Hemififths/Chords: Difference between revisions

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autopatrolled, Sysops
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added C as the chord root
TallKite (talk | contribs)
autopatrolled, Sysops
3,992 edits
→Triads: added more chord names
Line 4: Line 4:


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.
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.
The "As (sub)harmonics" column describes otonal chords as harmonics and utonal chords as subharmonics.
{| class="wikitable"
{| class="wikitable"
|+Hemififth's genchain
|+Hemififth's genchain
Line 124: Line 126:
|-
|-
! #
! #
! Chord
! Genspans
! Transversal
! Transversal
! Type
! Type
!Name
!Name
!Inversion
!Inversion
!As (sub)harmonics
|-
|-
| 1
| 1
Line 135: Line 138:
| rastmic
| rastmic
|C~
|C~
|
|
|
|-
|-
Line 143: Line 147:
|C~7no5
|C~7no5
|
|
|11/9/6
|-
|-
| 3
| 3
Line 150: Line 155:
|C~7no3
|C~7no3
|
|
|6:9:11
|-
|-
| 4
| 4
Line 156: Line 162:
| rastmic
| rastmic
|C~,9no5
|C~,9no5
|
|
|
|-
|-
Line 164: Line 171:
|C2 <u>or</u> C4
|C2 <u>or</u> C4
|1-4/3-9/8
|1-4/3-9/8
|
|-
|-
| 6
| 6
Line 170: Line 178:
| rastmic
| rastmic
|C~9no35
|C~9no35
|
|
|
|-
|-
Line 178: Line 187:
|C~(\b5)
|C~(\b5)
|
|
|11/9/8
|-
|-
| 8
| 8
Line 185: Line 195:
|C~7sus4no5
|C~7sus4no5
|1-4/3-11/6
|1-4/3-11/6
|6:8:11
|-
|-
| 9
| 9
Line 192: Line 203:
|C~2
|C~2
|1-12/11-3/2
|1-12/11-3/2
|12/11/8
|-
|-
| 10
| 10
Line 199: Line 211:
|C~,7no5
|C~,7no5
|1-11/9-16/9
|1-11/9-16/9
|9:11:16
|-
|-
| 11
| 11
Line 205: Line 218:
| hemimin
| hemimin
|C,~7no5
|C,~7no5
|
|
|
|-
|-
Line 212: Line 226:
| pentacircle
| pentacircle
|C,9no5
|C,9no5
|
|
|
|-
|-
Line 219: Line 234:
| hemimin
| hemimin
|C(\b5)
|C(\b5)
|
|
|
|-
|-
Line 227: Line 243:
|C~(^5)
|C~(^5)
|
|
|9:11:14
|-
|-
| 15
| 15
Line 234: Line 251:
|C7~4no5
|C7~4no5
|1-11/8-16/9
|1-11/8-16/9
|
|-
|-
| 16
| 16
Line 244: Line 262:


1-9/7-16/9
1-9/7-16/9
|
|-
|-
| 17
| 17
Line 251: Line 270:
|C(^5)
|C(^5)
|
|
|14/11/9
|-
|-
| 18
| 18
Line 258: Line 278:
|C\m
|C\m
|
|
|6:7:9
|-
|-
| 19
| 19
Line 265: Line 286:
|C\m~7no5
|C\m~7no5
|
|
|6:7:11
|-
|-
| 20
| 20
Line 272: Line 294:
|C~2/6
|C~2/6
|1-12/11-12/7
|1-12/11-12/7
|12/11/7
|-
|-
| 21
| 21
Line 279: Line 302:
|C/
|C/
|1-9/7-3/2
|1-9/7-3/2
|9/7/6
|-
|-
| 22
| 22
Line 285: Line 309:
| swetismic
| swetismic
|C~(\~5)
|C~(\~5)
|
|
|
|-
|-
Line 293: Line 318:
|C/(b5)
|C/(b5)
|1-9/7-7/5
|1-9/7-7/5
|
|-
|-
| 24
| 24
Line 299: Line 325:
| werckismic
| werckismic
|C2(\~5)
|C2(\~5)
|
|
|
|-
|-
Line 306: Line 333:
| werckismic
| werckismic
|C(\~5)
|C(\~5)
|
|
|
|-
|-
Line 314: Line 342:
|C~2(b5)
|C~2(b5)
|1-12/11-7/5
|1-12/11-7/5
|
|-
|-
| 27
| 27
Line 320: Line 349:
| swetismic
| swetismic
|C\m(\~5)
|C\m(\~5)
|
|
|
|-
|-
Line 327: Line 357:
| werckismic
| werckismic
|C~,\7no5
|C~,\7no5
|
|
|
|-
|-
Line 335: Line 366:
|C\7no3
|C\7no3
|
|
|4:6:7
|-
|-
| 30
| 30
Line 342: Line 374:
|C\9no35
|C\9no35
|
|
|4:7:9
|-
|-
| 31
| 31
Line 349: Line 382:
|C(~5)
|C(~5)
|1-14/11-16/11
|1-14/11-16/11
|11:14:16
|-
|-
| 32
| 32
Line 356: Line 390:
|C,\7
|C,\7
|
|
|14/11/8
|-
|-
| 33
| 33
Line 363: Line 398:
|C/,2no5
|C/,2no5
|1-9/8-9/7
|1-9/8-9/7
|9/8/7
|-
|-
| 34
| 34
Line 370: Line 406:
|C\m7no5
|C\m7no5
|
|
|7/6/4
|-
|-
| 35
| 35
Line 377: Line 414:
|C~(b5)
|C~(b5)
|1-11/9-7/5
|1-11/9-7/5
|
|-
|-
| 36
| 36
Line 384: Line 422:
|C,\~7no5
|C,\~7no5
|
|
|11:14:20
|-
|-
| 37
| 37
Line 389: Line 428:
| 1-14/9-20/11
| 1-14/9-20/11
| swetismic
| swetismic
|
|
|
|
|
Line 397: Line 437:
| swetismic
| swetismic
|C\m\~7no5
|C\m\~7no5
|
|
|
|-
|-
Line 405: Line 446:
|C(b5)
|C(b5)
|
|
|20/14/11
|-
|-
| 40
| 40
Line 412: Line 454:
|C~,\9no5
|C~,\9no5
|
|
|9:10:11
|-
|-
| 41
| 41
Line 418: Line 461:
| werckismic
| werckismic
|C,\9no5
|C,\9no5
|
|
|
|-
|-
Line 426: Line 470:
|C/(\~5)
|C/(\~5)
|1-9/7-10/7
|1-9/7-10/7
|7:9:10
|-
|-
| 43
| 43
Line 433: Line 478:
|C\2(\~5)
|C\2(\~5)
|
|
|10/9/7
|-
|-
| 44
| 44
Line 439: Line 485:
| werckismic
| werckismic
|C\2\m7no5
|C\2\m7no5
|
|
|
|-
|-
Line 447: Line 494:
|
|
|
|
|20/18/11
|-
|-
| 46
| 46
Line 454: Line 502:
|C\m7no5
|C\m7no5
|1-6/5-9/5
|1-6/5-9/5
|5:6:9
|-
|-
| 47
| 47
Line 461: Line 510:
|
|
|
|
|6:10:11
|-
|-
| 48
| 48
Line 468: Line 518:
|C\m6no5
|C\m6no5
|
|
|6:7:10
|-
|-
| 49
| 49
Line 475: Line 526:
|C/dim
|C/dim
|1-7/6-7/5
|1-7/6-7/5
|10/7/6
|-
|-
| 50
| 50
Line 482: Line 534:
|
|
|
|
|20/12/11
|-
|-
| 51
| 51
Line 489: Line 542:
|C/7no3
|C/7no3
|1-3/2-9/5
|1-3/2-9/5
|9/6/5
|-
|-
| 52
| 52
Line 496: Line 550:
|C\
|C\
|
|
|4:5:6
|-
|-
| 53
| 53
Line 503: Line 558:
|C\,9no5
|C\,9no5
|
|
|4:5:9
|-
|-
| 54
| 54
Line 510: Line 566:
|C\(\b5)
|C\(\b5)
|
|
|8:10:11
|-
|-
| 55
| 55
Line 517: Line 574:
|C\(\~5)
|C\(\~5)
|
|
|10/8/7
|-
|-
| 56
| 56
Line 524: Line 582:
|C\7no5
|C\7no5
|
|
|4:5:6
|-
|-
| 57
| 57
Line 531: Line 590:
|C\,\~7no5
|C\,\~7no5
|
|
|20/11/16
|-
|-
| 58
| 58
Line 538: Line 598:
|C/9no35
|C/9no35
|1-9/5-9/4
|1-9/5-9/4
|9/5/4
|-
|-
| 59
| 59
Line 545: Line 606:
|C/m
|C/m
|1-6/5-3/2
|1-6/5-3/2
|6/5/4
|}
|}


