1131edo: Difference between revisions

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~~'''1131edo''' divides the octave into 1131 equal parts of 1.0610 cents each.~~

~~Using the patent val, it tempers out 1600000/1594323 (~~[[~~amity comma~~]]~~) in~~ the [[5-limit]]~~, 2401/2400 (~~[[~~breedsma~~]]~~) and 4802000/4782969 (~~[[~~canousma~~]]~~) in the~~ [[~~7-limit~~]], ~~3025/3024 (lehmerisma), 41503/41472, and 151262/151250 in the~~ [[~~11-limit~~]]~~. It provides the~~ [[~~optimal patent val~~]] ~~for~~ [[~~amicable~~]] ~~temperament~~, ~~the rank-~~2 ~~temperament that tempers out 2401/2400 and 1600000/1594323, and for~~ [[~~canou family|canou temperament~~]]~~, the rank-3 temperament that tempers out 4802000/4782969~~.

1131edo is in[[consistent]] to the [[5-odd-limit]] and [[harmonic]] [[3/1|3]] is about halfway between its steps. Otherwise, it has good approximations to harmonics [[5/1|5]], [[7/1|7]], [[9/1|9]], [[13/1|13]], making it suitable for a 2.9.5.7.13 [[subgroup]] interpretation.

1131 factors into ~~3 × 13 × 29 with divisors~~ 3, 13, 29, 39, 87 and 377, and it shares the ~~major third of [[~~5~~/4]]~~ with [[87edo]].

Meanwhile using the [[patent val]], the equal temperament [[Tempering out|tempers out]] 1600000/1594323 ([[amity comma]]) in the [[5-limit]], 2401/2400 ([[breedsma]]) and 4802000/4782969 ([[canousma]]) in the [[7-limit]], [[3025/3024]], [[41503/41472]], and 151262/151250 in the [[11-limit]]. It provides the [[optimal patent val]] for [[amicable]] temperament, the rank-2 temperament that tempers out 2401/2400 and 1600000/1594323, and for [[canou temperament]], the rank-3 temperament that tempers out 4802000/4782969.

=== Odd harmonics ===

=== Subsets and supersets ===

Since 1131 factors into {{factorization|1131}}, 1131edo has subset edos 3, 13, 29, 39, 87 and 377, and it shares the excellent approximation to harmonic 5 with [[87edo]].

~~[[Category:Equal divisions of the octave]]~~

[[Category:Amicable]]

[[Category:Canou]]

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-'''1131edo''' divides the octave into 1131 equal parts of 1.0610 cents each.
+{{Infobox ET}}
+{{ED intro}}
-Using the patent val, it tempers out 1600000/1594323 ([[amity comma]]) in the [[5-limit]], 2401/2400 ([[breedsma]]) and 4802000/4782969 ([[canousma]]) in the [[7-limit]], 3025/3024 (lehmerisma), 41503/41472, and 151262/151250 in the [[11-limit]]. It provides the [[optimal patent val]] for [[amicable]] temperament, the rank-2 temperament that tempers out 2401/2400 and 1600000/1594323, and for [[canou family|canou temperament]], the rank-3 temperament that tempers out 4802000/4782969.
+edo is in[[consistent]] to the [[5-odd-limit]] and [[harmonic]] [[3/1|3]] is about halfway between its steps. Otherwise, it has good approximations to harmonics [[5/1|5]], [[7/1|7]], [[9/1|9]], [[13/1|13]], making it suitable for a 2.9.5.7.13 [[subgroup]] interpretation.
-factors into 3 × 13 × 29 with divisors 3, 13, 29, 39, 87 and 377, and it shares the major third of [[5/4]] with [[87edo]].
+Meanwhile using the [[patent val]], the equal temperament [[Tempering out|tempers out]] 1600000/1594323 ([[amity comma]]) in the [[5-limit]], 2401/2400 ([[breedsma]]) and 4802000/4782969 ([[canousma]]) in the [[7-limit]], [[3025/3024]], [[41503/41472]], and 151262/151250 in the [[11-limit]]. It provides the [[optimal patent val]] for [[amicable]] temperament, the rank-2 temperament that tempers out 2401/2400 and 1600000/1594323, and for [[canou temperament]], the rank-3 temperament that tempers out 4802000/4782969.
+=== Odd harmonics ===
+{{Harmonics in equal|1131}}
+=== Subsets and supersets ===
+Since 1131 factors into {{factorization|1131}}, 1131edo has subset edos 3, 13, 29, 39, 87 and 377, and it shares the excellent approximation to harmonic 5 with [[87edo]].
-[[Category:Equal divisions of the octave]]
 [[Category:Amicable]]
 [[Category:Canou]]