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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 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)
|}
|}


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