Transversal: Difference between revisions
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In the language of mathematics, a [http://en.wikipedia.org/wiki/Transversal 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 [http://en.wikipedia.org/wiki/Transversal 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. | ||
[[Category:Math]] | [[Category:Math]] | ||
[[Category:Theory]] | [[Category:Theory]] | ||
Revision as of 13:41, 5 December 2020
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.