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]], and those requiring both 441/440 and 896/891 are labeled pele. The label "nofives" refers to the unnamed rank-three temperament tempering out 243/242, 896/891 and 1344/1331, and if any two of these are needed the chord is so labled. "Nofives" refers to the fact that it is in essence a no-fives version of hemififths; 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 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.
 
{| class="wikitable center-all"
|+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<br>16/13
| 3/2
| 11/6<br>24/13
| 9/8
| 11/8<br>18/13
| 27/16<br>22/13
| 28/27<br>33/32
| 14/11
| 14/9
| 40/21<br>21/11
| 7/6
| 10/7
| 7/4
| …
| 20/11
| 10/9
| …
| 5/3
| …
| 5/4
|-
! Interval
| P1
| ~3
| P5
| ~7
| M2
| ~4<br>\b5
| M6
| ^1<br>\m2
| M3
| ^5<br>\m6
| M7
| ^M2<br>\m3
| A4<br>\~5
| ^M6<br>\m7
| …
| A6<br>\~7
| ^A1<br>\M2
| …
| ^A5<br>\M6
| …
| ^A2<br>\M3
|}
{{Todo|complete table|inline=1}}


== Triads ==
== Triads ==
Line 7: Line 107:
|-
|-
! #
! #
! Chord
! Genspans
! Transversal
! Transversal
! Type
! Type
! Name
! Inversion
! As harmonics<br>or subharmonics
|-
|-
| 1
| 1
Line 15: Line 118:
| 1-11/9-3/2
| 1-11/9-3/2
| rastmic
| rastmic
| C~
|
|
|-
|-
| 2
| 2
Line 20: Line 126:
| 1-11/9-11/6
| 1-11/9-11/6
| utonal
| utonal
| C~7no5
|
| 1/(11:9:6)
|-
|-
| 3
| 3
Line 25: Line 134:
| 1-3/2-11/6
| 1-3/2-11/6
| otonal
| otonal
| C~7no3
|
| 6:9:11
|-
|-
| 4
| 4
Line 30: Line 142:
| 1-11/9-9/8
| 1-11/9-9/8
| rastmic
| rastmic
| C~,9no5
|
|
|-
|-
| 5
| 5
Line 35: Line 150:
| 1-3/2-9/8
| 1-3/2-9/8
| ambitonal
| ambitonal
| C2 ''or'' C4
| 1-4/3-3/2
|
|-
|-
| 6
| 6
Line 40: Line 158:
| 1-11/6-9/8
| 1-11/6-9/8
| rastmic
| rastmic
| C~9no35
|
|
|-
|-
| 7
| 7
Line 45: Line 166:
| 1-11/9-11/8
| 1-11/9-11/8
| utonal
| utonal
| C~(\b5)
|
| 1/(11:9:8)
|-
|-
| 8
| 8
Line 50: Line 174:
| 1-3/2-11/8
| 1-3/2-11/8
| otonal
| otonal
| C~7sus4no5
| 1-4/3-11/6
| 6:8:11
|-
|-
| 9
| 9
Line 55: Line 182:
| 1-11/6-11/8
| 1-11/6-11/8
| utonal
| utonal
| C~2
| 1-12/11-3/2
| 1/(12:11:8)
|-
|-
| 10
| 10
Line 60: Line 190:
| 1-9/8-11/8
| 1-9/8-11/8
| otonal
| otonal
| C~,7no5
| 1-11/9-16/9
| 9:11:16
|-
|-
| 11
| 11
Line 65: Line 198:
| 1-11/6-14/11
| 1-11/6-14/11
| hemimin
| hemimin
| C,~7no5
|
|
|-
|-
| 12
| 12
Line 70: Line 206:
| 1-9/8-14/11
| 1-9/8-14/11
| pentacircle
| pentacircle
| C,9no5
|
|
|-
|-
| 13
| 13
Line 75: Line 214:
| 1-11/8-14/11
| 1-11/8-14/11
| hemimin
| hemimin
| C(\b5)
|
|
|-
|-
| 14
| 14
Line 80: Line 222:
| 1-11/9-14/9
| 1-11/9-14/9
| otonal
| otonal
| C~(^5)
|
| 9:11:14
|-
|-
| 15
| 15
Line 85: Line 230:
| 1-9/8-14/9
| 1-9/8-14/9
| pentacircle
| pentacircle
| C7~4no5
| 1-11/8-16/9
|
|-
|-
| 16
| 16
Line 90: Line 238:
| 1-11/8-14/9
| 1-11/8-14/9
| pentacircle
| pentacircle
| C2(~5) ''or''<br>C/,7no5
| 1-9/8-13/9<br>1-9/7-16/9
|
|-
|-
| 17
| 17
Line 95: Line 246:
| 1-14/11-14/9
| 1-14/11-14/9
| utonal
| utonal
| C(^5)
|
| 1/(14:11:9)
|-
|-
| 18
| 18
Line 100: Line 254:
| 1-3/2-7/6
| 1-3/2-7/6
| otonal
| otonal
| C\m
|
| 6:7:9
|-
|-
