Chords of magic: Difference between revisions

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Below are listed the [[11-odd-limit]] [[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 [[keemic chords|keemic]]. 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]].
 
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.


[[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.
[[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.
Line 161: Line 164:
! Transversal
! Transversal
! Type
! Type
! Comments
! Kite's name
! Kite's name
! Comments
|-
|-
| 1
| 1
Line 168: Line 171:
| 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
| 1–6/5–14/9
| Sensamagic
| Sensamagic
|
| C^m(vv#5)
| C^m(vv#5)
|
|-
|-
| 3
| 3
Line 182: Line 185:
| 1–5/4–3/2
| 1–5/4–3/2
| Otonal
| Otonal
| [[4:5:6]]
| Cv
| Cv
|
|-
|-
| 4
| 4
Line 189: Line 192:
| 1–6/5–3/2
| 1–6/5–3/2
| Utonal
| Utonal
| [[10:12:15|1/(6:5:4)]]
| C^m
| 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)]]
| C/
| C/
| 1–9/7–3/2
|-
|-
| 6
| 6
| 0–5–7
| 0–5–7
| 1–3/2–7/6
| 1–7/6–3/2
| Otonal
| Otonal
| [[6:7:9]]
| C\m
| C\m
|
|-
|-
| 7
| 7
Line 210: Line 213:
| 1–5/4–16/11
| 1–5/4–16/11
| Keenanismic
| Keenanismic
|
| Cv(^^b5)
| Cv(^^b5)
|
|-
|-
| 8
| 8
Line 217: Line 220:
| 1–6/5–16/11
| 1–6/5–16/11
| Ptolemismic
| Ptolemismic
|
| C^m(^^b5)
| C^m(^^b5)
|
|-
|-
| 9
| 9
Line 224: Line 227:
| 1–7/6–16/11
| 1–7/6–16/11
| Keenanismic
| Keenanismic
|
| C\m(^^b5)
| C\m(^^b5)
|
|-
|-
| 10
| 10
Line 231: Line 234:
| 1–5/4–20/11
| 1–5/4–20/11
| Utonal
| Utonal
|
| Cv^7no5
| Cv^7no5
|
|-
|-
| 11
| 11
Line 238: Line 241:
| 1–14/9–9/5
| 1–14/9–9/5
| Sensamagic
| Sensamagic
|
| C^m7(vv#5)no3
| C^m7(vv#5)no3
|
|-
|-
| 12
| 12
Line 245: Line 248:
| 1–6/5–9/5
| 1–6/5–9/5
| Otonal
| Otonal
| C^m7no5
| [[6:9:10]]
| ''or'' 1–3/2–5/3 = Cv6no3
| C^m7no5 ''or'' Cv6no3
|-
|-
| 13
| 13
Line 252: Line 255:
| 1–3/2–9/5
| 1–3/2–9/5
| Utonal
| Utonal
| [[10:15:18|1/(9:6:5)]]
| C^m7no3
| C^m7no3
|
|-
|-
| 14
| 14
Line 259: Line 262:
| 1–7/6–9/5
| 1–7/6–9/5
| Sensamagic
| Sensamagic
|
| C\mv7no5
| C\mv7no5
|
|-
|-
| 15
| 15
Line 266: Line 269:
| 1–16/11–20/11
| 1–16/11–20/11
| Otonal
| Otonal
| 1–5/4–11/8
| Cv(\b5)
| Cv(\b5)
| 1–5/4–11/8
|-
|-
| 16
| 16
| 0–1–10
| 0–1–10
| 1–5/4–9/8
| 1–9/8–5/4
| Otonal
| Otonal
|
| Cv,9no5
| Cv,9no5
|
|-
|-
| 17
| 17
| 0–2–10
| 0–2–10
| 1–14/9–9/8
| 1–9/8–14/9
| Pentacircle
| Pentacircle
|
| C2(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
| [[6:8:9]], [[8:9:12]]
| C2
| C2
|
|-
|-
| 19
| 19
| 0–8–10
| 0–8–10
| 1–16/11–9/8
| 1–9/8–16/11
| Pentacircle
| Pentacircle
|
| C2(^^b5)
| C2(^^b5)
|
|-
|-
| 20
| 20
| 0–9–10
| 0–9–10
| 1–9/5–9/8
| 1–9/8–9/5
| Utonal
| Utonal
| C^9no35
|
| ''or'' C^7sus2no5
| C^9no35 ''or'' C^7sus2no5
|-
|-
| 21
| 21
Line 308: Line 311:
| 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
| 1–7/5–14/9
| Utonal
| Utonal
| 1–9/7–9/5
| C/,^7no5
| C/,^7no5
| 1–9/7–9/5
|-
|-
| 23
| 23
Line 322: Line 325:
| 1–6/5–7/5
| 1–6/5–7/5
| Otonal
| Otonal
| [[5:6:7]]
| C^m(^\b5)
| C^m(^\b5)
|
|-
|-
| 24
| 24
Line 329: Line 332:
| 1–7/6–7/5
| 1–7/6–7/5
| Utonal
| Utonal
| [[30:35:42|1/(7:6:5)]]
| C\m(^\b5)
| C\m(^\b5)
|
|-
|-
| 25
| 25
| 0–9–11
| 0–9–11
| 1–9/5–7/5
| 1–7/5–9/5
| Otonal
| Otonal
| 1–9/7–10/7
| C/(^b5)
| C/(^b5)
| 1–9/7–10/7
|-
|-
| 26
| 26
Line 343: Line 346:
| 1–9/8–7/5
| 1–9/8–7/5
| Marvel
| Marvel
| 1–5/4–16/9
| Cv,7no5
| Cv,7no5
| 1–5/4–16/9
|-
|-
| 27
| 27
Line 350: Line 353:
| 1–5/4–7/4
| 1–5/4–7/4
| Otonal
| Otonal
| [[4:5:7]]
| Cv,\7no5
| Cv,\7no5
|
|-
|-
| 28
| 28
Line 357: Line 360:
| 1–14/9–7/4
| 1–14/9–7/4
| Utonal
| Utonal
| 1–9/8–9/7
| C/,9no5
| C/,9no5
| 1–9/8–9/7
|-
|-
| 29
| 29
Line 364: Line 367:
| 1–6/5–7/4
| 1–6/5–7/4
| Keenanismic
| Keenanismic
|
| C^m\7
| C^m\7
|
|-
|-
| 30
| 30
Line 371: Line 374:
| 1–3/2–7/4
| 1–3/2–7/4
| Otonal
| Otonal
| [[4:6:7]]
| C\7no3
| C\7no3
|
|-
|-
| 31
| 31
Line 378: Line 381:
| 1–7/6–7/4
| 1–7/6–7/4
| Utonal
| Utonal
| [[14:18:21|1/(12:8:7)]]
| C\m7no5
| C\m7no5
|
|-
|-
| 32
| 32
Line 385: Line 388:
| 1–16/11–7/4
| 1–16/11–7/4
| Keenanismic
| Keenanismic
| 1–6/5–11/8
| C^m(\b5)
| C^m(\b5)
| 1–6/5–11/8
|-
|-
| 33
| 33
Line 392: Line 395:
| 1–9/8–7/4
| 1–9/8–7/4
| Otonal
| Otonal
|
| C\7sus2
| C\7sus2
|
|-
|-
| 34
| 34
Line 399: Line 402:
| 1–7/5–7/4
| 1–7/5–7/4
| Utonal
| Utonal
| [[28:35:40|1/(10:8:7)]]
| C\7(^\b5)no3
| C\7(^\b5)no3
|
|-
|-
| 35
| 35
| 0–1–13
| 0–1–13
| 1–5/4–12/11
| 1–12/11–5/4
| Keenanismic
| Keenanismic
|  
|  
Line 411: Line 414:
| 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
| C/(^\b5)
| C/(^\b5)
| 1–9/7–7/5
|-
|-
| 37
| 37
| 0–4–13
| 0–4–13
| 1–6/5–12/11
| 1–12/11–6/5
| Utonal
| Utonal
|  
|  
Line 425: Line 428:
| 38
| 38
| 0–5–13
| 0–5–13
| 1–3/2–12/11
| 1–12/11–3/2
| Utonal
| Utonal
|
| C^^b2
| 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
| Cvv#4
| 1–11/8–3/2
|-
|-
| 40
| 40
| 0–9–13
| 0–9–13
| 1–20/11–12/11
| 1–12/11–20/11
| Otonal
| Otonal
|  
|  
Line 446: Line 449:
| 41
| 41
| 0–11–13
| 0–11–13
| 1–7/5–12/11
| 1–12/11–7/5
| Swetismic
| Swetismic
|  
|  
Line 453: Line 456:
| 42
| 42
| 0–12–13
| 0–12–13
| 1–7/4–12/11
| 1–12/11–7/4
| Keenanismic
| Keenanismic
|  
|  
Line 481: Line 484:
| 46
| 46
| 0–9–18
| 0–9–18
| 1–9/5–18/11
| 1–18/11–9/5
| Utonal
| Utonal
|  
|  
Line 509: Line 512:
| 50
| 50
| 0–2–20
| 0–2–20
| 1–14/9–14/11
| 1–14/11–14/9
| Utonal
| Utonal
|  
|  
Line 523: Line 526:
| 52
| 52
| 0–8–20
| 0–8–20
| 1–16/11–14/11
| 1–14/11–16/11
| Otonal
| Otonal
|  
|  
Line 530: Line 533:
