265edo
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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
| ← 264edo | 265edo | 266edo → |
265 equal divisions of the octave (265edo), or 265-tone equal temperament (265tet), 265 equal temperament (265et) when viewed from a regular temperament perspective, is the tuning system that divides the octave into 265 equal parts of about 4.53 ¢ each.
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
| 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) | |