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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | 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. |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| | [[Category:just]] |
| : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2014-06-14 10:31:48 UTC</tt>.<br>
| | [[Category:math]] |
| : The original revision id was <tt>513936958</tt>.<br>
| | [[Category:theory]] |
| : The revision comment was: <tt></tt><br>
| | [[Category:todo:add_examples]] |
| The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
| | [[Category:transversal]] |
| <h4>Original Wikitext content:</h4>
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| <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">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.</pre></div>
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| <h4>Original HTML content:</h4>
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| <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><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></pre></div>
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