Hemififths/Chords: Difference between revisions

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Below are listed the [[dyadic chord]]s 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 chords|swetismic]], by [[441/440]] [[Werckismic chords|werckismic]], by [[896/891]] [[Pentacircle chords|pentacircle]], by [[243/242]] [[Rastmic chords|rastmic]], and by [[1344/1331]] [[Hemimin chords|hemimin]]. Those requiring tempering by any two of 540/539, 441/440 or 243/242 are labeled [[Jove chords|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".
Below are listed the [[11-odd-limit]] [[dyadic chord]]s 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 chords|swetismic]], by [[441/440]] [[werckismic chords|werckismic]], by [[896/891]] [[pentacircle chords|pentacircle]], by [[243/242]] [[rastmic chords|rastmic]], and by [[1344/1331]] [[hemimin chords|hemimin]]. Those requiring tempering by any two of 540/539, 441/440 or 243/242 are labeled [[jove chords|jove]]. Those requiring both 441/440 and 896/891 are labeled [[pele chords|pele]]. Those requiring any two of 243/242, 896/891 or 1344/1331 are labeled [[parahemif chords|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.
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 scale]]s 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, 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 second. Enharmonic equivalences: vvA1 and v\m2. Cents: ^1 = 50¢ + 3.5c and /1 = 50¢ - 8.5c, where c equals 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.
The ''As harmonics or subharmonics'' column describes otonal chords as harmonics and utonal chords as subharmonics.
{| class="wikitable"
 
{| class="wikitable center-all"
|+Hemififth's genchain
|+Hemififth's genchain
!Genspan
! Genspan
!0
! 0
!1
! 1
!2
! 2
!3
! 3
!4
! 4
!5
! 5
!6
! 6
!7
! 7
!8
! 8
!9
! 9
!10
! 10
!11
! 11
!12
! 12
!13
! 13
!...
! …
!20
! 20
!21
! 21
!...
! …
!23
! 23
!...
! …
!25
! 25
|-
|-
!Cents (41edo)
! Cents (41edo)
|0
| 0
|351
| 351
|702
| 702
|1054
| 1054
|205
| 205
|556
| 556
|907
| 907
|59
| 59
|410
| 410
|761
| 761
|1112
| 1112
|263
| 263
|615
| 615
|966
| 966
!
| …
|1024
| 1024
|176
| 176
!
| …
|878
| 878
!
| …
|380
| 380
|-
|-
!Ratio
! Ratio
|1/1
| 1/1
|11/9
| 11/9<br>16/13
16/13
| 3/2
|3/2
| 11/6<br>24/13
|11/6
| 9/8
24/13
| 11/8<br>18/13
|9/8
| 27/16<br>22/13
|11/8
| 28/27<br>33/32
18/13
| 14/11
|27/16
| 14/9
22/13
| 40/21<br>21/11
|28/27
| 7/6
33/32
| 10/7
|14/11
| 7/4
|14/9
| …
|40/21
| 20/11
21/11
| 10/9
|7/6
| …
|10/7
| 5/3
|7/4
| …
!
| 5/4
|20/11
|10/9
!
|5/3
!
|5/4
|-
|-
!Interval
! Interval
|P1
| P1
|~3
| ~3
|P5
| P5
|~7
| ~7
|M2
| M2
|~4
| ~4<br>\b5
\b5
| M6
|M6
| ^1<br>\m2
|^1
| M3
\m2
| ^5<br>\m6
|M3
| M7
|^5
| ^M2<br>\m3
\m6
| A4<br>\~5
|M7
| ^M6<br>\m7
|^M2
| …
\m3
| A6<br>\~7
|A4
| ^A1<br>\M2
\~5
| …
|^M6
| ^A5<br>\M6
\m7
| …
!
| ^A2<br>\M3
|A6
 
\~7
|^A1
 
\M2
!
|^A5
 
\M6
!
|^A2
 
\M3
|}
|}
'''''TODO: Complete the tables'''''
{{Todo|complete table|inline=1}}


== Triads ==
== Triads ==
Line 129: Line 110:
! Transversal
! Transversal
! Type
! Type
!Name
! Name
!Inversion
! Inversion
!As (sub)harmonics
! As harmonics<br>or subharmonics
|-
|-
| 1
| 1
Line 137: Line 118:
| 1-11/9-3/2
| 1-11/9-3/2
| rastmic
| rastmic
|C~
| C~
|
|  
|
|  
|-
|-
| 2
| 2
Line 145: Line 126:
| 1-11/9-11/6
| 1-11/9-11/6
| utonal
| utonal
|C~7no5
| C~7no5
|
|  
|11/9/6
| 1/(11:9:6)
|-
|-
| 3
| 3
Line 153: Line 134:
| 1-3/2-11/6
| 1-3/2-11/6
| otonal
| otonal
|C~7no3
| C~7no3
|
|  
|6:9:11
| 6:9:11
|-
|-
| 4
| 4
Line 161: Line 142:
| 1-11/9-9/8
| 1-11/9-9/8
| rastmic
| rastmic
|C~,9no5
| C~,9no5
|
|  
|
|  
|-
|-
| 5
| 5
Line 169: Line 150:
| 1-3/2-9/8
| 1-3/2-9/8
| ambitonal
| ambitonal
|C2 <u>or</u> C4
| C2 ''or'' C4
|1-4/3-9/8
| 1-4/3-3/2
|
|
|-
|-
Line 177: Line 158:
| 1-11/6-9/8
| 1-11/6-9/8
| rastmic
| rastmic
|C~9no35
| C~9no35
|
|  
|
|  
|-
|-
| 7
| 7
Line 185: Line 166:
| 1-11/9-11/8
| 1-11/9-11/8
| utonal
| utonal
|C~(\b5)
| C~(\b5)
|
|  
|11/9/8
| 1/(11:9:8)
|-
|-
| 8
| 8
Line 193: Line 174:
| 1-3/2-11/8
| 1-3/2-11/8
| otonal
| otonal
|C~7sus4no5
| C~7sus4no5
|1-4/3-11/6
| 1-4/3-11/6
|6:8:11
| 6:8:11
|-
|-
| 9
| 9
Line 201: Line 182:
| 1-11/6-11/8
| 1-11/6-11/8
| utonal
| utonal
|C~2
| C~2
|1-12/11-3/2
| 1-12/11-3/2
|12/11/8
| 1/(12:11:8)
|-
|-
| 10
| 10
Line 209: Line 190:
| 1-9/8-11/8
| 1-9/8-11/8
| otonal
| otonal
|C~,7no5
| C~,7no5
|1-11/9-16/9
| 1-11/9-16/9
|9:11:16
| 9:11:16
|-
|-
| 11
| 11
Line 217: Line 198:
| 1-11/6-14/11
| 1-11/6-14/11
| hemimin
| hemimin
|C,~7no5
| C,~7no5
|
|  
|
|  
|-
|-
| 12
| 12
Line 225: Line 206:
| 1-9/8-14/11
| 1-9/8-14/11
| pentacircle
| pentacircle
|C,9no5
| C,9no5
|
|  
|
|  
|-
|-
| 13
| 13
Line 233: Line 214:
| 1-11/8-14/11
| 1-11/8-14/11
| hemimin
| hemimin
|C(\b5)
| C(\b5)
|
|  
|
|  
|-
|-
| 14
| 14
Line 241: Line 222:
| 1-11/9-14/9
| 1-11/9-14/9
| otonal
| otonal
|C~(^5)
| C~(^5)
|
|  
|9:11:14
| 9:11:14
|-
|-
| 15
| 15
Line 249: Line 230:
| 1-9/8-14/9
| 1-9/8-14/9
| pentacircle
| pentacircle
|C7~4no5
| C7~4no5
|1-11/8-16/9
| 1-11/8-16/9
|
|  
|-
|-
| 16
| 16
Line 257: Line 238:
| 1-11/8-14/9
| 1-11/8-14/9
| pentacircle
| pentacircle
|C2(~5) <u>or</u>
| C2(~5) ''or''<br>C/,7no5
C/,7no5
| 1-9/8-13/9<br>1-9/7-16/9
|1-9/8-13/9
|  
 
