Extension and restriction: Difference between revisions

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Some extensions are so "canonical" that it makes little sense to speak of any other way to extend to their expanded subgroup, and often little sense to speak of the original temperament in the restricted subgroup (an example of that being [[Ennealimma#Ennealimmal|Ennealimmal]], which while technically a 5-limit temperament, it is practically always referred in its [[Ennealimmal|7-limit form]].)

In any case, a strong extension has the same [[mapping]] as the original temperament with the original primes, while weak extensions have a mapping that ~~either subdivides either the [[equave]] or the/~~a [[Generator-offset property|generator]]. Additionally, a strong extension's [[pergen]] is the same as the original temperament's pergen.

In any case, a strong extension has the same [[mapping]] as the original temperament with the original primes, while weak extensions have a mapping that splits a [[Generator-offset property|generator]] or the [[equave]]. Additionally, a strong extension's [[pergen]] is the same as the original temperament's pergen, while a weak extension might either split the fifth, or use a completely different generator, such as [[Ploidacot/Omega-tricot|(P8, P4/3)]].

== See also ==

@@ Line 23: / Line 23: @@
 Some extensions are so "canonical" that it makes little sense to speak of any other way to extend to their expanded subgroup, and often little sense to speak of the original temperament in the restricted subgroup (an example of that being [[Ennealimma#Ennealimmal|Ennealimmal]], which while technically a 5-limit temperament, it is practically always referred in its [[Ennealimmal|7-limit form]].)
-In any case, a strong extension has the same [[mapping]] as the original temperament with the original primes, while weak extensions have a mapping that either subdivides either the [[equave]] or the/a [[Generator-offset property|generator]]. Additionally, a strong extension's [[pergen]] is the same as the original temperament's pergen.
+In any case, a strong extension has the same [[mapping]] as the original temperament with the original primes, while weak extensions have a mapping that splits a [[Generator-offset property|generator]] or the [[equave]]. Additionally, a strong extension's [[pergen]] is the same as the original temperament's pergen, while a weak extension might either split the fifth, or use a completely different generator, such as [[Ploidacot/Omega-tricot|(P8, P4/3)]].
 == See also ==