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 (sub)harmonics" 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|inline=1|comment=Complete the tables. }}


== Triads ==
== Triads ==
Line 129: Line 109:
! Transversal
! Transversal
! Type
! Type
!Name
! Name
!Inversion
! Inversion
!As (sub)harmonics
! As (sub)harmonics
|-
|-
| 1
| 1
Line 137: Line 117:
| 1-11/9-3/2
| 1-11/9-3/2
| rastmic
| rastmic
|C~
| C~
|
|  
|
|  
|-
|-
| 2
| 2
Line 145: Line 125:
| 1-11/9-11/6
| 1-11/9-11/6
| utonal
| utonal
|C~7no5
| C~7no5
|
|  
|11/9/6
| 11/9/6
|-
|-
| 3
| 3
Line 153: Line 133:
| 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 141:
| 1-11/9-9/8
| 1-11/9-9/8
| rastmic
| rastmic
|C~,9no5
| C~,9no5
|
|  
|
|  
|-
|-
| 5
| 5
Line 169: Line 149:
| 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
| 1-4/3-9/8
|
|
|-
|-
Line 177: Line 157:
| 1-11/6-9/8
| 1-11/6-9/8
| rastmic
| rastmic
|C~9no35
| C~9no35
|
|  
|
|  
|-
|-
| 7
| 7
Line 185: Line 165:
| 1-11/9-11/8
| 1-11/9-11/8
| utonal
| utonal
|C~(\b5)
| C~(\b5)
|
|  
|11/9/8
| 11/9/8
|-
|-
| 8
| 8
Line 193: Line 173:
| 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 181:
| 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
| 12/11/8
|-
|-
| 10
| 10
Line 209: Line 189:
| 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 197:
| 1-11/6-14/11
| 1-11/6-14/11
| hemimin
| hemimin
|C,~7no5
| C,~7no5
|
|  
|
|  
|-
|-
| 12
| 12
Line 225: Line 205:
| 1-9/8-14/11
| 1-9/8-14/11
| pentacircle
| pentacircle
|C,9no5
| C,9no5
|
|  
|
|  
|-
|-
| 13
| 13
Line 233: Line 213:
| 1-11/8-14/11
| 1-11/8-14/11
| hemimin
| hemimin
|C(\b5)
| C(\b5)
|
|  
|
|  
|-
|-
| 14
| 14
Line 241: Line 221:
| 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 229:
| 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 237:
| 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 245:
| 1-14/11-14/9
| 1-14/11-14/9
| utonal
| utonal
|C(^5)
| C(^5)
|
|  
|14/11/9
| 14/11/9
|-
|-
| 18
| 18
Line 276: Line 253:
| 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 261:
| 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 269:
| 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
| 12/11/7
|-
|-
| 21
| 21
Line 300: Line 277:
| 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
| 9/7/6
|-
|-
| 22
| 22
Line 308: Line 285:
| 1-11/9-10/7
| 1-11/9-10/7
| swetismic
| swetismic
|C~(\~5)
| C~(\~5)
|
|  
|
|  
|-
|-
| 23
| 23
Line 316: Line 293:
| 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 301:
| 1-9/8-10/7
| 1-9/8-10/7
| werckismic
| werckismic
|C2(\~5)
| C2(\~5)
|
|  
|
|  
|-
|-
| 25
| 25
Line 332: Line 309:
| 1-14/11-10/7
| 1-14/11-10/7
| werckismic
| werckismic
|C(\~5)
| C(\~5)
|
|  
|
|  
|-
|-
| 26
| 26
Line 340: Line 317:
| 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 325:
| 1-7/6-10/7
| 1-7/6-10/7
| swetismic
| swetismic
|C\m(\~5)
| C\m(\~5)
|
|  
|
|  
|-
|-
| 28
| 28
Line 356: Line 333:
| 1-11/9-7/4
| 1-11/9-7/4
| werckismic
| werckismic
|C~,\7no5
| C~,\7no5
|
|  
|
|  
|-
|-
| 29
| 29
Line 364: Line 341:
| 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 349:
| 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 357:
| 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
| 11:14:16
|-
|-
| 32
| 32
Line 388: Line 365:
| 1-14/11-7/4
| 1-14/11-7/4
| utonal
| utonal
|C,\7
| C,\7
|
|  
|14/11/8
| 14/11/8
|-
|-
| 33
| 33
Line 396: Line 373:
| 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
| 9/8/7
|-
|-
| 34
| 34
Line 404: Line 381:
| 1-7/6-7/4
| 1-7/6-7/4
| utonal
| utonal
|C\m7no5
| C\m7no5
|
|  
|7/6/4
| 7/6/4
|-
|-
| 35
| 35
Line 412: Line 389:
| 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 397:
| 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 405:
| 1-14/9-20/11
| 1-14/9-20/11
| swetismic
| swetismic
|
|  
|
|  
|
|  
|-
|-
| 38
| 38
Line 436: Line 413:
| 1-7/6-20/11
| 1-7/6-20/11
| swetismic
| swetismic
|C\m\~7no5
| C\m\~7no5
|
|  
|
|  
|-
|-
| 39
| 39
Line 444: Line 421:
| 1-10/7-20/11
| 1-10/7-20/11
| utonal
| utonal
|C(b5)
| C(b5)
|
|  
|20/14/11
| 20/14/11
|-
|-
| 40
| 40
