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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. 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
! Note (in C)
(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 111: 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 121: 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
|^mv9no5
| C^mv9no5
|-
|-
| 0-1-3
| 0-1-3
Line 129: 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
|^m7no5
| C^m7no5
|-
|-
| 0-2-3
| 0-2-3
Line 137: 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'''
|^m7no3
| C^m7no3
|-
|-
| 0-1-4
| 0-1-4
Line 145: 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'''
|^4
| C^4
|-
|-
| 0-2-4
| 0-2-4
Line 153: 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
|^m(v5)
| C^m(v5)
|-
|-
| 0-3-4
| 0-3-4
Line 161: 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
|v2
| Cv2
|-
|-
| 0-1-5
| 0-1-5
Line 169: 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
|^7(v5)no3
| C^7(v5)no3
|-
|-
| 0-2-5
| 0-2-5
Line 177: 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'''
|v
| Cv
|-
|-
| 0-3-5
| 0-3-5
Line 185: 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
|^m
| C^m
|-
|-
| 0-4-5
| 0-4-5
Line 193: 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'''
|v^7no5
| Cv^7no5
|-
|-
| 0-1-6
| 0-1-6
Line 201: 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'''
|v,9no5
| Cv,9no5
|-
|-
| 0-2-6
| 0-2-6
Line 209: 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'''
|sus2(v5)
| Csus2(v5)
|-
|-
| 0-3-6
| 0-3-6
Line 217: 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'''
|4 <u>or</u> 2
| C4 ''or'' C2
|-
|-
| 0-4-6
| 0-4-6
Line 225: 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
|^m^4no5
| C^m^4no5
|-
|-
| 0-5-6
| 0-5-6
Line 233: 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'''
|^m9no35
| C^m9no35
|-
|-
| 0-2-8
| 0-2-8
Line 241: 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
|vM9no35
| CvM9no35
|-
|-
| 0-3-8
| 0-3-8
Line 249: 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
|vM7no5
| CvM7no5
|-
|-
| 0-4-8
| 0-4-8
Line 257: 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'''
|^4(v5)
| C^4(v5)
|-
|-
| 0-5-8
| 0-5-8
Line 265: 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
|vM7no3
| CvM7no3
|-
|-
| 0-6-8
| 0-6-8
Line 273: 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'''
|^m,9no5
| C^m,9no5
|-
|-
| 0-1-9
| 0-1-9
| 1-11/10-7/6
| 1-11/10-7/6
| valinorsmic
| valinorsmic
| 1/1-11/10-7/6
| '''1/1-11/10-7/6'''
| 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
|-
|-
| 0-3-9
| 0-3-9
Line 289: 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'''
|7no3
| C7no3
|-
|-
| 0-4-9
| 0-4-9
Line 297: 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
|v,6no5
| Cv,6no5
|-
|-
| 0-5-9
| 0-5-9
Line 305: 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'''
|v(v5)
| Cv(v5)
|-
|-
| 0-6-9
| 0-6-9
Line 313: 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
|m7no5
| Cm7no5
|-
|-
| 0-8-9
| 0-8-9
| 1-16/15-7/6
| 1-16/15-7/6
| valinorsmic
| valinorsmic
| 1/1-16/15-7/6
| '''1/1-16/15-7/6'''
| 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
|-
|-
| 0-1-10
| 0-1-10
Line 327: Line 324:
| otonal
| otonal
| 1/1-12/11-14/11
| 1/1-12/11-14/11
| 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
|-
|-
| 0-2-10
| 0-2-10
Line 336: Line 333:
| 1/1-6/5-14/11
| 1/1-6/5-14/11
| 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
|-
|-
| 0-4-10
| 0-4-10
Line 344: Line 341:
| 1/1-14/11-16/11
| 1/1-14/11-16/11
| 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
|-
|-
| 0-5-10
| 0-5-10
Line 352: Line 349:
| 1/1-14/11-8/5
| 1/1-14/11-8/5
| 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
|-
|-
| 0-6-10
| 0-6-10
| 1-7/4-14/11
| 1-7/4-14/11
| utonal
| utonal
| 1/1-14/11-7/4
| '''1/1-14/11-7/4'''
| 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
|-
|-
| 0-8-10
| 0-8-10
Line 367: Line 364:
| valinorsmic
| valinorsmic
| 1/1-16/15-14/11
| 1/1-16/15-14/11
| 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
|-
|-
| 0-9-10
| 0-9-10
| 1-7/6-14/11
| 1-7/6-14/11
| utonal
| utonal
| 1/1-7/6-14/11
| '''1/1-7/6-14/11'''
| 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
|-
|-
| 0-1-11
| 0-1-11
Line 383: Line 380:
| otonal
| otonal
| 1/1-11/10-7/5
| 1/1-11/10-7/5
| 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
|-
|-
| 0-2-11
| 0-2-11
Line 393: 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
|^m(vv5)
| C^m(vv5)
|-
|-
| 0-3-11
| 0-3-11
Line 399: Line 396:
| archytas
| archytas
| 1/1-4/3-7/5
| 1/1-4/3-7/5
| 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
|-
|-
| 0-5-11
| 0-5-11
Line 409: 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'''
|v,7no5
| Cv,7no5
|-
|-
| 0-6-11
| 0-6-11
| 1-7/4-7/5
| 1-7/4-7/5
| utonal
| utonal
| 1/1-7/5-7/4
| '''1/1-7/5-7/4'''
| 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
|-
|-
| 0-8-11
| 0-8-11
Line 425: 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
|vM7(4)
| CvM7(4)
|-
|-
| 0-9-11
| 0-9-11
Line 433: 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
|m(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 448: 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 456: 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 465: 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
|m
| Cm
|-
|-
| 0-4-12
| 0-4-12
Line 472: 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 481: 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'''
|9no35
| C9no35
|-
|-
| 0-8-12
| 0-8-12
Line 488: 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 497: 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'''
|(major)
| C
|-
|-
| 0-10-12
| 0-10-12
Line 504: 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 512: 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 607: Line 604:
! Second inversion
! Second inversion
! Third inversion
! Third inversion
!name
! Name
|-
|-
| 0-1-2-3
| 0-1-2-3
Line 616: 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'''
|v6^7no3
| Cv6^7no3
|-
|-
| 0-1-2-4
| 0-1-2-4
Line 625: 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'''
|v6(^4)
| Cv6(^4)
|-
|-
| 0-1-3-4
| 0-1-3-4
Line 634: 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  
|v2v6
| Cv2v6
|-
|-
| 0-1-2-5
| 0-1-2-5
Line 643: 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'''
|v^4
| Cv^4
|-
|-
| 0-1-3-5
| 0-1-3-5
Line 652: 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   
|^mv6
| C^mv6
|-
|-
| 0-1-4-5
| 0-1-4-5
Line 659: Line 656:
| 1/1-11/10-16/11-8/5   
| 1/1-11/10-16/11-8/5   
| 1/1-4/3-16/11-20/11  
| 1/1-4/3-16/11-20/11  
| 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
|-
|-
| 0-2-3-5
| 0-2-3-5
Line 670: 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'''
|v6 <u>or</u> ^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'''
|v^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) ''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
|7sus4
| C7sus4
|-
| 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 ''or'' C6
|-
|-
| 0-4-8-12
| 0-4-8-12
Line 705: 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
|}
|}


== Pentads ==
== Pentads ==
{{todo|inline=1| clarify | comment=investigate what's missing there }}
{| class="wikitable"
{| class="wikitable"
|-
|-
Line 717: 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"