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Porcupine/Chords: Difference between revisions

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Below are listed the [[dyadic chord]]s of 11-limit [[porcupine|porcupine temperament]] that do not have generator steps 7 or 13 as dyads. Typing the chords requires consideration of the fact that porcupine conflates 10/9, 11/10 and 12/11 and also 16/9 and 7/4. 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 a chord is essentially tempered, the chord is analyzed in terms of the transversals 11/10, 6/5, 16/11 and 7/4. Chords that require only [[64/63]] tempering are marked [[archytas chords|archytas]], by [[100/99]] [[ptolemismic chords|ptolemismic]], by [[121/120]] [[biyatismic chords|biyatismic]], by [[176/175]] [[valinorsmic chords|valinorsmic]], and by [[385/384]] [[keenanismic chords|keenanismic]]. Chords that require 64/63 and 176/175 tempering are marked ares, 100/99 and 385/384 tempered chords are [[supermagic chords|supermagic]], and 176/175 and 385/384 tempered chords are marked zeus. Chords that receive tempering by three independent commas above are labeled porcupine.
Below are listed the [[15-odd-limit]] [[dyadic chord]]s of [[11-limit]] [[porcupine|porcupine temperament]] that do not have generator steps 7 or 13 as [[dyad]]s. Typing the chords requires consideration of the fact that porcupine conflates [[10/9]], [[11/10]] and [[12/11]], [[11/9]] with [[6/5]], [[22/15]] with [[16/11]], and [[16/9]] with [[7/4]]. 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 a chord is essentially tempered, the chord is analyzed in terms of the transversals 11/10, 6/5, 16/11 and 7/4. Chords that require only [[64/63]] tempering are marked [[archytas chords|archytas]], by [[100/99]] [[ptolemismic chords|ptolemismic]], by [[121/120]] [[biyatismic chords|biyatismic]], by [[176/175]] [[valinorsmic chords|valinorsmic]], and by [[385/384]] [[keenanismic chords|keenanismic]]. Chords that require any two of 64/63, 100/99 and 176/175 tempering are marked [[ares chords|ares]], that require 100/99 and 385/384 tempering are marked [[keemic chords|keemic]], and that require any two of 121/120, 176/175 and 385/384 are marked [[zeus chords|zeus]]. Chords that receive tempering by three independent commas above are labeled porcupine.


The transversal is in generator order. This is useful because it tells how common the chords are: For instance, a chord that appears on the sixth generation will appear exactly once in porcupine[7], twice in porcupine[8], and nine times in porcupine[15].
The transversal is in generator order. This is useful because it tells how common the chords are: For instance, a chord that appears on the sixth generation will appear exactly once in Porcupine[7], twice in Porcupine[8], and nine times in Porcupine[15].


The "As generated" column takes the intervals that were generated and places them in size order. The 1st and 2nd inversion (and so on) columns show the inversions of those generated tones. Note that this gives different results than you might be used to: the major chord (1/1 - 5/4 - 3/2, or 4:5:6) is the second inversion of the generated 0-2-5 chord.  
The "As generated" column takes the intervals that were generated and places them in size order. The 1st and 2nd inversion (and so on) columns show the inversions of those generated tones. Note that this gives different results than you might be used to: the major chord (1–5/4–3/2, or 4:5:6) is the second inversion of the generated 0–2–5 chord.  


Though we're used to thinking of 4:5:6 as the definitive "major chord", with all inversions coming from that, there is nothing definitive about calling these lists below "chord" or "inversion". That's just the way the generators came out.  
Though we are used to thinking of 4:5:6 as the definitive "major chord", with all inversions coming from that, there is nothing definitive about calling these lists below "chord" or "inversion". That is just the way the generators came out.  


The '''bolded''' inversions are named using [[ups and downs]] as described on the [[Pergen|pergens]] page. The pergen is (P8, P4/3) third-of-a-4th, #7 in the [http://tallkite.com/misc_files/notation%20guide%20for%20rank-2%20pergens.pdf notation guide for rank-2 pergens]. One up is -7 generators, octave-reduced, which is a third-sharp. The generator is vM2 = 167¢ - c/3, where c = the amount in cents the tempered fifth exceeds 700¢. ^1 = 33¢ + 2.33c. The enharmonic interval is v<sup>3</sup>A1, thus ^<sup>3</sup>C = C#.  
