# 265edo

 ← 264edo 265edo 266edo →
Prime factorization 5 × 53
Step size 4.5283¢
Fifth 155\265 (701.887¢) (→31\53)
Semitones (A1:m2) 25:20 (113.2¢ : 90.57¢)
Consistency limit 9
Distinct consistency limit 9

265 equal divisions of the octave (abbreviated 265edo or 265ed2), also called 265-tone equal temperament (265tet) or 265 equal temperament (265et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 265 equal parts of about 4.53 ¢ each. Each step represents a frequency ratio of 21/265, or the 265th root of 2.

265 = 5 × 53, and 265edo is enfactored in the 5-limit, tempering out the same commas as 53edo, including 15625/15552 and 32805/32768. In the 7-limit it tempers out 16875/16807 and 420175/419904, so that it supports sqrtphi, for which it provides the optimal patent val. In the 11-limit it tempers out 540/539, 1375/1372 and 4375/4356, and gives the optimal patent val for 11-limit sqrtphi temperament.

### Prime harmonics

Approximation of prime harmonics in 265edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.00 -0.07 -1.41 +0.23 +1.13 +1.74 -0.80 +1.35 +1.16 -1.65 +0.62
Relative (%) +0.0 -1.5 -31.1 +5.1 +25.1 +38.3 -17.8 +29.9 +25.6 -36.5 +13.8
Steps
(reduced)
265
(0)
420
(155)
615
(85)
744
(214)
917
(122)
981
(186)
1083
(23)
1126
(66)
1199
(139)
1287
(227)
1313
(253)

### Subsets and supersets

265edo contains 5edo and 53edo as subsets. 795edo, which triples it, corrects its harmonic 5 to near-just quality.

A step of 265edo is exactly 40 türk sents.