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Chords of magic: Difference between revisions

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