| 19
| 19
Line 105: Line 262:
| 1-11/6-7/6
| 1-11/6-7/6
| otonal
| otonal
| C\m~7no5
|
| 6:7:11
|-
|-
| 20
| 20
Line 110: Line 270:
| 1-14/11-7/6
| 1-14/11-7/6
| utonal
| utonal
| C~2/6
| 1-12/11-12/7
| 1/(12:11:7)
|-
|-
| 21
| 21
Line 115: Line 278:
| 1-14/9-7/6
| 1-14/9-7/6
| utonal
| utonal
| C/
| 1-9/7-3/2
| 1/(9:7:6)
|-
|-
| 22
| 22
Line 120: Line 286:
| 1-11/9-10/7
| 1-11/9-10/7
| swetismic
| swetismic
| C~(\~5)
|
|
|-
|-
| 23
| 23
Line 125: Line 294:
| 1-11/6-10/7
| 1-11/6-10/7
| swetismic
| swetismic
| C/(b5)
| 1-9/7-7/5
|
|-
|-
| 24
| 24
Line 130: Line 302:
| 1-9/8-10/7
| 1-9/8-10/7
| werckismic
| werckismic
| C2(\~5)
|
|
|-
|-
| 25
| 25
Line 135: Line 310:
| 1-14/11-10/7
| 1-14/11-10/7
| werckismic
| werckismic
| C(\~5)
|
|
|-
|-
| 26
| 26
Line 140: Line 318:
| 1-14/9-10/7
| 1-14/9-10/7
| swetismic
| swetismic
| C~2(b5)
| 1-12/11-7/5
|
|-
|-
| 27
| 27
Line 145: Line 326:
| 1-7/6-10/7
| 1-7/6-10/7
| swetismic
| swetismic
| C\m(\~5)
|
|
|-
|-
| 28
| 28
Line 150: Line 334:
| 1-11/9-7/4
| 1-11/9-7/4
| werckismic
| werckismic
| C~,\7no5
|
|
|-
|-
| 29
| 29
Line 155: Line 342:
| 1-3/2-7/4
| 1-3/2-7/4
| otonal
| otonal
| C\7no3
|
| 4:6:7
|-
|-
| 30
| 30
Line 160: Line 350:
| 1-9/8-7/4
| 1-9/8-7/4
| otonal
| otonal
| C\9no35
|
| 4:7:9
|-
|-
| 31
| 31
Line 165: Line 358:
| 1-11/8-7/4
| 1-11/8-7/4
| otonal
| otonal
| C(~5)
| 1-14/11-16/11
| 8:11:14
|-
|-
| 32
| 32
Line 170: Line 366:
| 1-14/11-7/4
| 1-14/11-7/4
| utonal
| utonal
| C,\7
|
| 1/(14:11:8)
|-
|-
| 33
| 33
Line 175: Line 374:
| 1-14/9-7/4
| 1-14/9-7/4
| utonal
| utonal
| C/,2no5
| 1-9/8-9/7
| 1/(9:8:7)
|-
|-
| 34
| 34
Line 180: Line 382:
| 1-7/6-7/4
| 1-7/6-7/4
| utonal
| utonal
| C\m7no5
|
| 1/(7:6:4)
|-
|-
| 35
| 35
Line 185: Line 390:
| 1-10/7-7/4
| 1-10/7-7/4
| werckismic
| werckismic
| C~(b5)
| 1-11/9-7/5
|
|-
|-
| 36
| 36
Line 190: Line 398:
| 1-14/11-20/11
| 1-14/11-20/11
| otonal
| otonal
| C,\~7no5
|
| 11:14:20
|-
|-
| 37
| 37
Line 195: Line 406:
| 1-14/9-20/11
| 1-14/9-20/11
| swetismic
| swetismic
|
|
|
|-
|-
| 38
| 38
Line 200: Line 414:
| 1-7/6-20/11
| 1-7/6-20/11
| swetismic
| swetismic
| C\m\~7no5
|
|
|-
|-
| 39
| 39
Line 205: Line 422:
| 1-10/7-20/11
| 1-10/7-20/11
| utonal
| utonal
| C(b5)
|
| 1/(20:14:11)
|-
|-
| 40
| 40
Line 210: Line 430:
| 1-11/9-10/9
| 1-11/9-10/9
| otonal
| otonal
| C~,\9no5
|
| 9:10:11
|-
|-
| 41
| 41
Line 215: Line 438:
| 1-14/11-10/9
| 1-14/11-10/9
| werckismic
| werckismic
| C,\9no5
|
|
|-
|-
| 42
| 42
Line 220: Line 446:
| 1-14/9-10/9
| 1-14/9-10/9
| otonal
| otonal
| C/(\~5)
| 1-9/7-10/7
| 7:9:10
|-
|-
| 43
| 43
Line 225: Line 454:
| 1-10/7-10/9
| 1-10/7-10/9
| utonal
| utonal
| C\2(\~5)
|
| 1/(10:9:7)
|-
|-
| 44
| 44
Line 230: Line 462:
| 1-7/4-10/9
| 1-7/4-10/9
| werckismic
| werckismic
| C\2\m7no5
|
|
|-
|-
| 45
| 45
Line 235: Line 470:
| 1-20/11-10/9
| 1-20/11-10/9
| utonal
| utonal
|
|
| 1/(20:18:11)
|-
|-
| 46
| 46
Line 240: Line 478:
| 1-3/2-5/3
| 1-3/2-5/3
| otonal
| otonal
| C\m7no5
| 1-6/5-9/5
| 5:6:9
|-
|-
| 47
| 47
Line 245: Line 486:
| 1-11/6-5/3
| 1-11/6-5/3
| otonal
| otonal
