265edo: Difference between revisions

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.

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
Error	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)

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.

@@ Line 2: / Line 2: @@
 {{EDO intro|265}}
-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.
+= 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}}
+{{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:Equal divisions of the octave|###]] <!-- 3-digit number -->
+[[Category:Sqrtphi]]

Revision as of 04:50, 11 March 2024