72edo: Difference between revisions
m →Regular temperament properties: correct and improve some associated ratios |
added dupminor and dudmajor, other small changes too |
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| Line 129: | Line 129: | ||
| 133.333 | | 133.333 | ||
| 27/25, 13/12, 14/13 | | 27/25, 13/12, 14/13 | ||
| v~2 | | ^^m2, | ||
| downmid 2nd | v~2 | ||
| dupminor 2nd, | |||
downmid 2nd | |||
| ^^Eb | | ^^Eb | ||
| Om2 | | Om2 | ||
| Line 151: | Line 153: | ||
| 166.667 | | 166.667 | ||
| 11/10 | | 11/10 | ||
| ^~2 | | ^~2, | ||
| upmid 2nd | vvM2 | ||
| upmid 2nd, | |||
dudmajor 2nd | |||
| vvE | | vvE | ||
| oM2 | | oM2 | ||
| Line 261: | Line 265: | ||
| 333.333 | | 333.333 | ||
| 40/33, 17/14 | | 40/33, 17/14 | ||
| v~3 | | ^^m3, | ||
| downmid 3rd | v~3 | ||
| dupminor 3rd, | |||
downmid 3rd | |||
| ^^F | | ^^F | ||
| Om3 | | Om3 | ||
| Line 283: | Line 289: | ||
| 366.667 | | 366.667 | ||
| 99/80, 16/13, 21/17 | | 99/80, 16/13, 21/17 | ||
| ^~3 | | ^~3, | ||
| upmid 3rd | vvM3 | ||
| upmid 3rd, | |||
dudmajor 3rd | |||
| vvF# | | vvF# | ||
| oM3 | | oM3 | ||
| Line 427: | Line 435: | ||
| 7/5 | | 7/5 | ||
| vA4, vd5 | | vA4, vd5 | ||
| downaug 4th, downdim 5th | | downaug 4th, | ||
downdim 5th | |||
| vG#, vAb | | vG#, vAb | ||
| kA4, ld5 | | kA4, ld5 | ||
| Line 460: | Line 469: | ||
| 36/25, 13/9 | | 36/25, 13/9 | ||
| v~5, ^^d5 | | v~5, ^^d5 | ||
| downmid 5th, dupdim 5th | | downmid 5th, | ||
dupdim 5th | |||
| ^^Ab | | ^^Ab | ||
| SA4, KKd5 | | SA4, KKd5 | ||
| Line 591: | Line 601: | ||
| 833.333 | | 833.333 | ||
| 81/50, 13/8 | | 81/50, 13/8 | ||
| v~6 | | ^^m6, | ||
| downmid 6th | v~6 | ||
| dupminor 6th, | |||
downmid 6th | |||
| ^^Bb | | ^^Bb | ||
| Om6 | | Om6 | ||
| Line 613: | Line 625: | ||
| 866.667 | | 866.667 | ||
| 33/20, 28/17 | | 33/20, 28/17 | ||
| ^~6 | | ^~6, | ||
| upmid 6th | vvM6 | ||
| upmid 6th, | |||
dudmajor 6th | |||
| vvB | | vvB | ||
| oM6 | | oM6 | ||
| Line 723: | Line 737: | ||
| 1033.333 | | 1033.333 | ||
| 20/11 | | 20/11 | ||
| v~7 | | ^^m7, | ||
| downmid 7th | v~7 | ||
| dupminor 7th, | |||
downmid 7th | |||
| ^^C | | ^^C | ||
| Om7 | | Om7 | ||
| Line 745: | Line 761: | ||
| 1066.667 | | 1066.667 | ||
| 50/27 | | 50/27 | ||
| ^~7 | | ^~7, | ||
| upmid 7th | vvM7 | ||
| upmid 7th, | |||
dudmajor 7th | |||
| vvC# | | vvC# | ||
| oM7, sd8 | | oM7, sd8 | ||
| Line 857: | Line 875: | ||
| zo | | zo | ||
| (a b 0 1) | | (a b 0 1) | ||
| 7/6, 7/ | | 7/6, 7/4 | ||
|- | |- | ||
| minor | | minor | ||
| Line 869: | Line 887: | ||
| 6/5, 9/5 | | 6/5, 9/5 | ||
|- | |- | ||
| rowspan="2" |downmid | | rowspan="2" |dupminor, | ||