1-9/7-16/9
|
|-
|-
| 17
| 17
Line 268: Line 246:
| 1-14/11-14/9
| 1-14/11-14/9
| utonal
| utonal
|C(^5)
| C(^5)
|
|  
|14/11/9
| 1/(14:11:9)
|-
|-
| 18
| 18
Line 276: Line 254:
| 1-3/2-7/6
| 1-3/2-7/6
| otonal
| otonal
|C\m
| C\m
|
|  
|6:7:9
| 6:7:9
|-
|-
| 19
| 19
Line 284: Line 262:
| 1-11/6-7/6
| 1-11/6-7/6
| otonal
| otonal
|C\m~7no5
| C\m~7no5
|
|  
|6:7:11
| 6:7:11
|-
|-
| 20
| 20
Line 292: Line 270:
| 1-14/11-7/6
| 1-14/11-7/6
| utonal
| utonal
|C~2/6
| C~2/6
|1-12/11-12/7
| 1-12/11-12/7
|12/11/7
| 1/(12:11:7)
|-
|-
| 21
| 21
Line 300: Line 278:
| 1-14/9-7/6
| 1-14/9-7/6
| utonal
| utonal
|C/
| C/
|1-9/7-3/2
| 1-9/7-3/2
|9/7/6
| 1/(9:7:6)
|-
|-
| 22
| 22
Line 308: Line 286:
| 1-11/9-10/7
| 1-11/9-10/7
| swetismic
| swetismic
|C~(\~5)
| C~(\~5)
|
|  
|
|  
|-
|-
| 23
| 23
Line 316: Line 294:
| 1-11/6-10/7
| 1-11/6-10/7
| swetismic
| swetismic
|C/(b5)
| C/(b5)
|1-9/7-7/5
| 1-9/7-7/5
|
|  
|-
|-
| 24
| 24
Line 324: Line 302:
| 1-9/8-10/7
| 1-9/8-10/7
| werckismic
| werckismic
|C2(\~5)
| C2(\~5)
|
|  
|
|  
|-
|-
| 25
| 25
Line 332: Line 310:
| 1-14/11-10/7
| 1-14/11-10/7
| werckismic
| werckismic
|C(\~5)
| C(\~5)
|
|  
|
|  
|-
|-
| 26
| 26
Line 340: Line 318:
| 1-14/9-10/7
| 1-14/9-10/7
| swetismic
| swetismic
|C~2(b5)
| C~2(b5)
|1-12/11-7/5
| 1-12/11-7/5
|
|  
|-
|-
| 27
| 27
Line 348: Line 326:
| 1-7/6-10/7
| 1-7/6-10/7
| swetismic
| swetismic
|C\m(\~5)
| C\m(\~5)
|
|  
|
|  
|-
|-
| 28
| 28
Line 356: Line 334:
| 1-11/9-7/4
| 1-11/9-7/4
| werckismic
| werckismic
|C~,\7no5
| C~,\7no5
|
|  
|
|  
|-
|-
| 29
| 29
Line 364: Line 342:
| 1-3/2-7/4
| 1-3/2-7/4
| otonal
| otonal
|C\7no3
| C\7no3
|
|  
|4:6:7
| 4:6:7
|-
|-
| 30
| 30
Line 372: Line 350:
| 1-9/8-7/4
| 1-9/8-7/4
| otonal
| otonal
|C\9no35
| C\9no35
|
|  
|4:7:9
| 4:7:9
|-
|-
| 31
| 31
Line 380: Line 358:
| 1-11/8-7/4
| 1-11/8-7/4
| otonal
| otonal
|C(~5)
| C(~5)
|1-14/11-16/11
| 1-14/11-16/11
|11:14:16
| 8:11:14
|-
|-
| 32
| 32
Line 388: Line 366:
| 1-14/11-7/4
| 1-14/11-7/4
| utonal
| utonal
|C,\7
| C,\7
|
|  
|14/11/8
| 1/(14:11:8)
|-
|-
| 33
| 33
Line 396: Line 374:
| 1-14/9-7/4
| 1-14/9-7/4
| utonal
| utonal
|C/,2no5
| C/,2no5
|1-9/8-9/7
| 1-9/8-9/7
|9/8/7
| 1/(9:8:7)
|-
|-
| 34
| 34
Line 404: Line 382:
| 1-7/6-7/4
| 1-7/6-7/4
| utonal
| utonal
|C\m7no5
| C\m7no5
|
|  
|7/6/4
| 1/(7:6:4)
|-
|-
| 35
| 35
Line 412: Line 390:
| 1-10/7-7/4
| 1-10/7-7/4
| werckismic
| werckismic
|C~(b5)
| C~(b5)
|1-11/9-7/5
| 1-11/9-7/5
|
|  
|-
|-
| 36
| 36
Line 420: Line 398:
| 1-14/11-20/11
| 1-14/11-20/11
| otonal
| otonal
|C,\~7no5
| C,\~7no5
|
|  
|11:14:20
| 11:14:20
|-
|-
| 37
| 37
Line 428: Line 406:
| 1-14/9-20/11
| 1-14/9-20/11
| swetismic
| swetismic
|
|  
|
|  
|
|  
|-
|-
| 38
| 38
Line 436: Line 414:
| 1-7/6-20/11
| 1-7/6-20/11
| swetismic
| swetismic
|C\m\~7no5
| C\m\~7no5
|
|  
|
|  
|-
|-
| 39
| 39
Line 444: Line 422:
| 1-10/7-20/11
| 1-10/7-20/11
| utonal
| utonal
|C(b5)
| C(b5)
|
|  
|20/14/11
| 1/(20:14:11)
|-
|-
| 40
| 40
Line 452: Line 430:
| 1-11/9-10/9
| 1-11/9-10/9
| otonal
| otonal
|C~,\9no5
| C~,\9no5
|
|  
|9:10:11
| 9:10:11
|-
|-
| 41
| 41
Line 460: Line 438:
| 1-14/11-10/9
| 1-14/11-10/9
| werckismic
| werckismic
|C,\9no5
| C,\9no5
|
|  
|
|  
|-
|-
| 42
| 42
Line 468: Line 446:
| 1-14/9-10/9
| 1-14/9-10/9
| otonal
| otonal
|C/(\~5)
| C/(\~5)
|1-9/7-10/7
| 1-9/7-10/7
|7:9:10
| 7:9:10
|-
|-
| 43
| 43
Line 476: Line 454:
| 1-10/7-10/9
| 1-10/7-10/9
| utonal
| utonal
|C\2(\~5)
| C\2(\~5)
|
|  
|10/9/7
| 1/(10:9:7)
|-
|-
| 44
| 44
Line 484: Line 462:
| 1-7/4-10/9
| 1-7/4-10/9
| werckismic
| werckismic
|C\2\m7no5
| C\2\m7no5
|
|  
|
|  
|-
|-
| 45
| 45
Line 492: Line 470:
| 1-20/11-10/9
| 1-20/11-10/9
| utonal
| utonal
|
|  
|
|  
|20/18/11
| 1/(20:18:11)
|-
|-
| 46
| 46
Line 500: Line 478:
| 1-3/2-5/3
| 1-3/2-5/3
| otonal
| otonal
|C\m7no5
| C\m7no5
|1-6/5-9/5
| 1-6/5-9/5
|5:6:9
| 5:6:9
|-
|-
| 47
| 47
Line 508: Line 486:
| 1-11/6-5/3
| 1-11/6-5/3
| otonal
| otonal
|
|  
|
|  
|6:10:11
| 6:10:11
|-
|-
| 48
| 48
Line 516: Line 494:
| 1-7/6-5/3
| 1-7/6-5/3
| otonal
| otonal
|C\m6no5
| C\m6no5
|
|  
|6:7:10
| 6:7:10
|-
|-
| 49
| 49
Line 524: Line 502:
| 1-10/7-5/3
| 1-10/7-5/3
| utonal
| utonal
|C/dim
| C/dim
|1-7/6-7/5
| 1-7/6-7/5
|10/7/6
| 1/(10:7:6)
|-
|-
| 50
| 50
Line 532: Line 510:
| 1-20/11-5/3
| 1-20/11-5/3
| utonal
| utonal
|
|  
|
|  
|20/12/11
| 1/(20:12:11)
|-
|-
| 51
| 51
Line 540: Line 518:
| 1-10/9-5/3
| 1-10/9-5/3
| utonal
| utonal
|C/7no3
| C/7no3
|1-3/2-9/5
| 1-3/2-9/5
|9/6/5
| 1/(9:6:5)
|-
|-
| 52
| 52
Line 548: Line 526:
| 1-3/2-5/4
| 1-3/2-5/4
| otonal
| otonal
|C\
| C\
|
|  
|4:5:6
| 4:5:6
|-
|-
| 53
| 53
Line 556: Line 534:
| 1-9/8-5/4
| 1-9/8-5/4
| otonal
| otonal
|C\,9no5
| C\,9no5
|
|  
|4:5:9
| 4:5:9
|-
|-
| 54
| 54
Line 564: Line 542:
| 1-11/8-5/4
| 1-11/8-5/4
| otonal
| otonal
|C\(\b5)
| C\(\b5)
|
|  
|8:10:11
| 8:10:11
|-
|-
| 55
| 55
Line 572: Line 550:
| 1-10/7-5/4
| 1-10/7-5/4
| utonal
| utonal
|C\(\~5)
| C\(\~5)
|
|  
|10/8/7
| 1/(10:8:7)
|-
|-
| 56
| 56
Line 580: Line 558:
| 1-7/4-5/4
| 1-7/4-5/4
| otonal
| otonal
|C\7no5
| C\7no5
|
|  
|4:5:6
| 4:5:6
|-
|-
| 57
| 57
Line 588: Line 566:
| 1-20/11-5/4
| 1-20/11-5/4
| utonal
| utonal
|C\,\~7no5
| C\,\~7no5
|
|  
|20/11/16
| 1/(20:16:11)
|-
|-
| 58
| 58
Line 596: Line 574:
| 1-10/9-5/4
| 1-10/9-5/4
| utonal
| utonal
|C/9no35
| C/9no35
|1-9/5-9/4
| 1-9/5-9/4
|9/5/4
| 1/(9:5:4)
|-
|-
| 59
| 59
Line 604: Line 582:
| 1-5/3-5/4
| 1-5/3-5/4
| utonal
| utonal
|C/m
| C/m
|1-6/5-3/2
| 1-6/5-3/2
|6/5/4
| 1/(6:5:4)
|}
|}