Line 551: Line 613:
|-
|-
! #
! #
! Chord
! Genspans
! Transversal
! Transversal
! Type
! Type
!Name
!Name
!Name
!Inversion
!Inversion
!As (sub)harmonics
|-
|-
| 1
| 1
Line 563: Line 625:
| rastmic
| rastmic
|C~7
|C~7
|~7
|
|
|
|-
|-
Line 571: Line 633:
| rastmic
| rastmic
|C~,9
|C~,9
|~,9
|
|
|
|-
|-
Line 579: Line 641:
| rastmic
| rastmic
|C~9no5
|C~9no5
|~9no5
|
|
|
|-
|-
Line 587: Line 649:
| rastmic
| rastmic
|C~9no3
|C~9no3
|~9no3
|
|
|
|-
|-
Line 595: Line 657:
| rastmic
| rastmic
|C~,~11
|C~,~11
|~,~11
|
|
|
|-
|-
Line 603: Line 665:
| utonal
| utonal
|C2~6 <u>or</u>
|C2~6 <u>or</u>
C4~9|2~6 <u>or</u>
C4~9
4~9
|1-9/8-3/2-18/11
|1-9/8-3/2-13/8
1-4/3-3/2-24/11
1-4/3-3/2-24/11
|18/16/12/11
24/18/16/11
|-
|-
| 7
| 7
Line 613: Line 676:
| ambitonal
| ambitonal
|C~4~7
|C~4~7
|~4~7
|
|
|
|-
|-
Line 629: Line 692:
| otonal
| otonal
|C4~7
|C4~7
|4~7
|1-4/3-3/2-11/6
|1-4/3-3/2-11/6
|6:8:9:11
|-
|-
| 10
| 10
Line 637: Line 700:
| rastmic
| rastmic
|C~11no35
|C~11no35
|~11no35
|
|
|
|-
|-
Line 645: Line 708:
| parahemif
| parahemif
|C9(~7)no5
|C9(~7)no5
|9(~7)no5
|
|
|
|-
|-
Line 653: Line 716:
| hemimin
| hemimin
|C~2~11
|C~2~11
|~2~11
|1-12/11-11/8-3/2
|1-12/11-11/8-3/2
|
|-
|-
| 13
| 13
Line 661: Line 724:
| parahemif
| parahemif
|C~,~9
|C~,~9
|~,~9
|1-11/9-3/2-13/12
|1-11/9-3/2-13/12
|
|-
|-
| 14
| 14
Line 669: Line 732:
| parahemif
| parahemif
|C~,9(^5)
|C~,9(^5)
|~,9(^5)
|
|
|
|-
|-
Line 677: Line 740:
| pentacircle
| pentacircle
|C,~6,9no5
|C,~6,9no5
|,~6,9no5
|1-14/11-18/11-9/4
|1-14/11-18/11-9/4
|
|-
|-
| 16
| 16
Line 685: Line 748:
| pentacircle
| pentacircle
|C~,7(\b5)
|C~,7(\b5)
|~,7(\b5)
|1-11/9-11/8-16/9
|1-11/9-11/8-16/9
|
|-
|-
| 17
| 17
Line 709: Line 772:
| otonal
| otonal
|C\m~7
|C\m~7
|\m~7
|
|
|6:7:9:11
|-
|-
| 20
| 20
Line 725: Line 788:
| utonal
| utonal
|C/,~6
|C/,~6
|/,~6
|1-9/7-3/2-18/11
|1-9/7-3/2-18/11
|18/14/12/11
|-
|-
| 22
| 22
Line 733: Line 796:
| swetismic
| swetismic
|C\m~6
|C\m~6
|\m~6
|1-7/6-3/2-13/8
|1-7/6-3/2-13/8
|
|-
|-
| 23
| 23
Line 765: Line 828:
| pele
| pele
|C9no5
|C9no5
|9no5
|1-9/8-14/11-16/9
|1-9/8-14/11-16/9
|
|-
|-
| 27
| 27
Line 821: Line 884:
| jove
| jove
|C~,\7
|C~,\7
|~,\7
|
|
|
|-
|-
Line 837: Line 900:
| otonal
| otonal
|C\9no3
|C\9no3
|\9no3
|
|
|4:6:7:9
|-
|-
| 36
| 36
Line 853: Line 916:
| otonal
| otonal
|C~4,\7
|C~4,\7
|~4,\7
|
|
|8:11:12:14
|-
|-
| 38
| 38
Line 861: Line 924:
| otonal
| otonal
|C~4\7,9 <u>or</u> C~,7(^5)
|C~4\7,9 <u>or</u> C~,7(^5)
|~4\7,9 <u>or</u> ~,7(^5)
|1-11/9-14/9-16/9
|1-11/9-14/9-16/9
|9:11:14:16
|-
|-
| 39
| 39
Line 910: Line 973:
|
|
|
|
|
|14/11/9/8
|-
|-
| 45
| 45
Line 917: Line 980:
| ambitonal
| ambitonal
|C\m7
|C\m7
|\m7
|
|
|
|-
|-
Line 926: Line 989:
|
|
|
|
|
|14/12/11/8
|-
|-
| 47
| 47
Line 933: Line 996:
| utonal
| utonal
|C/,9
|C/,9
|/,9
|1-9/7-3/2-9/4
|1-9/7-3/2-9/4
|9/7/6/4
|-
|-
| 48
| 48
Line 973: Line 1,036:
| jove
| jove
|C~,/6
|C~,/6
|~,/6
|1-11/9-3/2-12/7
|1-11/9-3/2-12/7
|
|-
|-
| 53
| 53
Line 1,030: Line 1,093:
|
|
|
|
|
|9:10:11:14
|-
|-
| 60
| 60
Line 1,118: Line 1,181:
|
|
|
|
|
|20/18/14/11
|-
|-
| 71
| 71
Line 1,126: Line 1,189:
|
|
|
|
|
|6:9:10:11
|-
|-
| 72
| 72
Line 1,133: Line 1,196:
| otonal
| otonal
|C\m6
|C\m6
|\m6
|
|
|6:7:9:10
|-
|-
| 73
| 73
Line 1,141: Line 1,204:
| otonal
| otonal
|C\m6~7no5
|C\m6~7no5
|\m6~7no5
|
|
|6:7:10:11
|-
|-
| 74
| 74
Line 1,157: Line 1,220:
| swetismic
| swetismic
|C\m6(\~5)
|C\m6(\~5)
|\m6(\~5)
|
|
|
|-
|-
Line 1,174: Line 1,237:
|
|
|
|
|
|20/14/12/11
|-
|-
| 78
| 78
Line 1,181: Line 1,244:
| utonal
| utonal
|C/7
|C/7
|/7
|1-9/7-3/2-9/5
|1-9/7-3/2-9/5
|9/7/6/5
|-
|-
| 79
| 79
Line 1,189: Line 1,252:
| utonal
| utonal
|C/7~13no3
|C/7~13no3
|/7~13no3
|1-3/2-18/11-9/5
|1-3/2-18/11-9/5
|18/12/11/10
|-
|-
| 80
| 80
Line 1,197: Line 1,260:
| otonal
| otonal
|C\,9
|C\,9
|\,9
|
|
|4:5:6:9
|-
|-
| 81
| 81
Line 1,205: Line 1,268:
| otonal
| otonal
|C\,~11
|C\,~11
|\,~11
|
|
|8:10:11:12
|-
|-
|82
|82
Line 1,213: Line 1,276:
|otonal
|otonal
|C\,9(\b5)
|C\,9(\b5)
|\,9(\b5)
|
|
|8:9:10:11
|-
|-
|83
|83
Line 1,221: Line 1,284:
|werckismic
|werckismic
|C,9(\~5)
|C,9(\~5)
|,9(\~5)
|
|
|
|-
|-
Line 1,229: Line 1,292:
|otonal
|otonal
|C\7
|C\7
|\7
|
|
|4:5:6:7
|-
|-
| 85
| 85
Line 1,237: Line 1,300:
| otonal
| otonal
|C\9no5
|C\9no5
|\9no5
|
|
|4:5:7:9
|-
|-
| 86
| 86
Line 1,245: Line 1,308:
| otonal
| otonal
|C\7~11no5
|C\7~11no5
|\7~11no5
|
|
|4:5:7:11
|-
|-
| 87
| 87
Line 1,253: Line 1,316:
| werckismic
| werckismic
|C\7(\~5)
|C\7(\~5)
|\7(\~5)
|
|
|
|-
|-
Line 1,261: Line 1,324:
| utonal
| utonal
|C,\7(b5)
|C,\7(b5)
|,\7(b5)
|1-14/11-7/5-7/4
|1-14/11-7/5-7/4
|20/16/14/11
|-
|-
| 89
| 89
Line 1,269: Line 1,332:
| utonal
| utonal
|C/9no5
|C/9no5
|/9no5
|1-9/7-9/5-9/4
|1-9/7-9/5-9/4
|10/9/8/7
|-
|-
|90
|90
Line 1,277: Line 1,340:
|werckismic
|werckismic
|C\7\9no5
|C\7\9no5
|\7\9no5
|
|
|
|-
|-
Line 1,285: Line 1,348:
|utonal
|utonal
|C2~6^7no5
|C2~6^7no5
|2~6^7no5
|1-18/11-9/5-9/4
|1-18/11-9/5-9/4
|20/18/16/11
|-
|-
|92
|92
Line 1,293: Line 1,356:
|ambitonal
|ambitonal
|C\6 <u>or</u> C/m7
|C\6 <u>or</u> C/m7
|\6 <u>or</u> /m7
|1-6/5-3/2-9/5
|1-6/5-3/2-9/5
|
|-
|-
|93
|93
Line 1,301: Line 1,364:
|utonal
|utonal
|C/m6
|C/m6
C\m7(b5)|/m6
C\m7(b5)
\m7(b5)
|1-6/5-3/2-12/7
|1-6/5-3/2-12/7
1-7/6-7/5-7/4
1-7/6-7/5-7/4
|12/10/8/7
7/6/5/4
|-
|-
| 94
| 94
Line 1,311: Line 1,375:
| utonal
| utonal
|C/m,~9
|C/m,~9
|/m,~9
|1-6/5-3/2-24/11
|1-6/5-3/2-12/11
|24/20/18/11
|-
|-
| 95
| 95
Line 1,319: Line 1,383:
| utonal
| utonal
|C/9no3
|C/9no3
|/9no3
|1-3/2-9/5-9/4
|1-3/2-9/5-9/4
|9/6/5/4
|}
|}


