Hemififths/Chords: Difference between revisions

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autopatrolled, Sysops
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TallKite (talk | contribs)
autopatrolled, Sysops
3,992 edits
added C as the chord root
Line 3: Line 3:
A striking feature of these hemififths chords is that essentially just chords tend to be of higher complexity than essentially tempered chords. Hemififths has MOS of size 7, 10, 17 and 24, and even seven notes are well-supplied with chords, mostly but by no means entirely essentially tempered chords. Extending consideration to the 13-limit adds even more such chords.
A striking feature of these hemififths chords is that essentially just chords tend to be of higher complexity than essentially tempered chords. Hemififths has MOS of size 7, 10, 17 and 24, and even seven notes are well-supplied with chords, mostly but by no means entirely essentially tempered chords. Extending consideration to the 13-limit adds even more such chords.


Chords are named with ups and downs, using pergen #4 (P8, P5/2) 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. The tilde ~ means mid, half-way between major and minor. ~4 = ^4 = vA4 and ~5 = v5 = ^d5. The comma (the actual punctuation mark) is pronounced "add", thus C~,7 is "C mid add 7". To facilitate chord naming, lifts and drops are also used. Enharmonic equivalences: vvA1 and v\m2. Cents: ^1 = 50¢ + 3.5c and /1 = 50¢ - 8.5c, where c = the amount in cents the tempered fifth exceeds 700¢. /1 = ~81/80 = ~64/63 and ^1 = ~33/32. To convert to 41edo, ^1 = 2\41 and /1 = 1\41.
Chords are named with ups and downs, using pergen #4 (P8, P5/2) 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, which is a half-sharp. The tilde ~ means mid, half-way between major and minor. ~4 = ^4 = vA4 and ~5 = v5 = ^d5. The comma (the actual punctuation mark) is pronounced "add", thus C~,7 is "C mid add 7". To facilitate chord naming, lifts and drops are also used. One lift is -17 generators, a half-diminished 2nd. Enharmonic equivalences: vvA1 and v\m2. Cents: ^1 = 50¢ + 3.5c and /1 = 50¢ - 8.5c, where c = the amount in cents the tempered fifth exceeds 700¢. /1 = ~81/80 = ~64/63 and ^1 = ~33/32. To convert to 41edo, ^1 = 2\41 and /1 = 1\41.
{| class="wikitable"
{| class="wikitable"
|+Hemififth's genchain
|+Hemififth's genchain
Line 134: Line 134:
| 1-11/9-3/2
| 1-11/9-3/2
| rastmic
| rastmic
|~
|C~
|
|
|-
|-
Line 141: Line 141:
| 1-11/9-11/6
| 1-11/9-11/6
| utonal
| utonal
|~7no5
|C~7no5
|
|
|-
|-
Line 148: Line 148:
| 1-3/2-11/6
| 1-3/2-11/6
| otonal
| otonal
|~7no3
|C~7no3
|
|
|-
|-
Line 155: Line 155:
| 1-11/9-9/8
| 1-11/9-9/8
| rastmic
| rastmic
|~,9no5
|C~,9no5
|
|
|-
|-
Line 162: Line 162:
| 1-3/2-9/8
| 1-3/2-9/8
| ambitonal
| ambitonal
|2 <u>or</u> 4
|C2 <u>or</u> C4
|1-4/3-9/8
|1-4/3-9/8
|-
|-
Line 169: Line 169:
| 1-11/6-9/8
| 1-11/6-9/8
| rastmic
| rastmic
|~9no35
|C~9no35
|
|
|-
|-
Line 176: Line 176:
| 1-11/9-11/8
| 1-11/9-11/8
| utonal
| utonal
|~(\b5)
|C~(\b5)
|
|
|-
|-
Line 183: Line 183:
| 1-3/2-11/8
| 1-3/2-11/8
| otonal
| otonal
|~7sus4no5
|C~7sus4no5
|1-4/3-11/6
|1-4/3-11/6
|-
|-
Line 190: Line 190:
| 1-11/6-11/8
| 1-11/6-11/8
| utonal
| utonal
|~2
|C~2
|1-12/11-3/2
|1-12/11-3/2
|-
|-
Line 197: Line 197:
| 1-9/8-11/8
| 1-9/8-11/8
| otonal
| otonal
|~,7no5
|C~,7no5
|1-11/9-16/9
|1-11/9-16/9
|-
|-
Line 204: Line 204:
| 1-11/6-14/11
| 1-11/6-14/11
| hemimin
| hemimin
|,~7no5
|C,~7no5
|
|
|-
|-
Line 211: Line 211:
| 1-9/8-14/11
| 1-9/8-14/11
| pentacircle
| pentacircle
|,9no5
|C,9no5
|
|
|-
|-
Line 218: Line 218:
| 1-11/8-14/11
| 1-11/8-14/11
| hemimin
| hemimin
|(\b5)
|C(\b5)
|
|
|-
|-
Line 225: Line 225:
| 1-11/9-14/9
| 1-11/9-14/9
| otonal
| otonal
|~(^5)
|C~(^5)
|
|
|-
|-
Line 232: Line 232:
| 1-9/8-14/9
| 1-9/8-14/9
| pentacircle
| pentacircle
|7~4no5
|C7~4no5
|1-11/8-16/9
|1-11/8-16/9
|-
|-
Line 239: Line 239:
| 1-11/8-14/9
| 1-11/8-14/9
| pentacircle
| pentacircle
|2(~5) <u>or</u>
|C2(~5) <u>or</u>
/,7no5
C/,7no5
|1-9/8-13/9
|1-9/8-13/9


