491edo: Difference between revisions

Revision as of 06:08, 3 November 2023

In the 5-limit the equal temperament tempers out the parakleisma, [8 14 -13⟩; in the 7-limit 65625/65536 and 420175/419904; in the 11-limit 441/440 and 8019/8000; in the 13-limit 729/728 and 4225/4224, and provides the optimal patent val for 11-limit history, tempering out 441/440 and 4000/3993.

Approximation of odd harmonics in 491edo
Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	-0.53	-0.16	-1.01	-1.06	+1.02	+0.21	-0.69	+0.14	+0.65	+0.91	-0.17
Error	Relative (%)	-21.7	-6.7	-41.1	-43.3	+41.9	+8.4	-28.3	+5.6	+26.8	+37.2	-6.9
Steps (reduced)		778 (287)	1140 (158)	1378 (396)	1556 (83)	1699 (226)	1817 (344)	1918 (445)	2007 (43)	2086 (122)	2157 (193)	2221 (257)

491edo is the 94th prime edo.

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-'''491EDO''' is the [[EDO|equal division of the octave]] into 491 parts of 2.44399 [[cent]]s each. In the 5-limit it tempers out the parakleima, |8 14 -13&gt;; in the 7-limit 65625/65536 and 420175/419904; in the 11-limit 441/440 and 8019/8000; in the 13-limit 729/728 and 4225/4224, and provides the [[Optimal_patent_val|optimal patent val]] for 11-limit [[Werckismic_temperaments#History|history temperament]], tempering out 441/440 and 4000/3993.
+{{EDO intro|491}}
-EDO is the 94th [[prime EDO]].
+In the 5-limit the equal temperament [[tempering out|tempers out]] the [[parakleisma]], {{monzo| 8 14 -13 }}; in the 7-limit [[65625/65536]] and 420175/419904; in the 11-limit [[441/440]] and [[8019/8000]]; in the 13-limit [[729/728]] and [[4225/4224]], and provides the [[optimal patent val]] for 11-limit [[history (temperament)|history]], tempering out 441/440 and 4000/3993.
-[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
+=== Odd harmonics ===
-[[Category:Prime EDO]]
+{{Harmonics in equal|491}}
+=== Subsets and supersets ===
+edo is the 94th [[prime edo]].