Line 1,327: Line 1,391:
|-
|-
! #
! #
! Chord
! Genspans
! Transversal
! Transversal
! Type
! Type
!Name
!Name
!Inversion
!Inversion
!As (sub)harmonics
|-
|-
| 1
| 1
Line 1,338: Line 1,403:
| rastmic
| rastmic
|C~9
|C~9
|
|
|
|-
|-
Line 1,345: Line 1,411:
| rastmic
| rastmic
|C~11no9
|C~11no9
|
|
|
|-
|-
Line 1,352: Line 1,419:
| rastmic
| rastmic
|C~11no7
|C~11no7
|
|
|
|-
|-
Line 1,359: Line 1,427:
| rastmic
| rastmic
|C~11no5
|C~11no5
|
|
|
|-
|-
Line 1,366: Line 1,435:
| rastmic
| rastmic
|C~11no3
|C~11no3
|
|
|
|-
|-
Line 1,372: Line 1,442:
| 1-11/6-9/8-11/8-14/11
| 1-11/6-9/8-11/8-14/11
| parahemif
| parahemif
|
|
|
|
|
Line 1,379: Line 1,450:
| 1-11/9-9/8-11/8-14/9
| 1-11/9-9/8-11/8-14/9
| parahemif
| parahemif
|
|
|
|
|
Line 1,386: Line 1,458:
| 1-9/8-11/8-14/11-14/9
| 1-9/8-11/8-14/11-14/9
| parahemif
| parahemif
|
|
|
|
|
Line 1,393: Line 1,466:
| 1-11/9-11/6-9/8-10/7
| 1-11/9-11/6-9/8-10/7
| jove
| jove
|
|
|
|
|
Line 1,400: Line 1,474:
| 1-11/6-9/8-14/11-10/7
| 1-11/6-9/8-14/11-10/7
| hemififths
| hemififths
|
|
|
|
|
Line 1,407: Line 1,482:
| 1-11/9-9/8-14/9-10/7
| 1-11/9-9/8-14/9-10/7
| hemififths
| hemififths
|
|
|
|
|
Line 1,414: Line 1,490:
| 1-9/8-14/11-14/9-10/7
| 1-9/8-14/11-14/9-10/7
| hemififths
| hemififths
|
|
|
|
|
Line 1,421: Line 1,498:
| 1-11/6-14/11-7/6-10/7
| 1-11/6-14/11-7/6-10/7
| hemififths
| hemififths
|
|
|
|
|
Line 1,428: Line 1,506:
| 1-14/11-14/9-7/6-10/7
| 1-14/11-14/9-7/6-10/7
| jove
| jove
|
|
|
|
|
Line 1,436: Line 1,515:
| jove
| jove
|C~9(\m7)
|C~9(\m7)
|
|
|
|-
|-
Line 1,442: Line 1,522:
| 1-11/9-3/2-11/8-7/4
| 1-11/9-3/2-11/8-7/4
| jove
| jove
|
|
|
|
|
Line 1,449: Line 1,530:
| 1-11/9-9/8-11/8-7/4
| 1-11/9-9/8-11/8-7/4
| jove
| jove
|
|
|
|
|
Line 1,458: Line 1,540:
|C\9~11no3
|C\9~11no3
|
|
|4:6:7:9:11
|-
|-
| 19
| 19
Line 1,463: Line 1,546:
| 1-9/8-11/8-14/11-7/4
| 1-9/8-11/8-14/11-7/4
| parahemif
| parahemif
|
|
|
|
|
Line 1,470: Line 1,554:
| 1-11/9-9/8-14/9-7/4
| 1-11/9-9/8-14/9-7/4
| hemififths
| hemififths
|
|
|
|
|
Line 1,477: Line 1,562:
| 1-11/9-11/8-14/9-7/4
| 1-11/9-11/8-14/9-7/4
| pele
| pele
|
|
|
|
|
Line 1,484: Line 1,570:
| 1-9/8-11/8-14/9-7/4
| 1-9/8-11/8-14/9-7/4
| pentacircle
| pentacircle
|
|
|
|
|
Line 1,491: Line 1,578:
| 1-9/8-14/11-14/9-7/4
| 1-9/8-14/11-14/9-7/4
| pentacircle
| pentacircle
|
|
|
|
|
Line 1,498: Line 1,586:
| 1-11/8-14/11-14/9-7/4
| 1-11/8-14/11-14/9-7/4
| parahemif
| parahemif
|
|
|
|
|
Line 1,507: Line 1,596:
|C/,~6,9
|C/,~6,9
|1-9/7-3/2-18/11-9/4
|1-9/7-3/2-18/11-9/4
|18/14/12/11/8
|-
|-
| 26
| 26
Line 1,512: Line 1,602:
| 1-11/9-9/8-10/7-7/4
| 1-11/9-9/8-10/7-7/4
| jove
| jove
|
|
|
|
|
Line 1,519: Line 1,610:
| 1-9/8-14/11-10/7-7/4
| 1-9/8-14/11-10/7-7/4
| pele
| pele
|
|
|
|
|
Line 1,526: Line 1,618:
| 1-11/9-14/9-10/7-7/4
| 1-11/9-14/9-10/7-7/4
| jove
| jove
|
|
|
|
|
Line 1,533: Line 1,626:
| 1-9/8-14/9-10/7-7/4
| 1-9/8-14/9-10/7-7/4
| hemififths
| hemififths
|
|
|
|
|
Line 1,540: Line 1,634:
| 1-14/11-14/9-10/7-7/4
| 1-14/11-14/9-10/7-7/4
