Chords of magic: Difference between revisions

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clarifications, added a few chord names
Clarify that the scope of this article is currently the 11-odd-limit. -duplicate and out-of-scope chords. Style
Line 1: Line 1:
Below are listed the [[dyadic chord]]s of 11-limit [[magic|magic temperament]]. Typing the chords requires consideration of the fact that magic conflates [[10/9]] and [[11/10]] and so also [[9/5]] and [[20/11]]. If a [[transversal]] can be found which shows the chord to be essentially just, that transversal is listed along with a typing as otonal, utonal, or ambitonal. If the chord is essentially tempered, it is analyzed in terms of the transversal which employs 10/9 and 9/5.
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.


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


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


The chord names use arrows (ups and downs) as described on the [[Pergen|pergens]] page. The pergen is (P8, P12/5) fifth-of-a-12th, #37 in the [http://tallkite.com/misc_files/notation%20guide%20for%20rank-2%20pergens.pdf list of pergens]. 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 interval is ^<sup>5</sup>dd2, thus {{nowrap|^<sup>5</sup>C {{=}} B##}}.  
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 interval is ^<sup>5</sup>dd2, thus {{nowrap|^<sup>5</sup>C {{=}} B##}}.  


To simplify the chord names, slashes (lifts and drops) are also used. One lift is -22 generators, octave-reduced. Thus {{nowrap|/1 {{=}} &minus;25G + 3G {{=}} 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}}.  
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}}.  


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


{| class="wikitable"
{| class="wikitable"
|+ style="font-size: 105%;" | Cents values of Magic accidentals in various tunings
|+ style="font-size: 105%;" | Cents values of magic accidentals in various tunings
|-
|-
!  
!  
Line 48: Line 48:
| 20¢ + 3.8c
| 20¢ + 3.8c
| 40¢ &minus; 4.4c
| 40¢ &minus; 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. 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. So 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"
{| class="wikitable center-all"
|+ style="font-size: 105%;" |Magic's genchain
|+ style="font-size: 105%;" |Magic's genchain
Line 69: Line 70:
! 12
! 12
! 13
! 13
!...
! …
!18
! 18
!...
! …
!20
! 20
|-
|-
! Cents (41edo)
! Cents (41edo)
Line 89: Line 90:
| 966
| 966
| 146
| 146
! rowspan="4" |
| …
|849
| 849
! rowspan="4" |
| …
|410
| 410
|-
|-
! Ratio
! Ratio
Line 109: Line 110:
| 7/4
| 7/4
| 12/11
| 12/11
|18/11
| …
|14/11
| 18/11
| …
| 14/11
|-
|-
! Interval
! Interval
|'''P1'''
| '''P1'''
| vM3
| vM3
| vvA5<br />\m6
| vvA5<br>\m6
| ^^d8<br />/M7
| ^^d8<br>/M7
| ^m3
| ^m3
|'''P5'''
| '''P5'''
| vM7
| vM7
| vvA2<br />\m3
| vvA2<br>\m3
| ^^d5<br />/A4
| ^^d5<br>/A4
| ^m7
| ^m7
|'''M2'''
| '''M2'''
| vA4<br />^\d5
| vA4<br>^\d5
| vvA6<br />\m7
| vvA6<br>\m7
| ^^m2<br />/A1
| ^^m2<br>/A1
|^^m6
| …
/A5
| ^^m6<br>/A5
|'''M3'''
| …
| '''M3'''
|-
|-
! Note (in C)
! Note (in C)
|'''C'''
| '''C'''
| vE
| vE
| vvG#<br />\Ab
| vvG#<br>\Ab
| ^^Cb<br />/B
| ^^Cb<br>/B
| ^Eb
| ^Eb
|'''G'''
| '''G'''
| vB
| vB
| vvD#<br />\Eb
| vvD#<br>\Eb
| ^^Gb<br />/F#
| ^^Gb<br>/F#
| ^Bb
| ^Bb
|'''D'''
|'''D'''
| vF#<br />^\Gb
| vF#<br>^\Gb
| vvA#<br />\Bb
| vvA#<br>\Bb
| ^^Db<br />/C#
| ^^Db<br>/C#
|^^Ab
| …
/G#
| ^^Ab<br>/G#
|'''E'''
| …
| '''E'''
|}
|}
'''''TODO: complete the tables'''''
{{Todo|inline=1|complete table}}