|
|
| 6:10:11
|-
|-
| 48
| 48
Line 250: Line 494:
| 1-7/6-5/3
| 1-7/6-5/3
| otonal
| otonal
| C\m6no5
|
| 6:7:10
|-
|-
| 49
| 49
Line 255: Line 502:
| 1-10/7-5/3
| 1-10/7-5/3
| utonal
| utonal
| C/dim
| 1-7/6-7/5
| 1/(10:7:6)
|-
|-
| 50
| 50
Line 260: Line 510:
| 1-20/11-5/3
| 1-20/11-5/3
| utonal
| utonal
|
|
| 1/(20:12:11)
|-
|-
| 51
| 51
Line 265: Line 518:
| 1-10/9-5/3
| 1-10/9-5/3
| utonal
| utonal
| C/7no3
| 1-3/2-9/5
| 1/(9:6:5)
|-
|-
| 52
| 52
Line 270: Line 526:
| 1-3/2-5/4
| 1-3/2-5/4
| otonal
| otonal
| C\
|
| 4:5:6
|-
|-
| 53
| 53
Line 275: Line 534:
| 1-9/8-5/4
| 1-9/8-5/4
| otonal
| otonal
| C\,9no5
|
| 4:5:9
|-
|-
| 54
| 54
Line 280: Line 542:
| 1-11/8-5/4
| 1-11/8-5/4
| otonal
| otonal
| C\(\b5)
|
| 8:10:11
|-
|-
| 55
| 55
Line 285: Line 550:
| 1-10/7-5/4
| 1-10/7-5/4
| utonal
| utonal
| C\(\~5)
|
| 1/(10:8:7)
|-
|-
| 56
| 56
Line 290: Line 558:
| 1-7/4-5/4
| 1-7/4-5/4
| otonal
| otonal
| C\7no5
|
| 4:5:6
|-
|-
| 57
| 57
Line 295: Line 566:
| 1-20/11-5/4
| 1-20/11-5/4
| utonal
| utonal
| C\,\~7no5
|
| 1/(20:16:11)
|-
|-
| 58
| 58
Line 300: Line 574:
| 1-10/9-5/4
| 1-10/9-5/4
| utonal
| utonal
| C/9no35
| 1-9/5-9/4
| 1/(9:5:4)
|-
|-
| 59
| 59
Line 305: Line 582:
| 1-5/3-5/4
| 1-5/3-5/4
| utonal
| utonal
| C/m
| 1-6/5-3/2
| 1/(6:5:4)
|}
|}


Line 311: Line 591:
|-
|-
! #
! #
! Chord
! Genspans
! Transversal
! Transversal
! Type
! Type
! Name
! Inversion
! As harmonics<br>or subharmonics
|-
|-
| 1
| 1
Line 319: Line 602:
| 1-11/9-3/2-11/6
| 1-11/9-3/2-11/6
| rastmic
| rastmic
| C~7
|
|
|-
|-
| 2
| 2
Line 324: Line 610:
| 1-11/9-3/2-9/8
| 1-11/9-3/2-9/8
| rastmic
| rastmic
| C~,9
|
|
|-
|-
| 3
| 3
Line 329: Line 618:
| 1-11/9-11/6-9/8
| 1-11/9-11/6-9/8
| rastmic
| rastmic
| C~9no5
|
|
|-
|-
| 4
| 4
Line 334: Line 626:
| 1-3/2-11/6-9/8
| 1-3/2-11/6-9/8
| rastmic
| rastmic
| C~9no3
|
|
|-
|-
| 5
| 5
Line 339: Line 634:
| 1-11/9-3/2-11/8
| 1-11/9-3/2-11/8
| rastmic
| rastmic
| C~,~11
|
|
|-
|-
| 6
| 6
Line 344: Line 642:
| 1-11/9-11/6-11/8
| 1-11/9-11/6-11/8
| utonal
| utonal
| C2~6 ''or''<br>C4~9
| 1-9/8-3/2-18/11<br>1-4/3-3/2-24/11
| 1/(18:16:12:11)<br>1/(24:18:16:11)
|-
|-
| 7
| 7
Line 349: Line 650:
| 1-3/2-11/6-11/8
| 1-3/2-11/6-11/8
| ambitonal
| ambitonal
| C~4~7
|
|
|-
|-
| 8
| 8
Line 354: Line 658:
| 1-11/9-9/8-11/8
| 1-11/9-9/8-11/8
| rastmic
| rastmic
|
|
|
|-
|-
| 9
| 9
Line 359: Line 666:
| 1-3/2-9/8-11/8
| 1-3/2-9/8-11/8
| otonal
| otonal
| C4~7
| 1-4/3-3/2-11/6
| 6:8:9:11
|-
|-
| 10
| 10
Line 364: Line 674:
| 1-11/6-9/8-11/8
| 1-11/6-9/8-11/8
| rastmic
| rastmic
| C~11no35
|
|
|-
|-
| 11
| 11
| 0-3-4-8
| 0-3-4-8
| 1-11/6-9/8-14/11
| 1-11/6-9/8-14/11
| nofives
| parahemif
| C9(~7)no5
|
|
|-
|-
| 12
| 12
Line 374: Line 690:
| 1-11/6-11/8-14/11
| 1-11/6-11/8-14/11
| hemimin
| hemimin
| C~2~11
| 1-12/11-11/8-3/2
|
|-
|-
| 13
| 13
| 0-4-5-8
| 0-4-5-8
| 1-9/8-11/8-14/11
| 1-9/8-11/8-14/11
| nofives
| parahemif
| C~,~9
| 1-11/9-3/2-13/12
|
|-
|-
| 14
| 14
| 0-1-4-9
| 0-1-4-9
| 1-11/9-9/8-14/9
| 1-11/9-9/8-14/9
| nofives
| parahemif
| C~,9(^5)
|
|
|-
|-
| 15
| 15
Line 389: Line 714:
| 1-11/9-11/8-14/9
| 1-11/9-11/8-14/9
| pentacircle
| pentacircle
| C,~6,9no5
| 1-14/11-18/11-9/4
|
|-
|-
| 16
| 16
Line 394: Line 722:
| 1-9/8-11/8-14/9
| 1-9/8-11/8-14/9
| pentacircle
| pentacircle
| C~,7(\b5)
| 1-11/9-11/8-16/9
|
|-
|-
| 17
| 17
Line 399: Line 730:
| 1-9/8-14/11-14/9
| 1-9/8-14/11-14/9
| pentacircle
| pentacircle
|
|
|
|-
|-
| 18
| 18
| 0-5-8-9
| 0-5-8-9
| 1-11/8-14/11-14/9
| 1-11/8-14/11-14/9
| nofives
| parahemif
|
|
|
|-
|-
| 19
| 19
Line 409: Line 746:
| 1-3/2-11/6-7/6
| 1-3/2-11/6-7/6
| otonal
| otonal
| C\m~7
|
| 6:7:9:11
|-
|-
| 20
| 20
Line 414: Line 754:
| 1-11/6-14/11-7/6
| 1-11/6-14/11-7/6
| hemimin
| hemimin
|
|
|
|-
|-
| 21
| 21
Line 419: Line 762:
| 1-14/11-14/9-7/6
| 1-14/11-14/9-7/6
| utonal
| utonal
| C/,~6
| 1-9/7-3/2-18/11
| 1/(18:14:12:11)
|-
|-
| 22
| 22
Line 424: Line 770:
| 1-11/9-11/6-10/7
| 1-11/9-11/6-10/7
| swetismic
| swetismic
| C\m~6
| 1-7/6-3/2-13/8
|
|-
|-
| 23
| 23
Line 429: Line 778:
| 1-11/9-9/8-10/7
| 1-11/9-9/8-10/7
| jove
| jove
|
|
|
|-
|-
| 24
| 24
Line 434: Line 786:
| 1-11/6-9/8-10/7
| 1-11/6-9/8-10/7
| jove
| jove
|
|
|
|-
|-
| 25
| 25
Line 439: Line 794:
| 1-11/6-14/11-10/7
| 1-11/6-14/11-10/7
| hemififths
| hemififths
|
|
|
|-
|-
| 26
| 26
Line 444: Line 802:
| 1-9/8-14/11-10/7
| 1-9/8-14/11-10/7
| pele
| pele
| C9no5
| 1-9/8-14/11-16/9
|
|-
|-
| 27
| 27
Line 449: Line 810:
| 1-11/9-14/9-10/7
| 1-11/9-14/9-10/7
| swetismic
| swetismic
|
|
|
|-
|-
| 28
| 28
Line 454: Line 818:
| 1-9/8-14/9-10/7
| 1-9/8-14/9-10/7
| hemififths
| hemififths
|
|
|
|-
|-
| 29
| 29
Line 459: Line 826:
| 1-14/11-14/9-10/7
| 1-14/11-14/9-10/7
| jove
| jove
|
|
|
|-
|-
| 30
| 30
Line 464: Line 834:
| 1-11/6-7/6-10/7
| 1-11/6-7/6-10/7
| swetismic
| swetismic
|
|
|
|-
|-
| 31
| 31
Line 469: Line 842:
| 1-14/11-7/6-10/7
| 1-14/11-7/6-10/7
| jove
| jove
|
|
|
|-
|-
| 32
| 32
Line 474: Line 850:
| 1-14/9-7/6-10/7
| 1-14/9-7/6-10/7
| swetismic
| swetismic
|
|
|
|-
|-
| 33
| 33
Line 479: Line 858:
| 1-11/9-3/2-7/4
| 1-11/9-3/2-7/4
| jove
| jove
| C~,\7
|
|
|-
|-
| 34
| 34
Line 484: Line 866:
| 1-11/9-9/8-7/4
| 1-11/9-9/8-7/4
| jove
| jove
|
|
|
|-
|-
| 35
| 35
Line 489: Line 874:
| 1-3/2-9/8-7/4
| 1-3/2-9/8-7/4
| otonal
| otonal
| C\9no3
|
| 4:6:7:9
|-
|-
| 36
| 36
Line 494: Line 882:
| 1-11/9-11/8-7/4
| 1-11/9-11/8-7/4
| werckismic
| werckismic
|
|
|
|-
|-
| 37
| 37
Line 499: Line 890:
| 1-3/2-11/8-7/4
| 1-3/2-11/8-7/4
| otonal
| otonal
| C~4,\7
|
| 8:11:12:14
|-
|-
| 38
| 38
Line 504: Line 898:
| 1-9/8-11/8-7/4
| 1-9/8-11/8-7/4
| otonal
| otonal
| C~4\7,9 ''or'' C~,7(^5)
| 1-11/9-14/9-16/9
| 9:11:14:16
|-
|-
| 39
| 39
Line 509: Line 906:
| 1-9/8-14/11-7/4
| 1-9/8-14/11-7/4
| pentacircle
| pentacircle
|
|
|
|-
|-
| 40
| 40
Line 514: Line 914:
| 1-11/8-14/11-7/4
| 1-11/8-14/11-7/4
| hemimin
| hemimin
|
|
|
|-
|-
| 41
| 41
Line 519: Line 922:
| 1-11/9-14/9-7/4
| 1-11/9-14/9-7/4
| werckismic
| werckismic
|
|
|
|-
|-
| 42
| 42
Line 524: Line 930:
| 1-9/8-14/9-7/4
| 1-9/8-14/9-7/4
| pentacircle
| pentacircle
|
|
|
|-
|-
| 43
| 43
Line 529: Line 938:
| 1-11/8-14/9-7/4