| jove
| jove
|
|
|
|
|
Line 1,547: Line 1,642:
| 1-14/11-7/6-10/7-7/4
| 1-14/11-7/6-10/7-7/4
| jove
| jove
|
|
|
|
|
Line 1,554: Line 1,650:
| 1-14/9-7/6-10/7-7/4
| 1-14/9-7/6-10/7-7/4
| jove
| jove
|
|
|
|
|
Line 1,561: Line 1,658:
| 1-14/11-14/9-7/6-20/11
| 1-14/11-14/9-7/6-20/11
| swetismic
| swetismic
|
|
|
|
|
Line 1,568: Line 1,666:
| 1-14/11-14/9-10/7-20/11
| 1-14/11-14/9-10/7-20/11
| jove
| jove
|
|
|
|
|
Line 1,575: Line 1,674:
| 1-14/11-7/6-10/7-20/11
| 1-14/11-7/6-10/7-20/11
| jove
| jove
|
|
|
|
|
Line 1,582: Line 1,682:
| 1-14/9-7/6-10/7-20/11
| 1-14/9-7/6-10/7-20/11
| swetismic
| swetismic
|
|
|
|
|
Line 1,589: Line 1,690:
| 1-11/9-14/9-10/7-10/9
| 1-11/9-14/9-10/7-10/9
| swetismic
| swetismic
|
|
|
|
|
Line 1,596: Line 1,698:
| 1-14/11-14/9-10/7-10/9
| 1-14/11-14/9-10/7-10/9
| jove
| jove
|
|
|
|
|
Line 1,603: Line 1,706:
| 1-11/9-14/9-7/4-10/9
| 1-11/9-14/9-7/4-10/9
| werckismic
| werckismic
|
|
|
|
|
Line 1,610: Line 1,714:
| 1-14/11-14/9-7/4-10/9
| 1-14/11-14/9-7/4-10/9
| werckismic
| werckismic
|
|
|
|
|
Line 1,617: Line 1,722:
| 1-11/9-10/7-7/4-10/9
| 1-11/9-10/7-7/4-10/9
| jove
| jove
|
|
|
|
|
Line 1,624: Line 1,730:
| 1-14/11-10/7-7/4-10/9
| 1-14/11-10/7-7/4-10/9
| werckismic
| werckismic
|
|
|
|
|
Line 1,631: Line 1,738:
| 1-14/9-10/7-7/4-10/9
| 1-14/9-10/7-7/4-10/9
| jove
| jove
|
|
|
|
|
Line 1,638: Line 1,746:
| 1-14/11-14/9-20/11-10/9
| 1-14/11-14/9-20/11-10/9
| jove
| jove
|
|
|
|
|
Line 1,645: Line 1,754:
| 1-14/11-10/7-20/11-10/9
| 1-14/11-10/7-20/11-10/9
| werckismic
| werckismic
|
|
|
|
|
Line 1,652: Line 1,762:
| 1-14/9-10/7-20/11-10/9
| 1-14/9-10/7-20/11-10/9
| swetismic
| swetismic
|
|
|
|
|
Line 1,661: Line 1,772:
|C\m6~7
|C\m6~7
|
|
|6:7:9:10:11
|-
|-
| 48
| 48
Line 1,666: Line 1,778:
| 1-11/6-7/6-10/7-5/3
| 1-11/6-7/6-10/7-5/3
| swetismic
| swetismic
|
|
|
|
|
Line 1,673: Line 1,786:
| 1-7/6-10/7-20/11-5/3
| 1-7/6-10/7-20/11-5/3
| swetismic
| swetismic
|
|
|
|
|
Line 1,682: Line 1,796:
|C/7~6
|C/7~6
|1-9/7-3/2-18/11-9/5
|1-9/7-3/2-18/11-9/5
|18/14/12/11/10
|-
|-
| 51
| 51
Line 1,689: Line 1,804:
|C\,9~11
|C\,9~11
|
|
|4:5:6:9:11
|-
|-
| 52
| 52
Line 1,696: Line 1,812:
|C\9
|C\9
|
|
|4:5:6:7:9
|-
|-
| 53
| 53
Line 1,703: Line 1,820:
|C\7~11
|C\7~11
|
|
|4:5:6:7:11
|-
|-
| 54
| 54
Line 1,710: Line 1,828:
|C\9~11no5
|C\9~11no5
|
|
|4:5:7:9:11
|-
|-
| 55
| 55
Line 1,716: Line 1,835:
| werckismic
| werckismic
|C\9(\~5)
|C\9(\~5)
|
|
|
|-
|-
Line 1,722: Line 1,842:
| 1-10/7-7/4-10/9-5/4
| 1-10/7-7/4-10/9-5/4
| werckismic
| werckismic
|
|
|
|
|
Line 1,731: Line 1,852:
|C/9~6no5
|C/9~6no5
|1-9/7-18/11-9/5-9/4
|1-9/7-18/11-9/5-9/4
|18/14/11/10/8
|-
|-
| 58
| 58
Line 1,737: Line 1,859:
| utonal
| utonal
|C/m6~9
|C/m6~9
|1-6/5-3/2-12/7-13/6
|1-6/5-3/2-12/7-24/11
|24/20/16/14/11
|-
|-
| 59
| 59
Line 1,745: Line 1,868:
|C/9
|C/9
|1-9/7-3/2-9/5-9/4
|1-9/7-3/2-9/5-9/4
|9/7/6/5/4
|-
|-
| 60
| 60
Line 1,752: Line 1,876:
|C/9~6no3
|C/9~6no3
|1-3/2-18/11-9/5-9/4
|1-3/2-18/11-9/5-9/4
|18/12/11/10/8
|}
|}