| 53
| 53
| 0–9–20
| 0–9–20
| 1–20/11–14/11
| 1–14/11–20/11
| Otonal
| Otonal
|  
|  
Line 544: Line 547:
| 55
| 55
| 0–11–20
| 0–11–20
| 1–7/5–14/11
| 1–14/11–7/5
| Utonal
| Utonal
|  
|  
Line 551: Line 554:
| 56
| 56
| 0–12–20
| 0–12–20
| 1–7/4–14/11
| 1–14/11–7/4
| Utonal
| Utonal
|  
|  
Line 565: Line 568:
| 58
| 58
| 0–18–20
| 0–18–20
| 1–18/11–14/11
| 1–14/11–18/11
| Otonal
| Otonal
|  
|  
Line 578: Line 581:
! Transversal
! Transversal
! Type
! Type
! Comments
! Kite's name
! Kite's name
! Comments
|-
|-
| 1
| 1
Line 585: Line 588:
| 1–5/4–14/9–9/5
| 1–5/4–14/9–9/5
| Magic
| Magic
|
| Cv^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
|
| C^m7(vv#5)
| C^m7(vv#5)
|
|-
|-
| 3
| 3
Line 599: Line 602:
| 1–5/4–3/2–9/5
| 1–5/4–3/2–9/5
| Ptolemismic
| Ptolemismic
|
| Cv^7
| Cv^7
|
|-
|-
| 4
| 4
Line 606: Line 609:
| 1–6/5–3/2–9/5
| 1–6/5–3/2–9/5
| Ambitonal
| Ambitonal
| C^m7
| [[10:12:15:18]], [[12:15:18:20]]<br>[[9-odd-limit]] [[ASS]]
| ''or'' 1–5/4–3/2–5/3 = Cv6
| 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
| 1–9/7–3/2–7/3
| C/,vv#9
| C/,vv#9
| 1–9/7–3/2–7/3
|-
|-
| 6
| 6
| 0–5–7–9
| 0–5–7–9
| 1–3/2–7/6–9/5
| 1–7/6–3/2–9/5
| Sensamagic
| Sensamagic
|
| C\m^7
| C\m^7
|
|-
|-
| 7
| 7
Line 627: Line 630:
| 1–5/4–16/11–9/5
| 1–5/4–16/11–9/5
| Keemic
| Keemic
|
| Cv^7(^^b5)
| Cv^7(^^b5)
|
|-
|-
| 8
| 8
Line 634: Line 637:
| 1–6/5–16/11–9/5
| 1–6/5–16/11–9/5
| Ptolemismic
| Ptolemismic
|
| C^m7(^^b5)
| C^m7(^^b5)
|
|-
|-
| 9
| 9
Line 641: Line 644:
| 1–7/6–16/11–9/5
| 1–7/6–16/11–9/5
| Magic
| Magic
|
| C\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
|
| Cv,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
| [[4:5:6:9]]
| Cv,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
|
| Cv,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
| Cv^7,9no5
|
| <u>or</u> Cv9(^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
| C^9(vv#5)no3
|
| ''or'' C^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
| C^9no3
| [[20:30:36:45|1/(9:6:5:4)]]
| ''or'' C^7sus2 <u>or</u> C2,^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 695: Line 698:
| 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 702: Line 705:
| 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 709: Line 712:
| 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 723: Line 726:
| 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 730: Line 733:
| 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
| C^m7(^\b5)
| [[6:7:9:10]]
| ''or'' 1–7/6–3/2–5/3 = C\mv6
| 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 744: Line 747:
| 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 751: Line 754:
| 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 758: Line 761:
| 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 772: Line 775:
| 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 781: Line 784:
| 1–5/4–3/2–7/4
| 1–5/4–3/2–7/4
| Otonal
| Otonal
| [[4:5:6:7]]
| Cv,\7
| Cv,\7
|
|-
|-
| 30
| 30
Line 788: Line 791:
| 1–6/5–3/2–7/4
| 1–6/5–3/2–7/4
| Keenanismic
| Keenanismic
|
| C^m\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
|
| C\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
| [[12:14:18:21]], [[14:18:21:24]]<br>9-odd-limit ASS
| C\m7
| C\m7
|
|-
|-
| 33
| 33
Line 823: Line 826:
| 1–7/6–16/11–7/4
| 1–7/6–16/11–7/4
| Keenanismic
| Keenanismic
|
| C\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 842: Line 845:
| 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
| C2\7
| [[4:6:7:9]]
| ''or'' C\7sus2 ''or'' C\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 863: Line 866:
| 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)]]
|  
|  
|-
|-
Line 879: Line 882:
| 1–7/6–7/5–7/4
| 1–7/6–7/5–7/4
| Utonal
| Utonal
| C\m7(^\b5)
| [[70:84:105:120|1/(12:10:8:7)]]
| ''or'' 1–6/5–3/2–12/7 = C^m/6
| C\m7(^\b5) ''or'' C^m/6
|-
|-
| 44
| 44
Line 891: Line 894:
| 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
|  
|  
|  
|  
Line 898: Line 901:
| 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 905: Line 908:
| 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 912: Line 915:
| 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 919: Line 922:
| 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 926: Line 929:
| 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 933: Line 936:
| 51
| 51
| 0–1–9–13
| 0–1–9–13
| 1–5/4–9/5–12/11
| 1–12/11–5/4–9/5
| Keemic
| Keemic
|  
|  
Line 940: Line 943:
| 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 947: Line 950:
| 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 954: Line 957:
| 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 961: Line 964:
| 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 968: Line 971:
| 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
|  
|  
|  
|  
Line 975: Line 978:
| 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 982: Line 985:
| 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 989: Line 992:
| 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 996: Line 999:
| 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 1,003: Line 1,006:
| 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
|  
|  
|  
|  
Line 1,010: Line 1,013:
| 62
| 62
| 0–4–12–13
| 0–4–12–13
| 1–6/5–7/4–12/11
| 1–12/11–6/5–7/4
| Keemic
| Keemic
|  
|  
Line 1,017: Line 1,020:
| 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 1,024: Line 1,027:
| 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 1,031: Line 1,034:
| 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
