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autopatrolled, Sysops
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TallKite (talk | contribs)
autopatrolled, Sysops
4,192 edits
added more chord names, added C as the chord root
Line 7: Line 7:
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'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.  


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|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#.  
{| class="wikitable"
{| class="wikitable"
|+Porcupine's genchain
|+Porcupine's genchain
Line 83: Line 83:
|^d8
|^d8
|-
|-
!Note
!Note (in C)
(in C)
|'''C'''
|'''C'''
|vD
|vD
Line 113: Line 112:
! 1st Inversion
! 1st Inversion
! 2nd Inversion
! 2nd Inversion
!name
!Name
|-
|-
| 0-1-2
| 0-1-2
Line 121: Line 120:
| 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 128:
| '''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 136:
| 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 144:
| 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 152:
| 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 160:
| '''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 168:
| '''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 176:
| 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 184:
| '''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 192:
| 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 200:
| 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 208:
| 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 216:
| '''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 <u>or</u> C2
|-
|-
| 0-4-6
| 0-4-6
Line 225: Line 224:
| '''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 232:
| 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 240:
| '''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 248:
| '''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 256:
| 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 264:
| '''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 272:
| 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 288:
| 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 296:
| '''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 304:
| 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 312:
| 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 326:
| 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 335:
| 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 343:
| 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 351:
| 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 366:
| 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 382:
| 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 392:
| 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 398:
| 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 408:
| 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 424:
| '''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 432:
| 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
Line 465: Line 464:
| '''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 481: Line 480:
| 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 497: Line 496:
| 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 616: Line 615:
| 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 624:
| 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 633:
| '''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 642:
| 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 651:
| '''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 658:
| 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 669:
| '''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 <u>or</u> C^m7
|-
|-
|0-2-4-5
|0-2-4-5
Line 679: Line 678:
|
|
|
|
|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
| supermagic
| 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)
|-
|-
| 0-3-6-9
| 0-3-6-9
Line 697: Line 696:
| '''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
|-
|0-3-9-11
|
|
|
|
|
|
|Cm7
|-
|-
| 0-4-8-12
| 0-4-8-12
Line 706: Line 714:
| 1/1-16/15-11/8-22/15
| 1/1-16/15-11/8-22/15
| 1/1-9/7-15/11-15/8
| 1/1-9/7-15/11-15/8
|
|C,vM7^11no5
|}
|}


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