311edo/Ringer 311: Difference between revisions

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There are two known [[Ringer scale]]s based on [[311edo]]. Both include the complete mode 234 [[Overtone scale|of the harmonic series]] ([[234afdo]]) using non-[[patent val]]s of 311edo, which is believed to be the highest possible complete harmonic series mode mapped by a 311-form.

However, if one is looking for a Ringer scale, [[217edo#Ringer_217|217edo's corresponding Ringer 217]] may be preferred due to mapping all of mode 167 ([[167afdo]]), which is exceptional for its size (as a Ringer scale), just as [[311edo]] is exceptional for its size (as an [[edo]] interpreted as a temperament.

However, if one is looking for a Ringer scale, [[217edo#Ringer_217|217edo's corresponding Ringer 217]] may be preferred due to mapping all of mode 167 ([[167afdo]]), which is exceptional for its size (as a Ringer scale), just as [[311edo]] is exceptional for its size (as an [[edo]] interpreted as a [[temperament]]).

It's unknown whether Ringer 311 possesses any special properties that are not a direct result of 311edo's special properties as a temperament).

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==== Ringer 311[+61, &~~minus~~;67] ====

==== Ringer 311[+61, −67] ====

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[[Category:Just intonation scales]][[Category:311edo]]

[[Category:Just intonation scales]]

[[Category:Pages with mostly numerical content]][[Category:311edo]]

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+{{breadcrumb}}
 There are two known [[Ringer scale]]s based on [[311edo]]. Both include the complete mode 234 [[Overtone scale|of the harmonic series]] ([[234afdo]]) using non-[[patent val]]s of 311edo, which is believed to be the highest possible complete harmonic series mode mapped by a 311-form.
-However, if one is looking for a Ringer scale, [[217edo#Ringer_217|217edo's corresponding Ringer 217]] may be preferred due to mapping all of mode 167 ([[167afdo]]), which is exceptional for its size (as a Ringer scale), just as [[311edo]] is exceptional for its size (as an [[edo]] interpreted as a temperament.
+However, if one is looking for a Ringer scale, [[217edo#Ringer_217|217edo's corresponding Ringer 217]] may be preferred due to mapping all of mode 167 ([[167afdo]]), which is exceptional for its size (as a Ringer scale), just as [[311edo]] is exceptional for its size (as an [[edo]] interpreted as a [[temperament]]).
 It's unknown whether Ringer 311 possesses any special properties that are not a direct result of 311edo's special properties as a temperament).
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-==== Ringer 311[+61, &minus;67] ====
+==== Ringer 311[+61,&nbsp;−67] ====
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 {{col-end}}
-[[Category:Just intonation scales]][[Category:311edo]]
+[[Category:Just intonation scales]]
+[[Category:Pages with mostly numerical content]][[Category:311edo]]