The '''bolded''' inversions are named using [[ups and downs]] as described on the [[Pergen]] page. The pergen is (P8, P4/3) third-of-a-4th, #7 in the [http://tallkite.com/misc_files/notation%20guide%20for%20rank-2%20pergens.pdf notation guide for rank-2 pergens]. One up is -7 generators, octave-reduced, which is a third-sharp. Thus ^<sup>3</sup>C = C# and the [[enharmonic unison]] is v<sup>3</sup>A1. The generator is vM2 = 167¢ - ''c''/3, where ''c'' is the amount in cents the tempered fifth exceeds 700¢. ^1 = 33¢ + 2.33''c''. In 22edo, ^1 = 1\22 = 54.5¢.
{| class="wikitable"
 
In porcupine, 5/4 = vM3, 7/4 = m7 and 11/8 = ^4. Thus ^1 equals ~81/80 and ~33/32. This may not be true for other (P8, P4/3) temperaments. So the ratios in the table below are specific to Porcupine, but the chord names apply to any (P8, P4/3) temperament.  
 
{| class="wikitable center-all"
|+Porcupine's genchain
|+Porcupine's genchain
!Genspan
! Genspan
!0
! 0
!1
! 1
!2
! 2
!3
! 3
!4
! 4
!5
! 5
!6
! 6
!7
! 7
!8
! 8
!9
! 9
!10
! 10
!11
! 11
!12
! 12
!13
! 13
!14
! 14
|-
|-
!Cents (22edo)
! Cents (22edo)
|0
| 0
|164
| 164
|327
| 327
|491
| 491
|655
| 655
|818
| 818
|982
| 982
|1145
| 1145
|109
| 109
|273
| 273
|436
| 436
|600
| 600
|764
| 764
|927
| 927
|1091
| 1091
|-
|-
!Ratio
! Ratio
|1/1
| 1/1
|10/9
| 10/9<br>11/10
11/10
| 6/5<br>11/9
|6/5
| 4/3
11/9
| 16/11
|4/3
| 8/5
|16/11
| 16/9<br>7/4
|8/5
| 48/25<br>160/81
|16/9
| 16/15<br>21/20
7/4
| 7/6
|14/25
| 14/11
160/81
| 7/5
|16/15
| 14/9
21/20
|  
|7/6
| 28/15
|14/11
|7/5
|14/9
|
|28/15
|-
|-
!Interval
! Interval
|'''P1'''
| '''P1'''
|vM2
| vM2
|^m3
| ^m3
|'''P4'''
| '''P4'''
|v5
| v5
|^m6
| ^m6
|'''m7'''
| '''m7'''
|v8
| v8
|^m2
| ^m2
|'''m3'''
| '''m3'''
|v4
| v4
|^b5
| ^b5
|'''m6'''
| '''m6'''
|vm7
| vm7
|^d8
| ^d8
|-
|-
!Note (in C)
! Note (in C)
|'''C'''
| '''C'''
|vD
| vD
|^Eb
| ^Eb
|'''F'''
| '''F'''
|vG
| vG
|^Ab
| ^Ab
|'''Bb'''
| '''Bb'''
|vC
| vC
|^Db
| ^Db
|'''Eb'''
| '''Eb'''
|vF
| vF
|^Gb
| ^Gb
|'''Ab'''
| '''Ab'''
|vBb
| vBb
|^Cb
| ^Cb
|}
|}
'''''TODO: complete the tables'''''
