Generator preimage: Difference between revisions
Cmloegcmluin (talk | contribs) I agree it's no good that this page doesn't link to Detempering, but isn't it better to give the explanatory link in the opening, since it's half of the name for this concept? |
m typo again |
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Also known as a '''generator preimage transversal''' or a '''generator [[detempering]]'''. Every [[generator]] of a [[regular temperament]] has a [[preimage]], which is an infinite set of JI intervals that map to it. A [[transversal]] means a selection of one representative element from each of a list of sets. So if for each generator in our temperament's list of generators we choose one JI interval that maps to it, then we have a generator preimage transversal for that temperament. | Also known as a '''generator preimage transversal''' or a '''generator [[detempering]]'''. Every [[generator]] of a [[regular temperament]] has a [[preimage]], which is an infinite set of JI intervals that map to it. A [[transversal]] means a selection of one representative element from each of a list of sets. So if for each generator in our temperament's list of generators we choose one JI interval that maps to it, then we have a generator preimage transversal for that temperament. | ||
Generator preimages are commonly used to describe temperaments. For example, [[meantone]] is generated by an octave and fifth, and the corresponding generator preimage is [[2/1]] and [[3/2]]. [[Miracle]] is generated by an octave and a semitone, corresponding to [[2/1]] and [[16/15]]~[[15/14]]. | |||
=Technical Definition= | =Technical Definition= | ||