| 1-11/8-14/9-7/4
| pentacircle
| pentacircle
|
|
|
|-
|-
| 44
| 44
Line 534: Line 946:
| 1-14/11-14/9-7/4
| 1-14/11-14/9-7/4
| utonal
| utonal
|
|
| 1/(14:11:9:8)
|-
|-
| 45
| 45
Line 539: Line 954:
| 1-3/2-7/6-7/4
| 1-3/2-7/6-7/4
| ambitonal
| ambitonal
| C\m7
|
|
|-
|-
| 46
| 46
Line 544: Line 962:
| 1-14/11-7/6-7/4
| 1-14/11-7/6-7/4
| utonal
| utonal
|
|
| 1/(14:12:11:8)
|-
|-
| 47
| 47
Line 549: Line 970:
| 1-14/9-7/6-7/4
| 1-14/9-7/6-7/4
| utonal
| utonal
| C/,9
| 1-9/7-3/2-9/4
| 1/(9:7:6:4)
|-
|-
| 48
| 48
Line 554: Line 978:
| 1-11/9-10/7-7/4
| 1-11/9-10/7-7/4
| jove
| jove
|
|
|
|-
|-
| 49
| 49
Line 559: Line 986:
| 1-9/8-10/7-7/4
| 1-9/8-10/7-7/4
| werckismic
| werckismic
|
|
|
|-
|-
| 50
| 50
Line 564: Line 994:
| 1-14/11-10/7-7/4
| 1-14/11-10/7-7/4
| werckismic
| werckismic
|
|
|
|-
|-
| 51
| 51
Line 569: Line 1,002:
| 1-14/9-10/7-7/4
| 1-14/9-10/7-7/4
| jove
| jove
|
|
|
|-
|-
| 52
| 52
Line 574: Line 1,010:
| 1-7/6-10/7-7/4
| 1-7/6-10/7-7/4
| jove
| jove
| C~,/6
| 1-11/9-3/2-12/7
|
|-
|-
| 53
| 53
Line 579: Line 1,018:
| 1-14/11-14/9-20/11
| 1-14/11-14/9-20/11
| swetismic
| swetismic
|
|
|
|-
|-
| 54
| 54
Line 584: Line 1,026:
| 1-14/11-7/6-20/11
| 1-14/11-7/6-20/11
| swetismic
| swetismic
|
|
|
|-
|-
| 55
| 55
Line 589: Line 1,034:
| 1-14/9-7/6-20/11
| 1-14/9-7/6-20/11
| swetismic
| swetismic
|
|
|
|-
|-
| 56
| 56
Line 594: Line 1,042:
| 1-14/11-10/7-20/11
| 1-14/11-10/7-20/11
| werckismic
| werckismic
|
|
|
|-
|-
| 57
| 57
Line 599: Line 1,050:
| 1-14/9-10/7-20/11
| 1-14/9-10/7-20/11
| swetismic
| swetismic
|
|
|
|-
|-
| 58
| 58
Line 604: Line 1,058:
| 1-7/6-10/7-20/11
| 1-7/6-10/7-20/11
| swetismic
| swetismic
|
|
|
|-
|-
| 59
| 59
Line 609: Line 1,066:
| 1-11/9-14/9-10/9
| 1-11/9-14/9-10/9
| otonal
| otonal
|
|
| 9:10:11:14
|-
|-
| 60
| 60
Line 614: Line 1,074:
| 1-14/11-14/9-10/9
| 1-14/11-14/9-10/9
| werckismic
| werckismic
|
|
|
|-
|-
| 61
| 61
Line 619: Line 1,082:
| 1-11/9-10/7-10/9
| 1-11/9-10/7-10/9
| swetismic
| swetismic
|
|
|
|-
|-
| 62
| 62
Line 624: Line 1,090:
| 1-14/11-10/7-10/9
| 1-14/11-10/7-10/9
| werckismic
| werckismic
|
|
|
|-
|-
| 63
| 63
Line 629: Line 1,098:
| 1-14/9-10/7-10/9
| 1-14/9-10/7-10/9
| swetismic
| swetismic
|
|
|
|-
|-
| 64
| 64
Line 634: Line 1,106:
| 1-11/9-7/4-10/9
| 1-11/9-7/4-10/9
| werckismic
| werckismic
|
|
|
|-
|-
| 65
| 65
Line 639: Line 1,114:
| 1-14/11-7/4-10/9
| 1-14/11-7/4-10/9
| werckismic
| werckismic
|
|
|
|-
|-
| 66
| 66
Line 644: Line 1,122:
| 1-14/9-7/4-10/9
| 1-14/9-7/4-10/9
| werckismic
| werckismic
|
|
|
|-
|-
| 67
| 67
Line 649: Line 1,130:
| 1-10/7-7/4-10/9
| 1-10/7-7/4-10/9
| werckismic
| werckismic
|
|
|
|-
|-
| 68
| 68
Line 654: Line 1,138:
| 1-14/11-20/11-10/9
| 1-14/11-20/11-10/9
| werckismic
| werckismic
|
|
|
|-
|-
| 69
| 69
Line 659: Line 1,146:
| 1-14/9-20/11-10/9
| 1-14/9-20/11-10/9
| swetismic
| swetismic
|
|
|
|-
|-
| 70
| 70
Line 664: Line 1,154:
| 1-10/7-20/11-10/9
| 1-10/7-20/11-10/9
| utonal
| utonal
|
|
| 1/(20:18:14:11)
|-
|-
| 71
| 71
Line 669: Line 1,162:
| 1-3/2-11/6-5/3
| 1-3/2-11/6-5/3
