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Below are listed the [[Dyadic chord|dyadic chords]] 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, by [[100/99]] [[Ptolemismic triad|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, 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]] 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¢.
 
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
! Genspan
! 0
! 1
! 2
! 3
! 4
! 5
! 6
! 7
! 8
! 9
! 10
! 11
! 12
! 13
! 14
|-
! Cents (22edo)
| 0
| 164
| 327
| 491
| 655
| 818
| 982
| 1145
| 109
| 273
| 436
| 600
| 764
| 927
| 1091
|-
! Ratio
| 1/1
| 10/9<br>11/10
| 6/5<br>11/9
| 4/3
| 16/11
| 8/5
| 16/9<br>7/4
| 48/25<br>160/81
| 16/15<br>21/20
| 7/6
| 14/11
| 7/5
| 14/9
|
| 28/15
|-
! Interval
| '''P1'''
| vM2
| ^m3
| '''P4'''
| v5
| ^m6
| '''m7'''
| v8
| ^m2
| '''m3'''
| v4
| ^b5
| '''m6'''
| vm7
| ^d8
|-
! Note (in C)
| '''C'''
| vD
| ^Eb
| '''F'''
| vG
| ^Ab
| '''Bb'''
| vC
| ^Db
| '''Eb'''
| vF
| ^Gb
| '''Ab'''
| vBb
| ^Cb
|}
{{Todo|inline=1|complete table|research|comment=Both tetrads and pentads are incomplete. Add the missing chords.}}


== Triads ==
== Triads ==
Line 15: Line 108:
! Type
! Type
! As generated
! As generated
! 1st Inversion
! 1st inversion
! 2nd Inversion
! 2nd inversion
! Name
|-
|-
| 0-1-2
| 0-1-2
| 1-11/10-6/5
| 1-11/10-6/5
| otonal
| otonal
| 1/1-11/10-6/5
| '''1/1-11/10-6/5'''
| 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
|-
|-
| 0-1-3
| 0-1-3
Line 29: Line 124:
| otonal
| otonal
| 1/1-10/9-4/3
| 1/1-10/9-4/3
| 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
|-
|-
| 0-2-3
| 0-2-3
Line 37: Line 133:
| 1/1-11/9-4/3
| 1/1-11/9-4/3
| 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
|-
|-
| 0-1-4
| 0-1-4
Line 44: Line 141:
| 1/1-12/11-16/11
| 1/1-12/11-16/11
| 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
|-
|-
| 0-2-4
| 0-2-4
| 1-6/5-22/15
| 1-6/5-22/15
| otonal
| otonal
| 1/1-6/5-22/15
| '''1/1-6/5-22/15'''
| 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)
|-
|-
| 0-3-4
| 0-3-4
Line 57: Line 156:
| otonal
| otonal
| 1/1-4/3-22/15
| 1/1-4/3-22/15
| 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
|-
|-
| 0-1-5
| 0-1-5
Line 64: Line 164:
| otonal
| otonal
| 1/1-11/10-8/5
| 1/1-11/10-8/5
| 1/1-16/11-20/11
| '''1/1-16/11-9/5'''
| 1/1-5/4-11/8
| 1/1-5/4-11/8
| C^7(v5)no3
|-
|-
| 0-2-5
| 0-2-5
Line 72: Line 173:
| 1/1-6/5-8/5
| 1/1-6/5-8/5
| 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
|-
|-
| 0-3-5
| 0-3-5
Line 78: Line 180:
| utonal
| utonal
| 1/1-4/3-8/5
| 1/1-4/3-8/5
| 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
|-
|-
| 0-4-5
| 0-4-5
Line 86: Line 189:
| 1/1-22/15-8/5
| 1/1-22/15-8/5
| 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
|-
|-
| 0-1-6
| 0-1-6
Line 93: Line 197:
| 1/1-10/9-16/9
| 1/1-10/9-16/9
| 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
|-
|-
| 0-2-6
| 0-2-6
Line 99: Line 204:
| otonal
| otonal
| 1/1-11/9-16/9
| 1/1-11/9-16/9
| 1/1-16/11-18/11
| 1/1-16/11-5/3
| 1/1-9/8-11/8
| '''1/1-9/8-11/8'''
| Csus2(v5)
|-
|-
| 0-3-6
| 0-3-6
Line 106: Line 212:
| ambitonal
| ambitonal
| 1/1-4/3-16/9
| 1/1-4/3-16/9
| 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 ''or'' C2
|-
|-
| 0-4-6
| 0-4-6
Line 113: Line 220:
| utonal
| utonal
| 1/1-16/11-16/9
| 1/1-16/11-16/9
| 1/1-11/9-11/8
| '''1/1-11/9-11/8'''
| 1/1-9/8-18/11
| 1/1-9/8-5/3
| C^m^4no5
|-
|-
| 0-5-6
| 0-5-6
Line 121: Line 229:
| 1/1-8/5-16/9
| 1/1-8/5-16/9
| 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
|-
|-
| 0-2-8
| 0-2-8
Line 127: Line 236:
| otonal
| otonal
| 1/1-16/15-6/5
| 1/1-16/15-6/5
| 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
|-
|-
| 0-3-8
| 0-3-8
Line 134: Line 244:
| ambitonal
| ambitonal
| 1/1-16/15-4/3
| 1/1-16/15-4/3
| 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
|-
|-
| 0-4-8
| 0-4-8
Line 142: Line 253:
| 1/1-16/15-22/15
| 1/1-16/15-22/15
| 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)
|-
|-
| 0-5-8
| 0-5-8
Line 148: Line 260:
| ambitonal
| ambitonal
| 1/1-16/15-8/5
| 1/1-16/15-8/5
| 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
|-
|-
| 0-6-8
| 0-6-8
Line 156: Line 269:
| 1/1-16/15-16/9
| 1/1-16/15-16/9
| 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
|-
|-
| 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 170: Line 285:
| 1/1-7/6-4/3
| 1/1-7/6-4/3
| 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
|-
|-
| 0-4-9
| 0-4-9
Line 176: Line 292:
| keenanismic
| keenanismic
| 1/1-7/6-16/11
| 1/1-7/6-16/11
| 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
|-
|-
| 0-5-9
| 0-5-9
Line 184: Line 301:
| 1/1-7/6-8/5
| 1/1-7/6-8/5
| 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)
|-
|-
| 0-6-9
| 0-6-9
| 1-7/4-7/6
| 1-7/4-7/6
| utonal
| utonal
| 1/1-7/6-7/4
| '''1/1-7/6-7/4'''
| 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
|-
|-
| 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 204: 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 212: 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 219: 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 226: 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 239: 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 253: 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
| 1-6/5-7/5
| 1-6/5-7/5
| otonal
| otonal
| 1/1-6/5-7/5
| '''1/1-6/5-7/5'''
| 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)
|-
|-
| 0-3-11
| 0-3-11
Line 267: 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 275: Line 405:
| 1/1-7/5-8/5
| 1/1-7/5-8/5
| 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
|-
|-
| 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 288: Line 420:
| archytas
| archytas
| 1/1-16/15-7/5
| 1/1-16/15-7/5
| 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)
|-
|-
| 0-9-11
| 0-9-11
| 1-7/6-7/5
| 1-7/6-7/5
| utonal
| utonal
| 1/1-7/6-7/5
| '''1/1-7/6-7/5'''
| 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)
|-
|-
| 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 310: 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 317: 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 323: Line 460:
| otonal
| otonal
| 1/1-4/3-14/9
| 1/1-4/3-14/9
| 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
|-
|-
| 0-4-12
| 0-4-12
Line 331: 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 338: Line 477:
| 1/1-14/9-16/9
| 1/1-14/9-16/9
| 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
|-
|-
| 0-8-12
| 0-8-12
Line 345: 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 352: Line 493:
| 1/1-7/6-14/9
| 1/1-7/6-14/9
| 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
|-
|-
| 0-10-12
| 0-10-12
Line 359: 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 366: 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 374: Line 518:
| 1/1-14/9-5/3
| 1/1-14/9-5/3
| 1/1-15/14-9/7
| 1/1-15/14-9/7
|
|-
|-
| 0-3-14
| 0-3-14
Line 381: Line 526:
| 1/1-7/5-3/2
| 1/1-7/5-3/2
| 1/1-15/14-10/7
| 1/1-15/14-10/7
|
|-
|-
| 0-4-14
| 0-4-14
Line 388: Line 534:
| 1/1-14/11-15/11
| 1/1-14/11-15/11
| 1/1-15/14-11/7
| 1/1-15/14-11/7
|
|-
|-
| 0-5-14
| 0-5-14
Line 395: Line 542:
| 1/1-7/6-5/4
| 1/1-7/6-5/4
| 1/1-15/14-12/7
| 1/1-15/14-12/7
|
|-
|-
| 0-6-14
| 0-6-14
Line 402: Line 550:
| 1/1-16/15-8/7
| 1/1-16/15-8/7
| 1/1-15/14-15/8
| 1/1-15/14-15/8
|
|-
|-
| 0-8-14
| 0-8-14
Line 409: Line 558:
| 1/1-7/4-15/8
| 1/1-7/4-15/8
| 1/1-15/14-8/7
| 1/1-15/14-8/7
|
|-
|-
| 0-9-14
| 0-9-14
Line 416: Line 566:
| 1/1-8/5-12/7
| 1/1-8/5-12/7
| 1/1-15/14-5/4
| 1/1-15/14-5/4
|
|-
|-
| 0-10-14
| 0-10-14
Line 423: Line 574:
| 1/1-22/15-11/7
| 1/1-22/15-11/7
| 1/1-15/14-15/11
| 1/1-15/14-15/11
|
|-
|-
| 0-11-14
| 0-11-14
Line 430: Line 582:
| 1/1-4/3-10/7
| 1/1-4/3-10/7
| 1/1-15/14-3/2
| 1/1-15/14-3/2
|
|-
|-
| 0-12-14
| 0-12-14
Line 437: Line 590:
| 1/1-6/5-9/7
| 1/1-6/5-9/7
| 1/1-15/14-5/3
| 1/1-15/14-5/3
|
|}
|}


Line 450: Line 604:
! Second inversion
! Second inversion
! Third inversion
! Third inversion
! Name
|-
|-
| 0-1-2-3
| 0-1-2-3
Line 457: Line 612:
| 1/1-11/10-6/5-9/5   
| 1/1-11/10-6/5-9/5   
| 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
|-
|-
| 0-1-2-4
| 0-1-2-4
Line 465: Line 621:
| 1/1-10/9-4/3-20/11  
| 1/1-10/9-4/3-20/11  
| 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)
|-
|-
| 0-1-3-4
| 0-1-3-4
Line 472: Line 629:
| 1/1-10/9-4/3-22/15  
| 1/1-10/9-4/3-22/15  
| 1/1-6/5-4/3-9/5   
| 1/1-6/5-4/3-9/5   
| 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
|-
|-
| 0-1-2-5
| 0-1-2-5
Line 481: Line 639:
| 1/1-12/11-16/11-20/11  
| 1/1-12/11-16/11-20/11  
| 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
|-
|-
| 0-1-3-5
| 0-1-3-5
Line 488: Line 647:
| 1/1-11/10-4/3-8/5   
| 1/1-11/10-4/3-8/5   
| 1/1-6/5-16/11-20/11  
| 1/1-6/5-16/11-20/11  
| 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
|-
|-
| 0-1-4-5
| 0-1-4-5
Line 496: 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 504: Line 665:
| 1/1-6/5-4/3-8/5   
| 1/1-6/5-4/3-8/5   
| 1/1-10/9-4/3-5/3   
| 1/1-10/9-4/3-5/3   
| 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 ''or'' C^m7
|-
| 0-2-4-5
| 1-6/5-16/11-8/5
| ptolemismic
| 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
|-
|-
| 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
| 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
| 1-16/11-16/15-14/9
| 1-16/11-16/15-14/9
| zeus
| zeus
| 1/1-16/15-16/11-14/9
| 1/1-16/15-16/11-14/9
| 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 540: 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
|}
|}


[[Category:Chords]]
[[Category:Lists of chords]]
[[Category:Porcupine]]
[[Category:Porcupine]]
[[Category:Triad]]
[[Category:Triads]]
[[Category:Tetrad]]
[[Category:Tetrads]]
[[Category:Pentad]]
[[Category:Pentads]]
Retrieved from "https://en.xen.wiki/w/Porcupine/Chords"