Line 249: Line 249:
| 1-14/11-14/9
| 1-14/11-14/9
| utonal
| utonal
|(^5)
|C(^5)
|
|
|-
|-
Line 256: Line 256:
| 1-3/2-7/6
| 1-3/2-7/6
| otonal
| otonal
|\m
|C\m
|
|
|-
|-
Line 263: Line 263:
| 1-11/6-7/6
| 1-11/6-7/6
| otonal
| otonal
|\m~7no5
|C\m~7no5
|
|
|-
|-
Line 270: Line 270:
| 1-14/11-7/6
| 1-14/11-7/6
| utonal
| utonal
|~2/6
|C~2/6
|1-12/11-12/7
|1-12/11-12/7
|-
|-
Line 277: Line 277:
| 1-14/9-7/6
| 1-14/9-7/6
| utonal
| utonal
|/
|C/
|1-9/7-3/2
|1-9/7-3/2
|-
|-
Line 284: Line 284:
| 1-11/9-10/7
| 1-11/9-10/7
| swetismic
| swetismic
|~(\~5)
|C~(\~5)
|
|
|-
|-
Line 291: Line 291:
| 1-11/6-10/7
| 1-11/6-10/7
| swetismic
| swetismic
|/(b5)
|C/(b5)
|1-9/7-7/5
|1-9/7-7/5
|-
|-
Line 298: Line 298:
| 1-9/8-10/7
| 1-9/8-10/7
| werckismic
| werckismic
|2(\~5)
|C2(\~5)
|
|
|-
|-
Line 305: Line 305:
| 1-14/11-10/7
| 1-14/11-10/7
| werckismic
| werckismic
|(\~5)
|C(\~5)
|
|
|-
|-
Line 312: Line 312:
| 1-14/9-10/7
| 1-14/9-10/7
| swetismic
| swetismic
|~2(b5)
|C~2(b5)
|1-12/11-7/5
|1-12/11-7/5
|-
|-
Line 319: Line 319:
| 1-7/6-10/7
| 1-7/6-10/7
| swetismic
| swetismic
|\m(\~5)
|C\m(\~5)
|
|
|-
|-
Line 326: Line 326:
| 1-11/9-7/4
| 1-11/9-7/4
| werckismic
| werckismic
|~,\7no5
|C~,\7no5
|
|
|-
|-
Line 333: Line 333:
| 1-3/2-7/4
| 1-3/2-7/4
| otonal
| otonal
|\7no3
|C\7no3
|
|
|-
|-
Line 340: Line 340:
| 1-9/8-7/4
| 1-9/8-7/4
| otonal
| otonal
|\9no35
|C\9no35
|
|
|-
|-
Line 347: Line 347:
| 1-11/8-7/4
| 1-11/8-7/4
| otonal
| otonal
|(~5)
|C(~5)
|1-14/11-16/11
|1-14/11-16/11
|-
|-
Line 354: Line 354:
| 1-14/11-7/4
| 1-14/11-7/4
| utonal
| utonal
|,\7
|C,\7
|
|
|-
|-
Line 361: Line 361:
| 1-14/9-7/4
| 1-14/9-7/4
| utonal
| utonal
|/,2no5
|C/,2no5
|1-9/8-9/7
|1-9/8-9/7
|-
|-
Line 368: Line 368:
| 1-7/6-7/4
| 1-7/6-7/4
| utonal
| utonal
|\m7no5
|C\m7no5
|
|
|-
|-
Line 375: Line 375:
| 1-10/7-7/4
| 1-10/7-7/4
| werckismic
| werckismic
|~(b5)
|C~(b5)
|1-11/9-7/5
|1-11/9-7/5
|-
|-
Line 382: Line 382:
| 1-14/11-20/11
| 1-14/11-20/11
| otonal
| otonal
|,\~7no5
|C,\~7no5
|
|
|-
|-
Line 396: Line 396:
| 1-7/6-20/11
| 1-7/6-20/11
| swetismic
| swetismic
|\m\~7no5
|C\m\~7no5
|
|
|-
|-
Line 403: Line 403:
| 1-10/7-20/11
| 1-10/7-20/11
| utonal
| utonal
|(b5)
|C(b5)
|
|
|-
|-
Line 410: Line 410:
| 1-11/9-10/9
| 1-11/9-10/9
| otonal
| otonal
|~,\9no5
|C~,\9no5
|
|
|-
|-
Line 417: Line 417:
| 1-14/11-10/9
| 1-14/11-10/9
| werckismic
| werckismic
|,\9no5
|C,\9no5
|
|
|-
|-
Line 424: Line 424:
| 1-14/9-10/9
| 1-14/9-10/9
| otonal
| otonal
|/(\~5)
|C/(\~5)
|1-9/7-10/7
|1-9/7-10/7
|-
|-
Line 431: Line 431:
| 1-10/7-10/9
| 1-10/7-10/9
| utonal
| utonal
|\2(\~5)
|C\2(\~5)
|
|
|-
|-
Line 438: Line 438:
| 1-7/4-10/9
| 1-7/4-10/9
| werckismic
| werckismic
|\2\m7no5
|C\2\m7no5
|
|
|-
|-
Line 452: Line 452:
| 1-3/2-5/3
| 1-3/2-5/3
| otonal
| otonal
|\m7no5
|C\m7no5
|1-6/5-9/5
|1-6/5-9/5
|-
|-
Line 466: Line 466:
| 1-7/6-5/3
| 1-7/6-5/3
| otonal
| otonal
|\m6no5
|C\m6no5
|
|
|-
|-
Line 473: Line 473:
| 1-10/7-5/3
| 1-10/7-5/3
| utonal
| utonal
|/dim
|C/dim
|1-7/6-7/5
|1-7/6-7/5
|-
|-
Line 487: Line 487:
| 1-10/9-5/3
| 1-10/9-5/3
| utonal
| utonal
|/7no3
|C/7no3
|1-3/2-9/5
|1-3/2-9/5
|-
|-
Line 494: Line 494:
| 1-3/2-5/4
| 1-3/2-5/4
| otonal
| otonal
|\
|C\
|
|
|-
|-
Line 501: Line 501:
| 1-9/8-5/4
| 1-9/8-5/4
| otonal
| otonal
|\,9no5
|C\,9no5
|
|
|-
|-
Line 508: Line 508:
| 1-11/8-5/4
| 1-11/8-5/4
| otonal
| otonal
|\(\b5)
|C\(\b5)
|
|
|-
|-
Line 515: Line 515:
| 1-10/7-5/4
| 1-10/7-5/4
| utonal
| utonal
|\(\~5)
|C\(\~5)
|
|
|-
|-
Line 522: Line 522:
| 1-7/4-5/4
| 1-7/4-5/4
| otonal
| otonal
|\7no5
|C\7no5
|
|
|-
|-
Line 529: Line 529:
| 1-20/11-5/4
| 1-20/11-5/4
| utonal
| utonal
|\,\~7no5
|C\,\~7no5
|
|
|-
|-
Line 536: Line 536:
| 1-10/9-5/4
| 1-10/9-5/4
| utonal
| utonal
|/9no35
|C/9no35
|1-9/5-9/4
|1-9/5-9/4
|-
|-
Line 543: Line 543:
| 1-5/3-5/4
| 1-5/3-5/4
| utonal
| utonal
|/m
|C/m
|1-6/5-3/2
|1-6/5-3/2
|}
|}
Line 554: Line 554:
! Transversal
! Transversal
! Type
! Type
!Name
!Name
!Name
!Inversion
!Inversion
Line 561: Line 562:
| 1-11/9-3/2-11/6
| 1-11/9-3/2-11/6
| rastmic
| rastmic
|C~7
|~7
|~7
|
|
Line 568: Line 570:
| 1-11/9-3/2-9/8
| 1-11/9-3/2-9/8
| rastmic
| rastmic
|C~,9
|~,9
|~,9
|
|
Line 575: Line 578:
| 1-11/9-11/6-9/8
| 1-11/9-11/6-9/8
| rastmic