== Triads ==
== Triads ==
{| class="wikitable center-1"
{| class="wikitable center-1"
|-
|-
! &#35;
! #
! Chord
! Chord
! Transversal
! Transversal
! Type
! Type
!Name
! Name
! Comments
! Comments
|-
|-
Line 166: Line 171:
| 1-5/4-14/9
| 1-5/4-14/9
| Marvel
| Marvel
|Cv(vv#5)
| Cv(vv#5)
|
|
|-
|-
Line 173: Line 178:
| 1-14/9-6/5
| 1-14/9-6/5
| Sensamagic
| Sensamagic
|C^m(vv#5)
| C^m(vv#5)
|
|
|-
|-
Line 180: Line 185:
| 1-5/4-3/2
| 1-5/4-3/2
| Otonal
| Otonal
|Cv
| Cv
|
|
|-
|-
Line 187: Line 192:
| 1-6/5-3/2
| 1-6/5-3/2
| Utonal
| Utonal
|C^m
| C^m
|
|
|-
|-
Line 194: Line 199:
| 1-14/9-7/6
| 1-14/9-7/6
| Utonal
| Utonal
|C/
| C/
| 1-9/7-3/2
| 1-9/7-3/2
|-
|-
Line 201: Line 206:
| 1-3/2-7/6
| 1-3/2-7/6
| Otonal
| Otonal
|C\m
| C\m
|
|
|-
|-
Line 208: Line 213:
| 1-5/4-16/11
| 1-5/4-16/11
| Keenanismic
| Keenanismic
|Cv(^^b5)
| Cv(^^b5)
|
|
|-
|-
Line 215: Line 220:
| 1-6/5-16/11
| 1-6/5-16/11
| Ptolemismic
| Ptolemismic
|C^m(^^b5)
| C^m(^^b5)
|
|
|-
|-
Line 222: Line 227:
| 1-7/6-16/11
| 1-7/6-16/11
| Keenanismic
| Keenanismic
|C\m(^^b5)
| C\m(^^b5)
|
|
|-
|-
Line 229: Line 234:
| 1-5/4-20/11
| 1-5/4-20/11
| Utonal
| Utonal
|Cv^7no5
| Cv^7no5
|
|
|-
|-
Line 236: Line 241:
| 1-14/9-9/5
| 1-14/9-9/5
| Sensamagic
| Sensamagic
|C^m7(vv#5)no3
| C^m7(vv#5)no3
|
|
|-
|-
Line 243: Line 248:
| 1-6/5-9/5
| 1-6/5-9/5
| Otonal
| Otonal
|C^m7no5
| C^m7no5
| <u>or</u> 1-3/2-5/3 = Cv6no3
| ''or'' 1-3/2-5/3 = Cv6no3
|-
|-
| 13
| 13
Line 250: Line 255:
| 1-3/2-9/5
| 1-3/2-9/5
| Utonal
| Utonal
|C^m7no3
| C^m7no3
|
|
|-
|-
Line 257: Line 262:
| 1-7/6-9/5
| 1-7/6-9/5
| Sensamagic
| Sensamagic
|C\mv7no5
| C\mv7no5
|
|
|-
|-
Line 264: Line 269:
| 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
|-
|-
Line 271: Line 276:
| 1-5/4-9/8
| 1-5/4-9/8
| Otonal
| Otonal
|Cv,9no5
| Cv,9no5
|
|
|-
|-
Line 278: Line 283:
| 1-14/9-9/8
| 1-14/9-9/8
| Pentacircle
| Pentacircle
|C2(vv#5)
| C2(vv#5)
|
|
|-
|-
Line 285: Line 290:
| 1-3/2-9/8
| 1-3/2-9/8
| Ambitonal
| Ambitonal
|C2
| C2
|
|
|-
|-
Line 292: Line 297:
| 1-16/11-9/8
| 1-16/11-9/8
| Pentacircle
| Pentacircle
|C2(^^b5)
| C2(^^b5)
|
|
|-
|-
Line 299: Line 304:
| 1-9/5-9/8
| 1-9/5-9/8
| Utonal
| Utonal
|C^9no35
| C^9no35
| <u>or</u> C^7sus2no5
| ''or'' C^7sus2no5
|-
|-
| 21
| 21
Line 306: Line 311:
| 1-5/4-7/5
| 1-5/4-7/5
| Marvel
| Marvel
|Cv(^\b5)
| Cv(^\b5)
|
|
|-
|-
Line 313: Line 318:
| 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
|-
|-
Line 320: Line 325:
| 1-6/5-7/5
| 1-6/5-7/5
| Otonal
| Otonal
|C^m(^\b5)
| C^m(^\b5)
|
|
|-
|-
Line 327: Line 332:
| 1-7/6-7/5
| 1-7/6-7/5
| Utonal
| Utonal
|C\m(^\b5)
| C\m(^\b5)
|
|
|-
|-
Line 334: Line 339:
| 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
|-
|-
Line 341: Line 346:
| 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
|-
|-
Line 348: Line 353:
| 1-5/4-7/4
| 1-5/4-7/4
| Otonal
| Otonal
|Cv,\7no5
| Cv,\7no5
|
|
|-
|-
Line 355: Line 360:
| 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
|-
|-
Line 362: Line 367:
| 1-6/5-7/4
| 1-6/5-7/4
| Keenanismic
| Keenanismic
|C^m\7
| C^m\7
|
|
|-
|-
Line 369: Line 374:
| 1-3/2-7/4
| 1-3/2-7/4
| Otonal
| Otonal
|C\7no3
| C\7no3
|
|
|-
|-
Line 376: Line 381:
| 1-7/6-7/4
| 1-7/6-7/4
| Utonal
| Utonal
|C\m7no5
| C\m7no5
|
|
|-
|-
Line 383: Line 388:
| 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
|-
|-
Line 390: Line 395:
| 1-9/8-7/4
| 1-9/8-7/4
| Otonal
| Otonal
|C\7sus2
| C\7sus2
|
|
|-
|-
Line 397: Line 402:
| 1-7/5-7/4
| 1-7/5-7/4
| Utonal
| Utonal
|C\7(^\b5)no3
| C\7(^\b5)no3
|
|
|-
|-
Line 411: Line 416:
| 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
|-
|-
Line 425: Line 430:
| 1-3/2-12/11
| 1-3/2-12/11
| Utonal
| Utonal
|C^^b2
| C^^b2
|
|
|-
|-
Line 432: Line 437:
| 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
Line 576: Line 581:
! Transversal
! Transversal
! Type
! Type
!Name
! Name
! Comments
! Comments
|-
|-
|1
| 1
|0-1-5-6
|1-5/4-3/2-15/8
|Ambitonal
|CvM7
|
|-
| 2
| 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)
|  
|  
|-
|-
| 3
| 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)
|  
|  
|-
|-
| 4
| 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
|  
|  
|-
|-
| 5
| 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
|<u>or</u> 1-5/4-3/2-5/3 = Cv6
| ''or'' 1-5/4-3/2-5/3 = Cv6
|-
|-
| 6
| 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
|-
|-
| 7
| 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
|  
|  
|-
|-
| 8
| 7
| 0-1-8-9
| 0-1-8-9
| 1-5/4-16/11-9/5
| 1-5/4-16/11-9/5
| Supermagic
| Supermagic
|Cv^7(^^b5)
| Cv^7(^^b5)
|  
|  
|-
|-
| 9
| 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)
|  
|  
|-
|-
| 10
| 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)
|  
|  
|-
|-
| 11
| 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)
|  
|  
|-
|-
| 12
| 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
|  
|  
|-
|-
| 13
| 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)
|  
|  
|-
|-
| 14
| 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
| <u>or</u> Cv9(^7)no5
| <u>or</u> Cv9(^7)no5
|-
|-
| 15
| 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
| <u>or</u> C^7(vv#5)sus2
| ''or'' C^7(vv#5)sus2
|-
|-
| 16
| 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
|<u>or</u> C^7sus2 <u>or</u> C2,^7
| ''or'' C^7sus2 <u>or</u> C2,^7