{{Todo|inline=1|complete table|research|comment=Both tetrads and pentads are incomplete. Add the missing chords.}}


== Triads ==
== Triads ==
Line 110: Line 108:
! Type
! Type
! As generated
! As generated
! 1st Inversion
! 1st inversion
! 2nd Inversion
! 2nd inversion
!Name
! Name
|-
|-
| 0-1-2
| 0-1-2
Line 120: Line 118:
| 1/1-12/11-20/11
| 1/1-12/11-20/11
| 1/1-5/3-11/6
| 1/1-5/3-11/6
|C^mv9no5
| C^mv9no5
|-
|-
| 0-1-3
| 0-1-3
Line 128: Line 126:
| '''1/1-6/5-9/5'''
| '''1/1-6/5-9/5'''
| 1/1-3/2-5/3
| 1/1-3/2-5/3
|C^m7no5
| C^m7no5
|-
|-
| 0-2-3
| 0-2-3
Line 136: Line 134:
| 1/1-12/11-18/11
| 1/1-12/11-18/11
| '''1/1-3/2-11/6'''
| '''1/1-3/2-11/6'''
|C^m7no3
| C^m7no3
|-
|-
| 0-1-4
| 0-1-4
Line 144: Line 142:
| 1/1-4/3-11/6
| 1/1-4/3-11/6
| '''1/1-11/8-3/2'''
| '''1/1-11/8-3/2'''
|C^4
| C^4
|-
|-
| 0-2-4
| 0-2-4
Line 152: Line 150:
| 1/1-11/9-5/3
| 1/1-11/9-5/3
| 1/1-15/11-18/11
| 1/1-15/11-18/11
|C^m(v5)
| C^m(v5)
|-
|-
| 0-3-4
| 0-3-4
Line 160: Line 158:
| '''1/1-11/10-3/2'''
| '''1/1-11/10-3/2'''
| 1/1-15/11-20/11
| 1/1-15/11-20/11
|Cv2
| Cv2
|-
|-
| 0-1-5
| 0-1-5
Line 168: Line 166:
| '''1/1-16/11-9/5'''
| '''1/1-16/11-9/5'''
| 1/1-5/4-11/8
| 1/1-5/4-11/8
|C^7(v5)no3
| C^7(v5)no3
|-
|-
| 0-2-5
| 0-2-5
Line 176: Line 174:
| 1/1-4/3-5/3
| 1/1-4/3-5/3
| '''1/1-5/4-3/2'''
| '''1/1-5/4-3/2'''
|Cv
| Cv
|-
|-
| 0-3-5
| 0-3-5
Line 184: Line 182:
| '''1/1-6/5-3/2'''
| '''1/1-6/5-3/2'''
| 1/1-5/4-5/3
| 1/1-5/4-5/3
|C^m
| C^m
|-
|-
| 0-4-5
| 0-4-5
Line 192: Line 190:
| 1/1-12/11-15/11
| 1/1-12/11-15/11
| '''1/1-5/4-11/6'''
| '''1/1-5/4-11/6'''
|Cv^7no5
| Cv^7no5
|-
|-
| 0-1-6
| 0-1-6
Line 200: Line 198:
| 1/1-8/5-9/5
| 1/1-8/5-9/5
| '''1/1-9/8-5/4'''
| '''1/1-9/8-5/4'''
|Cv,9no5
| Cv,9no5
|-
|-
| 0-2-6
| 0-2-6
Line 208: Line 206:
| 1/1-16/11-5/3
| 1/1-16/11-5/3
| '''1/1-9/8-11/8'''
| '''1/1-9/8-11/8'''
|Csus2(v5)
| Csus2(v5)
|-
|-
| 0-3-6
| 0-3-6
Line 216: Line 214:
| '''1/1-4/3-3/2'''
| '''1/1-4/3-3/2'''
| '''1/1-9/8-3/2'''
| '''1/1-9/8-3/2'''
|C4 <u>or</u> C2
| C4 ''or'' C2
|-
|-
| 0-4-6
| 0-4-6
Line 224: Line 222:
| '''1/1-11/9-11/8'''
| '''1/1-11/9-11/8'''
