185edo: Difference between revisions

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'''185edo''' is the [[EDO|equal division of the octave]] into 185 parts of 6.4865 [[cent]]s each. It [[tempering out|tempers out]] the [[comma]]s 126/125, 1029/1024, 6144/6125 and 243/242, making it useful for various purposes. It is an excellent tuning for [[Starling family|starling temperament]], the [[7-limit]] [[Planar Temperament|planar temperament]] tempering out 126/125; [[Starling family#Valentine temperament|valentine temperament]], which also tempers out 1029/1024; and the rank three 89&154&185 temperament tempering out 126/125 and 243/242. With 185cff, the val <185 293 429 519 640 686|, it makes for a first-class tuning of the 13-limit [[Gamelismic clan#Miracle-Miraculous|miraculous temperament]].

=== ~~Prime~~ harmonics ===

== Theory ==

The [[patent val]] of 185edo [[tempering out|tempers out]] [[126/125]], [[1029/1024]], [[6144/6125]] in the 7-limit, and [[243/242]] in the 11-limit, making it useful for various purposes. It is an excellent tuning for [[starling]], the [[7-limit]] [[planar temperament]] tempering out 126/125; [[valentine]], which also tempers out 1029/1024; and [[cuckoo]], tempering out 126/125 and 243/242.

Using the 185c val, it tempers out [[225/224]] and 1029/1024 in the 7-limit, 243/242, [[385/384]], [[441/440]], and [[540/539]] in the 11-limit, providing a great alternative to [[72edo]] for [[miracle]]. With the 185cf val {{val| 185 293 '''429''' 519 640 '''684''' }}, it makes for an excellent tuning of 13-limit [[manna]]. Meanwhile the 185cff val {{val| 185 293 '''429''' 519 640 '''686''' }} is a first-class tuning of 13-limit [[miraculous]].

=== Odd harmonics ===

=== Subsets and supersets ===

Since 185 factors into {{factorization|185}}, 185edo contains [[5edo]] and [[37edo]] as its subsets.

== Scales ==

* [[nova]]

* [[novadene]]

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

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 {{Infobox ET}}
-'''185edo''' is the [[EDO|equal division of the octave]] into 185 parts of 6.4865 [[cent]]s each. It [[tempering out|tempers out]] the [[comma]]s 126/125, 1029/1024, 6144/6125 and 243/242, making it useful for various purposes. It is an excellent tuning for [[Starling family|starling temperament]], the [[7-limit]] [[Planar Temperament|planar temperament]] tempering out 126/125; [[Starling family#Valentine temperament|valentine temperament]], which also tempers out 1029/1024; and the rank three 89&amp;154&amp;185 temperament tempering out 126/125 and 243/242. With 185cff, the val &lt;185 293 429 519 640 686|, it makes for a first-class tuning of the 13-limit [[Gamelismic clan#Miracle-Miraculous|miraculous temperament]].
+{{ED intro}}
-=== Prime harmonics ===
+== Theory ==
+The [[patent val]] of 185edo [[tempering out|tempers out]] [[126/125]], [[1029/1024]], [[6144/6125]] in the 7-limit, and [[243/242]] in the 11-limit, making it useful for various purposes. It is an excellent tuning for [[starling]], the [[7-limit]] [[planar temperament]] tempering out 126/125; [[valentine]], which also tempers out 1029/1024; and [[cuckoo]], tempering out 126/125 and 243/242.
+Using the 185c val, it tempers out [[225/224]] and 1029/1024 in the 7-limit, 243/242, [[385/384]], [[441/440]], and [[540/539]] in the 11-limit, providing a great alternative to [[72edo]] for [[miracle]]. With the 185cf val {{val| 185 293 '''429''' 519 640 '''684''' }}, it makes for an excellent tuning of 13-limit [[manna]]. Meanwhile the 185cff val {{val| 185 293 '''429''' 519 640 '''686''' }} is a first-class tuning of 13-limit [[miraculous]].
+=== Odd harmonics ===
 {{Harmonics in equal|185}}
+=== Subsets and supersets ===
+Since 185 factors into {{factorization|185}}, 185edo contains [[5edo]] and [[37edo]] as its subsets.
 == Scales ==
 * [[nova]]
 * [[novadene]]
-[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->