Porcupine/Chords: Difference between revisions

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autopatrolled, Sysops
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added chord names
Line 6: Line 6:


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 applied to [[Pergen|pergens]]. The genchain of intervals is: 
... <u>M3</u> vA4 ^5 <u>M6</u> vM7 ^1 <u>M2</u> vM3 ^4 <u>P5</u> vM6 ^m7 '''<u>P1</u>''' vM2 ^m3 <u>P4</u> v5 ^m6 <u>m7</u> v8 ^m2 <u>m3</u> v4 ^d5 <u>m6</u> ...


== Triads ==
== Triads ==
Line 17: Line 21:
! 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
|^m,v9no5
|-
|-
| 0-1-3
| 0-1-3
Line 29: Line 35:
| 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
|^m7no5
|-
|-
| 0-2-3
| 0-2-3
Line 37: Line 44:
| 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'''
|^m7no3
|-
|-
| 0-1-4
| 0-1-4
Line 44: Line 52:
| 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'''
|^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
|^m(v5)
|-
|-
| 0-3-4
| 0-3-4
Line 57: Line 67:
| 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
|v2
|-
|-
| 0-1-5
| 0-1-5
Line 66: Line 77:
| 1/1-16/11-20/11
| 1/1-16/11-20/11
| 1/1-5/4-11/8
| 1/1-5/4-11/8
|
|-
|-
| 0-2-5
| 0-2-5
Line 72: Line 84:
| 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'''
|v
|-
|-
| 0-3-5
| 0-3-5
Line 78: Line 91:
| 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
|^m
|-
|-
| 0-4-5
| 0-4-5
Line 86: Line 100:
| 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'''
|v^7no5
|-
|-
| 0-1-6
| 0-1-6
Line 93: Line 108:
| 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'''
|v,9no5
|-
|-
| 0-2-6
| 0-2-6
Line 101: Line 117:
| 1/1-16/11-18/11
| 1/1-16/11-18/11
| 1/1-9/8-11/8
| 1/1-9/8-11/8
|
|-
|-
| 0-3-6
| 0-3-6
Line 106: Line 123:
| 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'''
|4 <u>or</u> 2
|-
|-
| 0-4-6
| 0-4-6
Line 115: Line 133:
| 1/1-11/9-11/8
| 1/1-11/9-11/8
| 1/1-9/8-18/11
| 1/1-9/8-18/11
|
|-
|-
| 0-5-6
| 0-5-6
Line 121: Line 140:
| 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'''
|^m9no35
|-
|-
| 0-2-8
| 0-2-8
Line 129: Line 149:
| 1/1-9/8-15/8
| 1/1-9/8-15/8
| 1/1-5/3-16/9
| 1/1-5/3-16/9
|
|-
|-
| 0-3-8
| 0-3-8
Line 134: Line 155:
| 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
|vM7no5
|-
|-
| 0-4-8
| 0-4-8
Line 142: Line 164:
| 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'''
|^4(v5)
|-
|-
| 0-5-8
| 0-5-8
Line 148: Line 171:
| 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
|vM7no3
|-
|-
| 0-6-8
| 0-6-8
Line 157: Line 181:
| 1/1-5/3-15/8
| 1/1-5/3-15/8
| 1/1-9/8-6/5
| 1/1-9/8-6/5
|
|-
|-
| 0-1-9
| 0-1-9
Line 164: Line 189:
| 1/1-16/15-20/11
| 1/1-16/15-20/11
| 1/1-12/7-15/8
| 1/1-12/7-15/8
|
|-
|-
| 0-3-9
| 0-3-9
Line 170: Line 196:
| 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'''
|7no3
|-
|-
| 0-4-9
| 0-4-9
Line 176: Line 203:
| 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
|v,6no5
|-
|-
| 0-5-9
| 0-5-9
Line 184: Line 212:
| 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'''
|v(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
|m7no5
|-
|-
| 0-8-9
| 0-8-9
Line 199: Line 229:
| 1/1-11/10-15/8
| 1/1-11/10-15/8
| 1/1-12/7-20/11
| 1/1-12/7-20/11
|
|-
|-
| 0-1-10
| 0-1-10
Line 206: Line 237:
| 1/1-7/6-11/6
| 1/1-7/6-11/6
| 1/1-11/7-12/7
| 1/1-11/7-12/7
|
|-
|-
| 0-2-10
| 0-2-10
Line 213: Line 245:
| 1/1-16/15-5/3
| 1/1-16/15-5/3
| 1/1-11/7-15/8
| 1/1-11/7-15/8
|
|-
|-
| 0-4-10
| 0-4-10
Line 220: Line 253:
| 1/1-8/7-11/7
| 1/1-8/7-11/7
| 1/1-11/8-7/4
| 1/1-11/8-7/4
|
|-
|-
| 0-5-10
| 0-5-10
Line 227: Line 261:
| 1/1-5/4-11/7
| 1/1-5/4-11/7
| 1/1-5/4-8/5
| 1/1-5/4-8/5
|
|-
|-
| 0-6-10
| 0-6-10
Line 234: Line 269:
| 1/1-11/8-11/7
| 1/1-11/8-11/7
| 1/1-8/7-16/11
| 1/1-8/7-16/11
|
|-
|-
| 0-8-10
| 0-8-10
Line 241: Line 277:
| 1/1-6/5-15/8
| 1/1-6/5-15/8
| 1/1-11/7-5/3
| 1/1-11/7-5/3
|
|-
|-
| 0-9-10
| 0-9-10
Line 248: Line 285:
| 1/1-12/11-12/7
| 1/1-12/11-12/7
| 1/1-11/7-11/6
| 1/1-11/7-11/6
|
|-
|-
| 0-1-11
| 0-1-11
Line 255: Line 293:
| 1/1-14/11-20/11
| 1/1-14/11-20/11
| 1/1-10/7-11/7
| 1/1-10/7-11/7
|
|-
|-
| 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
|^m(vv5)
|-
|-
| 0-3-11
| 0-3-11
Line 269: Line 309:
| 1/1-16/15-3/2
| 1/1-16/15-3/2
| 1/1-10/7-15/8
| 1/1-10/7-15/8
|
|-
|-
| 0-5-11
| 0-5-11
Line 275: Line 316:
| 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'''
|v,7no5
|-
|-
| 0-6-11
| 0-6-11
Line 283: Line 325:
| 1/1-5/4-10/7
| 1/1-5/4-10/7
| 1/1-8/7-8/5
| 1/1-8/7-8/5
|
|-
|-
| 0-8-11
| 0-8-11
Line 288: Line 331:
| 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
|vM7(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
|m(vv5)
|-
|-
| 0-10-11
| 0-10-11
Line 304: Line 349:
| 1/1-11/10-11/7
| 1/1-11/10-11/7
| 1/1-10/7-20/11
| 1/1-10/7-20/11
|
|-
|-
| 0-1-12
| 0-1-12
Line 311: Line 357:
| 1/1-7/5-9/5
| 1/1-7/5-9/5
| 1/1-9/7-10/7
| 1/1-9/7-10/7
|
|-
|-
| 0-2-12
| 0-2-12
Line 318: Line 365:
| 1/1-14/11-18/11
| 1/1-14/11-18/11
| 1/1-9/7-11/7
| 1/1-9/7-11/7
|
|-
|-
| 0-3-12
| 0-3-12
Line 323: Line 371:
| 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
|m
|-
|-
| 0-4-12
| 0-4-12
Line 332: Line 381:
| 1/1-16/15-11/8
| 1/1-16/15-11/8
| 1/1-9/7-15/8
| 1/1-9/7-15/8
|
|-
|-
| 0-6-12
| 0-6-12
Line 338: Line 388:
| 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'''
|9no35
|-
|-
| 0-8-12
| 0-8-12
Line 346: Line 397:
| 1/1-16/11-15/8
| 1/1-16/11-15/8
| 1/1-9/7-11/8
| 1/1-9/7-11/8
|
|-
|-
| 0-9-12
| 0-9-12
Line 352: Line 404:
| 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'''
|(major)
|-
|-
| 0-10-12
| 0-10-12
Line 360: Line 413:
| 1/1-11/9-11/7
| 1/1-11/9-11/7
| 1/1-9/7-18/11
| 1/1-9/7-18/11
|
|-
|-
| 0-11-12
| 0-11-12
Line 367: Line 421:
| 1/1-10/9-10/7
| 1/1-10/9-10/7
| 1/1-9/7-9/5
| 1/1-9/7-9/5
|
|-
|-
| 0-2-14
| 0-2-14
Line 374: Line 429:
| 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 437:
| 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 445:
| 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 453:
| 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 461:
| 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 469:
| 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 477:
| 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 485:
| 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 493:
| 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 501:
| 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 515:
! Second inversion
! Second inversion
! Third inversion
! Third inversion
!name
|-
|-
| 0-1-2-3
| 0-1-2-3
Line 458: Line 524:
| 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   
|
|-
|-
| 0-1-2-4
| 0-1-2-4
Line 465: Line 532:
| 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'''
|v6(^4)
|-
|-
| 0-1-3-4
| 0-1-3-4
Line 472: Line 540:
| 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  
|v2v6
|-
|-
| 0-1-2-5
| 0-1-2-5
Line 481: Line 550:
| 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'''
|v^4
|-
|-
| 0-1-3-5
| 0-1-3-5
Line 488: Line 558:
| 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   
|^mv6
|-
|-
| 0-1-4-5
| 0-1-4-5
Line 498: Line 569:
| 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  
|
|-
|-
| 0-2-3-5
| 0-2-3-5
Line 504: Line 576:
| 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'''
|v6 or ^m7
|-
|0-2-4-5
|
|
|
|
|
|
|v^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
|
|-
|-
| 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
| 1/1-7/6-4/3-7/4
| 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
|-
|-
| 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
| 1/1-9/7-15/11-15/8
|
|}
|}