| 1/1-9/8-5/3
| 1/1-9/8-5/3
|C^m^4no5
| C^m^4no5
|-
|-
| 0-5-6
| 0-5-6
Line 232: Line 230:
| 1/1-10/9-5/4
| 1/1-10/9-5/4
| '''1/1-9/8-9/5'''
| '''1/1-9/8-9/5'''
|C^m9no35
| C^m9no35
|-
|-
| 0-2-8
| 0-2-8
Line 240: Line 238:
| '''1/1-9/8-15/8'''
| '''1/1-9/8-15/8'''
| 1/1-5/3-16/9
| 1/1-5/3-16/9
|CvM9no35
| CvM9no35
|-
|-
| 0-3-8
| 0-3-8
Line 248: Line 246:
| '''1/1-5/4-15/8'''
| '''1/1-5/4-15/8'''
| 1/1-3/2-8/5
| 1/1-3/2-8/5
|CvM7no5
| CvM7no5
|-
|-
| 0-4-8
| 0-4-8
Line 256: Line 254:
| 1/1-11/8-15/8
| 1/1-11/8-15/8
| '''1/1-15/11-16/11'''
| '''1/1-15/11-16/11'''
|C^4(v5)
| C^4(v5)
|-
|-
| 0-5-8
| 0-5-8
Line 264: Line 262:
| '''1/1-3/2-15/8'''
| '''1/1-3/2-15/8'''
| 1/1-5/4-4/3
| 1/1-5/4-4/3
|CvM7no3
| CvM7no3
|-
|-
| 0-6-8
| 0-6-8
Line 272: Line 270:
| 1/1-5/3-15/8
| 1/1-5/3-15/8
| '''1/1-9/8-6/5'''
| '''1/1-9/8-6/5'''
|C^m,9no5
| C^m,9no5
|-
|-
| 0-1-9
| 0-1-9
Line 280: Line 278:
| 1/1-16/15-20/11
| 1/1-16/15-20/11
| 1/1-12/7-15/8
| 1/1-12/7-15/8
|Cmv9no5
| Cmv9no5
|-
|-
| 0-3-9
| 0-3-9
Line 288: Line 286:
| 1/1-8/7-12/7
| 1/1-8/7-12/7
| '''1/1-3/2-7/4'''
| '''1/1-3/2-7/4'''
|C7no3
| C7no3
|-
|-
| 0-4-9
| 0-4-9
Line 296: Line 294:
| '''1/1-5/4-12/7'''
| '''1/1-5/4-12/7'''
| 1/1-11/8-8/5
| 1/1-11/8-8/5
|Cv,6no5
| Cv,6no5
|-
|-
| 0-5-9
| 0-5-9
Line 304: Line 302:
| 1/1-11/8-12/7
| 1/1-11/8-12/7
| '''1/1-5/4-16/11'''
| '''1/1-5/4-16/11'''
|Cv(v5)
| Cv(v5)
|-
|-
| 0-6-9
| 0-6-9
Line 312: Line 310:
| 1/1-3/2-12/7
| 1/1-3/2-12/7
| 1/1-8/7-4/3
| 1/1-8/7-4/3
|Cm7no5
| Cm7no5
|-
|-
| 0-8-9
| 0-8-9
Line 320: Line 318:
| 1/1-11/10-15/8
| 1/1-11/10-15/8
| 1/1-12/7-20/11
| 1/1-12/7-20/11
|Cm^b9no5
| Cm^b9no5
|-
|-
| 0-1-10
| 0-1-10
Line 328: Line 326:
| '''1/1-7/6-11/6'''
| '''1/1-7/6-11/6'''
| 1/1-11/7-12/7
| 1/1-11/7-12/7
|Cm^7no5
| Cm^7no5
|-
|-
| 0-2-10
| 0-2-10
Line 336: Line 334:
| 1/1-16/15-5/3
| 1/1-16/15-5/3
| '''1/1-11/7-15/8'''
| '''1/1-11/7-15/8'''
|CvM7(^5)no3
| CvM7(^5)no3
|-
|-
| 0-4-10
| 0-4-10
Line 344: Line 342:
| 1/1-8/7-11/7
| 1/1-8/7-11/7
| '''1/1-11/8-7/4'''
| '''1/1-11/8-7/4'''
|C7(^4)no5
| C7(^4)no5
|-
|-
| 0-5-10
| 0-5-10
