24edt: Difference between revisions
Jump to navigation
Jump to search
Created page with "'''24EDT''' is the equal division of the third harmonic into 24 parts of 79.2481 cents each, corresponding to 15.1423 edo (similar to every seventh step o..." Tags: Mobile edit Mobile web edit |
No edit summary Tags: Mobile edit Mobile web edit |
||
| Line 1: | Line 1: | ||
'''24EDT''' is the [[Edt|equal division of the third harmonic]] into 24 parts of 79.2481 [[cent|cents]] each, corresponding to 15.1423 [[edo]] (similar to every seventh step of [[106edo]]). | '''24EDT''' is the [[Edt|equal division of the third harmonic]] into 24 parts of 79.2481 [[cent|cents]] each, corresponding to 15.1423 [[edo]] (similar to every seventh step of [[106edo]]). It is related to the rank-three temperament which tempers out 325/324, 625/624, and 468512/468195 in the 13-limit, which is supported by [[15edo|15]], [[106edo|106]], [[121edo|121]], [[212edo|212]], and [[227edo|227]] EDOs. | ||
{| class="wikitable" | {| class="wikitable" | ||
| Line 133: | Line 133: | ||
| | [[3/2|just perfect fifth]] plus an octave | | | [[3/2|just perfect fifth]] plus an octave | ||
|} | |} | ||
==Related temperament== | |||
===11-limit 15&106&212=== | |||
Commas: 15625/15552, 585640/583443 | |||
POTE generators: ~7/4 = 968.8778, ~22/21 = 79.2597 | |||
Map: [<1 0 1 0 -1|, <0 24 20 0 25|, <0 0 0 1 1|] | |||
EDOs: 15, 106, 121, 212, 227 | |||
===13-limit 15&106&212=== | |||
Commas: 325/324, 625/624, 468512/468195 | |||
POTE generators: ~7/4 = 968.8187, ~22/21 = 79.2727 | |||
Map: [<1 0 1 0 -1 0|, <0 24 20 0 25 56|, <0 0 0 1 1 0|] | |||
EDOs: 15, 106, 121, 212, 227 | |||
[[Category:Edt]] | [[Category:Edt]] | ||
[[Category:Edonoi]] | [[Category:Edonoi]] | ||
Revision as of 12:28, 13 February 2019
24EDT is the equal division of the third harmonic into 24 parts of 79.2481 cents each, corresponding to 15.1423 edo (similar to every seventh step of 106edo). It is related to the rank-three temperament which tempers out 325/324, 625/624, and 468512/468195 in the 13-limit, which is supported by 15, 106, 121, 212, and 227 EDOs.
| degree | cents value | corresponding JI intervals |
comments |
|---|---|---|---|
| 0 | 0.0000 | exact 1/1 | |
| 1 | 79.2481 | 22/21 | |
| 2 | 158.4963 | ||
| 3 | 237.7444 | 39/34 | |
| 4 | 316.9925 | 6/5 | |
| 5 | 396.2406 | 44/35 | |
| 6 | 475.4888 | ||
| 7 | 554.7369 | ||
| 8 | 633.9850 | 75/52 | |
| 9 | 713.2331 | ||
| 10 | 792.4813 | 30/19, 19/12 | |
| 11 | 871.7294 | ||
| 12 | 950.9775 | 45/26, 26/15 | |
| 13 | 1030.2256 | ||
| 14 | 1109.4738 | 36/19, 19/10 | |
| 15 | 1188.7219 | ||
| 16 | 1267.9700 | 52/25 | |
| 17 | 1347.2181 | ||
| 18 | 1426.4663 | ||
| 19 | 1505.7144 | 105/44 | |
| 20 | 1584.9625 | 5/2 | |
| 21 | 1664.2106 | 34/13 | |
| 22 | 1743.4588 | ||
| 23 | 1822.7069 | 63/22 | |
| 24 | 1901.9550 | exact 3/1 | just perfect fifth plus an octave |
Related temperament
11-limit 15&106&212
Commas: 15625/15552, 585640/583443
POTE generators: ~7/4 = 968.8778, ~22/21 = 79.2597
Map: [<1 0 1 0 -1|, <0 24 20 0 25|, <0 0 0 1 1|]
EDOs: 15, 106, 121, 212, 227
13-limit 15&106&212
Commas: 325/324, 625/624, 468512/468195
POTE generators: ~7/4 = 968.8187, ~22/21 = 79.2727
Map: [<1 0 1 0 -1 0|, <0 24 20 0 25 56|, <0 0 0 1 1 0|]
EDOs: 15, 106, 121, 212, 227