Elf: Difference between revisions
Jump to navigation
Jump to search
Wikispaces>genewardsmith **Imported revision 398749630 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 398749698 - 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>2013-01-15 19:11: | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2013-01-15 19:11:41 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>398749698</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> | ||
| Line 73: | Line 73: | ||
=Rank three examples= | =Rank three examples= | ||
==11-limit | ==11-limit jove== | ||
[[elfjove7]] | [[elfjove7]] | ||
[[elfjove8d]] | [[elfjove8d]] | ||
| Line 99: | Line 99: | ||
<!-- ws:end:WikiTextTocRule:35 --><!-- ws:start:WikiTextTocRule:36: --><div style="margin-left: 2em;"><a href="#Rank two examples-11-limit valentine">11-limit valentine</a></div> | <!-- ws:end:WikiTextTocRule:35 --><!-- ws:start:WikiTextTocRule:36: --><div style="margin-left: 2em;"><a href="#Rank two examples-11-limit valentine">11-limit valentine</a></div> | ||
<!-- ws:end:WikiTextTocRule:36 --><!-- ws:start:WikiTextTocRule:37: --><div style="margin-left: 1em;"><a href="#Rank three examples">Rank three examples</a></div> | <!-- ws:end:WikiTextTocRule:36 --><!-- ws:start:WikiTextTocRule:37: --><div style="margin-left: 1em;"><a href="#Rank three examples">Rank three examples</a></div> | ||
<!-- ws:end:WikiTextTocRule:37 --><!-- ws:start:WikiTextTocRule:38: --><div style="margin-left: 2em;"><a href="#Rank three examples-11-limit | <!-- ws:end:WikiTextTocRule:37 --><!-- ws:start:WikiTextTocRule:38: --><div style="margin-left: 2em;"><a href="#Rank three examples-11-limit jove">11-limit jove</a></div> | ||
<!-- ws:end:WikiTextTocRule:38 --><!-- ws:start:WikiTextTocRule:39: --><div style="margin-left: 2em;"><a href="#Rank three examples-11-limit portent">11-limit portent</a></div> | <!-- ws:end:WikiTextTocRule:38 --><!-- ws:start:WikiTextTocRule:39: --><div style="margin-left: 2em;"><a href="#Rank three examples-11-limit portent">11-limit portent</a></div> | ||
<!-- ws:end:WikiTextTocRule:39 --><!-- ws:start:WikiTextTocRule:40: --></div> | <!-- ws:end:WikiTextTocRule:39 --><!-- ws:start:WikiTextTocRule:40: --></div> | ||
| Line 168: | Line 168: | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:20:&lt;h1&gt; --><h1 id="toc10"><a name="Rank three examples"></a><!-- ws:end:WikiTextHeadingRule:20 -->Rank three examples</h1> | <!-- ws:start:WikiTextHeadingRule:20:&lt;h1&gt; --><h1 id="toc10"><a name="Rank three examples"></a><!-- ws:end:WikiTextHeadingRule:20 -->Rank three examples</h1> | ||
<!-- ws:start:WikiTextHeadingRule:22:&lt;h2&gt; --><h2 id="toc11"><a name="Rank three examples-11-limit | <!-- ws:start:WikiTextHeadingRule:22:&lt;h2&gt; --><h2 id="toc11"><a name="Rank three examples-11-limit jove"></a><!-- ws:end:WikiTextHeadingRule:22 -->11-limit jove</h2> | ||
<a class="wiki_link" href="/elfjove7">elfjove7</a><br /> | <a class="wiki_link" href="/elfjove7">elfjove7</a><br /> | ||
<a class="wiki_link" href="/elfjove8d">elfjove8d</a><br /> | <a class="wiki_link" href="/elfjove8d">elfjove8d</a><br /> | ||
Revision as of 19:11, 15 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 2013-01-15 19:11:41 UTC.
- The original revision id was 398749698.