| rastmic
|C~9no5
|~9no5
|~9no5
|
|
Line 582: Line 586:
| 1-3/2-11/6-9/8
| 1-3/2-11/6-9/8
| rastmic
| rastmic
|C~9no3
|~9no3
|~9no3
|
|
Line 589: Line 594:
| 1-11/9-3/2-11/8
| 1-11/9-3/2-11/8
| rastmic
| rastmic
|C~,~11
|~,~11
|~,~11
|
|
Line 596: Line 602:
| 1-11/9-11/6-11/8
| 1-11/9-11/6-11/8
| utonal
| utonal
|2~6 <u>or</u>
|C2~6 <u>or</u>
C4~9|2~6 <u>or</u>
4~9
4~9
|1-9/8-3/2-13/8
|1-9/8-3/2-13/8
Line 605: Line 612:
| 1-3/2-11/6-11/8
| 1-3/2-11/6-11/8
| ambitonal
| ambitonal
|C~4~7
|~4~7
|~4~7
|
|
Line 612: Line 620:
| 1-11/9-9/8-11/8
| 1-11/9-9/8-11/8
| rastmic
| rastmic
|
|
|
|
|
Line 619: Line 628:
| 1-3/2-9/8-11/8
| 1-3/2-9/8-11/8
| otonal
| otonal
|C4~7
|4~7
|4~7
|1-4/3-3/2-11/6
|1-4/3-3/2-11/6
Line 626: Line 636:
| 1-11/6-9/8-11/8
| 1-11/6-9/8-11/8
| rastmic
| rastmic
|C~11no35
|~11no35
|~11no35
|
|
Line 633: Line 644:
| 1-11/6-9/8-14/11
| 1-11/6-9/8-14/11
| parahemif
| parahemif
|C9(~7)no5
|9(~7)no5
|9(~7)no5
|
|
Line 640: Line 652:
| 1-11/6-11/8-14/11
| 1-11/6-11/8-14/11
| hemimin
| hemimin
|C~2~11
|~2~11
|~2~11
|1-12/11-11/8-3/2
|1-12/11-11/8-3/2
Line 647: Line 660:
| 1-9/8-11/8-14/11
| 1-9/8-11/8-14/11
| parahemif
| parahemif
|C~,~9
|~,~9
|~,~9
|1-11/9-3/2-13/12
|1-11/9-3/2-13/12
Line 654: Line 668:
| 1-11/9-9/8-14/9
| 1-11/9-9/8-14/9
| parahemif
| parahemif
|C~,9(^5)
|~,9(^5)
|~,9(^5)
|
|
Line 661: Line 676:
| 1-11/9-11/8-14/9
| 1-11/9-11/8-14/9
| pentacircle
| pentacircle
|C,~6,9no5
|,~6,9no5
|,~6,9no5
|1-14/11-18/11-9/4
|1-14/11-18/11-9/4
Line 668: Line 684:
| 1-9/8-11/8-14/9
| 1-9/8-11/8-14/9
| pentacircle
| pentacircle
|C~,7(\b5)
|~,7(\b5)
|~,7(\b5)
|1-11/9-11/8-16/9
|1-11/9-11/8-16/9
Line 675: Line 692:
| 1-9/8-14/11-14/9
| 1-9/8-14/11-14/9
| pentacircle
| pentacircle
|
|
|
|
|
Line 682: Line 700:
| 1-11/8-14/11-14/9
| 1-11/8-14/11-14/9
| parahemif
| parahemif
|
|
|
|
|
Line 689: Line 708:
| 1-3/2-11/6-7/6
| 1-3/2-11/6-7/6
| otonal
| otonal
|C\m~7
|\m~7
|\m~7
|
|
Line 696: Line 716:
| 1-11/6-14/11-7/6
| 1-11/6-14/11-7/6
| hemimin
| hemimin
|
|
|
|
|
Line 703: Line 724:
| 1-14/11-14/9-7/6
| 1-14/11-14/9-7/6
| utonal
| utonal
|C/,~6
|/,~6
|/,~6
|1-9/7-3/2-18/11
|1-9/7-3/2-18/11
Line 710: Line 732:
| 1-11/9-11/6-10/7
| 1-11/9-11/6-10/7
| swetismic
| swetismic
|C\m~6
|\m~6
|\m~6
|1-7/6-3/2-13/8
|1-7/6-3/2-13/8
Line 717: Line 740:
| 1-11/9-9/8-10/7
| 1-11/9-9/8-10/7
| jove
| jove
|
|
|
|
|
Line 724: Line 748:
| 1-11/6-9/8-10/7
| 1-11/6-9/8-10/7
| jove
| jove
|
|
|
|
|
Line 731: Line 756:
| 1-11/6-14/11-10/7
| 1-11/6-14/11-10/7
| hemififths
| hemififths
|
|
|
|
|
Line 738: Line 764:
| 1-9/8-14/11-10/7
| 1-9/8-14/11-10/7
| pele
| pele
|C9no5
|9no5
|9no5
|1-9/8-14/11-16/9
|1-9/8-14/11-16/9
Line 745: Line 772:
| 1-11/9-14/9-10/7
| 1-11/9-14/9-10/7
| swetismic
| swetismic
|
|
|
|
|
Line 752: Line 780:
| 1-9/8-14/9-10/7
| 1-9/8-14/9-10/7
| hemififths
| hemififths
|
|
|
|
|
Line 759: Line 788:
| 1-14/11-14/9-10/7
| 1-14/11-14/9-10/7
| jove
| jove
|
|
|
|
|
Line 766: Line 796:
| 1-11/6-7/6-10/7
| 1-11/6-7/6-10/7
| swetismic
| swetismic
|
|
|
|
|
Line 773: Line 804:
| 1-14/11-7/6-10/7
| 1-14/11-7/6-10/7
| jove
| jove
|
|
|
|
|
Line 780: Line 812:
| 1-14/9-7/6-10/7
| 1-14/9-7/6-10/7
| swetismic
| swetismic
|
|
|
|
|
Line 787: Line 820:
| 1-11/9-3/2-7/4
| 1-11/9-3/2-7/4
| jove
| jove
|C~,\7
|~,\7
|~,\7
|
|
Line 794: Line 828:
| 1-11/9-9/8-7/4
| 1-11/9-9/8-7/4
| jove
| jove
|
|
|
|
|
Line 801: Line 836:
| 1-3/2-9/8-7/4
| 1-3/2-9/8-7/4
| otonal
| otonal
|C\9no3
|\9no3
|\9no3
|
|
Line 808: Line 844:
| 1-11/9-11/8-7/4
| 1-11/9-11/8-7/4
| werckismic
| werckismic
|
|
|
|
|
Line 815: Line 852:
| 1-3/2-11/8-7/4
| 1-3/2-11/8-7/4
| otonal
| otonal
|C~4,\7
|~4,\7
|~4,\7
|
|
Line 822: Line 860:
| 1-9/8-11/8-7/4
| 1-9/8-11/8-7/4
| otonal
| otonal
|C~4\7,9 <u>or</u> C~,7(^5)
|~4\7,9 <u>or</u> ~,7(^5)
|~4\7,9 <u>or</u> ~,7(^5)
|1-11/9-14/9-16/9
|1-11/9-14/9-16/9
Line 829: Line 868:
| 1-9/8-14/11-7/4
| 1-9/8-14/11-7/4
| pentacircle
| pentacircle
|
|
|
|
|
Line 836: Line 876:
| 1-11/8-14/11-7/4
| 1-11/8-14/11-7/4
| hemimin
| hemimin
|
|
|
|
|
Line 843: Line 884:
| 1-11/9-14/9-7/4
| 1-11/9-14/9-7/4
| werckismic
| werckismic
|
|
|
|
|
Line 850: Line 892:
| 1-9/8-14/9-7/4
| 1-9/8-14/9-7/4
| pentacircle
| pentacircle
|
|
|
|
|
Line 857: Line 900:
| 1-11/8-14/9-7/4
| 1-11/8-14/9-7/4
| pentacircle
| pentacircle
|
|
|
|
|
Line 864: Line 908:
| 1-14/11-14/9-7/4
| 1-14/11-14/9-7/4
| utonal
| utonal
|
|
|
|
|
Line 871: Line 916:
| 1-3/2-7/6-7/4
| 1-3/2-7/6-7/4
| ambitonal
| ambitonal
|C\m7
|\m7
|\m7
|
|
Line 878: Line 924:
| 1-14/11-7/6-7/4
| 1-14/11-7/6-7/4
| utonal
| utonal
|
|
|
|
|
Line 885: Line 932:
| 1-14/9-7/6-7/4
| 1-14/9-7/6-7/4
| utonal
| utonal
|C/,9
|/,9
|/,9
|1-9/7-3/2-9/4
|1-9/7-3/2-9/4
Line 892: Line 940:
| 1-11/9-10/7-7/4
| 1-11/9-10/7-7/4
| jove
| jove
|
|
|
|
|
Line 899: Line 948:
| 1-9/8-10/7-7/4
| 1-9/8-10/7-7/4
| werckismic
| werckismic
|
|
|
|
|
Line 906: Line 956:
| 1-14/11-10/7-7/4
| 1-14/11-10/7-7/4
| werckismic
| werckismic
|
|
|
|
|
Line 913: Line 964:
| 1-14/9-10/7-7/4
| 1-14/9-10/7-7/4
| jove
| jove
|
|
|
|
|
Line 920: Line 972:
| 1-7/6-10/7-7/4
| 1-7/6-10/7-7/4
| jove
| jove
|C~,/6
|~,/6
|~,/6
|1-11/9-3/2-12/7
|1-11/9-3/2-12/7
Line 927: Line 980:
| 1-14/11-14/9-20/11
| 1-14/11-14/9-20/11
| swetismic
| swetismic
|
|
|
|
|
Line 934: Line 988:
| 1-14/11-7/6-20/11
| 1-14/11-7/6-20/11
| swetismic
| swetismic
|
|
|
|
|
Line 941: Line 996:
| 1-14/9-7/6-20/11
| 1-14/9-7/6-20/11
| swetismic
| swetismic
|
|
|
|
|
Line 948: Line 1,004:
| 1-14/11-10/7-20/11
| 1-14/11-10/7-20/11
| werckismic
| werckismic
|
|
|
|
|
Line 955: Line 1,012:
| 1-14/9-10/7-20/11
| 1-14/9-10/7-20/11
| swetismic
| swetismic
|
|
|
|
|
Line 962: Line 1,020:
| 1-7/6-10/7-20/11
| 1-7/6-10/7-20/11
| swetismic
| swetismic
|
|
|
|
|
Line 969: Line 1,028:
| 1-11/9-14/9-10/9
| 1-11/9-14/9-10/9
| otonal
| otonal
|
|
|
|
|
Line 976: Line 1,036:
| 1-14/11-14/9-10/9
| 1-14/11-14/9-10/9
| werckismic
| werckismic
|
|
|
|
|
Line 983: Line 1,044:
| 1-11/9-10/7-10/9
| 1-11/9-10/7-10/9
| swetismic
| swetismic
|
|
|
|
|
Line 990: Line 1,052:
| 1-14/11-10/7-10/9
| 1-14/11-10/7-10/9
| werckismic
| werckismic
|
|
|
|
|
Line 997: Line 1,060:
| 1-14/9-10/7-10/9
| 1-14/9-10/7-10/9
| swetismic
| swetismic
|
|
|
|
|
Line 1,004: Line 1,068:
| 1-11/9-7/4-10/9
| 1-11/9-7/4-10/9
| werckismic
| werckismic
|
|
|
|
|
Line 1,011: Line 1,076:
| 1-14/11-7/4-10/9
| 1-14/11-7/4-10/9
| werckismic
| werckismic
|
|
|
|
|
Line 1,018: Line 1,084:
| 1-14/9-7/4-10/9
| 1-14/9-7/4-10/9
| werckismic
| werckismic
|
|
|
|
|
Line 1,025: Line 1,092:
| 1-10/7-7/4-10/9
| 1-10/7-7/4-10/9
| werckismic
| werckismic
|
|
|
|
|
Line 1,032: Line 1,100:
| 1-14/11-20/11-10/9
| 1-14/11-20/11-10/9
| werckismic
| werckismic
|
|
|
|
|
Line 1,039: Line 1,108:
| 1-14/9-20/11-10/9
| 1-14/9-20/11-10/9
| swetismic
| swetismic
|
|
|
|
|
Line 1,046: Line 1,116:
| 1-10/7-20/11-10/9
| 1-10/7-20/11-10/9
| utonal
| utonal
|
|
|
|
|
Line 1,053: Line 1,124:
| 1-3/2-11/6-5/3
| 1-3/2-11/6-5/3
| otonal
| otonal
|
|
|
|
|
Line 1,060: Line 1,132:
| 1-3/2-7/6-5/3
| 1-3/2-7/6-5/3
| otonal
| otonal
|C\m6
|\m6
|\m6
|
|
Line 1,067: Line 1,140:
| 1-11/6-7/6-5/3
| 1-11/6-7/6-5/3
| otonal
| otonal
|C\m6~7no5
|\m6~7no5
|\m6~7no5
|
|
Line 1,074: Line 1,148:
| 1-11/6-10/7-5/3
| 1-11/6-10/7-5/3
| swetismic
| swetismic
|
|
|
|
|
Line 1,081: Line 1,156:
| 1-7/6-10/7-5/3
| 1-7/6-10/7-5/3
| swetismic
| swetismic
|C\m6(\~5)
|\m6(\~5)
|\m6(\~5)
|
|
Line 1,088: Line 1,164:
| 1-7/6-20/11-5/3
| 1-7/6-20/11-5/3
| swetismic
| swetismic
|
|
|
|
|
Line 1,095: Line 1,172:
| 1-10/7-20/11-5/3
| 1-10/7-20/11-5/3
| utonal
| utonal
|
|
|
|
|
Line 1,102: Line 1,180:
| 1-10/7-10/9-5/3
| 1-10/7-10/9-5/3
| utonal
| utonal
|C/7
|/7
|/7
|1-9/7-3/2-9/5
|1-9/7-3/2-9/5
Line 1,109: Line 1,188:
| 1-20/11-10/9-5/3
| 1-20/11-10/9-5/3
| utonal
| utonal
|C/7~13no3
|/7~13no3
|/7~13no3
|1-3/2-18/11-9/5
|1-3/2-18/11-9/5
Line 1,116: Line 1,196:
| 1-3/2-9/8-5/4
| 1-3/2-9/8-5/4
| otonal
| otonal
|C\,9
|\,9
|\,9
|
|
Line 1,123: Line 1,204:
| 1-3/2-11/8-5/4
| 1-3/2-11/8-5/4
| otonal
| otonal
|C\,~11
|\,~11
|\,~11
|
|
Line 1,130: Line 1,212:
|1-9/8-11/8-5/4
|1-9/8-11/8-5/4
|otonal
|otonal
|C\,9(\b5)
|\,9(\b5)
|\,9(\b5)
|
|
Line 1,137: Line 1,220:
|1-9/8-10/7-5/4
|1-9/8-10/7-5/4
|werckismic
|werckismic
|C,9(\~5)
|,9(\~5)
|,9(\~5)
|
|
Line 1,144: Line 1,228:
|1-3/2-7/4-5/4
|1-3/2-7/4-5/4
|otonal
|otonal
|C\7
|\7
|\7
|
|
Line 1,151: Line 1,236:
| 1-9/8-7/4-5/4
| 1-9/8-7/4-5/4
| otonal
| otonal
|C\9no5
|\9no5
|\9no5
|
|