Line 616: Line 594:
! Transversal
! Transversal
! Type
! Type
!Name
! Name
!Inversion
! Inversion
!As (sub)harmonics
! As harmonics<br>or subharmonics
|-
|-
| 1
| 1
Line 624: Line 602:
| 1-11/9-3/2-11/6
| 1-11/9-3/2-11/6
| rastmic
| rastmic
|C~7
| C~7
|
|  
|
|  
|-
|-
| 2
| 2
Line 632: Line 610:
| 1-11/9-3/2-9/8
| 1-11/9-3/2-9/8
| rastmic
| rastmic
|C~,9
| C~,9
|
|  
|
|  
|-
|-
| 3
| 3
Line 640: Line 618:
| 1-11/9-11/6-9/8
| 1-11/9-11/6-9/8
| rastmic
| rastmic
|C~9no5
| C~9no5
|
|  
|
|  
|-
|-
| 4
| 4
Line 648: Line 626:
| 1-3/2-11/6-9/8
| 1-3/2-11/6-9/8
| rastmic
| rastmic
|C~9no3
| C~9no3
|
|  
|
|  
|-
|-
| 5
| 5
Line 656: Line 634:
| 1-11/9-3/2-11/8
| 1-11/9-3/2-11/8
| rastmic
| rastmic
|C~,~11
| C~,~11
|
|  
|
|  
|-
|-
| 6
| 6
Line 664: Line 642:
| 1-11/9-11/6-11/8
| 1-11/9-11/6-11/8
| utonal
| utonal
|C2~6 <u>or</u>
| C2~6 ''or''<br>C4~9
C4~9
| 1-9/8-3/2-18/11<br>1-4/3-3/2-24/11
|1-9/8-3/2-18/11
| 1/(18:16:12:11)<br>1/(24:18:16:11)
1-4/3-3/2-24/11
|18/16/12/11
24/18/16/11
|-
|-
| 7
| 7
Line 675: Line 650:
| 1-3/2-11/6-11/8
| 1-3/2-11/6-11/8
| ambitonal
| ambitonal
|C~4~7
| C~4~7
|
|  
|
|  
|-
|-
| 8
| 8
Line 683: Line 658:
| 1-11/9-9/8-11/8
| 1-11/9-9/8-11/8
| rastmic
| rastmic
|
|  
|
|  
|
|  
|-
|-
| 9
| 9
Line 691: Line 666:
| 1-3/2-9/8-11/8
| 1-3/2-9/8-11/8
| otonal
| otonal
|C4~7
| C4~7
|1-4/3-3/2-11/6
| 1-4/3-3/2-11/6
|6:8:9:11
| 6:8:9:11
|-
|-
| 10
| 10
Line 699: Line 674:
| 1-11/6-9/8-11/8
| 1-11/6-9/8-11/8
| rastmic
| rastmic
|C~11no35
| C~11no35
|
|  
|
|  
|-
|-
| 11
| 11
Line 707: Line 682:
| 1-11/6-9/8-14/11
| 1-11/6-9/8-14/11
| parahemif
| parahemif
|C9(~7)no5
| C9(~7)no5
|
|  
|
|  
|-
|-
| 12
| 12
Line 715: Line 690:
| 1-11/6-11/8-14/11
| 1-11/6-11/8-14/11
| hemimin
| hemimin
|C~2~11
| C~2~11
|1-12/11-11/8-3/2
| 1-12/11-11/8-3/2
|
|  
|-
|-
| 13
| 13
Line 723: Line 698:
| 1-9/8-11/8-14/11
| 1-9/8-11/8-14/11
| parahemif
| parahemif
|C~,~9
| C~,~9
|1-11/9-3/2-13/12
| 1-11/9-3/2-13/12
|
|  
|-
|-
| 14
| 14
Line 731: Line 706:
| 1-11/9-9/8-14/9
| 1-11/9-9/8-14/9
| parahemif
| parahemif
|C~,9(^5)
| C~,9(^5)
|
|  
|
|  
|-
|-
| 15
| 15
Line 739: Line 714:
| 1-11/9-11/8-14/9
| 1-11/9-11/8-14/9
| pentacircle
| pentacircle
|C,~6,9no5
| C,~6,9no5
|1-14/11-18/11-9/4
| 1-14/11-18/11-9/4
|
|  
|-
|-
| 16
| 16
Line 747: Line 722:
| 1-9/8-11/8-14/9
| 1-9/8-11/8-14/9
| pentacircle
| pentacircle
|C~,7(\b5)
| C~,7(\b5)
|1-11/9-11/8-16/9
| 1-11/9-11/8-16/9
|
|  
|-
|-
| 17
| 17
Line 755: Line 730:
| 1-9/8-14/11-14/9
| 1-9/8-14/11-14/9
| pentacircle
| pentacircle
|
|  
|
|  
|
|  
|-
|-
| 18
| 18
Line 763: Line 738:
| 1-11/8-14/11-14/9
| 1-11/8-14/11-14/9
| parahemif
| parahemif
|
|  
|
|  
|
|  
|-
|-
| 19
| 19
Line 771: Line 746:
| 1-3/2-11/6-7/6
| 1-3/2-11/6-7/6
| otonal
| otonal
|C\m~7
| C\m~7
|
|  
|6:7:9:11
| 6:7:9:11
|-
|-
| 20
| 20
Line 779: Line 754:
| 1-11/6-14/11-7/6
| 1-11/6-14/11-7/6
| hemimin
| hemimin
|
|  
|
|  
|
|  
|-
|-
| 21
| 21
Line 787: Line 762:
| 1-14/11-14/9-7/6
| 1-14/11-14/9-7/6
| utonal
| utonal
|C/,~6
| C/,~6
|1-9/7-3/2-18/11
| 1-9/7-3/2-18/11
|18/14/12/11
| 1/(18:14:12:11)
|-
|-
| 22
| 22
Line 795: Line 770:
| 1-11/9-11/6-10/7
| 1-11/9-11/6-10/7
| swetismic
| swetismic
|C\m~6
| C\m~6
|1-7/6-3/2-13/8
| 1-7/6-3/2-13/8
|
|  
|-
|-
| 23
| 23
Line 803: Line 778:
| 1-11/9-9/8-10/7
| 1-11/9-9/8-10/7
| jove
| jove
|
|  
|
|  
|
|  
|-
|-
| 24
| 24
Line 811: Line 786:
| 1-11/6-9/8-10/7
| 1-11/6-9/8-10/7
| jove
| jove
|
|  
|
|  
|
|  
|-
|-
| 25
| 25
Line 819: Line 794:
| 1-11/6-14/11-10/7
| 1-11/6-14/11-10/7
| hemififths
| hemififths
|
|  
|
|  
|
|  
|-
|-
| 26
| 26
Line 827: Line 802:
| 1-9/8-14/11-10/7
| 1-9/8-14/11-10/7
| pele
| pele
|C9no5
| C9no5
|1-9/8-14/11-16/9
| 1-9/8-14/11-16/9
|
|  
|-
|-
| 27
| 27
Line 835: Line 810:
| 1-11/9-14/9-10/7
| 1-11/9-14/9-10/7
| swetismic
| swetismic
|
|  
|
|  
|
|  
|-
|-
| 28
| 28
Line 843: Line 818:
| 1-9/8-14/9-10/7
| 1-9/8-14/9-10/7
| hemififths
| hemififths
|
|  
|
|  
|
|  
|-
|-
| 29
| 29
Line 851: Line 826:
| 1-14/11-14/9-10/7
| 1-14/11-14/9-10/7
| jove
| jove
|
|  
|
|  
|
|  
|-
|-
| 30
| 30
Line 859: Line 834:
| 1-11/6-7/6-10/7
| 1-11/6-7/6-10/7
| swetismic
| swetismic
|
|  
|
|  
|
|  
|-
|-
| 31
| 31
Line 867: Line 842:
| 1-14/11-7/6-10/7
| 1-14/11-7/6-10/7
| jove
| jove
|
|  
|
|  
|
|  
|-
|-
| 32
| 32
