12 1–5/4–7/4 Otonal Cv,\7no5
28 0–2–12 1–14/9–7/4 Utonal C/,9no5 1–9/8–9/7
29 0–4–12 1–6/5–7/4 Keenanismic C^m\7
30 0–5–12 1–3/2–7/4 Otonal C\7no3
31 0–7–12 1–7/6–7/4 Utonal C\m7no5
32 0–8–12 1–16/11–7/4 Keenanismic C^m(\b5) 1–6/5–11/8
33 0–10–12 1–9/8–7/4 Otonal C\7sus2
34 0–11–12 1–7/5–7/4 Utonal C\7(^\b5)no3
35 0–1–13 1–5/4–12/11 Keenanismic
36 0–2–13 1–14/9–12/11 Swetismic C/(^\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 C^^b2
39 0–8–13 1–16/11–12/11 Otonal Cvv#4 1–11/8–3/2
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

# Generators Transversal Type Kite's name Comments
1 0–1–2–9 1–5/4–14/9–9/5 Magic Cv^7(vv#5)
2 0–2–4–9 1–14/9–6/5–9/5 Sensamagic C^m7(vv#5)
3 0–1–5–9 1–5/4–3/2–9/5 Ptolemismic Cv^7
4 0–4–5–9 1–6/5–3/2–9/5 Ambitonal C^m7 or 1–5/4–3/2–5/3 = Cv6
5 0–2–7–9 1–14/9–7/6–9/5 Sensamagic C/,vv#9 1–9/7–3/2–7/3
6 0–5–7–9 1–3/2–7/6–9/5 Sensamagic C\m^7
7 0–1–8–9 1–5/4–16/11–9/5 Keemic Cv^7(^^b5)
8 0–4–8–9 1–6/5–16/11–9/5 Ptolemismic C^m7(^^b5)
9 0–7–8–9 1–7/6–16/11–9/5 Magic C\m^7(^^b5)
10 0–1–2–10 1–5/4–14/9–9/8 Apollo Cv,9(vv#5)
11 0–1–5–10 1–5/4–3/2–9/8 Otonal Cv,9
12 0–1–8–10 1–5/4–16/11–9/8 Sensamagic11 Cv,9(^^b5)
13 0–1–9–10 1–5/4–9/5–9/8 Ptolemismic Cv^7,9no5 or Cv9(^7)no5
14 0–2–9–10 1–14/9–9/5–9/8 Sensamagic11 C^9(vv#5)no3 or C^7(vv#5)sus2
15 0–5–9–10 1–3/2–9/5–9/8 Utonal C^9no3 or C^7sus2 or C2,^7
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 C^m7(^\b5) or 1–7/6–3/2–5/3 = C\mv6
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 Cv,\7
30 0–4–5–12 1–6/5–3/2–7/4 Keenanismic C^m\7
31 0–2–7–12 1–14/9–7/6–7/4 Utonal C\m7(vv#5)
32 0–5–7–12 1–3/2–7/6–7/4 Ambitonal C\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 Keemic
35 0–7–8–12 1–7/6–16/11–7/4 Keenanismic C\m7(^^b5)
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 C2\7 or C\7sus2 or C\9no3
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 C\m7(^\b5) or 1–6/5–3/2–12/7 = C^m/6
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 Keemic
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 Keemic
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

# Generators Transversal Type Kite's name Comments
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 Cv9(^7)
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 Cv9(\7)
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 C/9(^7) 1–9/7–3/2–9/5–9/4
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 Keemic
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 Keemic
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 Keemic
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 Keemic
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

# Generators Transversal Type Comment
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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