Defactoring: Difference between revisions

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== enfactored mappings vs. enfactored comma-bases ==

One may pose the question: what is the relationship between an enfactored mapping and an enfactored comma-basis? Can you have one but not the other? Must you? Or must you not? Or does the question even make sense? Certainly at least some ~~thinkers~~ have suggested these cases are meaningfully independent<ref>such as ~~in [[Kite Giedraitis]]'s writings on~~ [[Color_notation/Temperament_Names|color notation]], which ~~read~~ "it's possible that there is both torsion and contorsion"</ref>.

One may pose the question: what is the relationship between an enfactored mapping and an enfactored comma-basis? Can you have one but not the other? Must you? Or must you not? Or does the question even make sense? Certainly at least some have suggested these cases are meaningfully independent<ref>such as the page [[Color_notation/Temperament_Names|color notation]], which reads "it's possible that there is both torsion and contorsion"</ref>.

The conclusion we arrive at here is that because enfactored comma-bases don't make any sense, or at least don't represent any legitimately new musical information of any kind that their unenfactored version doesn't already represent, it is not generally useful to think of enfactored mappings and enfactored comma-bases as independent phenomena. It only makes sense to speak of enfactored temperaments. Of course, one will often use the term "enfactored mapping" because enfactored mappings are the kind which do have some musical purpose, and often the enfactored mapping will be being used to represent the enfactored temperament — or temperoid, that is.

@@ Line 155: / Line 155: @@
 == enfactored mappings vs. enfactored comma-bases ==
-One may pose the question: what is the relationship between an enfactored mapping and an enfactored comma-basis? Can you have one but not the other? Must you? Or must you not? Or does the question even make sense? Certainly at least some thinkers have suggested these cases are meaningfully independent<ref>such as in [[Kite Giedraitis]]'s writings on [[Color_notation/Temperament_Names|color notation]], which read "it's possible that there is both torsion and contorsion"</ref>.
+One may pose the question: what is the relationship between an enfactored mapping and an enfactored comma-basis? Can you have one but not the other? Must you? Or must you not? Or does the question even make sense? Certainly at least some have suggested these cases are meaningfully independent<ref>such as the page [[Color_notation/Temperament_Names|color notation]], which reads "it's possible that there is both torsion and contorsion"</ref>.
 The conclusion we arrive at here is that because enfactored comma-bases don't make any sense, or at least don't represent any legitimately new musical information of any kind that their unenfactored version doesn't already represent, it is not generally useful to think of enfactored mappings and enfactored comma-bases as independent phenomena. It only makes sense to speak of enfactored temperaments. Of course, one will often use the term "enfactored mapping" because enfactored mappings are the kind which do have some musical purpose, and often the enfactored mapping will be being used to represent the enfactored temperament — or temperoid, that is.