Line 875: Line 850:
| 1-14/9-7/6-10/7
| 1-14/9-7/6-10/7
| swetismic
| swetismic
|
|  
|
|  
|
|  
|-
|-
| 33
| 33
Line 883: Line 858:
| 1-11/9-3/2-7/4
| 1-11/9-3/2-7/4
| jove
| jove
|C~,\7
| C~,\7
|
|  
|
|  
|-
|-
| 34
| 34
Line 891: Line 866:
| 1-11/9-9/8-7/4
| 1-11/9-9/8-7/4
| jove
| jove
|
|  
|
|  
|
|  
|-
|-
| 35
| 35
Line 899: Line 874:
| 1-3/2-9/8-7/4
| 1-3/2-9/8-7/4
| otonal
| otonal
|C\9no3
| C\9no3
|
|  
|4:6:7:9
| 4:6:7:9
|-
|-
| 36
| 36
Line 907: Line 882:
| 1-11/9-11/8-7/4
| 1-11/9-11/8-7/4
| werckismic
| werckismic
|
|  
|
|  
|
|  
|-
|-
| 37
| 37
Line 915: Line 890:
| 1-3/2-11/8-7/4
| 1-3/2-11/8-7/4
| otonal
| otonal
|C~4,\7
| C~4,\7
|
|  
|8:11:12:14
| 8:11:12:14
|-
|-
| 38
| 38
Line 923: Line 898:
| 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)
| C~4\7,9 ''or'' C~,7(^5)
|1-11/9-14/9-16/9
| 1-11/9-14/9-16/9
|9:11:14:16
| 9:11:14:16
|-
|-
| 39
| 39
Line 931: Line 906:
| 1-9/8-14/11-7/4
| 1-9/8-14/11-7/4
| pentacircle
| pentacircle
|
|  
|
|  
|
|  
|-
|-
| 40
| 40
Line 939: Line 914:
| 1-11/8-14/11-7/4
| 1-11/8-14/11-7/4
| hemimin
| hemimin
|
|  
|
|  
|
|  
|-
|-
| 41
| 41
Line 947: Line 922:
| 1-11/9-14/9-7/4
| 1-11/9-14/9-7/4
| werckismic
| werckismic
|
|  
|
|  
|
|  
|-
|-
| 42
| 42
Line 955: Line 930:
| 1-9/8-14/9-7/4
| 1-9/8-14/9-7/4
| pentacircle
| pentacircle
|
|  
|
|  
|
|  
|-
|-
| 43
| 43
Line 963: Line 938:
| 1-11/8-14/9-7/4
| 1-11/8-14/9-7/4
| pentacircle
| pentacircle
|
|  
|
|  
|
|  
|-
|-
| 44
| 44
Line 971: Line 946:
| 1-14/11-14/9-7/4
| 1-14/11-14/9-7/4
| utonal
| utonal
|
|  
|
|  
|14/11/9/8
| 1/(14:11:9:8)
|-
|-
| 45
| 45
Line 979: Line 954:
| 1-3/2-7/6-7/4
| 1-3/2-7/6-7/4
| ambitonal
| ambitonal
|C\m7
| C\m7
|
|  
|
|  
|-
|-
| 46
| 46
Line 987: Line 962:
| 1-14/11-7/6-7/4
| 1-14/11-7/6-7/4
| utonal
| utonal
|
|  
|
|  
|14/12/11/8
| 1/(14:12:11:8)
|-
|-
| 47
| 47
Line 995: Line 970:
| 1-14/9-7/6-7/4
| 1-14/9-7/6-7/4
| utonal
| utonal
|C/,9
| C/,9
|1-9/7-3/2-9/4
| 1-9/7-3/2-9/4
|9/7/6/4
| 1/(9:7:6:4)
|-
|-
| 48
| 48
Line 1,003: Line 978:
| 1-11/9-10/7-7/4
| 1-11/9-10/7-7/4
| jove
| jove
|
|  
|
|  
|
|  
|-
|-
| 49
| 49
Line 1,011: Line 986:
| 1-9/8-10/7-7/4
| 1-9/8-10/7-7/4
| werckismic
| werckismic
|
|  
|
|  
|
|  
|-
|-
| 50
| 50
Line 1,019: Line 994:
| 1-14/11-10/7-7/4
| 1-14/11-10/7-7/4
| werckismic
| werckismic
|
|  
|
|  
|
|  
|-
|-
| 51
| 51
Line 1,027: Line 1,002:
| 1-14/9-10/7-7/4
| 1-14/9-10/7-7/4
| jove
| jove
|
|  
|
|  
|
|  
|-
|-
| 52
| 52
Line 1,035: Line 1,010:
| 1-7/6-10/7-7/4
| 1-7/6-10/7-7/4
| jove
| jove
|C~,/6
| C~,/6
|1-11/9-3/2-12/7
| 1-11/9-3/2-12/7
|
|  
|-
|-
| 53
| 53
Line 1,043: Line 1,018:
| 1-14/11-14/9-20/11
| 1-14/11-14/9-20/11
| swetismic
| swetismic
|
|  
|
|  
|
|  
|-
|-
| 54
| 54
Line 1,051: Line 1,026:
| 1-14/11-7/6-20/11
| 1-14/11-7/6-20/11
| swetismic
| swetismic
|
|  
|
|  
|
|  
|-
|-
| 55
| 55
Line 1,059: Line 1,034:
| 1-14/9-7/6-20/11
| 1-14/9-7/6-20/11
| swetismic
| swetismic
|
|  
|
|  
|
|  
|-
|-
| 56
| 56
Line 1,067: Line 1,042:
| 1-14/11-10/7-20/11
| 1-14/11-10/7-20/11
| werckismic
| werckismic
|
|  
|
|  
|
|  
|-
|-
| 57
| 57
Line 1,075: Line 1,050:
| 1-14/9-10/7-20/11
| 1-14/9-10/7-20/11
| swetismic
| swetismic
|
|  
|
|  
|
|  
|-
|-
| 58
| 58
Line 1,083: Line 1,058:
| 1-7/6-10/7-20/11
| 1-7/6-10/7-20/11
| swetismic
| swetismic
|
|  
|
|  
|
|  
|-
|-
| 59
| 59
Line 1,091: Line 1,066:
| 1-11/9-14/9-10/9
| 1-11/9-14/9-10/9
| otonal
| otonal
|
|  
|
|  
|9:10:11:14
| 9:10:11:14
|-
|-
| 60
| 60
Line 1,099: Line 1,074:
| 1-14/11-14/9-10/9
| 1-14/11-14/9-10/9
| werckismic
| werckismic
|
|  
|
|  
|
|  
|-
|-
| 61
| 61
Line 1,107: Line 1,082:
| 1-11/9-10/7-10/9
| 1-11/9-10/7-10/9
| swetismic
| swetismic
|
|  
|
|  
|
|  
|-
|-
| 62
| 62
Line 1,115: Line 1,090:
| 1-14/11-10/7-10/9
| 1-14/11-10/7-10/9
| werckismic
| werckismic
|
|  
|
|  
|
|  
|-
|-
| 63
| 63
Line 1,123: Line 1,098:
| 1-14/9-10/7-10/9
| 1-14/9-10/7-10/9
| swetismic
| swetismic
|
|  
|
|  
|
|  
|-
|-
| 64
| 64
Line 1,131: Line 1,106:
| 1-11/9-7/4-10/9
| 1-11/9-7/4-10/9
| werckismic
| werckismic
|
|  
|
|  
|
|  
|-
|-
| 65
| 65
Line 1,139: Line 1,114:
| 1-14/11-7/4-10/9
| 1-14/11-7/4-10/9
| werckismic
| werckismic
|
|  
|
|  
|
|  
|-
|-
| 66
| 66
Line 1,147: Line 1,122:
| 1-14/9-7/4-10/9
| 1-14/9-7/4-10/9
| werckismic