|  
|  
|  
|  
Line 1,038: Line 1,041:
| 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 1,046: Line 1,049:
| 0–7–8–18
| 0–7–8–18
| 1–7/6–16/11–18/11
| 1–7/6–16/11–18/11
| Unimarvel
| Marvel11
|  
|  
|  
|  
Line 1,052: Line 1,055:
| 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 1,059: Line 1,062:
| 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 1,066: Line 1,069:
| 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 1,073: Line 1,076:
| 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 1,080: Line 1,083:
| 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 1,087: Line 1,090:
| 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 1,101: Line 1,104:
| 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 1,109: Line 1,112:
| 0–10–11–18
| 0–10–11–18
| 1–9/8–7/5–18/11
| 1–9/8–7/5–18/11
| Unimarvel
| Marvel11
|  
|  
|  
|  
Line 1,115: Line 1,118:
| 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 1,122: Line 1,125:
| 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 1,129: Line 1,132:
| 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 1,136: Line 1,139:
| 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 1,143: Line 1,146:
| 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 1,150: Line 1,153:
| 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 1,157: Line 1,160:
| 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 1,164: Line 1,167:
| 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 1,171: Line 1,174:
| 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 1,178: Line 1,181:
| 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 1,185: Line 1,188:
| 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 1,192: Line 1,195:
| 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 1,199: Line 1,202:
| 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 1,206: Line 1,209:
| 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 1,213: Line 1,216:
| 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 1,220: Line 1,223:
| 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 1,227: Line 1,230:
| 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 1,234: Line 1,237:
| 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 1,241: Line 1,244:
| 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 1,248: Line 1,251:
| 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 1,255: Line 1,258:
| 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 1,262: Line 1,265:
| 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 1,269: Line 1,272:
| 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 1,276: Line 1,279:
| 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 1,283: Line 1,286:
| 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 1,290: Line 1,293:
| 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 1,297: Line 1,300:
| 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 1,304: Line 1,307:
| 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 1,311: Line 1,314:
| 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 1,318: Line 1,321:
| 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 1,325: Line 1,328:
| 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 1,332: Line 1,335:
| 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 1,342: Line 1,345:
|-
|-
! #
! #
! Generators
! Generators
! Transversal
! Transversal
! Type
! Type
! Kite's name
! Comments
! 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
| 0–1–5–9–10
| 1–9/8–5/4–3/2–9/5
| Ptolemismic
|  
|  
|-
| 2
| 0–1–5–9–10
| 1–5/4–3/2–9/5–9/8
| 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
| 1–9/8–5/4–16/11–9/5
| Magic
| Magic
|  
|  
Line 1,371: Line 1,374:
| 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
|  
|  
Line 1,378: Line 1,381:
| 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
|  
|  
Line 1,385: Line 1,388:
| 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
|  
|  
Line 1,392: Line 1,395:
| 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
|  
|  
Line 1,399: Line 1,402:
| 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
|  
|  
Line 1,406: Line 1,409:
| 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
|  
|  
Line 1,413: Line 1,416:
| 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
|  
|  
Line 1,420: Line 1,423:
| 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)
| 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
|  
|  
Line 1,434: Line 1,437:
| 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
|  
|  
Line 1,441: Line 1,444:
| 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
|  
|  
Line 1,448: Line 1,451:
| 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)
| C/9(^7)
| 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
| 1–9/8–5/4–7/5–7/4
| Marvel
| Marvel
|  
|  
Line 1,462: Line 1,465:
| 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
|  
|  
Line 1,469: Line 1,472:
| 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
|  
|  
Line 1,476: Line 1,479:
| 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
|  
|  
Line 1,483: Line 1,486:
| 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
| Keemic
| Keemic
|  
|  
Line 1,490: Line 1,493:
| 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
|  
|  
Line 1,497: Line 1,500:
| 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
| Keemic
| Keemic
|  
|  
Line 1,504: Line 1,507:
| 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
|  
|  
Line 1,511: Line 1,514:
| 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
|  
|  
|  
|  
Line 1,518: Line 1,521:
| 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
|  
|  
Line 1,525: Line 1,528:
| 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
|  
|  
Line 1,532: Line 1,535:
| 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
|  
|  
Line 1,539: Line 1,542:
| 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
|  
|  
Line 1,546: Line 1,549:
| 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
|  
|  
|  
|  
Line 1,553: Line 1,556:
| 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
|  
|  
Line 1,560: Line 1,563:
| 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
|  
|  
Line 1,567: Line 1,570:
| 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
| Keemic
| Keemic
|  
|  
Line 1,574: Line 1,577:
| 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
|  
|  
Line 1,581: Line 1,584:
| 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
| Keemic
| Keemic
|  
|  
Line 1,588: Line 1,591:
| 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
|  
|  
|  
|  
Line 1,595: Line 1,598:
| 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
|  
|  
|  
|  
Line 1,602: Line 1,605:
| 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
|  
|  
Line 1,609: Line 1,612:
| 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
|  
|  
Line 1,616: Line 1,619:
| 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
|  
|  
Line 1,623: Line 1,626:
| 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
|  
|  
Line 1,637: Line 1,640:
| 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
|  
|  
Line 1,644: Line 1,647:
| 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
|  
|  
Line 1,651: Line 1,654:
| 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
|  
|  
Line 1,658: Line 1,661:
| 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
|  
|  
Line 1,672: Line 1,675:
| 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
|  
|  
Line 1,679: Line 1,682:
| 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
|  
|  
Line 1,686: Line 1,689:
| 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
|  
|  
Line 1,693: Line 1,696:
| 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
|  
|  
Line 1,700: Line 1,703:
| 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
|  
|  
Line 1,714: Line 1,717:
| 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
|  
|  
Line 1,721: Line 1,724:
| 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
|  
|  
Line 1,728: Line 1,731:
| 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
|  
|  
Line 1,735: Line 1,738:
| 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
|  
|  
Line 1,749: Line 1,752:
| 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
|  
|  
Line 1,756: Line 1,759:
| 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
|  
|  
Line 1,763: Line 1,766:
| 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
|  
|  
Line 1,784: Line 1,787:
| 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
|  
|  
Line 1,791: Line 1,794:
| 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
|  
|  
Line 1,805: Line 1,808:
| 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
|  
|  
Line 1,812: Line 1,815:
| 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
|  
|  
|  
|  
Line 1,819: Line 1,822:
| 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
|  
|  
Line 1,826: Line 1,829:
| 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
|  
|  
Line 1,833: Line 1,836:
| 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
|  
|  
|  
|  
Line 1,840: Line 1,843:
| 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
|  
|  
Line 1,847: Line 1,850:
| 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
|  
|  
Line 1,861: Line 1,864:
| 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
|  
|  
Line 1,868: Line 1,871:
| 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
|  
|  
Line 1,875: Line 1,878:
| 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
|  
|  
Line 1,882: Line 1,885:
| 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
|  
|  
Line 1,889: Line 1,892:
| 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
|  
|  
Line 1,920: Line 1,923:
| 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
|  
|  
Line 1,926: Line 1,929:
| 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
|  
|  
Line 1,932: Line 1,935:
| 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
|  
|  
Line 1,938: Line 1,941:
| 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
|  
|  
Line 1,944: Line 1,947:
| 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
|  
|  
Line 1,956: Line 1,959:
| 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
|  
|  
Line 1,962: Line 1,965:
| 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
|  
|  
Line 1,968: Line 1,971:
| 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
|  
|  
Line 1,980: Line 1,983:
| 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
|  
|  
Line 1,986: Line 1,989:
| 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
|  
|  
Line 1,992: Line 1,995:
| 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
|  
|  
Line 1,998: Line 2,001:
| 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
|  
|  
Line 2,004: Line 2,007:
| 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
|  
|  
Line 2,010: Line 2,013:
| 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
|  
|  
Line 2,016: Line 2,019:
| 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
|  
|  