Line 1,158: Line 1,244:
| 1-11/8-7/4-5/4
| 1-11/8-7/4-5/4
| otonal
| otonal
|C\7~11no5
|\7~11no5
|\7~11no5
|
|
Line 1,165: Line 1,252:
| 1-10/7-7/4-5/4
| 1-10/7-7/4-5/4
| werckismic
| werckismic
|C\7(\~5)
|\7(\~5)
|\7(\~5)
|
|
Line 1,172: Line 1,260:
| 1-10/7-20/11-5/4
| 1-10/7-20/11-5/4
| utonal
| utonal
|C,\7(b5)
|,\7(b5)
|,\7(b5)
|1-14/11-7/5-7/4
|1-14/11-7/5-7/4
Line 1,179: Line 1,268:
| 1-10/7-10/9-5/4
| 1-10/7-10/9-5/4
| utonal
| utonal
|C/9no5
|/9no5
|/9no5
|1-9/7-9/5-9/4
|1-9/7-9/5-9/4
Line 1,186: Line 1,276:
|1-7/4-10/9-5/4
|1-7/4-10/9-5/4
|werckismic
|werckismic
|C\7\9no5
|\7\9no5
|\7\9no5
|
|
Line 1,193: Line 1,284:
|1-20/11-10/9-5/4
|1-20/11-10/9-5/4
|utonal
|utonal
|C2~6^7no5
|2~6^7no5
|2~6^7no5
|1-18/11-9/5-9/4
|1-18/11-9/5-9/4
Line 1,200: Line 1,292:
|1-3/2-5/3-5/4
|1-3/2-5/3-5/4
|ambitonal
|ambitonal
|C\6 <u>or</u> C/m7
|\6 <u>or</u> /m7
|\6 <u>or</u> /m7
|1-6/5-3/2-9/5
|1-6/5-3/2-9/5
Line 1,207: Line 1,300:
|1-10/7-5/3-5/4
|1-10/7-5/3-5/4
|utonal
|utonal
|/m6
|C/m6
C\m7(b5)|/m6
\m7(b5)
\m7(b5)
|1-6/5-3/2-12/7
|1-6/5-3/2-12/7
Line 1,216: Line 1,310:
| 1-20/11-5/3-5/4
| 1-20/11-5/3-5/4
| utonal
| utonal
|C/m,~9
|/m,~9
|/m,~9
|1-6/5-3/2-12/11
|1-6/5-3/2-12/11
Line 1,223: Line 1,318:
| 1-10/9-5/3-5/4
| 1-10/9-5/3-5/4
| utonal
| utonal
|C/9no3
|/9no3
|/9no3
|1-3/2-9/5-9/4
|1-3/2-9/5-9/4
Line 1,241: Line 1,337:
| 1-11/9-3/2-11/6-9/8
| 1-11/9-3/2-11/6-9/8
| rastmic
| rastmic
|~9
|C~9
|
|
|-
|-
Line 1,248: Line 1,344:
| 1-11/9-3/2-11/6-11/8
| 1-11/9-3/2-11/6-11/8
| rastmic
| rastmic
|~11no9
|C~11no9
|
|
|-
|-
Line 1,255: Line 1,351:
| 1-11/9-3/2-9/8-11/8
| 1-11/9-3/2-9/8-11/8
| rastmic
| rastmic
|~11no7
|C~11no7
|
|
|-
|-
Line 1,262: Line 1,358:
| 1-11/9-11/6-9/8-11/8
| 1-11/9-11/6-9/8-11/8
| rastmic
| rastmic
|~11no5
|C~11no5
|
|
|-
|-
Line 1,269: Line 1,365:
| 1-3/2-11/6-9/8-11/8
| 1-3/2-11/6-9/8-11/8
| rastmic
| rastmic
|~11no3
|C~11no3
|
|
|-
|-
Line 1,339: Line 1,435:
| 1-11/9-3/2-9/8-7/4
| 1-11/9-3/2-9/8-7/4
| jove
| jove
|~9(\m7)
|C~9(\m7)
|
|
|-
|-
Line 1,360: Line 1,456:
| 1-3/2-9/8-11/8-7/4
| 1-3/2-9/8-11/8-7/4
| otonal
| otonal
|\9~11no3
|C\9~11no3
|
|
|-
|-
Line 1,409: Line 1,505:
| 1-14/11-14/9-7/6-7/4
| 1-14/11-14/9-7/6-7/4
| utonal
| utonal
|/,~6,9
|C/,~6,9
|1-9/7-3/2-18/11-9/4
|1-9/7-3/2-18/11-9/4
|-
|-
Line 1,563: Line 1,659:
| 1-3/2-11/6-7/6-5/3
| 1-3/2-11/6-7/6-5/3
| otonal
| otonal
|\m6~7
|C\m6~7
|
|
|-
|-
Line 1,584: Line 1,680:
| 1-10/7-20/11-10/9-5/3
| 1-10/7-20/11-10/9-5/3
| utonal
| utonal
|/7~6
|C/7~6
|1-9/7-3/2-18/11-9/5
|1-9/7-3/2-18/11-9/5
|-
|-
Line 1,591: Line 1,687:
| 1-3/2-9/8-11/8-5/4
| 1-3/2-9/8-11/8-5/4
| otonal
| otonal
|\,9~11
|C\,9~11
|
|
|-
|-
Line 1,598: Line 1,694:
| 1-3/2-9/8-7/4-5/4
| 1-3/2-9/8-7/4-5/4
| otonal
| otonal
|\9
|C\9
|
|
|-
|-
Line 1,605: Line 1,701:
| 1-3/2-11/8-7/4-5/4
| 1-3/2-11/8-7/4-5/4
| otonal
| otonal
|\7~11
|C\7~11
|
|
|-
|-
Line 1,612: Line 1,708:
| 1-9/8-11/8-7/4-5/4
| 1-9/8-11/8-7/4-5/4
| otonal
| otonal
|\9~11no5
|C\9~11no5
|
|
|-
|-
Line 1,619: Line 1,715:
| 1-9/8-10/7-7/4-5/4
| 1-9/8-10/7-7/4-5/4
| werckismic
| werckismic
|\9(\~5)
|C\9(\~5)
|
|
|-
|-
Line 1,633: Line 1,729:
| 1-10/7-20/11-10/9-5/4
| 1-10/7-20/11-10/9-5/4
| utonal
| utonal
|/9~6no5
|C/9~6no5
|1-9/7-18/11-9/5-9/4
|1-9/7-18/11-9/5-9/4
|-
|-
Line 1,640: Line 1,736:
| 1-10/7-20/11-5/3-5/4
| 1-10/7-20/11-5/3-5/4
| utonal
| utonal
|/m6~9
|C/m6~9
|1-6/5-3/2-12/7-13/6
|1-6/5-3/2-12/7-13/6
|-
|-
Line 1,647: Line 1,743:
| 1-10/7-10/9-5/3-5/4
| 1-10/7-10/9-5/3-5/4
| utonal
| utonal
|/9
|C/9
|1-9/7-3/2-9/5-9/4
|1-9/7-3/2-9/5-9/4
|-
|-
Line 1,654: Line 1,750:
| 1-20/11-10/9-5/3-5/4
| 1-20/11-10/9-5/3-5/4
| utonal
| utonal
|/9~6no3
|C/9~6no3
|1-3/2-18/11-9/5-9/4
|1-3/2-18/11-9/5-9/4
|}
|}
Line 1,672: Line 1,768:
| 1-11/9-3/2-11/6-9/8-11/8
| 1-11/9-3/2-11/6-9/8-11/8
| rastmic
| rastmic
|~11
|C~11
|
|
|-
|-
Line 1,679: Line 1,775:
| 1-11/9-3/2-9/8-11/8-7/4
| 1-11/9-3/2-9/8-11/8-7/4
| jove
| jove
|~11(\m7)
|C~11(\m7)
|
|
|-
|-
Line 1,749: Line 1,845:
| 1-3/2-9/8-11/8-7/4-5/4
| 1-3/2-9/8-11/8-7/4-5/4
| otonal
| otonal
|\9~11
|C\9~11
|
|
|-
|-
Line 1,756: Line 1,852:
| 1-10/7-20/11-10/9-5/3-5/4
| 1-10/7-20/11-10/9-5/3-5/4
| utonal
| utonal
|/9~6
|C/9~6
|1-9/7-3/2-18/11-9/5-9/4
|1-9/7-3/2-18/11-9/5-9/4
|}
|}