Line 452: Line 429:
| 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 437:
| 1-14/11-10/9
| 1-14/11-10/9
| werckismic
| werckismic
|C,\9no5
| C,\9no5
|
|  
|
|  
|-
|-
| 42
| 42
Line 468: Line 445:
| 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 453:
| 1-10/7-10/9
| 1-10/7-10/9
| utonal
| utonal
|C\2(\~5)
| C\2(\~5)
|
|  
|10/9/7
| 10/9/7
|-
|-
| 44
| 44
Line 484: Line 461:
| 1-7/4-10/9
| 1-7/4-10/9
| werckismic
| werckismic
|C\2\m7no5
| C\2\m7no5
|
|  
|
|  
|-
|-
| 45
| 45
Line 492: Line 469:
| 1-20/11-10/9
| 1-20/11-10/9
| utonal
| utonal
|
|  
|
|  
|20/18/11
| 20/18/11
|-
|-
| 46
| 46
Line 500: Line 477:
| 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 485:
| 1-11/6-5/3
| 1-11/6-5/3
| otonal
| otonal
|
|  
|
|  
|6:10:11
| 6:10:11
|-
|-
| 48
| 48
Line 516: Line 493:
| 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 501:
| 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
| 10/7/6
|-
|-
| 50
| 50
Line 532: Line 509:
| 1-20/11-5/3
| 1-20/11-5/3
| utonal
| utonal
|
|  
|
|  
|20/12/11
| 20/12/11
|-
|-
| 51
| 51
Line 540: Line 517:
| 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
| 9/6/5
|-
|-
| 52
| 52
Line 548: Line 525:
| 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 533:
| 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 541:
| 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 549:
| 1-10/7-5/4
| 1-10/7-5/4
| utonal
| utonal
|C\(\~5)
| C\(\~5)
|
|  
|10/8/7
| 10/8/7
|-
|-
| 56
| 56
Line 580: Line 557:
| 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 565:
| 1-20/11-5/4
| 1-20/11-5/4
| utonal
| utonal
|C\,\~7no5
| C\,\~7no5
|
|  
|20/11/16
| 20/11/16
|-
|-
| 58
| 58
Line 596: Line 573:
| 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
| 9/5/4
|-
|-
| 59
| 59
Line 604: Line 581:
| 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
| 6/5/4
|}
|}


Line 616: Line 593:
! Transversal
! Transversal
! Type
! Type
!Name
! Name
!Inversion
! Inversion
!As (sub)harmonics
! As (sub)harmonics
|-
|-
| 1
| 1
Line 624: Line 601:
| 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 609:
| 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 617:
| 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 625:
| 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 633:
| 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 641:
| 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
| 18/16/12/11<br>24/18/16/11
1-4/3-3/2-24/11
|18/16/12/11
24/18/16/11
|-
|-
| 7
| 7
Line 675: Line 649:
| 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 657:
| 1-11/9-9/8-11/8
| 1-11/9-9/8-11/8
| rastmic
| rastmic
|
|  
|
|  
|
|  
|-
|-
| 9
| 9
Line 691: Line 665:
| 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 673:
| 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 681:
| 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 689:
| 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 697:
| 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 705:
| 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 713:
| 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 721:
| 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 729:
| 1-9/8-14/11-14/9
| 1-9/8-14/11-14/9
| pentacircle
| pentacircle
|
|  
|
|  
|
|  
|-
|-
| 18
| 18
Line 763: Line 737:
| 1-11/8-14/11-14/9
| 1-11/8-14/11-14/9
| parahemif
| parahemif
|
|  
|
|  
|
|  
|-
|-
| 19
| 19
Line 771: Line 745:
| 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 753:
| 1-11/6-14/11-7/6
| 1-11/6-14/11-7/6
| hemimin
| hemimin
|
|  
|
|  
|
|  
|-
|-
| 21
| 21
Line 787: Line 761:
| 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
| 18/14/12/11
|-
|-
| 22
| 22
Line 795: Line 769:
| 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 777:
| 1-11/9-9/8-10/7
| 1-11/9-9/8-10/7
| jove
| jove
|
|  
|
|  
|
|  
|-
|-
| 24
| 24
Line 811: Line 785:
| 1-11/6-9/8-10/7
| 1-11/6-9/8-10/7
| jove
| jove
|
|  
|
|  
|
|  
|-
|-
| 25
| 25
Line 819: Line 793:
| 1-11/6-14/11-10/7
| 1-11/6-14/11-10/7
| hemififths
| hemififths
|
|  
|
|  
|
|  
|-
|-
| 26
| 26
Line 827: Line 801:
| 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 809:
| 1-11/9-14/9-10/7
| 1-11/9-14/9-10/7
| swetismic
| swetismic
|
|  
|
|  
|
|  
|-
|-
| 28
| 28
Line 843: Line 817:
| 1-9/8-14/9-10/7
| 1-9/8-14/9-10/7
| hemififths
| hemififths
|
|  
|
|  
|
|  
|-
|-
| 29
| 29
Line 851: Line 825:
| 1-14/11-14/9-10/7
| 1-14/11-14/9-10/7
| jove
| jove
|
|  
|
|  
|
|  
|-
|-
| 30
| 30
Line 859: Line 833:
| 1-11/6-7/6-10/7
| 1-11/6-7/6-10/7
| swetismic
| swetismic
|
|  
|
|  
|
|  
|-
|-
| 31
| 31
Line 867: Line 841:
| 1-14/11-7/6-10/7
| 1-14/11-7/6-10/7
| jove
| jove
|
|  
|
|  
|
|  
|-
|-
| 32
| 32
Line 875: Line 849:
| 1-14/9-7/6-10/7
| 1-14/9-7/6-10/7
| swetismic
| swetismic
|
|  
|
|  
|
|  
|-
|-
| 33
| 33
Line 883: Line 857:
| 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 865:
| 1-11/9-9/8-7/4
| 1-11/9-9/8-7/4
| jove
| jove
|
|  
|
|  
|
|  
|-
|-
| 35
| 35
Line 899: Line 873:
| 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 881:
| 1-11/9-11/8-7/4
| 1-11/9-11/8-7/4
| werckismic
| werckismic
|
|  
|
|  
|
|  
|-
|-
| 37
| 37
Line 915: Line 889:
| 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 897:
| 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 <u>or</u> 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 905:
| 1-9/8-14/11-7/4
| 1-9/8-14/11-7/4
| pentacircle
| pentacircle
|
|  
|
|  
|
|  
|-
|-
| 40
| 40
Line 939: Line 913:
| 1-11/8-14/11-7/4
| 1-11/8-14/11-7/4
| hemimin
| hemimin
|
|  
|
|  
|
|  
|-
|-
| 41
| 41
Line 947: Line 921:
| 1-11/9-14/9-7/4
| 1-11/9-14/9-7/4
| werckismic
| werckismic
|
|  
|
|  
|
|  
|-
|-
| 42
| 42
Line 955: Line 929:
| 1-9/8-14/9-7/4
| 1-9/8-14/9-7/4
| pentacircle
| pentacircle
|
|  
|
|  
|
|  
|-
|-
| 43
| 43
Line 963: Line 937:
| 1-11/8-14/9-7/4
| 1-11/8-14/9-7/4
| pentacircle
| pentacircle
|
|  
|
|  
|
|  
|-
|-
| 44
| 44
Line 971: Line 945:
| 1-14/11-14/9-7/4
| 1-14/11-14/9-7/4
| utonal
| utonal
|
|  
|
|  
|14/11/9/8
| 14/11/9/8
|-
|-
| 45
| 45
Line 979: Line 953:
| 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 961:
| 1-14/11-7/6-7/4
| 1-14/11-7/6-7/4
| utonal
| utonal
|
|  
|
|  
|14/12/11/8
| 14/12/11/8
|-
|-
| 47
| 47
Line 995: Line 969:
| 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
| 9/7/6/4
|-
|-
| 48
| 48
Line 1,003: Line 977:
| 1-11/9-10/7-7/4
| 1-11/9-10/7-7/4
| jove
| jove
|
|  
|
|  
|
|  
|-
|-
| 49
| 49
Line 1,011: Line 985:
| 1-9/8-10/7-7/4
| 1-9/8-10/7-7/4
| werckismic
| werckismic
|
|  
|
|  
|
|  
|-
|-
| 50
| 50
Line 1,019: Line 993:
| 1-14/11-10/7-7/4
| 1-14/11-10/7-7/4
| werckismic
| werckismic
|
|  
|
|  
|
|  
|-
|-
| 51
| 51
Line 1,027: Line 1,001:
| 1-14/9-10/7-7/4
| 1-14/9-10/7-7/4
| jove
| jove
|
|  
|
|  
|
|  
|-
|-
| 52
| 52
Line 1,035: Line 1,009:
| 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 1,017:
| 1-14/11-14/9-20/11
| 1-14/11-14/9-20/11
| swetismic
| swetismic
|
|  
|
|  
|
|  
|-
|-
| 54
| 54
Line 1,051: Line 1,025:
| 1-14/11-7/6-20/11
| 1-14/11-7/6-20/11
| swetismic
| swetismic
|
|  
|
|  
|
|  
|-
|-
| 55
| 55
Line 1,059: Line 1,033:
| 1-14/9-7/6-20/11
| 1-14/9-7/6-20/11
| swetismic
| swetismic
|
|  
|
|  
|
|  
|-
|-
| 56
| 56
Line 1,067: Line 1,041:
| 1-14/11-10/7-20/11
| 1-14/11-10/7-20/11
| werckismic
| werckismic
|
|  
|
|  
|
|  
|-
|-
| 57
| 57
Line 1,075: Line 1,049:
| 1-14/9-10/7-20/11
| 1-14/9-10/7-20/11
| swetismic
| swetismic
|
|  
|
|  
|
|  
|-
|-
| 58
| 58
Line 1,083: Line 1,057:
| 1-7/6-10/7-20/11
| 1-7/6-10/7-20/11
| swetismic
| swetismic
|
|  
|
|  
|
|  
|-
|-
| 59
| 59
Line 1,091: Line 1,065:
| 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 1,073:
| 1-14/11-14/9-10/9
| 1-14/11-14/9-10/9
| werckismic
| werckismic
|
|  
|
|  
|
|  
|-
|-
| 61
| 61
Line 1,107: Line 1,081:
| 1-11/9-10/7-10/9
| 1-11/9-10/7-10/9
| swetismic
| swetismic
|
|  
|
|  
|
|  
|-
|-
| 62
| 62
Line 1,115: Line 1,089:
| 1-14/11-10/7-10/9
| 1-14/11-10/7-10/9
| werckismic
| werckismic
|
|  
|
|  
|
|  
|-
|-
| 63
| 63
Line 1,123: Line 1,097:
| 1-14/9-10/7-10/9
| 1-14/9-10/7-10/9
| swetismic
| swetismic
|
|  
|
|  
|
|  
|-
|-
| 64
| 64