downmid | |||
| luyo | | luyo | ||
| (a b 1 0 -1) | | (a b 1 0 -1) | ||
| Line 880: | Line 899: | ||
| rowspan="2" | mid | | rowspan="2" | mid | ||
| ilo | | ilo | ||
| (a | | (a b 0 0 1) | ||
| 11/9, 11/6 | | 11/9, 11/6 | ||
|- | |- | ||
| lu | | lu | ||
| (a | | (a b 0 0 -1) | ||
| 12/11, 18/11 | | 12/11, 18/11 | ||
|- | |- | ||
| rowspan="2" |upmid | | rowspan="2" |upmid, | ||
dudmajor | |||
| logu | | logu | ||
| (a b -1 0 1) | | (a b -1 0 1) | ||
| Line 908: | Line 928: | ||
| dupmajor | | dupmajor | ||
| ru | | ru | ||
| (a | | (a b 0 -1) | ||
| 9/7, 12/7 | | 9/7, 12/7 | ||
|- | |||
| rowspan="2" |trupmajor, | |||
trudminor | |||
|thogu | |||
|(a b -1 0 0 1) | |||
|13/10 | |||
|- | |||
|thuyo | |||
|(a b 1 0 0 -1) | |||
|15/13 | |||
|} | |} | ||
All 72edo chords can be named using ups and downs. An up, down or mid after the chord root affects the 3rd, 6th, 7th, and/or the 11th (every other note of a stacked-3rds chord 6-1-3-5-7-9-11-13). Alterations are always enclosed in parentheses, additions never are. Here are the zo, gu, ilo, yo and ru triads: | All 72edo chords can be named using ups and downs. An up, down or mid after the chord root affects the 3rd, 6th, 7th, and/or the 11th (every other note of a stacked-3rds chord 6-1-3-5-7-9-11-13). Alterations are always enclosed in parentheses, additions never are. Here are the zo, gu, ilo, yo and ru triads: | ||
| Line 959: | Line 989: | ||
For a more complete list, see [[Ups and Downs Notation #Chord names in other EDOs]]. | For a more complete list, see [[Ups and Downs Notation #Chord names in other EDOs]]. | ||
=== | === Relationship between primes and rings === | ||
In 72tet, there are 6 [[Ring number|rings]]. 12edo is the plain ring; thus every 6 degrees is the 3-limit. | |||
Then, after each subsequent degree in reverse, a new prime limit is unveiled from it: | Then, after each subsequent degree in reverse, a new prime limit is unveiled from it: | ||
* -1 degree corrects 5/4 | * -1 degree (the down ring) corrects 81/64 to 5/4 via 80/81 | ||
* -2 degrees corrects 7/4 | * -2 degrees (the dud ring) corrects 16/9 to 7/4 via 63/64 | ||
* +3 degrees corrects 11/8 | * +3 degrees (the trup ring)corrects 4/3 to 11/8 via 33/32 | ||
* +2 degrees corrects 13/8 | * +2 degrees (the dup ring) corrects 128/81 to 13/8 via 1053/1024 | ||
* 0 | * 0 degrees (the plain ring) corrects 256/243 to 17/16 via 4131/4096 | ||
* 0 degrees (the plain ring) corrects 32/27 to 19/16 via 513/512 | |||
Thus the product of a ratio's monzo with (0 0 -1 -2 3 2 0 0), modulo 6, specifies which ring the ratio lies on. | |||
== Notations == | == Notations == | ||