Transversal: Difference between revisions

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In the language of mathematics, a '''transversal''' is a selection of one representative element from each set of a collection of sets. Transversals may be used to define scales tempered by a [[regular temperament]] in a way which is precise, useful for several purposes, and independent of the exact tuning used by the temperament. For each note of a scale which is defined in ''p''-limit temperament, there is a set of ''p''-limit rational intervals which is tempered by the temperament to that note. This gives us a collection of sets, and selecting a representative element from each set gives us a transversal. Transversals may also be used to denote all of the intervals of a regular temperament, usually by confining the intervals of the transversal to a subgroup of the group tempered by the temperament. For instance, Pythagorean tuning provides a transversal for meantone.

== See also ==

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[[Category:Transversal scales| ]]

~~[[Category:~~Todo:review]]

~~[[Category:Todo:~~add examples]]

~~[[Category:Todo:add introduction]] ~~

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-In the language of mathematics, a '''transversal''' is a selection of one representative element from each set of a collection of sets. Transversals may be used to define scales tempered by a [[regular temperament]] in a way which is precise, useful for several purposes, and independent of the exact tuning used by the temperament. For each note of a scale which is defined in ''p''-limit temperament, there is a set of ''p''-limit rational intervals which is tempered by the temperament to that note. This gives us a collection of sets, and selecting a representative element from each set gives us a transversal. Transversals may also be used to denote all  of the intervals of a regular temperament, usually by confining the intervals of the transversal to a subgroup of the group tempered by the temperament. For instance, Pythagorean tuning provides a transversal for meantone.
+In the language of mathematics, a '''transversal''' is a selection of one representative element from each set of a collection of sets. Transversals may be used to define scales tempered by a [[regular temperament]] in a way which is precise, useful for several purposes, and independent of the exact tuning used by the temperament. For each note of a scale which is defined in ''p''-limit temperament, there is a set of ''p''-limit rational intervals which is tempered by the temperament to that note. This gives us a collection of sets, and selecting a representative element from each set gives us a transversal. Transversals may also be used to denote all of the intervals of a regular temperament, usually by confining the intervals of the transversal to a subgroup of the group tempered by the temperament. For instance, Pythagorean tuning provides a transversal for meantone.
 == See also ==
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 [[Category:Transversal scales| ]]  <!-- sort order in category: this page shows above A -->
-[[Category:Todo:review]]
+{{Todo| review | add examples }}
-[[Category:Todo:add examples]]
-[[Category:Todo:add introduction]] <!-- Isn't this page about traversal scales? -->