Transversal
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author genewardsmith and made on 2014-06-14 10:31:48 UTC.
- The original revision id was 513936958.
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The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.
Original Wikitext content:
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 temperaments|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.
Original HTML content:
<html><head><title>Transversal</title></head><body>In the language of mathematics, a <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Transversal" rel="nofollow">transversal</a> 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 <a class="wiki_link" href="/Regular%20temperaments">regular temperament</a> 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.</body></html>