# 279edo

← 278edo | 279edo | 280edo → |

^{2}× 31**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 2^{1/279}, 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 (%) | +0.0 | -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) |

### Subsets and supersets

Since 279 factors into 3^{2} × 31, 279edo has subset edos 3, 9, 31, and 93.