|-
|-
| 17
| 16
| 0-8-9-10
| 0-8-9-10
| 1-16/11-9/5-9/8
| 1-16/11-9/5-9/8
Line 698: Line 696:
|  
|  
|-
|-
| 18
| 17
| 0-1-2-11
| 0-1-2-11
| 1-5/4-14/9-7/5
| 1-5/4-14/9-7/5
Line 705: Line 703:
|  
|  
|-
|-
| 19
| 18
| 0-2-4-11
| 0-2-4-11
| 1-14/9-6/5-7/5
| 1-14/9-6/5-7/5
Line 712: Line 710:
|  
|  
|-
|-
| 20
| 19
| 0-2-7-11
| 0-2-7-11
| 1-14/9-7/6-7/5
| 1-14/9-7/6-7/5
Line 719: Line 717:
|  
|  
|-
|-
| 21
| 20
| 0-1-9-11
| 0-1-9-11
| 1-5/4-9/5-7/5
| 1-5/4-9/5-7/5
Line 726: Line 724:
|  
|  
|-
|-
| 22
| 21
| 0-2-9-11
| 0-2-9-11
| 1-14/9-9/5-7/5
| 1-14/9-9/5-7/5
Line 733: Line 731:
|  
|  
|-
|-
| 23
| 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)
| <u>or</u> 1-7/6-3/2-5/3 = C\mv6
| ''or'' 1-7/6-3/2-5/3 = C\mv6
|-
|-
| 24
| 23
| 0-7-9-11
| 0-7-9-11
| 1-7/6-9/5-7/5
| 1-7/6-9/5-7/5
Line 747: Line 745:
|  
|  
|-
|-
| 25
| 24
| 0-1-10-11
| 0-1-10-11
| 1-5/4-9/8-7/5
| 1-5/4-9/8-7/5
Line 754: Line 752:
|  
|  
|-
|-
| 26
| 25
| 0-2-10-11
| 0-2-10-11
| 1-14/9-9/8-7/5
| 1-14/9-9/8-7/5
Line 761: Line 759:
|  
|  
|-
|-
| 27
| 26
| 0-9-10-11
| 0-9-10-11
| 1-9/5-9/8-7/5
| 1-9/5-9/8-7/5
Line 768: Line 766:
|  
|  
|-
|-
| 28
| 27
| 0-1-2-12
| 0-1-2-12
| 1-5/4-14/9-7/4
| 1-5/4-14/9-7/4
Line 775: Line 773:
|  
|  
|-
|-
| 29
| 28
| 0-2-4-12
| 0-2-4-12
| 1-14/9-6/5-7/4
| 1-14/9-6/5-7/4
Line 782: Line 780:
|  
|  
|-
|-
| 30
| 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
|  
|  
|-
|-
| 31
| 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
|  
|  
|-
|-
| 32
| 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)
|  
|  
|-
|-
| 33
| 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
|  
|  
|-
|-
| 34
| 33
| 0-1-8-12
| 0-1-8-12
| 1-5/4-16/11-7/4
| 1-5/4-16/11-7/4
Line 817: Line 815:
|  
|  
|-
|-
| 35
| 34
| 0-4-8-12
| 0-4-8-12
| 1-6/5-16/11-7/4
| 1-6/5-16/11-7/4
Line 824: Line 822:
|  
|  
|-
|-
| 36
| 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)
|  
|  
|-
|-
|37
| 36
|0-7-11-12
|1-7/6-7/5-7/4
|Otonal
|C\m7(^\b5)
|<u>or</u> 1-6/5-3/2-12/7 = C^m/6
|-
| 38
| 0-1-10-12
| 0-1-10-12
| 1-5/4-9/8-7/4
| 1-5/4-9/8-7/4
Line 845: Line 836:
|  
|  
|-
|-
| 39
| 37
| 0-2-10-12
| 0-2-10-12
| 1-14/9-9/8-7/4
| 1-14/9-9/8-7/4
Line 852: Line 843:
|  
|  
|-
|-
| 40
| 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
|<u>or</u> C\7sus2 <u>or</u> C\9no3
| ''or'' C\7sus2 ''or'' C\9no3
|-
|-
| 41
| 39
| 0-8-10-12
| 0-8-10-12
| 1-16/11-9/8-7/4
| 1-16/11-9/8-7/4
Line 866: Line 857:
|  
|  
|-
|-
| 42
| 40
| 0-1-11-12
| 0-1-11-12
| 1-5/4-7/5-7/4
| 1-5/4-7/5-7/4
Line 873: Line 864:
|  
|  
|-
|-
| 43
| 41
| 0-2-11-12
| 0-2-11-12
| 1-14/9-7/5-7/4
| 1-14/9-7/5-7/4