Line 1,758: Line 1,883:
|-
|-
! #
! #
! Chord
! Genspans
! Transversal
! Transversal
! Type
! Type
!Name
!Name
!Inversion
!Inversion
!As (sub)harmonics
|-
|-
| 1
| 1
Line 1,769: Line 1,895:
| rastmic
| rastmic
|C~11
|C~11
|
|
|
|-
|-
Line 1,776: Line 1,903:
| jove
| jove
|C~11(\m7)
|C~11(\m7)
|
|
|
|-
|-
Line 1,782: Line 1,910:
| 1-11/9-9/8-11/8-14/9-7/4
| 1-11/9-9/8-11/8-14/9-7/4
| hemififths
| hemififths
|
|
|
|
|
Line 1,789: Line 1,918:
| 1-9/8-11/8-14/11-14/9-7/4
| 1-9/8-11/8-14/11-14/9-7/4
| nofives
| nofives
|
|
|
|
|
Line 1,796: Line 1,926:
| 1-11/9-9/8-14/9-10/7-7/4
| 1-11/9-9/8-14/9-10/7-7/4
| hemififths
| hemififths
|
|
|
|
|
Line 1,803: Line 1,934:
| 1-9/8-14/11-14/9-10/7-7/4
| 1-9/8-14/11-14/9-10/7-7/4
| hemififths
| hemififths
|
|
|
|
|
Line 1,810: Line 1,942:
| 1-14/11-14/9-7/6-10/7-7/4
| 1-14/11-14/9-7/6-10/7-7/4
| jove
| jove
|
|
|
|
|
Line 1,817: Line 1,950:
| 1-14/11-14/9-7/6-10/7-20/11
| 1-14/11-14/9-7/6-10/7-20/11
| jove
| jove
|
|
|
|
|
Line 1,824: Line 1,958:
| 1-11/9-14/9-10/7-7/4-10/9
| 1-11/9-14/9-10/7-7/4-10/9
| jove
| jove
|
|
|
|
|
Line 1,831: Line 1,966:
| 1-14/11-14/9-10/7-7/4-10/9
| 1-14/11-14/9-10/7-7/4-10/9
| jove
| jove
|
|
|
|
|
Line 1,838: Line 1,974:
| 1-14/11-14/9-10/7-20/11-10/9
| 1-14/11-14/9-10/7-20/11-10/9
| jove
| jove
|
|
|
|
|
Line 1,847: Line 1,984:
|C\9~11
|C\9~11
|
|
|4:5:6:7:9:11
|-
|-
| 13
| 13
Line 1,854: Line 1,992:
|C/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
|18/14/12/11/10/8
|}
|}