Line 1,131: Line 1,105:
| 1-11/9-7/4-10/9
| 1-11/9-7/4-10/9
| werckismic
| werckismic
|
|  
|
|  
|
|  
|-
|-
| 65
| 65
Line 1,139: Line 1,113:
| 1-14/11-7/4-10/9
| 1-14/11-7/4-10/9
| werckismic
| werckismic
|
|  
|
|  
|
|  
|-
|-
| 66
| 66
Line 1,147: Line 1,121:
| 1-14/9-7/4-10/9
| 1-14/9-7/4-10/9
| werckismic
| werckismic
|
|  
|
|  
|
|  
|-
|-
| 67
| 67
Line 1,155: Line 1,129:
| 1-10/7-7/4-10/9
| 1-10/7-7/4-10/9
| werckismic
| werckismic
|
|  
|
|  
|
|  
|-
|-
| 68
| 68
Line 1,163: Line 1,137:
| 1-14/11-20/11-10/9
| 1-14/11-20/11-10/9
| werckismic
| werckismic
|
|  
|
|  
|
|  
|-
|-
| 69
| 69
Line 1,171: Line 1,145:
| 1-14/9-20/11-10/9
| 1-14/9-20/11-10/9
| swetismic
| swetismic
|
|  
|
|  
|
|  
|-
|-
| 70
| 70
Line 1,179: Line 1,153:
| 1-10/7-20/11-10/9
| 1-10/7-20/11-10/9
| utonal
| utonal
|
|  
|
|  
|20/18/14/11
| 20/18/14/11
|-
|-
| 71
| 71
Line 1,187: Line 1,161:
| 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 1,169:
| 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 1,177:
| 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 1,185:
| 1-11/6-10/7-5/3
| 1-11/6-10/7-5/3
| swetismic
| swetismic
|
|  
|
|  
|
|  
|-
|-
| 75
| 75
Line 1,219: Line 1,193:
| 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 1,201:
| 1-7/6-20/11-5/3
| 1-7/6-20/11-5/3
| swetismic
| swetismic
|
|  
|
|  
|
|  
|-
|-
| 77
| 77
Line 1,235: Line 1,209:
| 1-10/7-20/11-5/3
| 1-10/7-20/11-5/3
| utonal
| utonal
|
|  
|
|  
|20/14/12/11
| 20/14/12/11
|-
|-
| 78
| 78
Line 1,243: Line 1,217:
| 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
| 9/7/6/5
|-
|-
| 79
| 79
Line 1,251: Line 1,225:
| 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
| 18/12/11/10
|-
|-
| 80
| 80
Line 1,259: Line 1,233:
| 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 1,241:
| 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 1,273:
| 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 1,281:
| 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 1,289:
| 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 1,297:
| 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
| 20/16/14/11
|-
|-
| 89
| 89
Line 1,331: Line 1,305:
| 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
| 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
| 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
| 12/10/8/7<br>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 1,345:
| 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
| 24/20/18/11
|-
|-
| 95
| 95
Line 1,382: Line 1,353:
| 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
| 9/6/5/4
|}
|}


Line 1,394: Line 1,365:
! Transversal
! Transversal
! Type
! Type
!Name
! Name
!Inversion
! Inversion
!As (sub)harmonics
! As (sub)harmonics
|-
|-
| 1
| 1
Line 1,402: Line 1,373:
| 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 1,381:
| 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 1,389:
| 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 1,397:
| 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 1,405:
| 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 1,413:
| 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 1,421:
| 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 1,429:
| 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 1,437:
| 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 1,445:
| 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 1,453:
| 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 1,461:
| 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 1,469:
| 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 1,477:
| 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 1,485:
| 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 1,493:
| 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 1,501:
| 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 1,509:
| 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 1,517:
| 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 1,525:
| 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 1,533:
| 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 1,541:
| 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 1,549:
| 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 1,557:
| 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 1,565:
| 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
| 18/14/12/11/8
|-
|-
| 26
| 26
Line 1,602: Line 1,573:
| 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 1,581:
| 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 1,589:
| 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 1,597:
| 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 1,605:
| 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 1,613:
| 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 1,621:
| 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 1,629:
| 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 1,637:
| 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 1,645:
| 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 1,653:
| 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 1,661:
| 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 1,669:
| 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 1,677:
| 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 1,685:
| 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 1,693:
| 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 1,701:
| 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 1,709:
| 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 1,717:
| 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 1,725:
| 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 1,733:
| 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 1,741:
| 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 1,749:
| 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 1,757:
| 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 1,765:
| 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
| 18/14/12/11/10
|-
|-
| 51
| 51
Line 1,802: Line 1,773:
| 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 1,781:
| 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 1,789:
| 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 1,797:
| 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 1,805:
| 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 1,813:
| 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 1,821:
| 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
| 18/14/11/10/8
|-
|-
| 58
| 58
Line 1,858: Line 1,829:
| 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
| 24/20/16/14/11
|-
|-
| 59
| 59
Line 1,866: Line 1,837:
| 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
| 9/7/6/5/4
|-
|-
| 60
| 60
Line 1,874: Line 1,845:
| 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
| 18/12/11/10/8
|}
|}


Line 1,886: Line 1,857:
! Transversal
! Transversal
! Type
! Type
!Name
! Name
!Inversion
! Inversion
!As (sub)harmonics
! As (sub)harmonics
|-
|-
| 1
| 1
Line 1,894: Line 1,865:
| 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 1,873:
| 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 1,881:
| 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
Line 1,918: Line 1,889:
| 1-9/8-11/8-14/11-14/9-7/4
| 1-9/8-11/8-14/11-14/9-7/4
| nofives
| nofives
|
|  
|
|  
|
|  
|-
|-
| 5
| 5
Line 1,926: Line 1,897:
| 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 1,905:
| 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 1,913:
| 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 1,921:
| 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 1,929:
| 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 1,937:
| 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 1,945:
| 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 1,953:
| 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 1,961:
| 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
| 18/14/12/11/10/8
|}
|}


Revision as of 14:10, 22 March 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 (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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