Line 880: Line 871:
|  
|  
|-
|-
| 44
| 42
| 0-4-11-12
| 0-4-11-12
| 1-6/5-7/5-7/4
| 1-6/5-7/5-7/4
Line 887: Line 878:
|  
|  
|-
|-
| 45
| 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)
|  
| ''or'' 1-6/5-3/2-12/7 = C^m/6
|-
|-
| 46
| 44
| 0-10-11-12
| 0-10-11-12
| 1-9/8-7/5-7/4
| 1-9/8-7/5-7/4
Line 901: Line 892:
|  
|  
|-
|-
| 47
| 45
| 0-1-2-13
| 0-1-2-13
| 1-5/4-14/9-12/11
| 1-5/4-14/9-12/11
Line 908: Line 899:
|  
|  
|-
|-
| 48
| 46
| 0-2-4-13
| 0-2-4-13
| 1-14/9-6/5-12/11
| 1-14/9-6/5-12/11
Line 915: Line 906:
|  
|  
|-
|-
| 49
| 47
| 0-1-5-13
| 0-1-5-13
| 1-5/4-3/2-12/11
| 1-5/4-3/2-12/11
Line 922: Line 913:
|  
|  
|-
|-
| 50
| 48
| 0-4-5-13
| 0-4-5-13
| 1-6/5-3/2-12/11
| 1-6/5-3/2-12/11
Line 929: Line 920:
|  
|  
|-
|-
| 51
| 49
| 0-1-8-13
| 0-1-8-13
| 1-5/4-16/11-12/11
| 1-5/4-16/11-12/11
Line 936: Line 927:
|  
|  
|-
|-
| 52
| 50
| 0-4-8-13
| 0-4-8-13
| 1-6/5-16/11-12/11
| 1-6/5-16/11-12/11
Line 943: Line 934:
|  
|  
|-
|-
| 53
| 51
| 0-1-9-13
| 0-1-9-13
| 1-5/4-9/5-12/11
| 1-5/4-9/5-12/11
Line 950: Line 941:
|  
|  
|-
|-
| 54
| 52
| 0-2-9-13
| 0-2-9-13
| 1-14/9-9/5-12/11
| 1-14/9-9/5-12/11
Line 957: Line 948:
|  
|  
|-
|-
| 55
| 53
| 0-4-9-13
| 0-4-9-13
| 1-6/5-9/5-12/11
| 1-6/5-9/5-12/11
Line 964: Line 955:
|  
|  
|-
|-
| 56
| 54
| 0-5-9-13
| 0-5-9-13
| 1-3/2-9/5-12/11
| 1-3/2-9/5-12/11
Line 971: Line 962:
|  
|  
|-
|-
| 57
| 55
| 0-8-9-13
| 0-8-9-13
| 1-16/11-20/11-12/11
| 1-16/11-20/11-12/11
Line 978: Line 969:
|  
|  
|-
|-
| 58
| 56
| 0-1-11-13
| 0-1-11-13
| 1-5/4-7/5-12/11
| 1-5/4-7/5-12/11
Line 985: Line 976:
|  
|  
|-
|-
| 59
| 57
| 0-2-11-13
| 0-2-11-13
| 1-14/9-7/5-12/11
| 1-14/9-7/5-12/11
Line 992: Line 983:
|  
|  
|-
|-
| 60
| 58
| 0-4-11-13
| 0-4-11-13
| 1-6/5-7/5-12/11
| 1-6/5-7/5-12/11
Line 999: Line 990:
|  
|  
|-
|-
| 61
| 59
| 0-9-11-13
| 0-9-11-13
| 1-9/5-7/5-12/11
| 1-9/5-7/5-12/11
Line 1,006: Line 997:
|  
|  
|-
|-
| 62
| 60
| 0-1-12-13
| 0-1-12-13
| 1-5/4-7/4-12/11
| 1-5/4-7/4-12/11
Line 1,013: Line 1,004:
|  
|  
|-
|-
| 63
| 61
| 0-2-12-13
| 0-2-12-13
| 1-14/9-7/4-12/11
| 1-14/9-7/4-12/11
Line 1,020: Line 1,011:
|  
|  
|-
|-
| 64
| 62
| 0-4-12-13
| 0-4-12-13
| 1-6/5-7/4-12/11
| 1-6/5-7/4-12/11
Line 1,027: Line 1,018:
|  
|  
|-
|-
| 65
| 63
| 0-5-12-13
| 0-5-12-13
| 1-3/2-7/4-12/11
| 1-3/2-7/4-12/11
Line 1,034: Line 1,025:
|  
|  
|-
|-
| 66
| 64
| 0-8-12-13
| 0-8-12-13
| 1-16/11-7/4-12/11
| 1-16/11-7/4-12/11
Line 1,041: Line 1,032:
|  
|  
|-
|-
| 67
| 65
| 0-11-12-13
| 0-11-12-13
| 1-7/5-7/4-12/11
| 1-7/5-7/4-12/11
Line 1,048: Line 1,039:
|  
|  
|-
|-
| 68
| 66
| 0-5-7-18
| 0-5-7-18
| 1-3/2-7/6-18/11