| werckismic
|
|  
|
|  
|
|  
|-
|-
| 67
| 67
Line 1,155: Line 1,130:
| 1-10/7-7/4-10/9
| 1-10/7-7/4-10/9
| werckismic
| werckismic
|
|  
|
|  
|
|  
|-
|-
| 68
| 68
Line 1,163: Line 1,138:
| 1-14/11-20/11-10/9
| 1-14/11-20/11-10/9
| werckismic
| werckismic
|
|  
|
|  
|
|  
|-
|-
| 69
| 69
Line 1,171: Line 1,146:
| 1-14/9-20/11-10/9
| 1-14/9-20/11-10/9
| swetismic
| swetismic
|
|  
|
|  
|
|  
|-
|-
| 70
| 70
Line 1,179: Line 1,154:
| 1-10/7-20/11-10/9
| 1-10/7-20/11-10/9
| utonal
| utonal
|
|  
|
|  
|20/18/14/11
| 1/(20:18:14:11)
|-
|-
| 71
| 71
Line 1,187: Line 1,162:
| 1-3/2-11/6-5/3
| 1-3/2-11/6-5/3
| otonal
| otonal
|
|  
|
|  
|6:9:10:11
| 6:9:10:11
|-
|-
| 72
| 72
Line 1,195: Line 1,170:
| 1-3/2-7/6-5/3
| 1-3/2-7/6-5/3
| otonal
| otonal
|C\m6
| C\m6
|
|  
|6:7:9:10
| 6:7:9:10
|-
|-
| 73
| 73
Line 1,203: Line 1,178:
| 1-11/6-7/6-5/3
| 1-11/6-7/6-5/3
| otonal
| otonal
|C\m6~7no5
| C\m6~7no5
|
|  
|6:7:10:11
| 6:7:10:11
|-
|-
| 74
| 74
Line 1,211: Line 1,186:
| 1-11/6-10/7-5/3
| 1-11/6-10/7-5/3
| swetismic
| swetismic
|
|  
|
|  
|
|  
|-
|-
| 75
| 75
Line 1,219: Line 1,194:
| 1-7/6-10/7-5/3
| 1-7/6-10/7-5/3
| swetismic
| swetismic
|C\m6(\~5)
| C\m6(\~5)
|
|  
|
|  
|-
|-
| 76
| 76
Line 1,227: Line 1,202:
| 1-7/6-20/11-5/3
| 1-7/6-20/11-5/3
| swetismic
| swetismic
|
|  
|
|  
|
|  
|-
|-
| 77
| 77
Line 1,235: Line 1,210:
| 1-10/7-20/11-5/3
| 1-10/7-20/11-5/3
| utonal
| utonal
|
|  
|
|  
|20/14/12/11
| 1/(20:14:12:11)
|-
|-
| 78
| 78
Line 1,243: Line 1,218:
| 1-10/7-10/9-5/3
| 1-10/7-10/9-5/3
| utonal
| utonal
|C/7
| C/7
|1-9/7-3/2-9/5
| 1-9/7-3/2-9/5
|9/7/6/5
| 1/(9:7:6:5)
|-
|-
| 79
| 79
Line 1,251: Line 1,226:
| 1-20/11-10/9-5/3
| 1-20/11-10/9-5/3
| utonal
| utonal
|C/7~13no3
| C/7~13no3
|1-3/2-18/11-9/5
| 1-3/2-18/11-9/5
|18/12/11/10
| 1/(18:12:11:10)
|-
|-
| 80
| 80
Line 1,259: Line 1,234:
| 1-3/2-9/8-5/4
| 1-3/2-9/8-5/4
| otonal
| otonal
|C\,9
| C\,9
|
|  
|4:5:6:9
| 4:5:6:9
|-
|-
| 81
| 81
Line 1,267: Line 1,242:
| 1-3/2-11/8-5/4
| 1-3/2-11/8-5/4
| otonal
| otonal
|C\,~11
| C\,~11
|
|  
|8:10:11:12
| 8:10:11:12
|-
|-
|82
| 82
|0-4-5-25
| 0-4-5-25
|1-9/8-11/8-5/4
| 1-9/8-11/8-5/4
|otonal
| otonal
|C\,9(\b5)
| C\,9(\b5)
|
|  
|8:9:10:11
| 8:9:10:11
|-
|-
|83
| 83
|0-4-12-25
| 0-4-12-25
|1-9/8-10/7-5/4
| 1-9/8-10/7-5/4
|werckismic
| werckismic
|C,9(\~5)
| C,9(\~5)
|
|  
|
|  
|-
|-
|84
| 84
|0-2-13-25
| 0-2-13-25
|1-3/2-7/4-5/4
| 1-3/2-7/4-5/4
|otonal
| otonal
|C\7
| C\7
|
|  
|4:5:6:7
| 4:5:6:7
|-
|-
| 85
| 85
Line 1,299: Line 1,274:
| 1-9/8-7/4-5/4
| 1-9/8-7/4-5/4
| otonal
| otonal
|C\9no5
| C\9no5
|
|  
|4:5:7:9
| 4:5:7:9
|-
|-
| 86
| 86
Line 1,307: Line 1,282:
| 1-11/8-7/4-5/4
| 1-11/8-7/4-5/4
| otonal
| otonal
|C\7~11no5
| C\7~11no5
|
|  
|4:5:7:11
| 4:5:7:11
|-
|-
| 87
| 87
Line 1,315: Line 1,290:
| 1-10/7-7/4-5/4
| 1-10/7-7/4-5/4
| werckismic
| werckismic
|C\7(\~5)
| C\7(\~5)
|
|  
|
|  
|-
|-
| 88
| 88
Line 1,323: Line 1,298:
| 1-10/7-20/11-5/4
| 1-10/7-20/11-5/4
| utonal
| utonal
|C,\7(b5)
| C,\7(b5)
|1-14/11-7/5-7/4
| 1-14/11-7/5-7/4
|20/16/14/11
| 1/(20:16:14:11)
|-
|-
| 89
| 89
Line 1,331: Line 1,306:
| 1-10/7-10/9-5/4
| 1-10/7-10/9-5/4
| utonal
| utonal
|C/9no5
| C/9no5
|1-9/7-9/5-9/4
| 1-9/7-9/5-9/4
|10/9/8/7
| 1/(10:9:8:7)
|-
|-
|90
| 90
|0-13-21-25
| 0-13-21-25
|1-7/4-10/9-5/4
| 1-7/4-10/9-5/4
|werckismic
| werckismic
|C\7\9no5
| C\7\9no5
|
|  
|
|  
|-
|-
|91
| 91
|0-20-21-25
| 0-20-21-25
|1-20/11-10/9-5/4
| 1-20/11-10/9-5/4
|utonal
| utonal
|C2~6^7no5
| C2~6^7no5
|1-18/11-9/5-9/4
| 1-18/11-9/5-9/4
|20/18/16/11
| 1/(20:18:16:11)
|-
|-
|92
| 92
|0-2-23-25
| 0-2-23-25
|1-3/2-5/3-5/4
| 1-3/2-5/3-5/4
|ambitonal
| ambitonal
|C\6 <u>or</u> C/m7
| C\6 <u>or</u> C/m7
|1-6/5-3/2-9/5
| 1-6/5-3/2-9/5
|
|  
|-
|-
|93
| 93
|0-12-23-25
| 0-12-23-25
|1-10/7-5/3-5/4
| 1-10/7-5/3-5/4
|utonal
| utonal
|C/m6
| C/m6<br>C\m7(b5)
C\m7(b5)
| 1-6/5-3/2-12/7<br>1-7/6-7/5-7/4
|1-6/5-3/2-12/7
| 1/(12:10:8:7)<br>1/(7:6:5:4)
1-7/6-7/5-7/4
|12/10/8/7
7/6/5/4
|-
|-
| 94
| 94
Line 1,374: Line 1,346:
| 1-20/11-5/3-5/4
| 1-20/11-5/3-5/4
| utonal
| utonal
|C/m,~9
| C/m,~9
|1-6/5-3/2-24/11
| 1-6/5-3/2-24/11
|24/20/18/11
| 1/(24:20:18:11)
|-
|-
| 95
| 95
Line 1,382: Line 1,354:
| 1-10/9-5/3-5/4
| 1-10/9-5/3-5/4
| utonal
| utonal
|C/9no3
| C/9no3
|1-3/2-9/5-9/4
| 1-3/2-9/5-9/4
|9/6/5/4
| 1/(9:6:5:4)
|}
|}