Revision as of 02:23, 17 October 2024

Below are listed the dyadic chords of 11-limit 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, by 121/120 biyatismic, by 176/175 valinorsmic, and by 385/384 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.

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.

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 applied to pergens. The genchain of intervals is:

... M3 vA4 ^5 M6 vM7 ^1 M2 vM3 ^4 P5 vM6 ^m7 P1 vM2 ^m3 P4 v5 ^m6 m7 v8 ^m2 m3 v4 ^d5 m6 ...

Triads

Chord Transversal Type As generated 1st Inversion 2nd Inversion name
0-1-2 1-11/10-6/5 otonal 1/1-11/10-6/5 1/1-12/11-20/11 1/1-5/3-11/6 ^m,v9no5
0-1-3 1-10/9-4/3 otonal 1/1-10/9-4/3 1/1-6/5-9/5 1/1-3/2-5/3 ^m7no5
0-2-3 1-11/9-4/3 otonal 1/1-11/9-4/3 1/1-12/11-18/11 1/1-3/2-11/6 ^m7no3
0-1-4 1-12/11-16/11 otonal 1/1-12/11-16/11 1/1-4/3-11/6 1/1-11/8-3/2 ^4
0-2-4 1-6/5-22/15 otonal 1/1-6/5-22/15 1/1-11/9-5/3 1/1-15/11-18/11 ^m(v5)
0-3-4 1-4/3-22/15 otonal 1/1-4/3-22/15 1/1-11/10-3/2 1/1-15/11-20/11 v2
0-1-5 1-11/10-8/5 otonal 1/1-11/10-8/5 1/1-16/11-20/11 1/1-5/4-11/8
0-2-5 1-6/5-8/5 otonal 1/1-6/5-8/5 1/1-4/3-5/3 1/1-5/4-3/2 v
0-3-5 1-4/3-8/5 utonal 1/1-4/3-8/5 1/1-6/5-3/2 1/1-5/4-5/3 ^m
0-4-5 1-22/15-8/5 otonal 1/1-22/15-8/5 1/1-12/11-15/11 1/1-5/4-11/6 v^7no5
0-1-6 1-10/9-16/9 otonal 1/1-10/9-16/9 1/1-8/5-9/5 1/1-9/8-5/4 v,9no5
0-2-6 1-11/9-16/9 otonal 1/1-11/9-16/9 1/1-16/11-18/11 1/1-9/8-11/8
0-3-6 1-4/3-16/9 ambitonal 1/1-4/3-16/9 1/1-4/3-3/2 1/1-9/8-3/2 4 or 2
0-4-6 1-16/11-16/9 utonal 1/1-16/11-16/9 1/1-11/9-11/8 1/1-9/8-18/11
0-5-6 1-8/5-16/9 utonal 1/1-8/5-16/9 1/1-10/9-5/4 1/1-9/8-9/5 ^m9no35
0-2-8 1-6/5-16/15 otonal 1/1-16/15-6/5 1/1-9/8-15/8 1/1-5/3-16/9
0-3-8 1-4/3-16/15 ambitonal 1/1-16/15-4/3 1/1-5/4-15/8 1/1-3/2-8/5 vM7no5
0-4-8 1-22/15-16/15 otonal 1/1-16/15-22/15 1/1-11/8-15/8 1/1-15/11-16/11 ^4(v5)
0-5-8 1-8/5-16/15 ambitonal 1/1-16/15-8/5 1/1-3/2-15/8 1/1-5/4-4/3 vM7no3
0-6-8 1-16/9-16/15 utonal 1/1-16/15-16/9 1/1-5/3-15/8 1/1-9/8-6/5
0-1-9 1-11/10-7/6 valinorsmic 1/1-11/10-7/6 1/1-16/15-20/11 1/1-12/7-15/8
0-3-9 1-4/3-7/6 otonal 1/1-7/6-4/3 1/1-8/7-12/7 1/1-3/2-7/4 7no3
0-4-9 1-16/11-7/6 keenanismic 1/1-7/6-16/11 1/1-5/4-12/7 1/1-11/8-8/5 v,6no5
0-5-9 1-8/5-7/6 keenanismic 1/1-7/6-8/5 1/1-11/8-12/7 1/1-5/4-16/11 v(v5)
0-6-9 1-7/4-7/6 utonal 1/1-7/6-7/4 1/1-3/2-12/7 1/1-8/7-4/3 m7no5
0-8-9 1-16/15-7/6 valinorsmic 1/1-16/15-7/6 1/1-11/10-15/8 1/1-12/7-20/11