Revision as of 23:16, 19 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.

The "As (sub)harmonics" column describes otonal chords as harmonics and utonal chords as subharmonics.

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

# Genspans Transversal Type Name Inversion As (sub)harmonics
1 0-1-2 1-11/9-3/2 rastmic C~
2 0-1-3 1-11/9-11/6 utonal C~7no5 11/9/6
3 0-2-3 1-3/2-11/6 otonal C~7no3 6:9:11
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) 11/9/8
8 0-2-5 1-3/2-11/8 otonal C~7sus4no5 1-4/3-11/6 6:8:11
9 0-3-5 1-11/6-11/8 utonal C~2 1-12/11-3/2 12/11/8
10 0-4-5 1-9/8-11/8 otonal C~,7no5 1-11/9-16/9 9:11:16
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) 9:11:14
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) 14/11/9
18 0-2-11 1-3/2-7/6 otonal C\m 6:7:9
19 0-3-11 1-11/6-7/6 otonal C\m~7no5 6:7:11
20 0-8-11 1-14/11-7/6 utonal C~2/6 1-12/11-12/7 12/11/7
21 0-9-11 1-14/9-7/6 utonal C/ 1-9/7-3/2 9/7/6
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 4:6:7
30 0-4-13 1-9/8-7/4 otonal C\9no35 4:7:9
31 0-5-13 1-11/8-7/4 otonal C(~5) 1-14/11-16/11 11:14:16
32 0-8-13 1-14/11-7/4 utonal C,\7 14/11/8
33 0-9-13 1-14/9-7/4 utonal C/,2no5 1-9/8-9/7 9/8/7
34 0-11-13 1-7/6-7/4 utonal C\m7no5 7/6/4
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 11:14:20
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) 20/14/11
40 0-1-21 1-11/9-10/9 otonal C~,\9no5 9:10:11
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 7:9:10
43 0-12-21 1-10/7-10/9 utonal C\2(\~5) 10/9/7
44 0-13-21 1-7/4-10/9 werckismic C\2\m7no5
45 0-20-21 1-20/11-10/9 utonal 20/18/11
46 0-2-23 1-3/2-5/3 otonal C\m7no5 1-6/5-9/5 5:6:9
47 0-3-23 1-11/6-5/3 otonal 6:10:11
48 0-11-23 1-7/6-5/3 otonal C\m6no5 6:7:10
49 0-12-23 1-10/7-5/3 utonal C/dim 1-7/6-7/5 10/7/6
50 0-20-23 1-20/11-5/3 utonal 20/12/11
51 0-21-23 1-10/9-5/3 utonal C/7no3 1-3/2-9/5 9/6/5
52 0-2-25 1-3/2-5/4 otonal C\ 4:5:6
53 0-4-25 1-9/8-5/4 otonal C\,9no5 4:5:9
54 0-5-25 1-11/8-5/4 otonal C\(\b5) 8:10:11
55 0-12-25 1-10/7-5/4 utonal C\(\~5) 10/8/7
56 0-13-25 1-7/4-5/4 otonal C\7no5 4:5:6
57 0-20-25 1-20/11-5/4 utonal C\,\~7no5 20/11/16
58 0-21-25 1-10/9-5/4 utonal C/9no35 1-9/5-9/4 9/5/4
59 0-23-25 1-5/3-5/4 utonal C/m 1-6/5-3/2 6/5/4

Tetrads

# Genspans Transversal Type Name Inversion As (sub)harmonics
1 0-1-2-3 1-11/9-3/2-11/6 rastmic C~7
2 0-1-2-4 1-11/9-3/2-9/8 rastmic C~,9
3 0-1-3-4 1-11/9-11/6-9/8 rastmic C~9no5
4 0-2-3-4 1-3/2-11/6-9/8 rastmic C~9no3
5 0-1-2-5 1-11/9-3/2-11/8 rastmic C~,~11
6 0-1-3-5 1-11/9-11/6-11/8 utonal C2~6 or