Line 1,394: Line 1,366:
! Transversal
! Transversal
! Type
! Type
!Name
! Name
!Inversion
! Inversion
!As (sub)harmonics
! As harmonics<br>or subharmonics
|-
|-
| 1
| 1
Line 1,402: Line 1,374:
| 1-11/9-3/2-11/6-9/8
| 1-11/9-3/2-11/6-9/8
| rastmic
| rastmic
|C~9
| C~9
|
|  
|
|  
|-
|-
| 2
| 2
Line 1,410: Line 1,382:
| 1-11/9-3/2-11/6-11/8
| 1-11/9-3/2-11/6-11/8
| rastmic
| rastmic
|C~11no9
| C~11no9
|
|  
|
|  
|-
|-
| 3
| 3
Line 1,418: Line 1,390:
| 1-11/9-3/2-9/8-11/8
| 1-11/9-3/2-9/8-11/8
| rastmic
| rastmic
|C~11no7
| C~11no7
|
|  
|
|  
|-
|-
| 4
| 4
Line 1,426: Line 1,398:
| 1-11/9-11/6-9/8-11/8
| 1-11/9-11/6-9/8-11/8
| rastmic
| rastmic
|C~11no5
| C~11no5
|
|  
|
|  
|-
|-
| 5
| 5
Line 1,434: Line 1,406:
| 1-3/2-11/6-9/8-11/8
| 1-3/2-11/6-9/8-11/8
| rastmic
| rastmic
|C~11no3
| C~11no3
|
|  
|
|  
|-
|-
| 6
| 6
Line 1,442: Line 1,414:
| 1-11/6-9/8-11/8-14/11
| 1-11/6-9/8-11/8-14/11
| parahemif
| parahemif
|
|  
|
|  
|
|  
|-
|-
| 7
| 7
Line 1,450: Line 1,422:
| 1-11/9-9/8-11/8-14/9
| 1-11/9-9/8-11/8-14/9
| parahemif
| parahemif
|
|  
|
|  
|
|  
|-
|-
| 8
| 8
Line 1,458: Line 1,430:
| 1-9/8-11/8-14/11-14/9
| 1-9/8-11/8-14/11-14/9
| parahemif
| parahemif
|
|  
|
|  
|
|  
|-
|-
| 9
| 9
Line 1,466: Line 1,438:
| 1-11/9-11/6-9/8-10/7
| 1-11/9-11/6-9/8-10/7
| jove
| jove
|
|  
|
|  
|
|  
|-
|-
| 10
| 10
Line 1,474: Line 1,446:
| 1-11/6-9/8-14/11-10/7
| 1-11/6-9/8-14/11-10/7
| hemififths
| hemififths
|
|  
|
|  
|
|  
|-
|-
| 11
| 11
Line 1,482: Line 1,454:
| 1-11/9-9/8-14/9-10/7
| 1-11/9-9/8-14/9-10/7
| hemififths
| hemififths
|
|  
|
|  
|
|  
|-
|-
| 12
| 12
Line 1,490: Line 1,462:
| 1-9/8-14/11-14/9-10/7
| 1-9/8-14/11-14/9-10/7
| hemififths
| hemififths
|
|  
|
|  
|
|  
|-
|-
| 13
| 13
Line 1,498: Line 1,470:
| 1-11/6-14/11-7/6-10/7
| 1-11/6-14/11-7/6-10/7
| hemififths
| hemififths
|
|  
|
|  
|
|  
|-
|-
| 14
| 14
Line 1,506: Line 1,478:
| 1-14/11-14/9-7/6-10/7
| 1-14/11-14/9-7/6-10/7
| jove
| jove
|
|  
|
|  
|
|  
|-
|-
| 15
| 15
Line 1,514: Line 1,486:
| 1-11/9-3/2-9/8-7/4
| 1-11/9-3/2-9/8-7/4
| jove
| jove
|C~9(\m7)
| C~9(\m7)
|
|  
|
|  
|-
|-
| 16
| 16
Line 1,522: Line 1,494:
| 1-11/9-3/2-11/8-7/4
| 1-11/9-3/2-11/8-7/4
| jove
| jove
|
|  
|
|  
|
|  
|-
|-
| 17
| 17
Line 1,530: Line 1,502:
| 1-11/9-9/8-11/8-7/4
| 1-11/9-9/8-11/8-7/4
| jove
| jove
|
|  
|
|  
|
|  
|-
|-
| 18
| 18
Line 1,538: Line 1,510:
| 1-3/2-9/8-11/8-7/4
| 1-3/2-9/8-11/8-7/4
| otonal
| otonal
|C\9~11no3
| C\9~11no3
|
|  
|4:6:7:9:11
| 4:6:7:9:11
|-
|-
| 19
| 19
Line 1,546: Line 1,518:
| 1-9/8-11/8-14/11-7/4
| 1-9/8-11/8-14/11-7/4
| parahemif
| parahemif
|
|  
|
|  
|
|  
|-
|-
| 20
| 20
Line 1,554: Line 1,526:
| 1-11/9-9/8-14/9-7/4
| 1-11/9-9/8-14/9-7/4
| hemififths
| hemififths
|
|  
|
|  
|
|  
|-
|-
| 21
| 21
Line 1,562: Line 1,534:
| 1-11/9-11/8-14/9-7/4
| 1-11/9-11/8-14/9-7/4
| pele
| pele
|
|  
|
|  
|
|  
|-
|-
| 22
| 22
Line 1,570: Line 1,542:
| 1-9/8-11/8-14/9-7/4
| 1-9/8-11/8-14/9-7/4
| pentacircle
| pentacircle
|
|  
|
|  
|
|  
|-
|-
| 23
| 23
Line 1,578: Line 1,550:
| 1-9/8-14/11-14/9-7/4
| 1-9/8-14/11-14/9-7/4
| pentacircle
| pentacircle
|
|  
|
|  
|
|  
|-
|-
| 24
| 24
Line 1,586: Line 1,558:
| 1-11/8-14/11-14/9-7/4
| 1-11/8-14/11-14/9-7/4
| parahemif
| parahemif
|
|  
|
|  
|
|  
|-
|-
| 25
| 25
Line 1,594: Line 1,566:
| 1-14/11-14/9-7/6-7/4
| 1-14/11-14/9-7/6-7/4
| utonal
| utonal
|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
| 1/(18:14:12:11:8)
|-
|-
| 26
| 26
Line 1,602: Line 1,574:
| 1-11/9-9/8-10/7-7/4
| 1-11/9-9/8-10/7-7/4
| jove
| jove
|
|  
|
|  
|
|  
|-
|-
| 27
| 27
Line 1,610: Line 1,582:
| 1-9/8-14/11-10/7-7/4
| 1-9/8-14/11-10/7-7/4
| pele
| pele
|
|  
|
|  
|
|  
|-
|-
| 28
| 28
Line 1,618: Line 1,590:
| 1-11/9-14/9-10/7-7/4
| 1-11/9-14/9-10/7-7/4
| jove
| jove
|
|  
|
|  
|
|  
|-
|-
| 29
| 29
Line 1,626: Line 1,598:
| 1-9/8-14/9-10/7-7/4
| 1-9/8-14/9-10/7-7/4
| hemififths
| hemififths
|
|  
|
|  
|
|  
|-
|-
| 30
| 30
Line 1,634: Line 1,606:
| 1-14/11-14/9-10/7-7/4
| 1-14/11-14/9-10/7-7/4
| jove
| jove
|
|  
|
|  
|
|  
|-
|-
| 31
| 31
Line 1,642: Line 1,614:
| 1-14/11-7/6-10/7-7/4
| 1-14/11-7/6-10/7-7/4
| jove
| jove
|
|  
|
|  
|
|  
|-
|-
| 32
| 32
Line 1,650: Line 1,622:
| 1-14/9-7/6-10/7-7/4
| 1-14/9-7/6-10/7-7/4
| jove
| jove
|
|  
|
|  
|
|  
|-
|-
| 33
| 33
Line 1,658: Line 1,630:
| 1-14/11-14/9-7/6-20/11
| 1-14/11-14/9-7/6-20/11
| swetismic
| swetismic
|
|  
|
|  
|
|  
|-
|-
| 34
| 34
Line 1,666: Line 1,638:
| 1-14/11-14/9-10/7-20/11
| 1-14/11-14/9-10/7-20/11
| jove
| jove
|
|  
|
|  
|
|  
|-
|-
| 35
| 35
Line 1,674: Line 1,646:
| 1-14/11-7/6-10/7-20/11
| 1-14/11-7/6-10/7-20/11
| jove
| jove
|
|  
|
|  
|
|  
|-
|-
| 36
| 36
Line 1,682: Line 1,654:
| 1-14/9-7/6-10/7-20/11
| 1-14/9-7/6-10/7-20/11
| swetismic
| swetismic
|
|  
|
|  
|
|  
|-
|-
| 37
| 37
Line 1,690: Line 1,662:
| 1-11/9-14/9-10/7-10/9
| 1-11/9-14/9-10/7-10/9
| swetismic
| swetismic
|
|  
|
|  
|
|  
|-
|-
| 38
| 38
Line 1,698: Line 1,670:
| 1-14/11-14/9-10/7-10/9
| 1-14/11-14/9-10/7-10/9
| jove
| jove
|
|  
|
|  
|
|  
|-
|-
| 39
| 39
Line 1,706: Line 1,678:
| 1-11/9-14/9-7/4-10/9
| 1-11/9-14/9-7/4-10/9
| werckismic
| werckismic
|
|  
|
|  
|
|  
|-
|-
| 40
| 40
Line 1,714: Line 1,686:
| 1-14/11-14/9-7/4-10/9
| 1-14/11-14/9-7/4-10/9
| werckismic
| werckismic
|
|  
|
|  
|
|  
|-
|-
| 41
| 41
Line 1,722: Line 1,694:
| 1-11/9-10/7-7/4-10/9
| 1-11/9-10/7-7/4-10/9
| jove
| jove
|
|  
|
|  
|
|  
|-
|-
| 42
| 42
Line 1,730: Line 1,702:
| 1-14/11-10/7-7/4-10/9
| 1-14/11-10/7-7/4-10/9
| werckismic
| werckismic
|
|  
|
|  
|
|  
|-
|-
| 43
| 43
Line 1,738: Line 1,710:
| 1-14/9-10/7-7/4-10/9
| 1-14/9-10/7-7/4-10/9
| jove
| jove
|
|  
|
|  
|
|  
|-
|-
| 44
| 44
Line 1,746: Line 1,718:
| 1-14/11-14/9-20/11-10/9
| 1-14/11-14/9-20/11-10/9
| jove
| jove
|
|  
|
|  
|
|  
|-
|-
| 45
| 45
Line 1,754: Line 1,726:
| 1-14/11-10/7-20/11-10/9
| 1-14/11-10/7-20/11-10/9
| werckismic
| werckismic
|
|  
|
|  
|
|  
|-
|-
| 46
| 46
Line 1,762: Line 1,734:
| 1-14/9-10/7-20/11-10/9
| 1-14/9-10/7-20/11-10/9
| swetismic
| swetismic
|
|  
|
|  
|
|  
|-
|-
| 47
| 47
Line 1,770: Line 1,742:
| 1-3/2-11/6-7/6-5/3
| 1-3/2-11/6-7/6-5/3
| otonal
| otonal
|C\m6~7
| C\m6~7
|
|  
|6:7:9:10:11
| 6:7:9:10:11
|-
|-
| 48
| 48
Line 1,778: Line 1,750:
| 1-11/6-7/6-10/7-5/3
| 1-11/6-7/6-10/7-5/3
| swetismic
| swetismic
|
|  
|
|  
|
|  
|-
|-
| 49
| 49
Line 1,786: Line 1,758:
| 1-7/6-10/7-20/11-5/3
| 1-7/6-10/7-20/11-5/3
| swetismic
| swetismic
|
|  
|
|  
|
|  
|-
|-
| 50
| 50
Line 1,794: Line 1,766:
| 1-10/7-20/11-10/9-5/3
| 1-10/7-20/11-10/9-5/3
| utonal
| utonal
|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
| 1/(18:14:12:11:10)
|-
|-
| 51
| 51
Line 1,802: Line 1,774:
| 1-3/2-9/8-11/8-5/4
| 1-3/2-9/8-11/8-5/4
| otonal
| otonal
|C\,9~11
| C\,9~11
|
|  
|4:5:6:9:11
| 4:5:6:9:11
|-
|-
| 52
| 52
Line 1,810: Line 1,782:
| 1-3/2-9/8-7/4-5/4
| 1-3/2-9/8-7/4-5/4
| otonal
| otonal
|C\9
| C\9
|
|  
|4:5:6:7:9
| 4:5:6:7:9
|-
|-
| 53
| 53
Line 1,818: Line 1,790:
| 1-3/2-11/8-7/4-5/4
| 1-3/2-11/8-7/4-5/4
| otonal
| otonal
|C\7~11
| C\7~11
|
|  
|4:5:6:7:11
| 4:5:6:7:11
|-
|-
| 54
| 54
Line 1,826: Line 1,798:
| 1-9/8-11/8-7/4-5/4
| 1-9/8-11/8-7/4-5/4
| otonal
| otonal
|C\9~11no5
| C\9~11no5
|
|  
|4:5:7:9:11
| 4:5:7:9:11
|-
|-
| 55
| 55
Line 1,834: Line 1,806:
| 1-9/8-10/7-7/4-5/4
| 1-9/8-10/7-7/4-5/4
| werckismic
| werckismic
|C\9(\~5)
| C\9(\~5)
|
|  
|
|  
|-
|-
| 56
| 56
Line 1,842: Line 1,814:
| 1-10/7-7/4-10/9-5/4
| 1-10/7-7/4-10/9-5/4
| werckismic
| werckismic
|
|  
|
|  
|
|  
|-
|-
| 57
| 57
Line 1,850: Line 1,822:
| 1-10/7-20/11-10/9-5/4
| 1-10/7-20/11-10/9-5/4
| utonal
| utonal
|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
| 1/(18:14:11:10:8)
|-
|-
| 58
| 58
Line 1,858: Line 1,830:
| 1-10/7-20/11-5/3-5/4
| 1-10/7-20/11-5/3-5/4
| utonal
| utonal
|C/m6~9
| C/m6~9
|1-6/5-3/2-12/7-24/11
| 1-6/5-3/2-12/7-24/11
|24/20/16/14/11
| 1/(24:20:16:14:11)
|-
|-
| 59
| 59
Line 1,866: Line 1,838:
| 1-10/7-10/9-5/3-5/4
| 1-10/7-10/9-5/3-5/4
| utonal
| utonal
|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
| 1/(9:7:6:5:4)
|-
|-
| 60
| 60
Line 1,874: Line 1,846:
| 1-20/11-10/9-5/3-5/4
| 1-20/11-10/9-5/3-5/4
| utonal
| utonal
|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
| 1/(18:12:11:10:8)
|}
|}


