265edo
| ← 264edo | 265edo | 266edo → |
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
| 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) | |
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.