Hemififths/Chords: Difference between revisions

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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.
Chords are named with ups and downs, using pergen #4 (P8, P5/2) in the [http://tallkite.com/misc_files/notation%20guide%20for%20rank-2%20pergens.pdf notation guide for rank-2 pergens]. One up is 7 generators, which is a half-sharp. The tilde ~ means mid, half-way between major and minor. ~4 = ^4 = vA4 and ~5 = v5 = ^d5. The comma (the actual punctuation mark) is pronounced "add", thus C~,7 is "C mid add 7". To facilitate chord naming, lifts and drops are also used. One lift is -17 generators, a half-diminished second. Enharmonic equivalences: vvA1 and v\m2. Cents: ^1 = 50¢ + 3.5c and /1 = 50¢ - 8.5c, where c equals the amount in cents the tempered fifth exceeds 700¢. /1 = ~81/80 = ~64/63 and ^1 = ~33/32. To convert to 41edo, ^1 = 2\41 and /1 = 1\41.


The "As (sub)harmonics" column describes otonal chords as harmonics and utonal chords as subharmonics.
The ''As harmonics or subharmonics'' column describes otonal chords as harmonics and utonal chords as subharmonics.
 
{| class="wikitable center-all"
{| class="wikitable center-all"
|+Hemififth's genchain
|+Hemififth's genchain
Line 100: Line 101:
| ^A2<br>\M3
| ^A2<br>\M3
|}
|}
{{Todo|inline=1|comment=Complete the tables. }}
{{Todo|complete table|inline=1}}


== Triads ==
== Triads ==
Line 111: Line 112:
! Name
! Name
! Inversion
! Inversion
! As (sub)harmonics
! As harmonics<br>or subharmonics
|-
|-
| 1
| 1
Line 127: Line 128:
| C~7no5
| C~7no5
|  
|  
| 11/9/6
| 1/(11:9:6)
|-
|-
| 3
| 3
Line 150: Line 151:
| ambitonal
| ambitonal
| C2 ''or'' C4
| C2 ''or'' C4
| 1-4/3-9/8
| 1-4/3-3/2
|
|
|-
|-
Line 167: Line 168:
| C~(\b5)
| C~(\b5)
|  
|  
| 11/9/8
| 1/(11:9:8)
|-
|-
| 8
| 8
Line 183: Line 184:
| C~2
| C~2
| 1-12/11-3/2
| 1-12/11-3/2
| 12/11/8
| 1/(12:11:8)
|-
|-
| 10
| 10
Line 247: Line 248:
| C(^5)
| C(^5)
|  
|  
| 14/11/9
| 1/(14:11:9)
|-
|-
| 18
| 18
Line 271: Line 272:
| C~2/6
| C~2/6
| 1-12/11-12/7
| 1-12/11-12/7
| 12/11/7
| 1/(12:11:7)
|-
|-
| 21
| 21
Line 279: Line 280:
| C/
| C/
| 1-9/7-3/2
| 1-9/7-3/2
| 9/7/6
| 1/(9:7:6)
|-
|-
| 22
| 22
Line 359: Line 360:
| C(~5)
| C(~5)
| 1-14/11-16/11
| 1-14/11-16/11
| 11:14:16
| 8:11:14
|-
|-
| 32
| 32
Line 367: Line 368:
| C,\7
| C,\7
|  
|  
| 14/11/8
| 1/(14:11:8)
|-
|-
| 33
| 33
Line 375: Line 376:
| C/,2no5
| C/,2no5
| 1-9/8-9/7
| 1-9/8-9/7
| 9/8/7
| 1/(9:8:7)
|-
|-
| 34
| 34
Line 383: Line 384:
| C\m7no5
| C\m7no5
|  
|  
| 7/6/4
| 1/(7:6:4)
|-
|-
| 35
| 35
Line 423: Line 424:
| C(b5)
| C(b5)
|  
|  
| 20/14/11
| 1/(20:14:11)
|-
|-
| 40
| 40
Line 455: Line 456:
| C\2(\~5)
| C\2(\~5)
|  
|  
| 10/9/7
| 1/(10:9:7)
|-
|-
| 44
| 44
Line 471: Line 472:
|  
|  
|  
|  
| 20/18/11
| 1/(20:18:11)
|-
|-
| 46
| 46
Line 503: Line 504:
| C/dim
| C/dim
| 1-7/6-7/5
| 1-7/6-7/5
| 10/7/6
| 1/(10:7:6)
|-
|-
| 50
| 50
Line 511: Line 512:
|  
|  
|  
|  
| 20/12/11
| 1/(20:12:11)
|-
|-
| 51
| 51
Line 519: Line 520:
| C/7no3
| C/7no3
| 1-3/2-9/5
| 1-3/2-9/5
| 9/6/5
| 1/(9:6:5)
|-
|-
| 52
| 52
Line 551: Line 552:
| C\(\~5)
| C\(\~5)
|  
|  
| 10/8/7
| 1/(10:8:7)
|-
|-
| 56
| 56
Line 567: Line 568:
| C\,\~7no5
| C\,\~7no5
|  
|  
| 20/11/16
| 1/(20:16:11)
|-
|-
| 58
| 58
Line 575: Line 576:
| C/9no35
| C/9no35
| 1-9/5-9/4
| 1-9/5-9/4
| 9/5/4
| 1/(9:5:4)
|-
|-
| 59
| 59
Line 583: Line 584:
| C/m
| C/m
| 1-6/5-3/2
| 1-6/5-3/2
| 6/5/4
| 1/(6:5:4)
|}
|}


