279edo
| ← 278edo | 279edo | 280edo → |
279 equal divisions of the octave (abbreviated 279edo or 279ed2), also called 279-tone equal temperament (279tet) or 279 equal temperament (279et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 279 equal parts of about 4.3 ¢ each. Each step represents a frequency ratio of 21/279, or the 279th root of 2.
279edo 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 is close to the syntonic comma, 81/80. Unfortunately, it is not compatible with the patent val, but the 279c val.
Prime harmonics
| 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 | -20 | +18 | -25 | -18 | -42 | -40 | -17 | -7 | -38 | -22 | |
| Steps (reduced) |
279 (0) |
442 (163) |
648 (90) |
783 (225) |
965 (128) |
1032 (195) |
1140 (24) |
1185 (69) |
1262 (146) |
1355 (239) |
1382 (266) | |
Subsets and supersets
Since 279 factors into 32 × 31, 279edo has subset edos 3, 9, 31, and 93.