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

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.

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

==== Ringer 311[+61] ====

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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; it's unknown whether Ringer 311 possesses any special properties that are not a direct result of 311edo's special properties as a temperament).
+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.
+It's unknown whether Ringer 311 possesses any special properties that are not a direct result of 311edo's special properties as a temperament).
 ==== Ringer 311[+61] ====