Generator preimage: Difference between revisions
m Sintel moved page Transversal generators to Generator preimage: Use more common term over transversal |
add some basic examples to intro |
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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, the preimage generators of [[meantone]] are [[2/1]] and [[3/2]], and those of [[miracle]] are [[2/1]] and [[16/15]]. | |||
=Technical Definition= | =Technical Definition= | ||