Line 1,886: Line 1,858:
! Transversal
! Transversal
! Type
! Type
!Name
! Name
!Inversion
! Inversion
!As (sub)harmonics
! As harmonics<br>or subharmonics
|-
|-
| 1
| 1
Line 1,894: Line 1,866:
| 1-11/9-3/2-11/6-9/8-11/8
| 1-11/9-3/2-11/6-9/8-11/8
| rastmic
| rastmic
|C~11
| C~11
|
|  
|
|  
|-
|-
| 2
| 2
Line 1,902: Line 1,874:
| 1-11/9-3/2-9/8-11/8-7/4
| 1-11/9-3/2-9/8-11/8-7/4
| jove
| jove
|C~11(\m7)
| C~11(\m7)
|
|  
|
|  
|-
|-
| 3
| 3
Line 1,910: Line 1,882:
| 1-11/9-9/8-11/8-14/9-7/4
| 1-11/9-9/8-11/8-14/9-7/4
| hemififths
| hemififths
|
|  
|
|  
|
|  
|-
|-
| 4
| 4
| 0-4-5-8-9-13
| 0-4-5-8-9-13
| 1-9/8-11/8-14/11-14/9-7/4
| 1-9/8-11/8-14/11-14/9-7/4
| nofives
| hemififths
|
|  
|
|  
|
|  
|-
|-
| 5
| 5
Line 1,926: Line 1,898:
| 1-11/9-9/8-14/9-10/7-7/4
| 1-11/9-9/8-14/9-10/7-7/4
| hemififths
| hemififths
|
|  
|
|  
|
|  
|-
|-
| 6
| 6
Line 1,934: Line 1,906:
| 1-9/8-14/11-14/9-10/7-7/4
| 1-9/8-14/11-14/9-10/7-7/4
| hemififths
| hemififths
|
|  
|
|  
|
|  
|-
|-
| 7
| 7
Line 1,942: Line 1,914:
| 1-14/11-14/9-7/6-10/7-7/4
| 1-14/11-14/9-7/6-10/7-7/4
| jove
| jove
|
|  
|
|  
|
|  
|-
|-
| 8
| 8
Line 1,950: Line 1,922:
| 1-14/11-14/9-7/6-10/7-20/11
| 1-14/11-14/9-7/6-10/7-20/11
| jove
| jove
|
|  
|
|  
|
|  
|-
|-
| 9
| 9
Line 1,958: Line 1,930:
| 1-11/9-14/9-10/7-7/4-10/9
| 1-11/9-14/9-10/7-7/4-10/9
| jove
| jove
|
|  
|
|  
|
|  
|-
|-
| 10
| 10
Line 1,966: Line 1,938:
| 1-14/11-14/9-10/7-7/4-10/9
| 1-14/11-14/9-10/7-7/4-10/9
| jove
| jove
|
|  
|
|  
|
|  
|-
|-
| 11
| 11
Line 1,974: Line 1,946:
| 1-14/11-14/9-10/7-20/11-10/9
| 1-14/11-14/9-10/7-20/11-10/9
| jove
| jove
|
|  
|
|  
|
|  
|-
|-
| 12
| 12
Line 1,982: Line 1,954:
| 1-3/2-9/8-11/8-7/4-5/4
| 1-3/2-9/8-11/8-7/4-5/4
| otonal
| otonal
|C\9~11
| C\9~11
|
|  
|4:5:6:7:9:11
| 4:5:6:7:9:11
|-
|-
| 13
| 13
Line 1,990: Line 1,962:
| 1-10/7-20/11-10/9-5/3-5/4
| 1-10/7-20/11-10/9-5/3-5/4
| utonal
| utonal
|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
| 1/(18:14:12:11:10:8)
|}
|}