Line 595: Line 596:
! Name
! Name
! Inversion
! Inversion
! As (sub)harmonics
! As harmonics<br>or subharmonics
|-
|-
| 1
| 1
Line 643: Line 644:
| C2~6 ''or''<br>C4~9
| C2~6 ''or''<br>C4~9
| 1-9/8-3/2-18/11<br>1-4/3-3/2-24/11
| 1-9/8-3/2-18/11<br>1-4/3-3/2-24/11
| 18/16/12/11<br>24/18/16/11
| 1/(18:16:12:11)<br>1/(24:18:16:11)
|-
|-
| 7
| 7
Line 763: Line 764:
| C/,~6
| C/,~6
| 1-9/7-3/2-18/11
| 1-9/7-3/2-18/11
| 18/14/12/11
| 1/(18:14:12:11)
|-
|-
| 22
| 22
Line 897: Line 898:
| 1-9/8-11/8-7/4
| 1-9/8-11/8-7/4
| otonal
| otonal
| C~4\7,9 <u>or</u> C~,7(^5)
| C~4\7,9 ''or'' C~,7(^5)
| 1-11/9-14/9-16/9
| 1-11/9-14/9-16/9
| 9:11:14:16
| 9:11:14:16
Line 947: Line 948:
|  
|  
|  
|  
| 14/11/9/8
| 1/(14:11:9:8)
|-
|-
| 45
| 45
Line 963: Line 964:
|  
|  
|  
|  
| 14/12/11/8
| 1/(14:12:11:8)
|-
|-
| 47
| 47
Line 971: Line 972:
| C/,9
| C/,9
| 1-9/7-3/2-9/4
| 1-9/7-3/2-9/4
| 9/7/6/4
| 1/(9:7:6:4)
|-
|-
| 48
| 48
Line 1,155: Line 1,156:
|  
|  
|  
|  
| 20/18/14/11
| 1/(20:18:14:11)
|-
|-
| 71
| 71
Line 1,211: Line 1,212:
|  
|  
|  
|  
| 20/14/12/11
| 1/(20:14:12:11)
|-
|-
| 78
| 78
Line 1,219: Line 1,220:
| C/7
| C/7
| 1-9/7-3/2-9/5
| 1-9/7-3/2-9/5
| 9/7/6/5
| 1/(9:7:6:5)
|-
|-
| 79
| 79
Line 1,227: Line 1,228:
| C/7~13no3
| C/7~13no3
| 1-3/2-18/11-9/5
| 1-3/2-18/11-9/5
| 18/12/11/10
| 1/(18:12:11:10)
|-
|-
| 80
| 80
Line 1,299: Line 1,300:
| C,\7(b5)
| C,\7(b5)
| 1-14/11-7/5-7/4
| 1-14/11-7/5-7/4
| 20/16/14/11
| 1/(20:16:14:11)
|-
|-
| 89
| 89
Line 1,307: Line 1,308:
| C/9no5
| C/9no5
| 1-9/7-9/5-9/4
| 1-9/7-9/5-9/4
| 10/9/8/7
| 1/(10:9:8:7)
|-
|-
| 90
| 90
Line 1,323: Line 1,324:
| C2~6^7no5
| C2~6^7no5
| 1-18/11-9/5-9/4
| 1-18/11-9/5-9/4
| 20/18/16/11
| 1/(20:18:16:11)
|-
|-
| 92
| 92
Line 1,339: Line 1,340:
| C/m6<br>C\m7(b5)
| C/m6<br>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<br>1-7/6-7/5-7/4
| 12/10/8/7<br>7/6/5/4
| 1/(12:10:8:7)<br>1/(7:6:5:4)
|-
|-
| 94
| 94
Line 1,347: Line 1,348:
| C/m,~9
| C/m,~9
| 1-6/5-3/2-24/11
| 1-6/5-3/2-24/11
| 24/20/18/11
| 1/(24:20:18:11)
|-
|-
| 95
| 95
Line 1,355: Line 1,356:
| C/9no3
| C/9no3
| 1-3/2-9/5-9/4
| 1-3/2-9/5-9/4
| 9/6/5/4
| 1/(9:6:5:4)
|}
|}


