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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
|
|}
|}


Retrieved from "https://en.xen.wiki/w/Chords_of_magic"