0-1-10 1-12/11-14/11 otonal 1/1-12/11-14/11 1/1-7/6-11/6 1/1-11/7-12/7
0-2-10 1-6/5-14/11 valinorsmic 1/1-6/5-14/11 1/1-16/15-5/3 1/1-11/7-15/8
0-4-10 1-16/11-14/11 otonal 1/1-14/11-16/11 1/1-8/7-11/7 1/1-11/8-7/4
0-5-10 1-8/5-14/11 valinorsmic 1/1-14/11-8/5 1/1-5/4-11/7 1/1-5/4-8/5
0-6-10 1-7/4-14/11 utonal 1/1-14/11-7/4 1/1-11/8-11/7 1/1-8/7-16/11
0-8-10 1-16/15-14/11 valinorsmic 1/1-16/15-14/11 1/1-6/5-15/8 1/1-11/7-5/3
0-9-10 1-7/6-14/11 utonal 1/1-7/6-14/11 1/1-12/11-12/7 1/1-11/7-11/6
0-1-11 1-11/10-7/5 otonal 1/1-11/10-7/5 1/1-14/11-20/11 1/1-10/7-11/7
0-2-11 1-6/5-7/5 otonal 1/1-6/5-7/5 1/1-7/6-5/3 1/1-10/7-12/7 ^m(vv5)
0-3-11 1-4/3-7/5 archytas 1/1-4/3-7/5 1/1-16/15-3/2 1/1-10/7-15/8
0-5-11 1-8/5-7/5 otonal 1/1-7/5-8/5 1/1-8/7-10/7 1/1-5/4-7/4 v,7no5
0-6-11 1-7/4-7/5 utonal 1/1-7/5-7/4 1/1-5/4-10/7 1/1-8/7-8/5
0-8-11 1-16/15-7/5 archytas 1/1-16/15-7/5 1/1-4/3-15/8 1/1-10/7-3/2 vM7(4)
0-9-11 1-7/6-7/5 utonal 1/1-7/6-7/5 1/1-6/5-12/7 1/1-10/7-5/3 m(vv5)
0-10-11 1-14/11-7/5 utonal 1/1-14/11-7/5 1/1-11/10-11/7 1/1-10/7-20/11
0-1-12 1-10/9-14/9 otonal 1/1-10/9-14/9 1/1-7/5-9/5 1/1-9/7-10/7
0-2-12 1-11/9-14/9 otonal 1/1-11/9-14/9 1/1-14/11-18/11 1/1-9/7-11/7
0-3-12 1-4/3-14/9 otonal 1/1-4/3-14/9 1/1-7/6-3/2 1/1-9/7-12/7 m
0-4-12 1-16/11-14/9 keenanismic 1/1-16/11-14/9 1/1-16/15-11/8 1/1-9/7-15/8
0-6-12 1-16/9-14/9 otonal 1/1-14/9-16/9 1/1-8/7-9/7 1/1-9/8-7/4 9no35
0-8-12 1-16/15-14/9 keenanismic 1/1-16/15-14/9 1/1-16/11-15/8 1/1-9/7-11/8
0-9-12 1-7/6-14/9 utonal 1/1-7/6-14/9 1/1-4/3-12/7 1/1-9/7-3/2 (major)
0-10-12 1-14/11-14/9 utonal 1/1-14/11-14/9 1/1-11/9-11/7 1/1-9/7-18/11
0-11-12 1-7/5-14/9 utonal 1/1-7/5-14/9 1/1-10/9-10/7 1/1-9/7-9/5
0-2-14 1-6/5-28/15 otonal 1/1-6/5-28/15 1/1-14/9-5/3 1/1-15/14-9/7
0-3-14 1-4/3-28/15 otonal 1/1-4/3-28/15 1/1-7/5-3/2 1/1-15/14-10/7
0-4-14 1-22/15-28/15 otonal 1/1-22/15-28/15 1/1-14/11-15/11 1/1-15/14-11/7
0-5-14 1-8/5-28/15 otonal 1/1-8/5-28/15 1/1-7/6-5/4 1/1-15/14-12/7
0-6-14 1-7/4-28/15 utonal 1/1-7/4-28/15 1/1-16/15-8/7 1/1-15/14-15/8
0-8-14 1-16/15-28/15 otonal 1/1-16/15-28/15 1/1-7/4-15/8 1/1-15/14-8/7
0-9-14 1-7/6-28/15 utonal 1/1-7/6-28/15 1/1-8/5-12/7 1/1-15/14-5/4
0-10-14 1-14/11-28/15 utonal 1/1-14/11-28/15 1/1-22/15-11/7 1/1-15/14-15/11
0-11-14 1-7/5-28/15 utonal 1/1-7/5-28/15 1/1-4/3-10/7 1/1-15/14-3/2
0-12-14 1-14/9-28/15 utonal 1/1-14/9-28/15 1/1-6/5-9/7 1/1-15/14-5/3