| 1-3/2-7/6-18/11
Line 1,055: Line 1,046:
|  
|  
|-
|-
| 69
| 67
| 0-7-8-18
| 0-7-8-18
| 1-7/6-16/11-18/11
| 1-7/6-16/11-18/11
Line 1,062: Line 1,053:
|  
|  
|-
|-
| 70
| 68
| 0-5-9-18
| 0-5-9-18
| 1-3/2-9/5-18/11
| 1-3/2-9/5-18/11
Line 1,069: Line 1,060:
|  
|  
|-
|-
| 71
| 69
| 0-7-9-18
| 0-7-9-18
| 1-7/6-9/5-18/11
| 1-7/6-9/5-18/11
Line 1,076: Line 1,067:
|  
|  
|-
|-
| 72
| 70
| 0-8-9-18
| 0-8-9-18
| 1-16/11-20/11-18/11
| 1-16/11-20/11-18/11
Line 1,083: Line 1,074:
|  
|  
|-
|-
| 73
| 71
| 0-5-10-18
| 0-5-10-18
| 1-3/2-9/8-18/11
| 1-3/2-9/8-18/11
Line 1,090: Line 1,081:
|  
|  
|-
|-
| 74
| 72
| 0-8-10-18
| 0-8-10-18
| 1-16/11-9/8-18/11
| 1-16/11-9/8-18/11
Line 1,097: Line 1,088:
|  
|  
|-
|-
| 75
| 73
| 0-9-10-18
| 0-9-10-18
| 1-9/5-9/8-18/11
| 1-9/5-9/8-18/11
Line 1,104: Line 1,095:
|  
|  
|-
|-
| 76
| 74
| 0-7-11-18
| 0-7-11-18
| 1-7/6-7/5-18/11
| 1-7/6-7/5-18/11
Line 1,111: Line 1,102:
|  
|  
|-
|-
| 77
| 75
| 0-9-11-18
| 0-9-11-18
| 1-9/5-7/5-18/11
| 1-9/5-7/5-18/11
Line 1,118: Line 1,109:
|  
|  
|-
|-
| 78
| 76
| 0-10-11-18
| 0-10-11-18
| 1-9/8-7/5-18/11
| 1-9/8-7/5-18/11
Line 1,125: Line 1,116:
|  
|  
|-
|-
| 79
| 77
| 0-5-13-18
| 0-5-13-18
| 1-3/2-12/11-18/11
| 1-3/2-12/11-18/11
Line 1,132: Line 1,123:
|  
|  
|-
|-
| 80
| 78
| 0-8-13-18
| 0-8-13-18
| 1-16/11-12/11-18/11
| 1-16/11-12/11-18/11
Line 1,139: Line 1,130:
|  
|  
|-
|-
| 81
| 79
| 0-9-13-18
| 0-9-13-18
| 1-20/11-12/11-18/11
| 1-20/11-12/11-18/11
Line 1,146: Line 1,137:
|  
|  
|-
|-
| 82
| 80
| 0-11-13-18
| 0-11-13-18
| 1-7/5-12/11-18/11
| 1-7/5-12/11-18/11
Line 1,153: Line 1,144:
|  
|  
|-
|-
| 83
| 81
| 0-2-7-20
| 0-2-7-20
| 1-14/9-7/6-14/11
| 1-14/9-7/6-14/11
Line 1,160: Line 1,151:
|  
|  
|-
|-
| 84
| 82
| 0-7-8-20
| 0-7-8-20
| 1-7/6-16/11-14/11
| 1-7/6-16/11-14/11
Line 1,167: Line 1,158:
|  
|  
|-
|-
| 85
| 83
| 0-2-9-20
| 0-2-9-20
| 1-14/9-9/5-14/11
| 1-14/9-9/5-14/11
Line 1,174: Line 1,165:
|  
|  
|-
|-
| 86
| 84
| 0-7-9-20
| 0-7-9-20
| 1-7/6-9/5-14/11
| 1-7/6-9/5-14/11
Line 1,181: Line 1,172:
|  
|  
|-
|-
| 87
| 85
| 0-8-9-20
| 0-8-9-20
| 1-16/11-20/11-14/11
| 1-16/11-20/11-14/11
Line 1,188: Line 1,179:
|  
|  
|-
|-
| 88
| 86
| 0-2-10-20
| 0-2-10-20
| 1-14/9-9/8-14/11
| 1-14/9-9/8-14/11
Line 1,195: Line 1,186:
|  
|  
|-
|-
| 89
| 87
| 0-8-10-20
| 0-8-10-20
| 1-16/11-9/8-14/11
| 1-16/11-9/8-14/11
Line 1,202: Line 1,193:
|  
|  
|-
|-
| 90
| 88
| 0-9-10-20
| 0-9-10-20
| 1-9/5-9/8-14/11
| 1-9/5-9/8-14/11
Line 1,209: Line 1,200:
|  
|  
|-
|-
| 91
| 89
| 0-2-11-20
| 0-2-11-20
| 1-14/9-7/5-14/11
| 1-14/9-7/5-14/11
Line 1,216: Line 1,207:
|  
|  
|-
|-
| 92
| 90
| 0-7-11-20
| 0-7-11-20
