Transversal: Difference between revisions
Jump to navigation
Jump to search
Wikispaces>genewardsmith **Imported revision 174652329 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 513936958 - Original comment: ** |
||
| Line 1: | Line 1: | ||
<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt> | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2014-06-14 10:31:48 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>513936958</tt>.<br> | ||
: The revision comment was: <tt></tt><br> | : The revision comment was: <tt></tt><br> | ||
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | ||
<h4>Original Wikitext content:</h4> | <h4>Original Wikitext content:</h4> | ||
<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</pre></div> | <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> | ||
<h4>Original HTML content:</h4> | <h4>Original HTML content:</h4> | ||
<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</body></html></pre></div> | <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> | ||
Revision as of 10:31, 14 June 2014
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.
- The revision comment was:
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>