1131edo: Difference between revisions

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'''1131edo''' divides the octave into 1131 equal parts of 1.0610 cents each.
{{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 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 ===
{{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|####]] <!-- 4-digit number -->
[[Category:Amicable]]
[[Category:Amicable]]
[[Category:Canou]]
[[Category:Canou]]