279edo: Difference between revisions
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'''279edo''' is the [[EDO|equal division of the octave]] into 279 parts of 4.3011 cents each | '''279edo''' is the [[EDO|equal division of the octave]] into 279 parts of 4.3011 cents each. | ||
[[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | == Theory == | ||
{{Harmonics in equal|279}} | |||
[[Category:Equal divisions of the octave|###]] | |||
It is closely related to [[31edo]], but the patent vals differ on the mapping for 3. It tempers out 78732/78125 (sensipent comma) and |-64 36 3> in the 5-limit, as well as |-68 18 17> (vavoom comma); 3136/3125, 19683/19600, and 823543/819200 in the 7-limit. Using the patent val, it tempers out 441/440, 5632/5625, 24057/24010, and 35937/35840 in the 11-limit; 351/350, 676/675, 1716/1715, 4225/4224, and 6656/6655 in the 13-limit. | |||
5 steps of 279edo closely represent the syntonic comma, [[81/80]].<!-- 3-digit number --> | |||
Revision as of 12:33, 15 September 2022
279edo is the equal division of the octave into 279 parts of 4.3011 cents each.
Theory
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | -0.88 | +0.78 | -1.08 | -0.78 | -1.82 | -1.73 | -0.74 | -0.32 | -1.62 | -0.95 |
| Relative (%) | +0.0 | -20.5 | +18.2 | -25.2 | -18.1 | -42.3 | -40.2 | -17.2 | -7.4 | -37.7 | -22.1 | |
| Steps (reduced) |
279 (0) |
442 (163) |
648 (90) |
783 (225) |
965 (128) |
1032 (195) |
1140 (24) |
1185 (69) |
1262 (146) |
1355 (239) |
1382 (266) | |
It is closely related to 31edo, but the patent vals differ on the mapping for 3. It tempers out 78732/78125 (sensipent comma) and |-64 36 3> in the 5-limit, as well as |-68 18 17> (vavoom comma); 3136/3125, 19683/19600, and 823543/819200 in the 7-limit. Using the patent val, it tempers out 441/440, 5632/5625, 24057/24010, and 35937/35840 in the 11-limit; 351/350, 676/675, 1716/1715, 4225/4224, and 6656/6655 in the 13-limit.
5 steps of 279edo closely represent the syntonic comma, 81/80.