| otonal
| otonal
|
|
| 6:9:10:11
|-
|-
| 72
| 72
Line 674: Line 1,170:
| 1-3/2-7/6-5/3
| 1-3/2-7/6-5/3
| otonal
| otonal
| C\m6
|
| 6:7:9:10
|-
|-
| 73
| 73
Line 679: Line 1,178:
| 1-11/6-7/6-5/3
| 1-11/6-7/6-5/3
| otonal
| otonal
| C\m6~7no5
|
| 6:7:10:11
|-
|-
| 74
| 74
Line 684: Line 1,186:
| 1-11/6-10/7-5/3
| 1-11/6-10/7-5/3
| swetismic
| swetismic
|
|
|
|-
|-
| 75
| 75
Line 689: Line 1,194:
| 1-7/6-10/7-5/3
| 1-7/6-10/7-5/3
| swetismic
| swetismic
| C\m6(\~5)
|
|
|-
|-
| 76
| 76
Line 694: Line 1,202:
| 1-7/6-20/11-5/3
| 1-7/6-20/11-5/3
| swetismic
| swetismic
|
|
|
|-
|-
| 77
| 77
Line 699: Line 1,210:
| 1-10/7-20/11-5/3
| 1-10/7-20/11-5/3
| utonal
| utonal
|
|
| 1/(20:14:12:11)
|-
|-
| 78
| 78
Line 704: Line 1,218:
| 1-10/7-10/9-5/3
| 1-10/7-10/9-5/3
| utonal
| utonal
| C/7
| 1-9/7-3/2-9/5
| 1/(9:7:6:5)
|-
|-
| 79
| 79
Line 709: Line 1,226:
| 1-20/11-10/9-5/3
| 1-20/11-10/9-5/3
| utonal
| utonal
| C/7~13no3
| 1-3/2-18/11-9/5
| 1/(18:12:11:10)
|-
|-
| 80
| 80
Line 714: Line 1,234:
| 1-3/2-9/8-5/4
| 1-3/2-9/8-5/4
| otonal
| otonal
| C\,9
|
| 4:5:6:9
|-
|-
| 81
| 81
Line 719: Line 1,242:
| 1-3/2-11/8-5/4
| 1-3/2-11/8-5/4
| otonal
| otonal
| C\,~11
|
| 8:10:11:12
|-
|-
| 82
| 82
Line 724: Line 1,250:
| 1-9/8-11/8-5/4
| 1-9/8-11/8-5/4
| otonal
| otonal
| C\,9(\b5)
|
| 8:9:10:11
|-
|-
| 83
| 83
Line 729: Line 1,258:
| 1-9/8-10/7-5/4
| 1-9/8-10/7-5/4
| werckismic
| werckismic
| C,9(\~5)
|
|
|-
|-
| 84
| 84
Line 734: Line 1,266:
| 1-3/2-7/4-5/4
| 1-3/2-7/4-5/4
| otonal
| otonal
| C\7
|
| 4:5:6:7
|-
|-
| 85
| 85
Line 739: Line 1,274:
| 1-9/8-7/4-5/4
| 1-9/8-7/4-5/4
| otonal
| otonal
| C\9no5
|
| 4:5:7:9
|-
|-
| 86
| 86
Line 744: Line 1,282:
| 1-11/8-7/4-5/4
| 1-11/8-7/4-5/4
| otonal
| otonal
| C\7~11no5
|
| 4:5:7:11
|-
|-
| 87
| 87
Line 749: Line 1,290:
| 1-10/7-7/4-5/4
| 1-10/7-7/4-5/4
| werckismic
| werckismic
| C\7(\~5)
|
|
|-
|-
| 88
| 88
Line 754: Line 1,298:
| 1-10/7-20/11-5/4
| 1-10/7-20/11-5/4
| utonal
| utonal
| C,\7(b5)
| 1-14/11-7/5-7/4
| 1/(20:16:14:11)
|-
|-
| 89
| 89
Line 759: Line 1,306:
| 1-10/7-10/9-5/4
| 1-10/7-10/9-5/4
| utonal
| utonal
| C/9no5
| 1-9/7-9/5-9/4
| 1/(10:9:8:7)
|-
|-
| 90
| 90
Line 764: Line 1,314:
| 1-7/4-10/9-5/4
| 1-7/4-10/9-5/4
| werckismic
| werckismic
| C\7\9no5
|
|
|-
|-
| 91
| 91
Line 769: Line 1,322:
| 1-20/11-10/9-5/4
| 1-20/11-10/9-5/4
| utonal
| utonal
| C2~6^7no5
| 1-18/11-9/5-9/4
| 1/(20:18:16:11)
|-
|-
| 92
| 92
Line 774: Line 1,330:
| 1-3/2-5/3-5/4
| 1-3/2-5/3-5/4
| ambitonal
| ambitonal
| C\6 <u>or</u> C/m7
| 1-6/5-3/2-9/5
|
|-
|-
| 93
| 93
Line 779: Line 1,338:
| 1-10/7-5/3-5/4
| 1-10/7-5/3-5/4
| utonal
| utonal
| C/m6<br>C\m7(b5)
| 1-6/5-3/2-12/7<br>1-7/6-7/5-7/4
| 1/(12:10:8:7)<br>1/(7:6:5:4)
|-
|-
| 94
| 94
Line 784: Line 1,346:
| 1-20/11-5/3-5/4
| 1-20/11-5/3-5/4
| utonal
| utonal
| C/m,~9
| 1-6/5-3/2-24/11
| 1/(24:20:18:11)
|-
|-
| 95
| 95
Line 789: Line 1,354:
| 1-10/9-5/3-5/4
| 1-10/9-5/3-5/4
| utonal
| utonal
| C/9no3
| 1-3/2-9/5-9/4
| 1/(9:6:5:4)
|}
|}


Line 795: Line 1,363:
|-
|-
! #
! #
! Chord
! Genspans
! Transversal
! Transversal
! Type
