265edo: Difference between revisions

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-The '''265 equal division''' divides the octave into 265 equal parts of 4.528 cents each. It is [[contorted]] in the 5-limit, tempering out the same commas as [[53edo|53edo]], including 15625/15552 and 32805/32768. In the 7-limit it tempers out 16875/16807 and 420175/419904, so that it [[support]]s [[Kleismic_family#Sqrtphi|sqrtphi temperament]], for which it provides the [[Optimal_patent_val|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.
+{{Infobox ET}}
+{{ED intro}}
-[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
+= 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 ===
+edo 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]]