Line 352: Line 350:
| 1/1-5/4-11/7
| 1/1-5/4-11/7
| '''1/1-5/4-8/5'''
| '''1/1-5/4-8/5'''
|Cv^b6
| Cv^b6
|-
|-
| 0-6-10
| 0-6-10
Line 360: Line 358:
| 1/1-11/8-11/7
| 1/1-11/8-11/7
| 1/1-8/7-16/11
| 1/1-8/7-16/11
|C7(v4)no5
| C7(v4)no5
|-
|-
| 0-8-10
| 0-8-10
Line 368: Line 366:
| '''1/1-6/5-15/8'''
| '''1/1-6/5-15/8'''
| 1/1-11/7-5/3
| 1/1-11/7-5/3
|C^mvM7
| C^mvM7
|-
|-
| 0-9-10
| 0-9-10
Line 376: Line 374:
| 1/1-12/11-12/7
| 1/1-12/11-12/7
| 1/1-11/7-11/6
| 1/1-11/7-11/6
|Cm,v11no5
| Cm,v11no5
|-
|-
| 0-1-11
| 0-1-11
Line 384: Line 382:
| '''1/1-14/11-20/11'''
| '''1/1-14/11-20/11'''
| 1/1-10/7-11/7
| 1/1-10/7-11/7
|C^7(v4)no5
| C^7(v4)no5
|-
|-
| 0-2-11
| 0-2-11
Line 392: Line 390:
| 1/1-7/6-5/3
| 1/1-7/6-5/3
| 1/1-10/7-12/7
| 1/1-10/7-12/7
|C^m(vv5)
| C^m(vv5)
|-
|-
| 0-3-11
| 0-3-11
Line 400: Line 398:
| '''1/1-16/15-3/2'''
| '''1/1-16/15-3/2'''
| 1/1-10/7-15/8
| 1/1-10/7-15/8
|C^b2
| C^b2
|-
|-
| 0-5-11
| 0-5-11
Line 408: Line 406:
| 1/1-8/7-10/7
| 1/1-8/7-10/7
| '''1/1-5/4-7/4'''
| '''1/1-5/4-7/4'''
|Cv,7no5
| Cv,7no5
|-
|-
| 0-6-11
| 0-6-11
Line 416: Line 414:
| 1/1-5/4-10/7
| 1/1-5/4-10/7
| 1/1-8/7-8/5
| 1/1-8/7-8/5
|C7(vv5)no3
| C7(vv5)no3
|-
|-
| 0-8-11
| 0-8-11
Line 424: Line 422:
| '''1/1-4/3-15/8'''
| '''1/1-4/3-15/8'''
| 1/1-10/7-3/2
| 1/1-10/7-3/2
|CvM7(4)
| CvM7(4)
|-
|-
| 0-9-11
| 0-9-11
Line 432: Line 430:
| 1/1-6/5-12/7
| 1/1-6/5-12/7
| 1/1-10/7-5/3
| 1/1-10/7-5/3
|Cm(vv5)
| Cm(vv5)
|-
|-
| 0-10-11
| 0-10-11
| 1-14/11-7/5
| 1-14/11-7/5
| utonal
| utonal
| 1/1-14/11-7/5
| '''1/1-14/11-7/5'''
| 1/1-11/10-11/7
| 1/1-11/10-11/7
| 1/1-10/7-20/11
| 1/1-10/7-20/11
|
| Cv4(vv5)
|-
|-
| 0-1-12
| 0-1-12
Line 447: Line 445:
| 1/1-10/9-14/9
| 1/1-10/9-14/9
| 1/1-7/5-9/5
| 1/1-7/5-9/5
| 1/1-9/7-10/7
| '''1/1-9/7-10/7'''
|
| C,^^11no5
|-
|-
| 0-2-12
| 0-2-12
Line 455: Line 453:
| 1/1-11/9-14/9
| 1/1-11/9-14/9
| 1/1-14/11-18/11
| 1/1-14/11-18/11
| 1/1-9/7-11/7
| '''1/1-9/7-11/7'''
|
| C(^5)
|-
|-
| 0-3-12
| 0-3-12
Line 464: Line 462:
| '''1/1-7/6-3/2'''
| '''1/1-7/6-3/2'''
| 1/1-9/7-12/7
| 1/1-9/7-12/7
|Cm
| Cm
|-
|-
| 0-4-12
