181edo: Difference between revisions

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== Theory ==

181edo is only consistent to the [[7-odd-limit]], though ~~besides~~ [[10/9]] and [[~~9/5~~]] ~~all intervals are~~ consistent in the 21-odd-limit, ~~and~~ it ~~has low errors~~ on primes ~~all the way up to~~ 43~~. It even does well beyond that~~, ~~with less than 30% error on all primes up~~ to ~~137~~, ~~besides 47, 61, 73, 97~~, and ~~113~~. 181et [[tempering out|tempers out]] 2109375/2097152 ([[semicomma]]) and {{monzo| 14 -22 9 }} in the 5-limit; [[2401/2400]], [[5120/5103]], and 390625/387072 in the 7-limit ([[support]]ing the [[hemififths]] and the [[cotritone]]). Using the patent val, it tempers out [[385/384]], 1375/1372, [[2200/2187]], and [[4000/3993]] in the 11-limit; [[325/324]], [[352/351]], [[847/845]], and [[1575/1573]] in the 13-limit.

181edo is only [[consistent]] to the [[7-odd-limit]], though except for [[9/5]], [[23/20]] and their [[octave complement]]s, it is consistent to the [[23-odd-limit]]. Beyond that, it does well on [[prime interval|primes]] [[37/1|37]] and [[43/1|43]], and has unambiguous though not accurate approximations to [[29/1|29]], [[31/1|31]], and [[41/1|41]].

As an equal temperament, 181et [[tempering out|tempers out]] 2109375/2097152 ([[semicomma]]) and {{monzo| 14 -22 9 }} in the 5-limit; [[2401/2400]], [[5120/5103]], and 390625/387072 in the 7-limit ([[support]]ing the [[hemififths]] and the [[cotritone]]). Using the patent val, it tempers out [[385/384]], 1375/1372, [[2200/2187]], and [[4000/3993]] in the 11-limit; [[325/324]], [[352/351]], [[847/845]], and [[1575/1573]] in the 13-limit.

=== Prime harmonics ===

{{Harmonics in equal|181|columns=11|start=12|collapsed=true|title=Approximation of prime harmonics in 181edo (continued)}}

=== Subsets and supersets ===

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 == Theory ==
-edo is only consistent to the [[7-odd-limit]], though besides [[10/9]] and [[9/5]] all intervals are consistent in the 21-odd-limit, and it has low errors on primes all the way up to 43. It even does well beyond that, with less than 30% error on all primes up to 137, besides 47, 61, 73, 97, and 113. 181et [[tempering out|tempers out]] 2109375/2097152 ([[semicomma]]) and {{monzo| 14 -22 9 }} in the 5-limit; [[2401/2400]], [[5120/5103]], and 390625/387072 in the 7-limit ([[support]]ing the [[hemififths]] and the [[cotritone]]). Using the patent val, it tempers out [[385/384]], 1375/1372, [[2200/2187]], and [[4000/3993]] in the 11-limit; [[325/324]], [[352/351]], [[847/845]], and [[1575/1573]] in the 13-limit.
+edo is only [[consistent]] to the [[7-odd-limit]], though except for [[9/5]], [[23/20]] and their [[octave complement]]s, it is consistent to the [[23-odd-limit]]. Beyond that, it does well on [[prime interval|primes]] [[37/1|37]] and [[43/1|43]], and has unambiguous though not accurate approximations to [[29/1|29]], [[31/1|31]], and [[41/1|41]].
+As an equal temperament, 181et [[tempering out|tempers out]] 2109375/2097152 ([[semicomma]]) and {{monzo| 14 -22 9 }} in the 5-limit; [[2401/2400]], [[5120/5103]], and 390625/387072 in the 7-limit ([[support]]ing the [[hemififths]] and the [[cotritone]]). Using the patent val, it tempers out [[385/384]], 1375/1372, [[2200/2187]], and [[4000/3993]] in the 11-limit; [[325/324]], [[352/351]], [[847/845]], and [[1575/1573]] in the 13-limit.
 === Prime harmonics ===
-{{Harmonics in equal|181}}{{Harmonics in equal|181|start=12}}{{Harmonics in equal|181|start=23}}
+{{Harmonics in equal|181|columns=11}}
+{{Harmonics in equal|181|columns=11|start=12|collapsed=true|title=Approximation of prime harmonics in 181edo (continued)}}
 === Subsets and supersets ===