| 1-7/6-7/5-14/11
| 1-7/6-7/5-14/11
Line 1,223: Line 1,214:
|  
|  
|-
|-
| 93
| 91
| 0-9-11-20
| 0-9-11-20
| 1-9/5-7/5-14/11
| 1-9/5-7/5-14/11
Line 1,230: Line 1,221:
|  
|  
|-
|-
| 94
| 92
| 0-10-11-20
| 0-10-11-20
| 1-9/8-7/5-14/11
| 1-9/8-7/5-14/11
Line 1,237: Line 1,228:
|  
|  
|-
|-
| 95
| 93
| 0-2-12-20
| 0-2-12-20
| 1-14/9-7/4-14/11
| 1-14/9-7/4-14/11
Line 1,244: Line 1,235:
|  
|  
|-
|-
| 96
| 94
| 0-7-12-20
| 0-7-12-20
| 1-7/6-7/4-14/11
| 1-7/6-7/4-14/11
Line 1,251: Line 1,242:
|  
|  
|-
|-
| 97
| 95
| 0-8-12-20
| 0-8-12-20
| 1-16/11-7/4-14/11
| 1-16/11-7/4-14/11
Line 1,258: Line 1,249:
|  
|  
|-
|-
| 98
| 96
| 0-10-12-20
| 0-10-12-20
| 1-9/8-7/4-14/11
| 1-9/8-7/4-14/11
Line 1,265: Line 1,256:
|  
|  
|-
|-
| 99
| 97
| 0-11-12-20
| 0-11-12-20
| 1-7/5-7/4-14/11
| 1-7/5-7/4-14/11
Line 1,272: Line 1,263:
|  
|  
|-
|-
| 100
| 98
| 0-2-13-20
| 0-2-13-20
| 1-14/9-12/11-14/11
| 1-14/9-12/11-14/11
Line 1,279: Line 1,270:
|  
|  
|-
|-
| 101
| 99
| 0-8-13-20
| 0-8-13-20
| 1-16/11-12/11-14/11
| 1-16/11-12/11-14/11
Line 1,286: Line 1,277:
|  
|  
|-
|-
| 102
| 100
| 0-9-13-20
| 0-9-13-20
| 1-20/11-12/11-14/11
| 1-20/11-12/11-14/11
Line 1,293: Line 1,284:
|  
|  
|-
|-
| 103
| 101
| 0-11-13-20
| 0-11-13-20
| 1-7/5-12/11-14/11
| 1-7/5-12/11-14/11
Line 1,300: Line 1,291:
|  
|  
|-
|-
| 104
| 102
| 0-12-13-20
| 0-12-13-20
| 1-7/4-12/11-14/11
| 1-7/4-12/11-14/11
Line 1,307: Line 1,298:
|  
|  
|-
|-
| 105
| 103
| 0-7-18-20
| 0-7-18-20
| 1-7/6-18/11-14/11
| 1-7/6-18/11-14/11
Line 1,314: Line 1,305:
|  
|  
|-
|-
| 106
| 104
| 0-8-18-20
| 0-8-18-20
| 1-16/11-18/11-14/11
| 1-16/11-18/11-14/11
Line 1,321: Line 1,312:
|  
|  
|-
|-
| 107
| 105
| 0-9-18-20
| 0-9-18-20
| 1-20/11-18/11-14/11
| 1-20/11-18/11-14/11
Line 1,328: Line 1,319:
|  
|  
|-
|-
| 108
| 106
| 0-10-18-20
| 0-10-18-20
| 1-9/8-18/11-14/11
| 1-9/8-18/11-14/11
Line 1,335: Line 1,326:
|  
|  
|-
|-
| 109
| 107
| 0-11-18-20
| 0-11-18-20
| 1-7/5-18/11-14/11
| 1-7/5-18/11-14/11
Line 1,342: Line 1,333:
|  
|  
|-
|-
| 110
| 108
| 0-13-18-20
| 0-13-18-20
| 1-12/11-18/11-14/11
| 1-12/11-18/11-14/11
Line 1,357: Line 1,348:
! Transversal
! Transversal
! Type
! Type
!Name
! Name
!Comments
! Comments
|-
|-
| 1
| 1
Line 1,371: Line 1,362:
| 1-5/4-3/2-9/5-9/8
| 1-5/4-3/2-9/5-9/8
| Ptolemismic
| Ptolemismic
|Cv9(^7)
| Cv9(^7)
|
|
|-
|-
Line 1,434: Line 1,425:
| 1-5/4-3/2-9/8-7/4
| 1-5/4-3/2-9/8-7/4
| Otonal
| Otonal
|Cv9(\7)
| Cv9(\7)
|
|
|-
|-
Line 1,462: Line 1,453:
| 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
Line 1,510: Line 1,501:
| 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
| supermagic
| Supermagic
|
|
|
|