| 0-4-12
Line 471: Line 469:
| 1/1-16/11-14/9
| 1/1-16/11-14/9
| 1/1-16/15-11/8
| 1/1-16/15-11/8
| 1/1-9/7-15/8
| '''1/1-9/7-15/8'''
|
| C,vM7no5
|-
|-
| 0-6-12
| 0-6-12
Line 480: Line 478:
| 1/1-8/7-9/7
| 1/1-8/7-9/7
| '''1/1-9/8-7/4'''
| '''1/1-9/8-7/4'''
|C9no35
| C9no35
|-
|-
| 0-8-12
| 0-8-12
Line 487: Line 485:
| 1/1-16/15-14/9
| 1/1-16/15-14/9
| 1/1-16/11-15/8
| 1/1-16/11-15/8
| 1/1-9/7-11/8
| '''1/1-9/7-11/8'''
|
| C,^11no5
|-
|-
| 0-9-12
| 0-9-12
Line 496: Line 494:
| 1/1-4/3-12/7
| 1/1-4/3-12/7
| '''1/1-9/7-3/2'''
| '''1/1-9/7-3/2'''
|C
| C
|-
|-
| 0-10-12
| 0-10-12
Line 503: Line 501:
| 1/1-14/11-14/9
| 1/1-14/11-14/9
| 1/1-11/9-11/7
| 1/1-11/9-11/7
| 1/1-9/7-18/11
| '''1/1-9/7-18/11'''
|
| C,v6no5
|-
|-
| 0-11-12
| 0-11-12
Line 511: Line 509:
| 1/1-7/5-14/9
| 1/1-7/5-14/9
| 1/1-10/9-10/7
| 1/1-10/9-10/7
| 1/1-9/7-9/5
| '''1/1-9/7-9/5'''
|
| C,^7no5
|-
|-
| 0-2-14
| 0-2-14
Line 606: Line 604:
! Second inversion
! Second inversion
! Third inversion
! Third inversion
!name
! Name
|-
|-
| 0-1-2-3
| 0-1-2-3
Line 615: Line 613:
| 1/1-12/11-18/11-20/11  
| 1/1-12/11-18/11-20/11  
| '''1/1-3/2-5/3-11/6'''
| '''1/1-3/2-5/3-11/6'''
|Cv6^7no3
| Cv6^7no3
|-
|-
| 0-1-2-4
| 0-1-2-4
Line 624: Line 622:
| 1/1-6/5-18/11-9/5   
| 1/1-6/5-18/11-9/5   
| '''1/1-15/11-3/2-5/3'''
| '''1/1-15/11-3/2-5/3'''
|Cv6(^4)
| Cv6(^4)
|-
|-
| 0-1-3-4
| 0-1-3-4
Line 633: Line 631:
| '''1/1-11/10-3/2-5/3'''
| '''1/1-11/10-3/2-5/3'''
| 1/1-15/11-3/2-20/11  
| 1/1-15/11-3/2-20/11  
|Cv2v6
| Cv2v6
|-
|-
| 0-1-2-5
| 0-1-2-5
Line 642: Line 640:
| 1/1-4/3-5/3-11/6   
| 1/1-4/3-5/3-11/6   
| '''1/1-5/4-11/8-3/2'''
| '''1/1-5/4-11/8-3/2'''
|Cv^4
| Cv^4
|-
|-
| 0-1-3-5
| 0-1-3-5
Line 651: Line 649:
| '''1/1-6/5-3/2-5/3'''
| '''1/1-6/5-3/2-5/3'''
| 1/1-5/4-11/8-5/3   
| 1/1-5/4-11/8-5/3   
|C^mv6
| C^mv6
|-
|-
| 0-1-4-5
| 0-1-4-5
Line 660: Line 658:
| '''1/1-11/10-11/8-3/2'''
| '''1/1-11/10-11/8-3/2'''
| 1/1-5/4-11/8-20/11  
| 1/1-5/4-11/8-20/11  
|C^4v9
| C^4v9
|-
|-
| 0-2-3-5
| 0-2-3-5
Line 669: Line 667:
| '''1/1-6/5-3/2-9/5'''
| '''1/1-6/5-3/2-9/5'''
| '''1/1-5/4-3/2-5/3'''