C4~9

1-9/8-3/2-18/11

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

18/16/12/11

24/18/16/11

7 0-2-3-5 1-3/2-11/6-11/8 ambitonal C~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 1-4/3-3/2-11/6 6:8:9:11
10 0-3-4-5 1-11/6-9/8-11/8 rastmic C~11no35
11 0-3-4-8 1-11/6-9/8-14/11 parahemif C9(~7)no5
12 0-3-5-8 1-11/6-11/8-14/11 hemimin C~2~11 1-12/11-11/8-3/2
13 0-4-5-8 1-9/8-11/8-14/11 parahemif C~,~9 1-11/9-3/2-13/12
14 0-1-4-9 1-11/9-9/8-14/9 parahemif C~,9(^5)
15 0-1-5-9 1-11/9-11/8-14/9 pentacircle C,~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) 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 6:7:9:11
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 1-9/7-3/2-18/11 18/14/12/11
22 0-1-3-12 1-11/9-11/6-10/7 swetismic C\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 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
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 4:6:7:9
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 8:11:12:14
38 0-4-5-13 1-9/8-11/8-7/4 otonal C~4\7,9 or C~,7(^5) 1-11/9-14/9-16/9 9:11:14:16
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 14/11/9/8
45 0-2-11-13 1-3/2-7/6-7/4 ambitonal C\m7
46 0-8-11-13 1-14/11-7/6-7/4 utonal 14/12/11/8
47 0-9-11-13 1-14/9-7/6-7/4 utonal C/,9 1-9/7-3/2-9/4 9/7/6/4
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 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 9:10:11:14
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 20/18/14/11
71 0-2-3-23 1-3/2-11/6-5/3 otonal 6:9:10:11
72 0-2-11-23 1-3/2-7/6-5/3 otonal C\m6 6:7:9:10
73 0-3-11-23 1-11/6-7/6-5/3 otonal C\m6~7no5 6:7:10:11
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)
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 20/14/12/11
78 0-12-21-23 1-10/7-10/9-5/3 utonal C/7 1-9/7-3/2-9/5 9/7/6/5
79 0-20-21-23 1-20/11-10/9-5/3 utonal C/7~13no3 1-3/2-18/11-9/5 18/12/11/10
80 0-2-4-25 1-3/2-9/8-5/4 otonal C\,9 4:5:6:9
81 0-2-5-25 1-3/2-11/8-5/4 otonal C\,~11 8:10:11:12
82 0-4-5-25 1-9/8-11/8-5/4 otonal C\,9(\b5) 8:9:10:11
83 0-4-12-25 1-9/8-10/7-5/4 werckismic C,9(\~5)
84 0-2-13-25 1-3/2-7/4-5/4 otonal C\7 4:5:6:7
85 0-4-13-25 1-9/8-7/4-5/4 otonal C\9no5 4:5:7:9
86 0-5-13-25 1-11/8-7/4-5/4 otonal C\7~11no5 4:5:7:11
87 0-12-13-25 1-10/7-7/4-5/4 werckismic C\7(\~5)
88 0-12-20-25 1-10/7-20/11-5/4 utonal C,\7(b5) 1-14/11-7/5-7/4 20/16/14/11
89 0-12-21-25 1-10/7-10/9-5/4 utonal C/9no5 1-9/7-9/5-9/4 10/9/8/7
90 0-13-21-25 1-7/4-10/9-5/4 werckismic C\7\9no5
91 0-20-21-25 1-20/11-10/9-5/4 utonal C2~6^7no5 1-18/11-9/5-9/4 20/18/16/11
92 0-2-23-25 1-3/2-5/3-5/4 ambitonal C\6 or C/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)

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

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

12/10/8/7

7/6/5/4

94 0-20-23-25 1-20/11-5/3-5/4 utonal C/m,~9 1-6/5-3/2-24/11 24/20/18/11
95 0-21-23-25 1-10/9-5/3-5/4 utonal C/9no3 1-3/2-9/5-9/4 9/6/5/4

Pentads

# Genspans Transversal Type Name Inversion As (sub)harmonics
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 4:6:7:9:11
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 18/14/12/11/8
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 6:7:9:10:11
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 18/14/12/11/10
51 0-2-4-5-25 1-3/2-9/8-11/8-5/4 otonal C\,9~11 4:5:6:9:11
52 0-2-4-13-25 1-3/2-9/8-7/4-5/4 otonal C\9 4:5:6:7:9
53 0-2-5-13-25 1-3/2-11/8-7/4-5/4 otonal C\7~11 4:5:6:7:11
54 0-4-5-13-25 1-9/8-11/8-7/4-5/4 otonal C\9~11no5 4:5:7:9:11
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 18/14/11/10/8
58 0-12-20-23-25 1-10/7-20/11-5/3-5/4 utonal C/m6~9 1-6/5-3/2-12/7-24/11 24/20/16/14/11
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 9/7/6/5/4
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 18/12/11/10/8

Hexads

# Genspans Transversal Type Name Inversion As (sub)harmonics
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 4:5:6:7:9:11
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 18/14/12/11/10/8
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