Revision as of 12:08, 17 December 2024

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 supermagic. Finally, anything requiring three independent commas among those discussed above is labeled magic.

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

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

To simplify the chord names, slashes (lifts and drops) are also used. One lift is -22 generators, octave-reduced. Thus /1 = −25G + 3G = m2 + ^^d8 = ^^d2. Thus a lift equals two ups minus a tempered pythagorean comma, 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. So 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

# Chord Transversal Type 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

# Chord Transversal Type 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 Supermagic 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 Supermagic
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 Supermagic
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 Supermagic
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

# Chord Transversal Type 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 Supermagic
21 0-4-5-9-13 1-6/5-3/2-9/5-12/11 Ptolemismic
22 0-1-8-9-13 1-5/4-16/11-9/5-12/11 Supermagic
23 0-4-8-9-13 1-6/5-16/11-9/5-12/11 Ptolemismic
24 0-1-2-11-13 1-5/4-14/9-7/5-12/11 Unimarvel
25 0-2-4-11-13 1-14/9-6/5-7/5-12/11 Octarod
26 0-1-9-11-13 1-5/4-9/5-7/5-12/11 Magic
27 0-2-9-11-13 1-14/9-9/5-7/5-12/11 Octarod
28 0-4-9-11-13 1-6/5-9/5-7/5-12/11 Octarod
29 0-1-2-12-13 1-5/4-14/9-7/4-12/11 Unimarvel
30 0-2-4-12-13 1-14/9-6/5-7/4-12/11 Magic
31 0-1-5-12-13 1-5/4-3/2-7/4-12/11 Keenanismic
32 0-4-5-12-13 1-6/5-3/2-7/4-12/11 Supermagic
33 0-1-8-12-13 1-5/4-16/11-7/4-12/11 Keenanismic
34 0-4-8-12-13 1-6/5-16/11-7/4-12/11 Supermagic
35 0-1-11-12-13 1-5/4-7/5-7/4-12/11 Unimarvel
36 0-2-11-12-13 1-14/9-7/5-7/4-12/11 Unimarvel
37 0-4-11-12-13 1-6/5-7/5-7/4-12/11 Magic
38 0-5-7-9-18 1-3/2-7/6-9/5-18/11 Octarod
39 0-7-8-9-18 1-7/6-16/11-9/5-18/11 Magic
40 0-5-9-10-18 1-3/2-9/5-9/8-18/11 Utonal
41 0-8-9-10-18 1-16/11-9/5-9/8-18/11 Apollo
42 0-7-9-11-18 1-7/6-9/5-7/5-18/11 Octarod
43 0-9-10-11-18 1-9/5-9/8-7/5-18/11 Magic
44 0-5-9-13-18 1-3/2-9/5-12/11-18/11 Ptolemismic
45 0-8-9-13-18 1-16/11-20/11-12/11-18/11 Otonal
46 0-9-11-13-18 1-9/5-7/5-12/11-18/11 Octarod
47 0-2-7-9-20 1-14/9-7/6-9/5-14/11 Octarod
48 0-7-8-9-20 1-7/6-16/11-9/5-14/11 Magic
49 0-2-9-10-20 1-14/9-9/5-9/8-14/11 Magic
50 0-8-9-10-20 1-16/11-9/5-9/8-14/11 Apollo
51 0-2-7-11-20 1-14/9-7/6-7/5-14/11 Utonal
52 0-2-9-11-20 1-14/9-9/5-7/5-14/11 Octarod
53 0-7-9-11-20 1-7/6-9/5-7/5-14/11 Octarod
54 0-2-10-11-20 1-14/9-9/8-7/5-14/11 Apollo
55 0-9-10-11-20 1-9/5-9/8-7/5-14/11 Apollo
56 0-2-7-12-20 1-14/9-7/6-7/4-14/11 Utonal
57 0-7-8-12-20 1-7/6-16/11-7/4-14/11 Keenanismic
58 0-2-10-12-20 1-14/9-9/8-7/4-14/11 Pentacircle
59 0-8-10-12-20 1-16/11-9/8-7/4-14/11 Sensamagic11
60 0-2-11-12-20 1-14/9-7/5-7/4-14/11 Utonal
61 0-7-11-12-20 1-7/6-7/5-7/4-14/11 Utonal
62 0-10-11-12-20 1-9/8-7/5-7/4-14/11 Apollo
63 0-2-9-13-20 1-14/9-9/5-12/11-14/11 Octarod
64 0-8-9-13-20 1-16/11-20/11-12/11-14/11 Otonal
65 0-2-11-13-20 1-14/9-7/5-12/11-14/11 Octarod
66 0-9-11-13-20 1-9/5-7/5-12/11-14/11 Octarod
67 0-2-12-13-20 1-14/9-7/4-12/11-14/11 Unimarvel
68 0-8-12-13-20 1-16/11-7/4-12/11-14/11 Keenanismic
69 0-11-12-13-20 1-7/5-7/4-12/11-14/11 Magic
70 0-7-8-18-20 1-7/6-16/11-18/11-14/11 Unimarvel
71 0-7-9-18-20 1-7/6-9/5-18/11-14/11 Octarod
72 0-8-9-18-20 1-16/11-20/11-18/11-14/11 Otonal
73 0-8-10-18-20 1-16/11-9/8-18/11-14/11 Pentacircle
74 0-9-10-18-20 1-9/5-9/8-18/11-14/11 Apollo
75 0-7-11-18-20 1-7/6-7/5-18/11-14/11 Octarod
76 0-9-11-18-20 1-9/5-7/5-18/11-14/11 Octarod
77 0-10-11-18-20 1-9/8-7/5-18/11-14/11 Magic
78 0-8-13-18-20 1-16/11-12/11-18/11-14/11 Otonal
79 0-9-13-18-20 1-20/11-12/11-18/11-14/11 Otonal
80 0-11-13-18-20 1-7/5-12/11-18/11-14/11 Octarod

Hexads

# Chord Transversal Type
1 0-1-2-9-10-11 1-5/4-14/9-9/5-9/8-7/5 Magic
2 0-1-2-10-11-12 1-5/4-14/9-9/8-7/5-7/4 Apollo
3 0-1-2-9-11-13 1-5/4-14/9-9/5-7/5-12/11 Magic
4 0-2-4-9-11-13 1-14/9-6/5-9/5-7/5-12/11 Octarod
5 0-1-2-11-12-13 1-5/4-14/9-7/5-7/4-12/11 Unimarvel
6 0-2-4-11-12-13 1-14/9-6/5-7/5-7/4-12/11 Magic
7 0-2-7-9-11-20 1-14/9-7/6-9/5-7/5-14/11 Octarod
8 0-2-9-10-11-20 1-14/9-9/5-9/8-7/5-14/11 Magic
9 0-2-7-11-12-20 1-14/9-7/6-7/5-7/4-14/11 Utonal
10 0-2-10-11-12-20 1-14/9-9/8-7/5-7/4-14/11 Apollo
11 0-2-9-11-13-20 1-14/9-9/5-7/5-12/11-14/11 Octarod
12 0-2-11-12-13-20 1-14/9-7/5-7/4-12/11-14/11 Magic
13 0-7-8-9-18-20 1-7/6-16/11-9/5-18/11-14/11 Magic
14 0-8-9-10-18-20 1-16/11-9/5-9/8-18/11-14/11 Apollo
15 0-7-9-11-18-20 1-7/6-9/5-7/5-18/11-14/11 Octarod
16 0-9-10-11-18-20 1-9/5-9/8-7/5-18/11-14/11 Magic
17 0-8-9-13-18-20 1-16/11-20/11-12/11-18/11-14/11 Otonal
18 0-9-11-13-18-20 1-9/5-7/5-12/11-18/11-14/11 Octarod
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