Line 1,367: Line 1,368:
! Name
! Name
! Inversion
! Inversion
! As (sub)harmonics
! As harmonics<br>or subharmonics
|-
|-
| 1
| 1
Line 1,567: Line 1,568:
| C/,~6,9
| C/,~6,9
| 1-9/7-3/2-18/11-9/4
| 1-9/7-3/2-18/11-9/4
| 18/14/12/11/8
| 1/(18:14:12:11:8)
|-
|-
| 26
| 26
Line 1,767: Line 1,768:
| C/7~6
| C/7~6
| 1-9/7-3/2-18/11-9/5
| 1-9/7-3/2-18/11-9/5
| 18/14/12/11/10
| 1/(18:14:12:11:10)
|-
|-
| 51
| 51
Line 1,823: Line 1,824:
| C/9~6no5
| C/9~6no5
| 1-9/7-18/11-9/5-9/4
| 1-9/7-18/11-9/5-9/4
| 18/14/11/10/8
| 1/(18:14:11:10:8)
|-
|-
| 58
| 58
Line 1,831: Line 1,832:
| C/m6~9
| C/m6~9
| 1-6/5-3/2-12/7-24/11
| 1-6/5-3/2-12/7-24/11
| 24/20/16/14/11
| 1/(24:20:16:14:11)
|-
|-
| 59
| 59
Line 1,839: Line 1,840:
| C/9
| C/9
| 1-9/7-3/2-9/5-9/4
| 1-9/7-3/2-9/5-9/4
| 9/7/6/5/4
| 1/(9:7:6:5:4)
|-
|-
| 60
| 60
Line 1,847: Line 1,848:
| C/9~6no3
| C/9~6no3
| 1-3/2-18/11-9/5-9/4
| 1-3/2-18/11-9/5-9/4
| 18/12/11/10/8
| 1/(18:12:11:10:8)
|}
|}


Line 1,859: Line 1,860:
! Name
! Name
! Inversion
! Inversion
! As (sub)harmonics
! As harmonics<br>or subharmonics
|-
|-
| 1
| 1
Line 1,888: Line 1,889:
| 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
|  
|  
|  
|  
Line 1,963: Line 1,964:
| C/9~6
| C/9~6
| 1-9/7-3/2-18/11-9/5-9/4
| 1-9/7-3/2-18/11-9/5-9/4
| 18/14/12/11/10/8
| 1/(18:14:12:11:10:8)
|}
|}


Latest revision as of 20:52, 29 July 2025

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

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

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

The As harmonics or subharmonics column describes otonal chords as harmonics and utonal chords as subharmonics.

