# 279edo

 ← 278edo 279edo 280edo →
Prime factorization 32 × 31
Step size 4.30108¢
Fifth 163\279 (701.075¢)
Semitones (A1:m2) 25:22 (107.5¢ : 94.62¢)
Consistency limit 7
Distinct consistency limit 7

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

Approximation of prime harmonics in 279edo
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 32 × 31, 279edo has subset edos 3, 9, 31, and 93.