Latest revision as of 12:18, 4 February 2026

< Magic

Below is a complete list of the 11-odd-limit dyadic chords of 11-limit 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 inversions; only one is listed, that being the inversion where all notes are a nonnegative number of major third generators above the root.

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.

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 100/99, 225/224 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 marvel11. 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 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.

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 Comments Kite's name
1 0–1–2 1–5/4–14/9 Marvel Cv(vv#5)
2 0–2–4 1–6/5–14/9 Sensamagic C^m(vv#5)
3 0–1–5 1–5/4–3/2 Otonal 4:5:6 Cv
4 0–4–5 1–6/5–3/2 Utonal 1/(6:5:4) C^m
5 0–2–7 1–7/6–14/9 Utonal 1/(9:7:6) C/
6 0–5–7 1–7/6–3/2 Otonal 6:7:9 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 6:9:10 C^m7no5 or Cv6no3
13 0–5–9 1–3/2–9/5 Utonal 1/(9:6:5) C^m7no3
14 0–7–9 1–7/6–9/5 Sensamagic C\mv7no5
15 0–8–9 1–16/11–20/11 Otonal 1–5/4–11/8 Cv(\b5)
16 0–1–10 1–9/8–5/4 Otonal Cv,9no5
17 0–2–10 1–9/8–14/9 Pentacircle C2(vv#5)
18 0–5–10 1–9/8–3/2 Ambitonal 6:8:9, 8:9:12 C2
19 0–8–10 1–9/8–16/11 Pentacircle C2(^^b5)
20 0–9–10 1–9/8–9/5 Utonal C^9no35 or C^7sus2no5
21 0–1–11 1–5/4–7/5 Marvel Cv(^\b5)
22 0–2–11 1–7/5–14/9 Utonal 1–9/7–9/5 C/,^7no5
23 0–4–11 1–6/5–7/5 Otonal 5:6:7 C^m(^\b5)
24 0–7–11 1–7/6–7/5 Utonal 1/(7:6:5) C\m(^\b5)
25 0–9–11 1–7/5–9/5 Otonal 1–9/7–10/7 C/(^b5)
26 0–10–11 1–9/8–7/5 Marvel 1–5/4–16/9 Cv,7no5
27 0–1–12 1–5/4–7/4 Otonal 4:5:7 Cv,\7no5
28 0–2–12 1–14/9–7/4 Utonal 1–9/8–9/7 C/,9no5
29 0–4–12 1–6/5–7/4 Keenanismic C^m\7
30 0–5–12 1–3/2–7/4 Otonal 4:6:7 C\7no3
31 0–7–12 1–7/6–7/4 Utonal 1/(12:8:7) C\m7no5
32 0–8–12 1–16/11–7/4 Keenanismic 1–6/5–11/8 C^m(\b5)
33 0–10–12 1–9/8–7/4 Otonal C\7sus2
34 0–11–12 1–7/5–7/4 Utonal 1/(10:8:7) C\7(^\b5)no3
35 0–1–13 1–12/11–5/4 Keenanismic
36 0–2–13 1–12/11–14/9 Swetismic 1–9/7–7/5 C/(^\b5)
37 0–4–13 1–12/11–6/5 Utonal
38 0–5–13 1–12/11–3/2 Utonal C^^b2
39 0–8–13 1–12/11–16/11 Otonal 1–11/8–3/2 Cvv#4
40 0–9–13 1–12/11–20/11 Otonal
41 0–11–13 1–12/11–7/5 Swetismic
42 0–12–13 1–12/11–7/4 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 1–18/11–9/5 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 1–14/11–14/9 Utonal
51 0–7–20 1–7/6–14/11 Utonal
52 0–8–20 1–14/11–16/11 Otonal
53 0–9–20 1–14/11–20/11 Otonal
54 0–10–20 1–9/8–14/11 Pentacircle
55 0–11–20 1–14/11–7/5 Utonal
56 0–12–20 1–14/11–7/4 Utonal
57 0–13–20 1–12/11–14/11 Otonal
58 0–18–20 1–14/11–18/11 Otonal