Hemififth's genchain
Genspan 0 1 2 3 4 5 6 7 8 9 10 11 12 13 … 20 21 … 23 … 25
Cents (41edo) 0 351 702 1054 205 556 907 59 410 761 1112 263 615 966 … 1024 176 … 878 … 380
Ratio 1/1 11/9
16/13 		3/2 11/6
24/13 		9/8 11/8
18/13 		27/16
22/13 		28/27
33/32 		14/11 14/9 40/21
21/11 		7/6 10/7 7/4 … 20/11 10/9 … 5/3 … 5/4
Interval P1 ~3 P5 ~7 M2 ~4
\b5 		M6 ^1
\m2 		M3 ^5
\m6 		M7 ^M2
\m3 		A4
\~5 		^M6
\m7 		… A6
\~7 		^A1
\M2 		… ^A5
\M6 		… ^A2
\M3
Todo: complete table

Triads

# Genspans Transversal Type Name Inversion As harmonics
or subharmonics
1 0-1-2 1-11/9-3/2 rastmic C~
2 0-1-3 1-11/9-11/6 utonal C~7no5 1/(11:9:6)
3 0-2-3 1-3/2-11/6 otonal C~7no3 6:9:11
4 0-1-4 1-11/9-9/8 rastmic C~,9no5
5 0-2-4 1-3/2-9/8 ambitonal C2 or C4 1-4/3-3/2
6 0-3-4 1-11/6-9/8 rastmic C~9no35
7 0-1-5 1-11/9-11/8 utonal C~(\b5) 1/(11:9:8)
8 0-2-5 1-3/2-11/8 otonal C~7sus4no5 1-4/3-11/6 6:8:11
9 0-3-5 1-11/6-11/8 utonal C~2 1-12/11-3/2 1/(12:11:8)
10 0-4-5 1-9/8-11/8 otonal C~,7no5 1-11/9-16/9 9:11:16
11 0-3-8 1-11/6-14/11 hemimin C,~7no5
12 0-4-8 1-9/8-14/11 pentacircle C,9no5
13 0-5-8 1-11/8-14/11 hemimin C(\b5)
14 0-1-9 1-11/9-14/9 otonal C~(^5) 9:11:14
15 0-4-9 1-9/8-14/9 pentacircle C7~4no5 1-11/8-16/9
16 0-5-9 1-11/8-14/9 pentacircle C2(~5) or
C/,7no5 		1-9/8-13/9
1-9/7-16/9
17 0-8-9 1-14/11-14/9 utonal C(^5) 1/(14:11:9)
18 0-2-11 1-3/2-7/6 otonal C\m 6:7:9
19 0-3-11 1-11/6-7/6 otonal C\m~7no5 6:7:11
20 0-8-11 1-14/11-7/6 utonal C~2/6 1-12/11-12/7 1/(12:11:7)
21 0-9-11 1-14/9-7/6 utonal C/ 1-9/7-3/2 1/(9:7:6)
22 0-1-12 1-11/9-10/7 swetismic C~(\~5)
23 0-3-12 1-11/6-10/7 swetismic C/(b5) 1-9/7-7/5
24 0-4-12 1-9/8-10/7 werckismic C2(\~5)
