265edo: Difference between revisions
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{{Infobox ET}} | |||
{{ED intro}} | |||
265 = 5 × 53, and 265edo is [[enfactoring|enfactored]] in the 5-limit, [[tempering out]] the same [[comma]]s as [[53edo]], including [[15625/15552]] and [[32805/32768]]. In the 7-limit it tempers out [[16875/16807]] and [[420175/419904]], so that it [[support]]s [[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 === | |||
{{Harmonics in equal|265}} | |||
=== 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 sent]]s. | |||
[[Category:Sqrtphi]] | |||
Latest revision as of 14:26, 20 February 2025
| ← 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 (%) | +0.0 | -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.