Elf: Difference between revisions
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Wikispaces>genewardsmith **Imported revision 397123474 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 397124154 - Original comment: ** |
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<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>2013-01-09 17: | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2013-01-09 17:55:29 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>397124154</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> | ||
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[[elfmagic7]] | [[elfmagic7]] | ||
[[elfmagic8]] | [[elfmagic8]] | ||
[[ | [[elfmagic8d]] | ||
[[elfmagic9]] | [[elfmagic9]] | ||
[[elfmagic10]] | [[elfmagic10]] | ||
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<a class="wiki_link" href="/elfmagic7">elfmagic7</a><br /> | <a class="wiki_link" href="/elfmagic7">elfmagic7</a><br /> | ||
<a class="wiki_link" href="/elfmagic8">elfmagic8</a><br /> | <a class="wiki_link" href="/elfmagic8">elfmagic8</a><br /> | ||
<a class="wiki_link" href="/ | <a class="wiki_link" href="/elfmagic8d">elfmagic8d</a><br /> | ||
<a class="wiki_link" href="/elfmagic9">elfmagic9</a><br /> | <a class="wiki_link" href="/elfmagic9">elfmagic9</a><br /> | ||
<a class="wiki_link" href="/elfmagic10">elfmagic10</a></body></html></pre></div> | <a class="wiki_link" href="/elfmagic10">elfmagic10</a></body></html></pre></div> | ||
Revision as of 17:55, 9 January 2013
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 2013-01-09 17:55:29 UTC.
- The original revision id was 397124154.
- 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:
An //elf// is a scale in a [[regular temperament]] which is tempered from a JI scale in the group of the temperament which is [[Periodic scale|epimorphic]] via a val V which may not be, and characteristically is not, a val supporting the temperament. This allows the elf to have more freedom in scale size and structure but still to possess the coherence induced by the epimorphic mapping. To construct an elf, take the intervals in the JI group of the temperament which lie within an octave and keep only the least complex (in terms of [[Benedetti height]]) representative for each corresponding interval of the temperament. Order the remaining JI intervals by increasing temperamental complexity, breaking ties by increasing Benedetti complexity. For each integer value 1 ≤ i ≤ V(2), set the ith element of a [[transversal]] for the scale to be the first interval c in the listing such that V(c) = i. The tempering of this transversal by a tuning map for the temperament is the elf. =Examples= ==11-limit magic== [[elfmagic7]] [[elfmagic8]] [[elfmagic8d]] [[elfmagic9]] [[elfmagic10]]
Original HTML content:
<html><head><title>Elves</title></head><body>An <em>elf</em> is a scale in a <a class="wiki_link" href="/regular%20temperament">regular temperament</a> which is tempered from a JI scale in the group of the temperament which is <a class="wiki_link" href="/Periodic%20scale">epimorphic</a> via a val V which may not be, and characteristically is not, a val supporting the temperament. This allows the elf to have more freedom in scale size and structure but still to possess the coherence induced by the epimorphic mapping.<br /> <br /> To construct an elf, take the intervals in the JI group of the temperament which lie within an octave and keep only the least complex (in terms of <a class="wiki_link" href="/Benedetti%20height">Benedetti height</a>) representative for each corresponding interval of the temperament. Order the remaining JI intervals by increasing temperamental complexity, breaking ties by increasing Benedetti complexity. For each integer value 1 ≤ i ≤ V(2), set the ith element of a <a class="wiki_link" href="/transversal">transversal</a> for the scale to be the first interval c in the listing such that V(c) = i. The tempering of this transversal by a tuning map for the temperament is the elf.<br /> <br /> <!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="Examples"></a><!-- ws:end:WikiTextHeadingRule:0 -->Examples</h1> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h2> --><h2 id="toc1"><a name="Examples-11-limit magic"></a><!-- ws:end:WikiTextHeadingRule:2 -->11-limit magic</h2> <a class="wiki_link" href="/elfmagic7">elfmagic7</a><br /> <a class="wiki_link" href="/elfmagic8">elfmagic8</a><br /> <a class="wiki_link" href="/elfmagic8d">elfmagic8d</a><br /> <a class="wiki_link" href="/elfmagic9">elfmagic9</a><br /> <a class="wiki_link" href="/elfmagic10">elfmagic10</a></body></html>