25 0-8-12 1-14/11-10/7 werckismic C(\~5)
26 0-9-12 1-14/9-10/7 swetismic C~2(b5) 1-12/11-7/5
27 0-11-12 1-7/6-10/7 swetismic C\m(\~5)
28 0-1-13 1-11/9-7/4 werckismic C~,\7no5
29 0-2-13 1-3/2-7/4 otonal C\7no3 4:6:7
30 0-4-13 1-9/8-7/4 otonal C\9no35 4:7:9
31 0-5-13 1-11/8-7/4 otonal C(~5) 1-14/11-16/11 8:11:14
32 0-8-13 1-14/11-7/4 utonal C,\7 1/(14:11:8)
33 0-9-13 1-14/9-7/4 utonal C/,2no5 1-9/8-9/7 1/(9:8:7)
34 0-11-13 1-7/6-7/4 utonal C\m7no5 1/(7:6:4)
35 0-12-13 1-10/7-7/4 werckismic C~(b5) 1-11/9-7/5
36 0-8-20 1-14/11-20/11 otonal C,\~7no5 11:14:20
37 0-9-20 1-14/9-20/11 swetismic
38 0-11-20 1-7/6-20/11 swetismic C\m\~7no5
39 0-12-20 1-10/7-20/11 utonal C(b5) 1/(20:14:11)
40 0-1-21 1-11/9-10/9 otonal C~,\9no5 9:10:11
41 0-8-21 1-14/11-10/9 werckismic C,\9no5
42 0-9-21 1-14/9-10/9 otonal C/(\~5) 1-9/7-10/7 7:9:10
43 0-12-21 1-10/7-10/9 utonal C\2(\~5) 1/(10:9:7)
44 0-13-21 1-7/4-10/9 werckismic C\2\m7no5
45 0-20-21 1-20/11-10/9 utonal 1/(20:18:11)
46 0-2-23 1-3/2-5/3 otonal C\m7no5 1-6/5-9/5 5:6:9
47 0-3-23 1-11/6-5/3 otonal 6:10:11
48 0-11-23 1-7/6-5/3 otonal C\m6no5 6:7:10
49 0-12-23 1-10/7-5/3 utonal C/dim 1-7/6-7/5 1/(10:7:6)
50 0-20-23 1-20/11-5/3 utonal 1/(20:12:11)
51 0-21-23 1-10/9-5/3 utonal C/7no3 1-3/2-9/5 1/(9:6:5)
52 0-2-25 1-3/2-5/4 otonal C\ 4:5:6
53 0-4-25 1-9/8-5/4 otonal C\,9no5 4:5:9
54 0-5-25 1-11/8-5/4 otonal C\(\b5) 8:10:11
55 0-12-25 1-10/7-5/4 utonal C\(\~5) 1/(10:8:7)
56 0-13-25 1-7/4-5/4 otonal C\7no5 4:5:6
57 0-20-25 1-20/11-5/4 utonal C\,\~7no5 1/(20:16:11)
58 0-21-25 1-10/9-5/4 utonal C/9no35 1-9/5-9/4 1/(9:5:4)
59 0-23-25 1-5/3-5/4 utonal C/m 1-6/5-3/2 1/(6:5:4)