! Type
! Name
! Inversion
! As harmonics<br>or subharmonics
|-
|-
| 1
| 1
Line 803: 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
|
|
|-
|-
| 2
| 2
Line 808: 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
|
|
|-
|-
| 3
| 3
Line 813: 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
|
|
|-
|-
| 4
| 4
Line 818: 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
|
|
|-
|-
| 5
| 5
Line 823: 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
|
|
|-
|-
| 6
| 6
| 0-3-4-5-8
| 0-3-4-5-8
| 1-11/6-9/8-11/8-14/11
| 1-11/6-9/8-11/8-14/11
| nofives
| parahemif
|
|
|
|-
|-
| 7
| 7
| 0-1-4-5-9
| 0-1-4-5-9
| 1-11/9-9/8-11/8-14/9
| 1-11/9-9/8-11/8-14/9
| nofives
| parahemif
|
|
|
|-
|-
| 8
| 8
| 0-4-5-8-9
| 0-4-5-8-9
| 1-9/8-11/8-14/11-14/9
| 1-9/8-11/8-14/11-14/9
| nofives
| parahemif
|
|
|
|-
|-
| 9
| 9
Line 843: 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 848: 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 853: 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 858: 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 863: 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 868: 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 873: 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)
|
|
|-
|-
| 16
| 16
Line 878: 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 883: 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 888: 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
|
| 4:6:7:9:11
|-
|-
| 19
| 19
| 0-4-5-8-13
| 0-4-5-8-13
| 1-9/8-11/8-14/11-7/4
| 1-9/8-11/8-14/11-7/4
| nofives
| parahemif
|
|
|
|-
|-
| 20
| 20
Line 898: 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 903: 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 908: 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 913: 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
| 0-5-8-9-13
| 0-5-8-9-13
| 1-11/8-14/11-14/9-7/4
| 1-11/8-14/11-14/9-7/4
| nofives
| parahemif
|
|
|
|-
|-
| 25
| 25
Line 923: 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
| 1-9/7-3/2-18/11-9/4
| 1/(18:14:12:11:8)
|-
|-
| 26
| 26
Line 928: 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 933: 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 938: 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 943: 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 948: 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 953: 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 958: 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 963: 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 968: 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 973: 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 978: 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 983: 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 988: 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 993: 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 998: 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 1,003: 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 1,008: 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 1,013: 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 1,018: 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 1,023: 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 1,028: 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 1,033: 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