| '''1/1-5/4-3/2-5/3'''
|Cv6 <u>or</u> C^m7
| Cv6 ''or'' C^m7
|-
|-
|0-2-4-5
| 0-2-4-5
|1-6/5-16/11-8/5
| 1-6/5-16/11-8/5
|
| ptolemismic
|1-6/5-16/11-8/5
| 1/1-6/5-16/11-8/5
|
| 1/1-6/5-4/3-5/3
|
| 1/1-11/10-11/8-5/3
|
| '''1/1-5/4-3/2-9/5'''
|Cv^7
| Cv^7
|-
|-
| 0-2-4-6
| 0-2-4-6
| 1-6/5-16/11-7/4
| 1-6/5-16/11-7/4
| supermagic
| keemic
| '''1/1-6/5-16/11-7/4'''
| '''1/1-6/5-16/11-7/4'''
| 1/1-6/5-16/11-5/3
| 1/1-6/5-16/11-5/3
| 1/1-6/5-11/8-5/3
| '''1/1-6/5-11/8-5/3'''
| 1/1-8/7-11/8-5/3
| 1/1-8/7-11/8-5/3
|C^m,7(v5)
| C^m,7(v5) ''or''<br>C^mv6^11no5
|-
|-
| 0-3-6-9
| 0-3-6-9
| 1-4/3-7/4-7/6
| 1-4/3-7/4-7/6
| archytas
| archytas
| 1/1-7/6-4/3-7/4
| 1/1/1-7/6-4/3-7/4
| 1/1-8/7-3/2-12/7
| 1/1-8/7-3/2-12/7
| '''1/1-4/3-3/2-7/4'''
| '''1/1-4/3-3/2-7/4'''
| 1/1-8/7-4/3-3/2
| 1/1-8/7-4/3-3/2
|C7sus4
| C7sus4
|-
|-
|0-3-9-11
| 0-3-9-12
|
| 1-4/3-7/6-14/9
|
| archytas
|
| 1/1-7/6-4/3-14/9
|
| '''1/1-7/6-3/2-7/4'''
|
| 1/1-9/8-4/3-12/7
|
| 1/1-9/7-3/2-12/7
|Cm7
| Cm7 ''or'' C6
|-
|-
| 0-4-8-12
| 0-4-8-12
Line 713: Line 711:
| 1/1-15/11-16/11-15/8
| 1/1-15/11-16/11-15/8
| 1/1-16/15-11/8-22/15
| 1/1-16/15-11/8-22/15
| 1/1-9/7-15/11-15/8
| '''1/1-9/7-11/8-15/8'''
|C,vM7^11no5
| C,vM7^11no5
|}
|}


== Pentads ==
== Pentads ==
{{todo|inline=1| clarify | comment=investigate what's missing there }}
{| class="wikitable"
{| class="wikitable"
|-
|-
Line 725: Line 721:
! Transversal
! Transversal
! Type
! Type
|-
! Name
|
|
|
|-
|-
| 0-1-2-3-6
| 0-1-2-3-6
| 1-10/9-11/9-4/3-16/9
| 1-10/9-11/9-4/3-16/9
| otonal
| otonal
| Cv,9^11
|-
|-
| 0-2-3-4-6
| 0-2-3-4-6
|  
| 1-6/5-4/3-16/11-16/9
|  
| keemic
| C^m,7,11(v5) ''or''<br>C4^7v9 ''or'' C^4v6,9
|-
|-
| 0-3-4-5-6
| 0-3-4-5-6
|  
| 1-4/3-16/11-8/5-16/9
|  
| utonal
| C^mv9,11
|-
|-
| 0-2-4-6-8
| 0-2-4-6-8
| 1-6/5-16/11-7/4-16/15
| 1-6/5-16/11-7/4-16/15
| porcupine
| porcupine
| C^m,7(v5) ''or''<br>C^mv6^11no5
|-
|-
| 0-3-6-9-12
| 0-3-6-9-12
| 1-4/3-7/4-7/6-14/9
| 1-4/3-7/4-7/6-14/9
| archytas
| archytas
| C9(4) ''or'' C6,9 ''or'' Cm7,11
|}
|}


Retrieved from "https://en.xen.wiki/w/Porcupine/Chords"