Tetrads

# Genspans Transversal Type Name Inversion As harmonics
or subharmonics
1 0-1-2-3 1-11/9-3/2-11/6 rastmic C~7
2 0-1-2-4 1-11/9-3/2-9/8 rastmic C~,9
3 0-1-3-4 1-11/9-11/6-9/8 rastmic C~9no5
4 0-2-3-4 1-3/2-11/6-9/8 rastmic C~9no3
5 0-1-2-5 1-11/9-3/2-11/8 rastmic C~,~11
6 0-1-3-5 1-11/9-11/6-11/8 utonal C2~6 or
C4~9 		1-9/8-3/2-18/11
1-4/3-3/2-24/11 		1/(18:16:12:11)
1/(24:18:16:11)
7 0-2-3-5 1-3/2-11/6-11/8 ambitonal C~4~7
8 0-1-4-5 1-11/9-9/8-11/8 rastmic
9 0-2-4-5 1-3/2-9/8-11/8 otonal C4~7 1-4/3-3/2-11/6 6:8:9:11
10 0-3-4-5 1-11/6-9/8-11/8 rastmic C~11no35
11 0-3-4-8 1-11/6-9/8-14/11 parahemif C9(~7)no5
12 0-3-5-8 1-11/6-11/8-14/11 hemimin C~2~11 1-12/11-11/8-3/2
13 0-4-5-8 1-9/8-11/8-14/11 parahemif C~,~9 1-11/9-3/2-13/12
14 0-1-4-9 1-11/9-9/8-14/9 parahemif C~,9(^5)
15 0-1-5-9 1-11/9-11/8-14/9 pentacircle C,~6,9no5 1-14/11-18/11-9/4
16 0-4-5-9 1-9/8-11/8-14/9 pentacircle C~,7(\b5) 1-11/9-11/8-16/9
17 0-4-8-9 1-9/8-14/11-14/9 pentacircle
18 0-5-8-9 1-11/8-14/11-14/9 parahemif
19 0-2-3-11 1-3/2-11/6-7/6 otonal C\m~7 6:7:9:11
20 0-3-8-11 1-11/6-14/11-7/6 hemimin
21 0-8-9-11 1-14/11-14/9-7/6 utonal C/,~6 1-9/7-3/2-18/11 1/(18:14:12:11)
22 0-1-3-12 1-11/9-11/6-10/7 swetismic C\m~6 1-7/6-3/2-13/8
23 0-1-4-12 1-11/9-9/8-10/7 jove
24 0-3-4-12 1-11/6-9/8-10/7 jove
25 0-3-8-12 1-11/6-14/11-10/7 hemififths
26 0-4-8-12 1-9/8-14/11-10/7 pele C9no5 1-9/8-14/11-16/9
27 0-1-9-12 1-11/9-14/9-10/7 swetismic
28 0-4-9-12 1-9/8-14/9-10/7 hemififths
29 0-8-9-12 1-14/11-14/9-10/7 jove
30 0-3-11-12 1-11/6-7/6-10/7 swetismic
31 0-8-11-12 1-14/11-7/6-10/7 jove
32 0-9-11-12 1-14/9-7/6-10/7 swetismic
33 0-1-2-13 1-11/9-3/2-7/4 jove C~,\7
34 0-1-4-13 1-11/9-9/8-7/4 jove
35 0-2-4-13 1-3/2-9/8-7/4 otonal C\9no3 4:6:7:9
36 0-1-5-13 1-11/9-11/8-7/4 werckismic
37 0-2-5-13 1-3/2-11/8-7/4 otonal C~4,\7 8:11:12:14
38 0-4-5-13 1-9/8-11/8-7/4 otonal C~4\7,9 or C~,7(^5) 1-11/9-14/9-16/9 9:11:14:16
39 0-4-8-13 1-9/8-14/11-7/4 pentacircle
40 0-5-8-13 1-11/8-14/11-7/4 hemimin
41 0-1-9-13 1-11/9-14/9-7/4 werckismic
42 0-4-9-13 1-9/8-14/9-7/4 pentacircle
43 0-5-9-13 1-11/8-14/9-7/4 pentacircle
44 0-8-9-13 1-14/11-14/9-7/4 utonal 1/(14:11:9:8)
45 0-2-11-13 1-3/2-7/6-7/4 ambitonal C\m7
46 0-8-11-13 1-14/11-7/6-7/4 utonal 1/(14:12:11:8)
47 0-9-11-13 1-14/9-7/6-7/4 utonal C/,9 1-9/7-3/2-9/4 1/(9:7:6:4)
48 0-1-12-13 1-11/9-10/7-7/4 jove
49 0-4-12-13 1-9/8-10/7-7/4 werckismic
50 0-8-12-13 1-14/11-10/7-7/4 werckismic
