Generator form manipulation: Difference between revisions

Line 1:

A [[~~User:Cmloegcmluin/Defactored_canonical_form~~|canonical mapping form]] is an important standard to have as community for uniquely identifying [[temperaments]], but it is not the only mapping form one should ever need, because one may wish to use differently-sized [[generators]]. Several such forms with different generator sizes have been presented, such as [[Normal_lists#Positive_generator_form|positive generator form]], [[Normal_lists#Equave-reduced_generator_form|equave-reduced generator form]], and [[Normal_lists#Minimal_generator_form|minimal-generator form]].

A [[canonical_form|canonical mapping form]] is an important standard to have as community for uniquely identifying [[temperaments]], but it is not the only mapping form one should ever need, because one may wish to use differently-sized [[generators]]. Several such forms with different generator sizes have been presented, such as [[Normal_lists#Positive_generator_form|positive generator form]], [[Normal_lists#Equave-reduced_generator_form|equave-reduced generator form]], and [[Normal_lists#Minimal_generator_form|minimal-generator form]].

If two mappings are equivalent, i.e. they have the same canonical form and therefore represent the same temperament, then their corresponding generators are equivalent too. That doesn't mean their generators are the same sizes; it only means that in combination with each other, their generators reach the same set of pitches.

Revision as of 21:33, 11 October 2021 view source Cmloegcmluin (talk \| contribs) autopatrolled, emailconfirmed 5,160 edits fix bad vector and map templates ← Older edit		Revision as of 23:44, 15 October 2021 view source Cmloegcmluin (talk \| contribs) autopatrolled, emailconfirmed 5,160 edits update link Newer edit →
Line 1:		Line 1:
	A [[~~User:Cmloegcmluin/Defactored_canonical_form~~\|canonical mapping form]] is an important standard to have as community for uniquely identifying [[temperaments]], but it is not the only mapping form one should ever need, because one may wish to use differently-sized [[generators]]. Several such forms with different generator sizes have been presented, such as [[Normal_lists#Positive_generator_form\|positive generator form]], [[Normal_lists#Equave-reduced_generator_form\|equave-reduced generator form]], and [[Normal_lists#Minimal_generator_form\|minimal-generator form]].		A [[canonical_form\|canonical mapping form]] is an important standard to have as community for uniquely identifying [[temperaments]], but it is not the only mapping form one should ever need, because one may wish to use differently-sized [[generators]]. Several such forms with different generator sizes have been presented, such as [[Normal_lists#Positive_generator_form\|positive generator form]], [[Normal_lists#Equave-reduced_generator_form\|equave-reduced generator form]], and [[Normal_lists#Minimal_generator_form\|minimal-generator form]].

	If two mappings are equivalent, i.e. they have the same canonical form and therefore represent the same temperament, then their corresponding generators are equivalent too. That doesn't mean their generators are the same sizes; it only means that in combination with each other, their generators reach the same set of pitches.		If two mappings are equivalent, i.e. they have the same canonical form and therefore represent the same temperament, then their corresponding generators are equivalent too. That doesn't mean their generators are the same sizes; it only means that in combination with each other, their generators reach the same set of pitches.