Latest revision as of 20:52, 29 July 2025

Below are listed the 11-odd-limit 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 scales 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 second. Enharmonic equivalences: vvA1 and v\m2. Cents: ^1 = 50¢ + 3.5c and /1 = 50¢ - 8.5c, where c equals 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 harmonics or subharmonics 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 table

Triads

# Genspans Transversal Type Name Inversion As harmonics
or subharmonics
1 0-1-2 1-11/9-3/2 rastmic C~
2 0-1-3 1-11/9-11/6 utonal C~7no5 1/(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 1-4/3-3/2
6 0-3-4 1-11/6-9/8 rastmic C~9no35
7 0-1-5 1-11/9-11/8 utonal C~(\b5) 1/(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 1/(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) 1/(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 1/(12:11:7)
21 0-9-11 1-14/9-7/6 utonal C/ 1-9/7-3/2 1/(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 8:11:14
32 0-8-13 1-14/11-7/4 utonal C,\7 1/(14:11:8)
33 0-9-13 1-14/9-7/4 utonal C/,2no5 1-9/8-9/7 1/(9:8:7)
34 0-11-13 1-7/6-7/4 utonal C\m7no5 1/(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) 1/(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) 1/(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 1/(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 1/(10:7:6)
50 0-20-23 1-20/11-5/3 utonal 1/(20:12:11)
51 0-21-23 1-10/9-5/3 utonal C/7no3 1-3/2-9/5 1/(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) 1/(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 1/(20:16:11)
58 0-21-25 1-10/9-5/4 utonal C/9no35 1-9/5-9/4 1/(9:5:4)
59 0-23-25 1-5/3-5/4 utonal C/m 1-6/5-3/2 1/(6:5:4)

Tetrads

# Genspans Transversal Type Name Inversion As harmonics
or subharmonics
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 		1/(18:16:12:11)
1/(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 1/(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 1/(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 1/(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 1/(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 1/(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 1/(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 1/(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 1/(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 1/(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 1/(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 1/(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 		1/(12:10:8:7)
1/(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 1/(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 1/(9:6:5:4)

Pentads

# Genspans Transversal Type Name Inversion As harmonics
or subharmonics
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 1/(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 1/(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 1/(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 1/(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 1/(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 1/(18:12:11:10:8)

Hexads

# Genspans Transversal Type Name Inversion As harmonics
or subharmonics
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 hemififths
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 1/(18:14:12:11:10:8)
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