Tetrads

# Generators Transversal Type Comments Kite's name
1 0–1–2–9 1–5/4–14/9–9/5 Magic Cv^7(vv#5)
2 0–2–4–9 1–6/5–14/9–9/5 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 10:12:15:18, 12:15:18:20
9-odd-limit ASS 		C^m7 or Cv6
5 0–2–7–9 1–7/6–14/9–9/5 Sensamagic 1–9/7–3/2–7/3 C/,vv#9
6 0–5–7–9 1–7/6–3/2–9/5 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 1–9/8–5/4–14/9 Apollo Cv,9(vv#5)
11 0–1–5–10 1–9/8–5/4–3/2 Otonal 4:5:6:9 Cv,9
12 0–1–8–10 1–9/8–5/4–16/11 Sensamagic11 Cv,9(^^b5)
13 0–1–9–10 1–9/8–5/4–9/5 Ptolemismic Cv^7,9no5 or Cv9(^7)no5
14 0–2–9–10 1–9/8–14/9–9/5 Sensamagic11 C^9(vv#5)no3 or C^7(vv#5)sus2
15 0–5–9–10 1–9/8–3/2–9/5 Utonal 1/(9:6:5:4) C^9no3 or C^7sus2 or C2,^7
16 0–8–9–10 1–9/8–16/11–9/5 Apollo
17 0–1–2–11 1–5/4–7/5–14/9 Marvel
18 0–2–4–11 1–6/5–7/5–14/9 Sensamagic
19 0–2–7–11 1–7/6–7/5–14/9 Utonal 1/(9:7:6:5)
20 0–1–9–11 1–5/4–7/5–9/5 Apollo
21 0–2–9–11 1–7/5–14/9–9/5 Sensamagic
22 0–4–9–11 1–6/5–7/5–9/5 Otonal 6:7:9:10 C^m7(^\b5) or C\mv6
23 0–7–9–11 1–7/6–7/5–9/5 Sensamagic
24 0–1–10–11 1–9/8–5/4–7/5 Marvel
25 0–2–10–11 1–9/8–7/5–14/9 Apollo
26 0–9–10–11 1–9/8–7/5–9/5 Marvel
27 0–1–2–12 1–5/4–14/9–7/4 Marvel
28 0–2–4–12 1–6/5–14/9–7/4 Sensamagic11
29 0–1–5–12 1–5/4–3/2–7/4 Otonal 4:5:6:7 Cv,\7
30 0–4–5–12 1–6/5–3/2–7/4 Keenanismic C^m\7
31 0–2–7–12 1–7/6–14/9–7/4 Utonal C\m7(vv#5)
32 0–5–7–12 1–7/6–3/2–7/4 Ambitonal 12:14:18:21, 14:18:21:24
9-odd-limit ASS 		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 1–9/8–5/4–7/4 Otonal 4:5:7:9
37 0–2–10–12 1–9/8–14/9–7/4 Pentacircle
38 0–5–10–12 1–9/8–3/2–7/4 Otonal 4:6:7:9 C2\7 or C\7sus2 or C\9no3
39 0–8–10–12 1–9/8–16/11–7/4 Sensamagic11
40 0–1–11–12 1–5/4–7/5–7/4 Marvel
41 0–2–11–12 1–7/5–14/9–7/4 Utonal 1/(9:7:5:4)
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 1/(12:10:8:7) C\m7(^\b5) or C^m/6
44 0–10–11–12 1–9/8–7/5–7/4 Marvel
45 0–1–2–13 1–12/11–5/4–14/9 Marvel11
46 0–2–4–13 1–12/11–6/5–14/9 Octarod
47 0–1–5–13 1–12/11–5/4–3/2 Keenanismic
48 0–4–5–13 1–12/11–6/5–3/2 Utonal
49 0–1–8–13 1–12/11–5/4–16/11 Keenanismic
50 0–4–8–13 1–12/11–6/5–16/11 Ptolemismic
51 0–1–9–13 1–12/11–5/4–9/5 Keemic
52 0–2–9–13 1–12/11–14/9–9/5 Octarod
53 0–4–9–13 1–12/11–6/5–9/5 Ptolemismic
54 0–5–9–13 1–12/11–3/2–9/5 Ptolemismic
55 0–8–9–13 1–12/11–16/11–20/11 Otonal
56 0–1–11–13 1–12/11–5/4–7/5 Marvel11
57 0–2–11–13 1–12/11–7/5–14/9 Swetismic
58 0–4–11–13 1–12/11–6/5–7/5 Octarod
59 0–9–11–13 1–12/11–7/5–9/5 Octarod
60 0–1–12–13 1–12/11–5/4–7/4 Keenanismic
61 0–2–12–13 1–12/11–14/9–7/4 Marvel11
62 0–4–12–13 1–12/11–6/5–7/4 Keemic
63 0–5–12–13 1–12/11–3/2–7/4 Keenanismic
64 0–8–12–13 1–12/11–16/11–7/4 Keenanismic
65 0–11–12–13 1–12/11–7/5–7/4 Marvel11
66 0–5–7–18 1–7/6–3/2–18/11 Swetismic
67 0–7–8–18 1–7/6–16/11–18/11 Marvel11
68 0–5–9–18 1–3/2–18/11–9/5 Utonal
69 0–7–9–18 1–7/6–18/11–9/5 Octarod
70 0–8–9–18 1–16/11–18/11–20/11 Otonal
71 0–5–10–18 1–9/8–3/2–18/11 Utonal
72 0–8–10–18 1–9/8–16/11–18/11 Pentacircle
73 0–9–10–18 1–9/8–18/11–9/5 Utonal
74 0–7–11–18 1–7/6–7/5–18/11 Swetismic
75 0–9–11–18 1–7/5–18/11–9/5 Octarod
76 0–10–11–18 1–9/8–7/5–18/11 Marvel11
77 0–5–13–18 1–12/11–3/2–18/11 Ambitonal
78 0–8–13–18 1–12/11–16/11–18/11 Otonal
79 0–9–13–18 1–12/11–18/11–20/11 Otonal
80 0–11–13–18 1–12/11–7/5–18/11 Swetismic
81 0–2–7–20 1–7/6–14/11–14/9 Utonal
82 0–7–8–20 1–7/6–14/11–16/11 Keenanismic
83 0–2–9–20 1–14/11–14/9–9/5 Octarod
84 0–7–9–20 1–7/6–14/11–9/5 Octarod
85 0–8–9–20 1–14/11–16/11–20/11 Otonal
86 0–2–10–20 1–9/8–14/11–14/9 Pentacircle
87 0–8–10–20 1–9/8–14/11–16/11 Pentacircle
88 0–9–10–20 1–9/8–14/11–9/5 Apollo
89 0–2–11–20 1–7/5–14/11–14/9 Utonal
90 0–7–11–20 1–7/6–14/11–7/5 Utonal
91 0–9–11–20 1–7/5–14/11–9/5 Ptolemismic
92 0–10–11–20 1–9/8–14/11–7/5 Apollo
93 0–2–12–20 1–14/11–14/9–7/4 Utonal
94 0–7–12–20 1–7/6–14/11–7/4 Utonal
95 0–8–12–20 1–14/11–16/11–7/4 Keenanismic
96 0–10–12–20 1–9/8–14/11–7/4 Pentacircle
97 0–11–12–20 1–14/11–7/5–7/4 Utonal
98 0–2–13–20 1–12/11–14/11–14/9 Swetismic
99 0–8–13–20 1–12/11–14/11–16/11 Otonal
100 0–9–13–20 1–12/11–14/11–20/11 Otonal
101 0–11–13–20 1–12/11–14/11–7/5 Octarod
102 0–12–13–20 1–12/11–14/11–7/4 Keenanismic
103 0–7–18–20 1–7/6–14/11–18/11 Swetismic
104 0–8–18–20 1–14/11–16/11–18/11 Otonal
105 0–9–18–20 1–14/11–18/11–20/11 Otonal
106 0–10–18–20 1–9/8–14/11–18/11 Pentacircle
107 0–11–18–20 1–14/11–7/5–18/11 Octarod
108 0–13–18–20 1–12/11–14/11–18/11 Otonal