51 0-9-12-13 1-14/9-10/7-7/4 jove
52 0-11-12-13 1-7/6-10/7-7/4 jove C~,/6 1-11/9-3/2-12/7
53 0-8-9-20 1-14/11-14/9-20/11 swetismic
54 0-8-11-20 1-14/11-7/6-20/11 swetismic
55 0-9-11-20 1-14/9-7/6-20/11 swetismic
56 0-8-12-20 1-14/11-10/7-20/11 werckismic
57 0-9-12-20 1-14/9-10/7-20/11 swetismic
58 0-11-12-20 1-7/6-10/7-20/11 swetismic
59 0-1-9-21 1-11/9-14/9-10/9 otonal 9:10:11:14
60 0-8-9-21 1-14/11-14/9-10/9 werckismic
61 0-1-12-21 1-11/9-10/7-10/9 swetismic
62 0-8-12-21 1-14/11-10/7-10/9 werckismic
63 0-9-12-21 1-14/9-10/7-10/9 swetismic
64 0-1-13-21 1-11/9-7/4-10/9 werckismic
65 0-8-13-21 1-14/11-7/4-10/9 werckismic
66 0-9-13-21 1-14/9-7/4-10/9 werckismic
67 0-12-13-21 1-10/7-7/4-10/9 werckismic
68 0-8-20-21 1-14/11-20/11-10/9 werckismic
69 0-9-20-21 1-14/9-20/11-10/9 swetismic
70 0-12-20-21 1-10/7-20/11-10/9 utonal 1/(20:18:14:11)
71 0-2-3-23 1-3/2-11/6-5/3 otonal 6:9:10:11
72 0-2-11-23 1-3/2-7/6-5/3 otonal C\m6 6:7:9:10
73 0-3-11-23 1-11/6-7/6-5/3 otonal C\m6~7no5 6:7:10:11
74 0-3-12-23 1-11/6-10/7-5/3 swetismic
75 0-11-12-23 1-7/6-10/7-5/3 swetismic C\m6(\~5)
76 0-11-20-23 1-7/6-20/11-5/3 swetismic
77 0-12-20-23 1-10/7-20/11-5/3 utonal 1/(20:14:12:11)
78 0-12-21-23 1-10/7-10/9-5/3 utonal C/7 1-9/7-3/2-9/5 1/(9:7:6:5)
79 0-20-21-23 1-20/11-10/9-5/3 utonal C/7~13no3 1-3/2-18/11-9/5 1/(18:12:11:10)
80 0-2-4-25 1-3/2-9/8-5/4 otonal C\,9 4:5:6:9
81 0-2-5-25 1-3/2-11/8-5/4 otonal C\,~11 8:10:11:12
82 0-4-5-25 1-9/8-11/8-5/4 otonal C\,9(\b5) 8:9:10:11
83 0-4-12-25 1-9/8-10/7-5/4 werckismic C,9(\~5)
84 0-2-13-25 1-3/2-7/4-5/4 otonal C\7 4:5:6:7
85 0-4-13-25 1-9/8-7/4-5/4 otonal C\9no5 4:5:7:9
86 0-5-13-25 1-11/8-7/4-5/4 otonal C\7~11no5 4:5:7:11
87 0-12-13-25 1-10/7-7/4-5/4 werckismic C\7(\~5)
88 0-12-20-25 1-10/7-20/11-5/4 utonal C,\7(b5) 1-14/11-7/5-7/4 1/(20:16:14:11)
89 0-12-21-25 1-10/7-10/9-5/4 utonal C/9no5 1-9/7-9/5-9/4 1/(10:9:8:7)
90 0-13-21-25 1-7/4-10/9-5/4 werckismic C\7\9no5
91 0-20-21-25 1-20/11-10/9-5/4 utonal C2~6^7no5 1-18/11-9/5-9/4 1/(20:18:16:11)
92 0-2-23-25 1-3/2-5/3-5/4 ambitonal C\6 or C/m7 1-6/5-3/2-9/5
93 0-12-23-25 1-10/7-5/3-5/4 utonal C/m6
C\m7(b5) 		1-6/5-3/2-12/7
1-7/6-7/5-7/4 		1/(12:10:8:7)
1/(7:6:5:4)
94 0-20-23-25 1-20/11-5/3-5/4 utonal C/m,~9 1-6/5-3/2-24/11 1/(24:20:18:11)
95 0-21-23-25 1-10/9-5/3-5/4 utonal C/9no3 1-3/2-9/5-9/4 1/(9:6:5:4)

Pentads

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

Hexads

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