473edo: Difference between revisions

473edo is inconsistent to the 5-odd-limit with large errors on both harmonics 3 and 5. The equal temperament is most notable for tempering out the kleisma, 15625/15552, in the 5-limit and 5120/5103 in the 7-limit, providing the optimal patent val for the 7-limit countercata temperament.

Approximation of odd harmonics in 473edo
Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	+0.79	-0.69	+0.31	-0.95	-0.79	-0.78	+0.10	-0.94	-0.68	+1.10	+0.90
Error	Relative (%)	+31.3	-27.2	+12.1	-37.5	-31.1	-30.8	+4.1	-37.0	-27.0	+43.4	+35.5
Steps (reduced)		750 (277)	1098 (152)	1328 (382)	1499 (80)	1636 (217)	1750 (331)	1848 (429)	1933 (41)	2009 (117)	2078 (186)	2140 (248)

Since 473 factors into 11 × 43, 473edo contains 11edo and 43edo as subsets.

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-The '''473 equal division''' divides the octave into 473 equal parts of 2.537 cents each. It tempers out the kleisma, 15625/15552, in the 5-limit and 5120/5103 in the 7-limit, providing the [[Optimal_patent_val|optimal patent val]] for 7-limit [[Kleismic_family#Countercata|countercata temperament]].
+{{EDO intro|473}}
+edo is in[[consistent]] to the [[5-odd-limit]] with large errors on both [[harmonic]]s [[3/1|3]] and [[5/1|5]]. The equal temperament is most notable for [[tempering out]] the kleisma, [[15625/15552]], in the 5-limit and [[5120/5103]] in the 7-limit, providing the [[optimal patent val]] for the 7-limit [[countercata]] temperament.
+=== Odd harmonics ===
+{{Harmonics in equal|473}}
+=== Subsets and supersets ===
+Since 473 factors into {{factorization|473}}, 473edo contains [[11edo]] and [[43edo]] as subsets.
-[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
 [[Category:Countercata]]
-[[Category:Kleisma]]
+[[Category:Kleismic]]
-[[category:todo:expand]]

Revision as of 06:38, 3 November 2023