Pentads

# Generators Transversal Type Comments Kite's name
1 0–1–2–9–10 1–9/8–5/4–14/9–9/5 Magic
2 0–1–5–9–10 1–9/8–5/4–3/2–9/5 Ptolemismic Cv9(^7)
3 0–1–8–9–10 1–9/8–5/4–16/11–9/5 Magic
4 0–1–2–9–11 1–5/4–7/5–14/9–9/5 Magic
5 0–2–4–9–11 1–6/5–7/5–14/9–9/5 Sensamagic
6 0–2–7–9–11 1–7/6–7/5–14/9–9/5 Sensamagic
7 0–1–2–10–11 1–9/8–5/4–7/5–14/9 Apollo
8 0–1–9–10–11 1–9/8–5/4–7/5–9/5 Apollo
9 0–2–9–10–11 1–9/8–7/5–14/9–9/5 Magic
10 0–1–2–10–12 1–9/8–5/4–14/9–7/4 Apollo
11 0–1–5–10–12 1–9/8–5/4–3/2–7/4 Otonal 4:5:6:7:9 Cv9(\7)
12 0–1–8–10–12 1–9/8–5/4–16/11–7/4 Sensamagic11
13 0–1–2–11–12 1–5/4–7/5–14/9–7/4 Marvel
14 0–2–4–11–12 1–6/5–7/5–14/9–7/4 Sensamagic11
15 0–2–7–11–12 1–7/6–7/5–14/9–7/4 Utonal 1/(24:20:16:14:9) C/9(^7)
16 0–1–10–11–12 1–9/8–5/4–7/5–7/4 Marvel
17 0–2–10–11–12 1–9/8–7/5–14/9–7/4 Apollo
18 0–1–2–9–13 1–12/11–5/4–14/9–9/5 Magic
19 0–2–4–9–13 1–12/11–6/5–14/9–9/5 Octarod
20 0–1–5–9–13 1–12/11–5/4–3/2–9/5 Keemic
21 0–4–5–9–13 1–12/11–6/5–3/2–9/5 Ptolemismic
22 0–1–8–9–13 1–12/11–5/4–16/11–9/5 Keemic
23 0–4–8–9–13 1–12/11–6/5–16/11–9/5 Ptolemismic
24 0–1–2–11–13 1–12/11–5/4–7/5–14/9 Marvel11
25 0–2–4–11–13 1–12/11–6/5–7/5–14/9 Octarod
26 0–1–9–11–13 1–12/11–5/4–7/5–9/5 Magic
27 0–2–9–11–13 1–12/11–7/5–14/9–9/5 Octarod
28 0–4–9–11–13 1–12/11–6/5–7/5–9/5 Octarod
29 0–1–2–12–13 1–12/11–5/4–14/9–7/4 Marvel11
30 0–2–4–12–13 1–12/11–6/5–14/9–7/4 Magic
31 0–1–5–12–13 1–12/11–5/4–3/2–7/4 Keenanismic
32 0–4–5–12–13 1–12/11–6/5–3/2–7/4 Keemic
33 0–1–8–12–13 1–12/11–5/4–16/11–7/4 Keenanismic
34 0–4–8–12–13 1–12/11–6/5–16/11–7/4 Keemic
35 0–1–11–12–13 1–12/11–5/4–7/5–7/4 Marvel11
36 0–2–11–12–13 1–12/11–7/5–14/9–7/4 Marvel11
37 0–4–11–12–13 1–12/11–6/5–7/5–7/4 Magic
38 0–5–7–9–18 1–7/6–3/2–18/11–9/5 Octarod
39 0–7–8–9–18 1–7/6–16/11–18/11–9/5 Magic
40 0–5–9–10–18 1–9/8–3/2–18/11–9/5 Utonal 1/(24:20:16:11:9)
41 0–8–9–10–18 1–9/8–16/11–18/11–9/5 Apollo
42 0–7–9–11–18 1–7/6–7/5–18/11–9/5 Octarod
43 0–9–10–11–18 1–9/8–7/5–18/11–9/5 Magic
44 0–5–9–13–18 1–3/2–12/11–18/11–9/5 Ptolemismic
45 0–8–9–13–18 1–12/11–16/11–18/11–20/11 Otonal 4:5:6:9:11
46 0–9–11–13–18 1–7/5–12/11–18/11–9/5 Octarod
47 0–2–7–9–20 1–7/6–14/11–14/9–9/5 Octarod
48 0–7–8–9–20 1–7/6–14/11–16/11–9/5 Magic
49 0–2–9–10–20 1–9/8–14/11–14/9–9/5 Magic
50 0–8–9–10–20 1–9/8–14/11–16/11–9/5 Apollo
51 0–2–7–11–20 1–7/6–7/5–14/11–14/9 Utonal 1/(24:20:14:11:9)
52 0–2–9–11–20 1–14/11–7/5–14/9–9/5 Octarod
53 0–7–9–11–20 1–7/6–14/11–7/5–9/5 Octarod
54 0–2–10–11–20 1–9/8–14/11–7/5–14/9 Apollo
55 0–9–10–11–20 1–9/8–14/11–7/5–9/5 Apollo
56 0–2–7–12–20 1–7/6–14/11–14/9–7/4 Utonal 1/(24:16:14:11:9)
57 0–7–8–12–20 1–7/6–14/11–16/11–7/4 Keenanismic
58 0–2–10–12–20 1–9/8–14/11–14/9–7/4 Pentacircle
59 0–8–10–12–20 1–9/8–14/11–16/11–7/4 Sensamagic11
60 0–2–11–12–20 1–14/11–7/5–14/9–7/4 Utonal 1/(20:16:14:11:9)
61 0–7–11–12–20 1–7/6–14/11–7/5–7/4 Utonal 1/(24:20:16:14:11)
62 0–10–11–12–20 1–9/8–14/11–7/5–7/4 Apollo
63 0–2–9–13–20 1–12/11–14/11–14/9–9/5 Octarod
64 0–8–9–13–20 1–12/11–14/11–16/11–20/11 Otonal 4:5:6:7:11
65 0–2–11–13–20 1–12/11–14/11–7/5–14/9 Octarod
66 0–9–11–13–20 1–12/11–14/11–7/5–9/5 Octarod
67 0–2–12–13–20 1–12/11–14/11–14/9–7/4 Marvel11
68 0–8–12–13–20 1–12/11–14/11–16/11–7/4 Keenanismic
69 0–11–12–13–20 1–12/11–14/11–7/5–7/4 Magic
70 0–7–8–18–20 1–7/6–14/11–16/11–18/11 Marvel11
71 0–7–9–18–20 1–7/6–14/11–18/11–9/5 Octarod
72 0–8–9–18–20 1–14/11–16/11–18/11–20/11 Otonal 4:5:7:9:11
73 0–8–10–18–20 1–9/8–14/11–16/11–18/11 Pentacircle
74 0–9–10–18–20 1–9/8–14/11–18/11–9/5 Apollo
75 0–7–11–18–20 1–7/6–14/11–7/5–18/11 Octarod
76 0–9–11–18–20 1–14/11–7/5–18/11–9/5 Octarod
77 0–10–11–18–20 1–9/8–14/11–7/5–18/11 Magic
78 0–8–13–18–20 1–12/11–14/11–16/11–18/11 Otonal 4:6:7:9:11
79 0–9–13–18–20 1–12/11–14/11–18/11–20/11 Otonal 5:6:7:9:11
80 0–11–13–18–20 1–12/11–14/11–7/5–18/11 Octarod