Revision as of 04:04, 17 December 2024

Below are listed the dyadic chords of 11-limit hemififths temperament. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering only by 540/539 are swetismic, by 441/440 werckismic, by 896/891 pentacircle, by 243/242 rastmic, and by 1344/1331 hemimin. Those requiring tempering by any two of 540/539, 441/440 or 243/242 are labeled jove. Those requiring both 441/440 and 896/891 are labeled pele. Those requiring any two of 243/242, 896/891 or 1344/1331 are labeled parahemif. If the full hemififths is required because of the tempering out of three independent hemififths commas, the chord is labeled "hemififths".

A striking feature of these hemififths chords is that essentially just chords tend to be of higher complexity than essentially tempered chords. Hemififths has MOS of size 7, 10, 17 and 24, and even seven notes are well-supplied with chords, mostly but by no means entirely essentially tempered chords. Extending consideration to the 13-limit adds even more such chords.

Chords are named with ups and downs, using pergen #4 (P8, P5/2) in the notation guide for rank-2 pergens. One up is 7 generators, which is a half-sharp. The tilde ~ means mid, half-way between major and minor. ~4 = ^4 = vA4 and ~5 = v5 = ^d5. The comma (the actual punctuation mark) is pronounced "add", thus C~,7 is "C mid add 7". To facilitate chord naming, lifts and drops are also used. One lift is -17 generators, a half-diminished 2nd. Enharmonic equivalences: vvA1 and v\m2. Cents: ^1 = 50¢ + 3.5c and /1 = 50¢ - 8.5c, where c = the amount in cents the tempered fifth exceeds 700¢. /1 = ~81/80 = ~64/63 and ^1 = ~33/32. To convert to 41edo, ^1 = 2\41 and /1 = 1\41.

Hemififth's genchain
Genspan 0 1 2 3 4 5 6 7 8 9 10 11 12 13 ... 20 21 ... 23 ... 25
Cents (41edo) 0 351 702 1054 205 556 907 59 410 761 1112 263 615 966 1024 176 878 380
Ratio 1/1 11/9

16/13

3/2 11/6

24/13

9/8 11/8

18/13

27/16

22/13

28/27

33/32

14/11 14/9 40/21

21/11

7/6 10/7 7/4 20/11 10/9 5/3 5/4
Interval P1 ~3 P5 ~7 M2 ~4

\b5

M6 ^1

\m2

M3 ^5

\m6

M7 ^M2

\m3

A4

\~5

^M6

\m7

A6

\~7

^A1

\M2

^A5

\M6

^A2

\M3

TODO: Complete the tables

Triads

# Chord Transversal Type Name Inversion
1 0-1-2 1-11/9-3/2 rastmic C~
2 0-1-3 1-11/9-11/6 utonal C~7no5
3 0-2-3 1-3/2-11/6 otonal C~7no3
4 0-1-4 1-11/9-9/8 rastmic C~,9no5
5 0-2-4 1-3/2-9/8 ambitonal C2 or C4 1-4/3-9/8
6 0-3-4 1-11/6-9/8 rastmic C~9no35
7 0-1-5 1-11/9-11/8 utonal C~(\b5)
8 0-2-5 1-3/2-11/8 otonal C~7sus4no5 1-4/3-11/6
9 0-3-5 1-11/6-11/8 utonal C~2 1-12/11-3/2
10 0-4-5 1-9/8-11/8 otonal C~,7no5 1-11/9-16/9
11 0-3-8 1-11/6-14/11 hemimin C,~7no5
12 0-4-8 1-9/8-14/11 pentacircle C,9no5
13 0-5-8 1-11/8-14/11 hemimin C(\b5)
14 0-1-9 1-11/9-14/9 otonal C~(^5)
15 0-4-9 1-9/8-14/9 pentacircle C7~4no5 1-11/8-16/9
16 0-5-9 1-11/8-14/9 pentacircle C2(~5) or

C/,7no5

1-9/8-13/9

1-9/7-16/9

17 0-8-9 1-14/11-14/9 utonal C(^5)
18 0-2-11 1-3/2-7/6 otonal C\m
19 0-3-11 1-11/6-7/6 otonal C\m~7no5
20 0-8-11 1-14/11-7/6 utonal C~2/6 1-12/11-12/7
21 0-9-11 1-14/9-7/6 utonal C/ 1-9/7-3/2
22 0-1-12 1-11/9-10/7 swetismic C~(\~5)
23 0-3-12 1-11/6-10/7 swetismic C/(b5) 1-9/7-7/5
24 0-4-12 1-9/8-10/7 werckismic C2(\~5)
25 0-8-12 1-14/11-10/7 werckismic C(\~5)
26 0-9-12 1-14/9-10/7 swetismic C~2(b5) 1-12/11-7/5
27 0-11-12 1-7/6-10/7 swetismic C\m(\~5)
28 0-1-13 1-11/9-7/4 werckismic C~,\7no5
29 0-2-13 1-3/2-7/4 otonal C\7no3
30 0-4-13 1-9/8-7/4 otonal C\9no35
31 0-5-13 1-11/8-7/4 otonal C(~5) 1-14/11-16/11
32 0-8-13 1-14/11-7/4 utonal C,\7
33 0-9-13 1-14/9-7/4 utonal C/,2no5 1-9/8-9/7
34 0-11-13 1-7/6-7/4 utonal C\m7no5
35 0-12-13 1-10/7-7/4 werckismic C~(b5) 1-11/9-7/5
36 0-8-20 1-14/11-20/11 otonal C,\~7no5
37 0-9-20 1-14/9-20/11 swetismic
38 0-11-20 1-7/6-20/11 swetismic C\m\~7no5
39 0-12-20 1-10/7-20/11 utonal C(b5)
40 0-1-21 1-11/9-10/9 otonal C~,\9no5
41 0-8-21 1-14/11-10/9 werckismic C,\9no5
42 0-9-21 1-14/9-10/9 otonal C/(\~5) 1-9/7-10/7
43 0-12-21 1-10/7-10/9 utonal C\2(\~5)
44 0-13-21 1-7/4-10/9 werckismic C\2\m7no5
45 0-20-21 1-20/11-10/9 utonal
46 0-2-23 1-3/2-5/3 otonal C\m7no5 1-6/5-9/5
47 0-3-23 1-11/6-5/3 otonal
48 0-11-23 1-7/6-5/3 otonal C\m6no5
49 0-12-23 1-10/7-5/3 utonal C/dim 1-7/6-7/5
50 0-20-23 1-20/11-5/3 utonal
51 0-21-23 1-10/9-5/3 utonal C/7no3 1-3/2-9/5
52 0-2-25 1-3/2-5/4 otonal C\
53 0-4-25 1-9/8-5/4 otonal C\,9no5
54 0-5-25 1-11/8-5/4 otonal C\(\b5)
55 0-12-25 1-10/7-5/4 utonal C\(\~5)
56 0-13-25 1-7/4-5/4 otonal C\7no5
57 0-20-25 1-20/11-5/4 utonal C\,\~7no5
58 0-21-25 1-10/9-5/4 utonal C/9no35 1-9/5-9/4
59 0-23-25 1-5/3-5/4 utonal C/m 1-6/5-3/2

Tetrads

# Chord Transversal Type Name Name Inversion
1 0-1-2-3 1-11/9-3/2-11/6 rastmic C~7 ~7
2 0-1-2-4 1-11/9-3/2-9/8 rastmic C~,9 ~,9
3 0-1-3-4 1-11/9-11/6-9/8 rastmic C~9no5 ~9no5
4 0-2-3-4 1-3/2-11/6-9/8 rastmic C~9no3 ~9no3
5 0-1-2-5 1-11/9-3/2-11/8 rastmic C~,~11 ~,~11
6 0-1-3-5 1-11/9-11/6-11/8 utonal C2~6 or