Tetrads

Chord Transversal Type As generated First inversion Second inversion Third inversion name
0-1-2-3 1-10/9-11/9-4/3 otonal 1/1-10/9-11/9-4/3 1/1-11/10-6/5-9/5 1/1-12/11-18/11-20/11 1/1-3/2-5/3-11/6
0-1-2-4 1-11/10-11/9-22/15 utonal 1/1-11/10-11/9-22/15 1/1-10/9-4/3-20/11 1/1-6/5-18/11-9/5 1/1-15/11-3/2-5/3 v6(^4)
0-1-3-4 1-10/9-4/3-22/15 ptolemismic 1/1-10/9-4/3-22/15 1/1-6/5-4/3-9/5 1/1-11/10-3/2-5/3 1/1-15/11-3/2-20/11 v2v6
0-1-2-5 1-11/10-6/5-8/5 otonal 1/1-11/10-6/5-8/5 1/1-12/11-16/11-20/11 1/1-4/3-5/3-11/6 1/1-5/4-11/8-3/2 v^4
0-1-3-5 1-11/10-4/3-8/5 ptolemismic 1/1-11/10-4/3-8/5 1/1-6/5-16/11-20/11 1/1-6/5-3/2-5/3 1/1-5/4-11/8-5/3 ^mv6
0-1-4-5 1-11/10-16/11-8/5 biyatismic 1/1-11/10-16/11-8/5 1/1-4/3-16/11-20/11 1/1-11/10-11/8-3/2 1/1-5/4-11/8-20/11
0-2-3-5 1-6/5-4/3-8/5 ambitonal 1/1-6/5-4/3-8/5 1/1-10/9-4/3-5/3 1/1-6/5-3/2-9/5 1/1-5/4-3/2-5/3 v6 or ^m7
0-2-4-5 v^7
0-2-4-6 1-6/5-16/11-7/4 supermagic 1/1-6/5-16/11-7/4 1/1-6/5-16/11-5/3 1/1-6/5-11/8-5/3 1/1-8/7-11/8-5/3
0-3-6-9 1-4/3-7/4-7/6 archytas 1/1-7/6-4/3-7/4 1/1-8/7-3/2-12/7 1/1-4/3-3/2-7/4 1/1-8/7-4/3-3/2 7sus4
0-4-8-12 1-16/11-16/15-14/9 zeus 1/1-16/15-16/11-14/9 1/1-15/11-16/11-15/8 1/1-16/15-11/8-22/15 1/1-9/7-15/11-15/8

Pentads

Todo: clarify

investigate what's missing there

Chord Transversal Type
0-1-2-3-6 1-10/9-11/9-4/3-16/9 otonal
0-2-3-4-6
0-3-4-5-6
0-2-4-6-8 1-6/5-16/11-7/4-16/15 porcupine
0-3-6-9-12 1-4/3-7/4-7/6-14/9 archytas
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