|
| 6:7:9:10:11
|-
|-
| 48
| 48
Line 1,038: 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 1,043: 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 1,048: 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
| 1-9/7-3/2-18/11-9/5
| 1/(18:14:12:11:10)
|-
|-
| 51
| 51
Line 1,053: 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
|
| 4:5:6:9:11
|-
|-
| 52
| 52
Line 1,058: 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
|
| 4:5:6:7:9
|-
|-
| 53
| 53
Line 1,063: 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
|
| 4:5:6:7:11
|-
|-
| 54
| 54
Line 1,068: 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
|
| 4:5:7:9:11
|-
|-
| 55
| 55
Line 1,073: 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)
|
|
|-
|-
| 56
| 56
Line 1,078: 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 1,083: 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
| 1-9/7-18/11-9/5-9/4
| 1/(18:14:11:10:8)
|-
|-
| 58
| 58
Line 1,088: 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
| 1-6/5-3/2-12/7-24/11
| 1/(24:20:16:14:11)
|-
|-
| 59
| 59
Line 1,093: 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
| 1-9/7-3/2-9/5-9/4
| 1/(9:7:6:5:4)
|-
|-
| 60
| 60
Line 1,098: 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
| 1-3/2-18/11-9/5-9/4
| 1/(18:12:11:10:8)
|}
|}


Line 1,104: Line 1,855:
|-
|-
! #
! #
! Chord
! Genspans
! Transversal
! Transversal
! Type
! Type
! Name
! Inversion
! As harmonics<br>or subharmonics
|-
|-
| 1
| 1
Line 1,112: 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
|
|
|-
|-
| 2
| 2
Line 1,117: 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)
|
|
|-
|-
| 3
| 3
Line 1,122: 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 1,132: 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 1,137: 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 1,142: 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 1,147: 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 1,152: 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 1,157: 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 1,162: 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 1,167: 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
|
| 4:5:6:7:9:11
|-
|-
| 13
| 13
Line 1,172: 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
| 1-9/7-3/2-18/11-9/5-9/4
| 1/(18:14:12:11:10:8)
|}
|}


[[Category:Chords]]
[[Category:Lists of chords]]
[[Category:Hemififths]]
[[Category:Hemififths]]
[[Category:Triad]]
[[Category:Triads]]
[[Category:Tetrad]]
[[Category:Tetrads]]
[[Category:Pentad]]
[[Category:Pentads]]
[[Category:Hexad]]
[[Category:Hexads]]

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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