C4~9|2~6 or 4~9

1-9/8-3/2-13/8

1-4/3-3/2-24/11

7 0-2-3-5 1-3/2-11/6-11/8 ambitonal C~4~7 ~4~7
8 0-1-4-5 1-11/9-9/8-11/8 rastmic
9 0-2-4-5 1-3/2-9/8-11/8 otonal C4~7 4~7 1-4/3-3/2-11/6
10 0-3-4-5 1-11/6-9/8-11/8 rastmic C~11no35 ~11no35
11 0-3-4-8 1-11/6-9/8-14/11 parahemif C9(~7)no5 9(~7)no5
12 0-3-5-8 1-11/6-11/8-14/11 hemimin C~2~11 ~2~11 1-12/11-11/8-3/2
13 0-4-5-8 1-9/8-11/8-14/11 parahemif C~,~9 ~,~9 1-11/9-3/2-13/12
14 0-1-4-9 1-11/9-9/8-14/9 parahemif C~,9(^5) ~,9(^5)
15 0-1-5-9 1-11/9-11/8-14/9 pentacircle C,~6,9no5 ,~6,9no5 1-14/11-18/11-9/4
16 0-4-5-9 1-9/8-11/8-14/9 pentacircle C~,7(\b5) ~,7(\b5) 1-11/9-11/8-16/9
17 0-4-8-9 1-9/8-14/11-14/9 pentacircle
18 0-5-8-9 1-11/8-14/11-14/9 parahemif
19 0-2-3-11 1-3/2-11/6-7/6 otonal C\m~7 \m~7
20 0-3-8-11 1-11/6-14/11-7/6 hemimin
21 0-8-9-11 1-14/11-14/9-7/6 utonal C/,~6 /,~6 1-9/7-3/2-18/11
22 0-1-3-12 1-11/9-11/6-10/7 swetismic C\m~6 \m~6 1-7/6-3/2-13/8
23 0-1-4-12 1-11/9-9/8-10/7 jove
24 0-3-4-12 1-11/6-9/8-10/7 jove
25 0-3-8-12 1-11/6-14/11-10/7 hemififths
26 0-4-8-12 1-9/8-14/11-10/7 pele C9no5 9no5 1-9/8-14/11-16/9
27 0-1-9-12 1-11/9-14/9-10/7 swetismic
28 0-4-9-12 1-9/8-14/9-10/7 hemififths
29 0-8-9-12 1-14/11-14/9-10/7 jove
30 0-3-11-12 1-11/6-7/6-10/7 swetismic
31 0-8-11-12 1-14/11-7/6-10/7 jove
32 0-9-11-12 1-14/9-7/6-10/7 swetismic
33 0-1-2-13 1-11/9-3/2-7/4 jove C~,\7 ~,\7
34 0-1-4-13 1-11/9-9/8-7/4 jove
35 0-2-4-13 1-3/2-9/8-7/4 otonal C\9no3 \9no3
36 0-1-5-13 1-11/9-11/8-7/4 werckismic
37 0-2-5-13 1-3/2-11/8-7/4 otonal C~4,\7 ~4,\7
38 0-4-5-13 1-9/8-11/8-7/4 otonal C~4\7,9 or C~,7(^5) ~4\7,9 or ~,7(^5) 1-11/9-14/9-16/9
39 0-4-8-13 1-9/8-14/11-7/4 pentacircle
40 0-5-8-13 1-11/8-14/11-7/4 hemimin
41 0-1-9-13 1-11/9-14/9-7/4 werckismic
42 0-4-9-13 1-9/8-14/9-7/4 pentacircle
43 0-5-9-13 1-11/8-14/9-7/4 pentacircle
44 0-8-9-13 1-14/11-14/9-7/4 utonal
45 0-2-11-13 1-3/2-7/6-7/4 ambitonal C\m7 \m7
46 0-8-11-13 1-14/11-7/6-7/4 utonal
47 0-9-11-13 1-14/9-7/6-7/4 utonal C/,9 /,9 1-9/7-3/2-9/4
48 0-1-12-13 1-11/9-10/7-7/4 jove
49 0-4-12-13 1-9/8-10/7-7/4 werckismic
50 0-8-12-13 1-14/11-10/7-7/4 werckismic
51 0-9-12-13 1-14/9-10/7-7/4 jove
52 0-11-12-13 1-7/6-10/7-7/4 jove C~,/6 ~,/6 1-11/9-3/2-12/7
53 0-8-9-20 1-14/11-14/9-20/11 swetismic
54 0-8-11-20 1-14/11-7/6-20/11 swetismic
55 0-9-11-20 1-14/9-7/6-20/11 swetismic
56 0-8-12-20 1-14/11-10/7-20/11 werckismic
57 0-9-12-20 1-14/9-10/7-20/11 swetismic
58 0-11-12-20 1-7/6-10/7-20/11 swetismic
59 0-1-9-21 1-11/9-14/9-10/9 otonal
60 0-8-9-21 1-14/11-14/9-10/9 werckismic
61 0-1-12-21 1-11/9-10/7-10/9 swetismic
62 0-8-12-21 1-14/11-10/7-10/9 werckismic
63 0-9-12-21 1-14/9-10/7-10/9 swetismic
64 0-1-13-21 1-11/9-7/4-10/9 werckismic
65 0-8-13-21 1-14/11-7/4-10/9 werckismic
66 0-9-13-21 1-14/9-7/4-10/9 werckismic
67 0-12-13-21 1-10/7-7/4-10/9 werckismic
68 0-8-20-21 1-14/11-20/11-10/9 werckismic
69 0-9-20-21 1-14/9-20/11-10/9 swetismic
70 0-12-20-21 1-10/7-20/11-10/9 utonal
71 0-2-3-23 1-3/2-11/6-5/3 otonal
72 0-2-11-23 1-3/2-7/6-5/3 otonal C\m6 \m6
73 0-3-11-23 1-11/6-7/6-5/3 otonal C\m6~7no5 \m6~7no5
74 0-3-12-23 1-11/6-10/7-5/3 swetismic
75 0-11-12-23 1-7/6-10/7-5/3 swetismic C\m6(\~5) \m6(\~5)
76 0-11-20-23 1-7/6-20/11-5/3 swetismic
77 0-12-20-23 1-10/7-20/11-5/3 utonal
78 0-12-21-23 1-10/7-10/9-5/3 utonal C/7 /7 1-9/7-3/2-9/5
79 0-20-21-23 1-20/11-10/9-5/3 utonal C/7~13no3 /7~13no3 1-3/2-18/11-9/5
80 0-2-4-25 1-3/2-9/8-5/4 otonal C\,9 \,9
81 0-2-5-25 1-3/2-11/8-5/4 otonal C\,~11 \,~11
82 0-4-5-25 1-9/8-11/8-5/4 otonal C\,9(\b5) \,9(\b5)
83 0-4-12-25 1-9/8-10/7-5/4 werckismic C,9(\~5) ,9(\~5)
84 0-2-13-25 1-3/2-7/4-5/4 otonal C\7 \7
85 0-4-13-25 1-9/8-7/4-5/4 otonal C\9no5 \9no5
86 0-5-13-25 1-11/8-7/4-5/4 otonal C\7~11no5 \7~11no5
87 0-12-13-25 1-10/7-7/4-5/4 werckismic C\7(\~5) \7(\~5)
88 0-12-20-25 1-10/7-20/11-5/4 utonal C,\7(b5) ,\7(b5) 1-14/11-7/5-7/4
89 0-12-21-25 1-10/7-10/9-5/4 utonal C/9no5 /9no5 1-9/7-9/5-9/4
90 0-13-21-25 1-7/4-10/9-5/4 werckismic C\7\9no5 \7\9no5
91 0-20-21-25 1-20/11-10/9-5/4 utonal C2~6^7no5 2~6^7no5 1-18/11-9/5-9/4
92 0-2-23-25 1-3/2-5/3-5/4 ambitonal C\6 or C/m7 \6 or /m7 1-6/5-3/2-9/5
93 0-12-23-25 1-10/7-5/3-5/4 utonal C/m6

