265edo

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← 264edo265edo266edo →
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 265-tone equal temperament (265tet), 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 of 265edo represents a frequency ratio of 21/265, or the 265th root of 2.

It is contorted 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 temperament, 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 -2 -31 +5 +25 +38 -18 +30 +26 -36 +14
Steps
(reduced)
265
(0)
420
(155)
615
(85)
744
(214)
917
(122)
981
(186)
1083
(23)
1126
(66)
1199
(139)
1287
(227)
1313
(253)