Hexads

# Generators Transversal Type Comment
1 0–1–2–9–10–11 1–9/8–5/4–7/5–14/9–9/5 Magic
2 0–1–2–10–11–12 1–9/8–5/4–7/5–14/9–7/4 Apollo
3 0–1–2–9–11–13 1–12/11–5/4–7/5–14/9–9/5 Magic
4 0–2–4–9–11–13 1–12/11–6/5–7/5–14/9–9/5 Octarod
5 0–1–2–11–12–13 1–12/11–5/4–7/5–14/9–7/4 Marvel11
6 0–2–4–11–12–13 1–12/11–6/5–7/5–14/9–7/4 Magic
7 0–2–7–9–11–20 1–7/6–14/11–7/5–14/9–9/5 Octarod
8 0–2–9–10–11–20 1–9/8–14/11–7/5–14/9–9/5 Magic
9 0–2–7–11–12–20 1–14/11–7/6–7/5–14/9–7/4 Utonal 1/(24:20:16:14:11:9)
10 0–2–10–11–12–20 1–9/8–14/11–7/5–14/9–7/4 Apollo
11 0–2–9–11–13–20 1–12/11–14/11–7/5–14/9–9/5 Octarod
12 0–2–11–12–13–20 1–12/11–14/11–7/5–14/9–7/4 Magic
13 0–7–8–9–18–20 1–7/6–14/11–16/11–18/11–9/5 Magic
14 0–8–9–10–18–20 1–9/8–14/11–16/11–18/11–9/5 Apollo
15 0–7–9–11–18–20 1–7/6–14/11–7/5–18/11–9/5 Octarod
16 0–9–10–11–18–20 1–9/8–14/11–7/5–18/11–9/5 Magic
17 0–8–9–13–18–20 1–12/11–14/11–16/11–18/11–20/11 Otonal 4:5:6:7:9:11
18 0–9–11–13–18–20 1–12/11–14/11–7/5–18/11–9/5 Octarod
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