C\m7(b5)|/m6 \m7(b5)

1-6/5-3/2-12/7

1-7/6-7/5-7/4

94 0-20-23-25 1-20/11-5/3-5/4 utonal C/m,~9 /m,~9 1-6/5-3/2-12/11
95 0-21-23-25 1-10/9-5/3-5/4 utonal C/9no3 /9no3 1-3/2-9/5-9/4

Pentads

# Chord Transversal Type Name Inversion
1 0-1-2-3-4 1-11/9-3/2-11/6-9/8 rastmic C~9
2 0-1-2-3-5 1-11/9-3/2-11/6-11/8 rastmic C~11no9
3 0-1-2-4-5 1-11/9-3/2-9/8-11/8 rastmic C~11no7
4 0-1-3-4-5 1-11/9-11/6-9/8-11/8 rastmic C~11no5
5 0-2-3-4-5 1-3/2-11/6-9/8-11/8 rastmic C~11no3
6 0-3-4-5-8 1-11/6-9/8-11/8-14/11 parahemif
7 0-1-4-5-9 1-11/9-9/8-11/8-14/9 parahemif
8 0-4-5-8-9 1-9/8-11/8-14/11-14/9 parahemif
9 0-1-3-4-12 1-11/9-11/6-9/8-10/7 jove
10 0-3-4-8-12 1-11/6-9/8-14/11-10/7 hemififths
11 0-1-4-9-12 1-11/9-9/8-14/9-10/7 hemififths
12 0-4-8-9-12 1-9/8-14/11-14/9-10/7 hemififths
13 0-3-8-11-12 1-11/6-14/11-7/6-10/7 hemififths
14 0-8-9-11-12 1-14/11-14/9-7/6-10/7 jove
15 0-1-2-4-13 1-11/9-3/2-9/8-7/4 jove C~9(\m7)
16 0-1-2-5-13 1-11/9-3/2-11/8-7/4 jove
17 0-1-4-5-13 1-11/9-9/8-11/8-7/4 jove
18 0-2-4-5-13 1-3/2-9/8-11/8-7/4 otonal C\9~11no3
19 0-4-5-8-13 1-9/8-11/8-14/11-7/4 parahemif
20 0-1-4-9-13 1-11/9-9/8-14/9-7/4 hemififths
21 0-1-5-9-13 1-11/9-11/8-14/9-7/4 pele
22 0-4-5-9-13 1-9/8-11/8-14/9-7/4 pentacircle
23 0-4-8-9-13 1-9/8-14/11-14/9-7/4 pentacircle
24 0-5-8-9-13 1-11/8-14/11-14/9-7/4 parahemif
25 0-8-9-11-13 1-14/11-14/9-7/6-7/4 utonal C/,~6,9 1-9/7-3/2-18/11-9/4
26 0-1-4-12-13 1-11/9-9/8-10/7-7/4 jove
27 0-4-8-12-13 1-9/8-14/11-10/7-7/4 pele
28 0-1-9-12-13 1-11/9-14/9-10/7-7/4 jove
29 0-4-9-12-13 1-9/8-14/9-10/7-7/4 hemififths
30 0-8-9-12-13 1-14/11-14/9-10/7-7/4 jove
31 0-8-11-12-13 1-14/11-7/6-10/7-7/4 jove
32 0-9-11-12-13 1-14/9-7/6-10/7-7/4 jove
33 0-8-9-11-20 1-14/11-14/9-7/6-20/11 swetismic
34 0-8-9-12-20 1-14/11-14/9-10/7-20/11 jove
35 0-8-11-12-20 1-14/11-7/6-10/7-20/11 jove
36 0-9-11-12-20 1-14/9-7/6-10/7-20/11 swetismic
37 0-1-9-12-21 1-11/9-14/9-10/7-10/9 swetismic
38 0-8-9-12-21 1-14/11-14/9-10/7-10/9 jove
39 0-1-9-13-21 1-11/9-14/9-7/4-10/9 werckismic
40 0-8-9-13-21 1-14/11-14/9-7/4-10/9 werckismic
41 0-1-12-13-21 1-11/9-10/7-7/4-10/9 jove
42 0-8-12-13-21 1-14/11-10/7-7/4-10/9 werckismic
43 0-9-12-13-21 1-14/9-10/7-7/4-10/9 jove
44 0-8-9-20-21 1-14/11-14/9-20/11-10/9 jove
45 0-8-12-20-21 1-14/11-10/7-20/11-10/9 werckismic
46 0-9-12-20-21 1-14/9-10/7-20/11-10/9 swetismic
47 0-2-3-11-23 1-3/2-11/6-7/6-5/3 otonal C\m6~7
48 0-3-11-12-23 1-11/6-7/6-10/7-5/3 swetismic
49 0-11-12-20-23 1-7/6-10/7-20/11-5/3 swetismic
50 0-12-20-21-23 1-10/7-20/11-10/9-5/3 utonal C/7~6 1-9/7-3/2-18/11-9/5
51 0-2-4-5-25 1-3/2-9/8-11/8-5/4 otonal C\,9~11
52 0-2-4-13-25 1-3/2-9/8-7/4-5/4 otonal C\9
53 0-2-5-13-25 1-3/2-11/8-7/4-5/4 otonal C\7~11
54 0-4-5-13-25 1-9/8-11/8-7/4-5/4 otonal C\9~11no5
55 0-4-12-13-25 1-9/8-10/7-7/4-5/4 werckismic C\9(\~5)
56 0-12-13-21-25 1-10/7-7/4-10/9-5/4 werckismic
57 0-12-20-21-25 1-10/7-20/11-10/9-5/4 utonal C/9~6no5 1-9/7-18/11-9/5-9/4
58 0-12-20-23-25 1-10/7-20/11-5/3-5/4 utonal C/m6~9 1-6/5-3/2-12/7-13/6
59 0-12-21-23-25 1-10/7-10/9-5/3-5/4 utonal C/9 1-9/7-3/2-9/5-9/4
60 0-20-21-23-25 1-20/11-10/9-5/3-5/4 utonal C/9~6no3 1-3/2-18/11-9/5-9/4

Hexads

# Chord Transversal Type Name Inversion
1 0-1-2-3-4-5 1-11/9-3/2-11/6-9/8-11/8 rastmic C~11
2 0-1-2-4-5-13 1-11/9-3/2-9/8-11/8-7/4 jove C~11(\m7)
3 0-1-4-5-9-13 1-11/9-9/8-11/8-14/9-7/4 hemififths
4 0-4-5-8-9-13 1-9/8-11/8-14/11-14/9-7/4 nofives
5 0-1-4-9-12-13 1-11/9-9/8-14/9-10/7-7/4 hemififths
6 0-4-8-9-12-13 1-9/8-14/11-14/9-10/7-7/4 hemififths
7 0-8-9-11-12-13 1-14/11-14/9-7/6-10/7-7/4 jove
8 0-8-9-11-12-20 1-14/11-14/9-7/6-10/7-20/11 jove
9 0-1-9-12-13-21 1-11/9-14/9-10/7-7/4-10/9 jove
10 0-8-9-12-13-21 1-14/11-14/9-10/7-7/4-10/9 jove
11 0-8-9-12-20-21 1-14/11-14/9-10/7-20/11-10/9 jove
12 0-2-4-5-13-25 1-3/2-9/8-11/8-7/4-5/4 otonal C\9~11
13 0-12-20-21-23-25 1-10/7-20/11-10/9-5/3-5/4 utonal C/9~6 1-9/7-3/2-18/11-9/5-9/4
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