- 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:
[[toc]] =Definition of elves= 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; which is to say, the interval of least temperamental complexity with ties broken by Benedetti height. The tempering of this transversal by a tuning map for the temperament is the elf. =Rank two examples= ==13-limit leapday== [[elfleapday7]] [[elfleapday8d]] [[elfleapday9]] [[elfleapday10]] [[elfleapday12f]] ==11-limit magic== [[elfmagic7]] [[elfmagic8]] [[elfmagic8d]] [[elfmagic9]] [[elfmagic10]] [[elfmagic12]] ==11-limit miracle== [[elfmiracle7]] [[elfmiracle8d]] [[elfmiracle9]] [[elfmiracle10]] [[elfmiracle12]] ==13-limit myna== [[elfmyna7]] [[elfmyna8d]] [[elfmyna9]] [[elfmyna10]] [[elfmyna12f]] ==13-limit octacot== [[elfoctacot7]] [[elfoctacot8d]] [[elfoctacot9]] [[elfoctacot10]] [[elfoctacot12f]] ==13-limit qilin== [[elfqilin7]] [[elfqilin8d]] [[elfqilin9]] [[elfqilin10]] [[elfqilin12f]] ==13-limit sensus== [[elfsensus7]] [[elfsensus8d]] [[elfsensus9]] [[elfsensus10]] [[elfsensus12]] [[elfsensus12f]] ==11-limit valentine== [[elfvalentine7]] [[elfvalentine8d]] [[elfvalentine9]] [[elfvalentine10]] [[elfvalentine12]] =Rank three examples= ==11-limit jove== [[elfjove7]] [[elfjove8d]] [[elfjove9]] [[elfjove10]] [[elfjove11c]] [[elfjove12]] ==11-limit portent== [[elfportent9]] [[elfportent10]] [[elfportent11c]] [[elfportent12]] [[elfportent15]]
Original HTML content:
<html><head><title>Elves</title></head><body><!-- ws:start:WikiTextTocRule:26:<img id="wikitext@@toc@@normal" class="WikiMedia WikiMediaToc" title="Table of Contents" src="/site/embedthumbnail/toc/normal?w=225&h=100"/> --><div id="toc"><h1 class="nopad">Table of Contents</h1><!-- ws:end:WikiTextTocRule:26 --><!-- ws:start:WikiTextTocRule:27: --><div style="margin-left: 1em;"><a href="#Definition of elves">Definition of elves</a></div> <!-- ws:end:WikiTextTocRule:27 --><!-- ws:start:WikiTextTocRule:28: --><div style="margin-left: 1em;"><a href="#Rank two examples">Rank two examples</a></div> <!-- ws:end:WikiTextTocRule:28 --><!-- ws:start:WikiTextTocRule:29: --><div style="margin-left: 2em;"><a href="#Rank two examples-13-limit leapday">13-limit leapday</a></div> <!-- ws:end:WikiTextTocRule:29 --><!-- ws:start:WikiTextTocRule:30: --><div style="margin-left: 2em;"><a href="#Rank two examples-11-limit magic">11-limit magic</a></div> <!-- ws:end:WikiTextTocRule:30 --><!-- ws:start:WikiTextTocRule:31: --><div style="margin-left: 2em;"><a href="#Rank two examples-11-limit miracle">11-limit miracle</a></div> <!-- ws:end:WikiTextTocRule:31 --><!-- ws:start:WikiTextTocRule:32: --><div style="margin-left: 2em;"><a href="#Rank two examples-13-limit myna">13-limit myna</a></div> <!-- ws:end:WikiTextTocRule:32 --><!-- ws:start:WikiTextTocRule:33: --><div style="margin-left: 2em;"><a href="#Rank two examples-13-limit octacot">13-limit octacot</a></div> <!-- ws:end:WikiTextTocRule:33 --><!-- ws:start:WikiTextTocRule:34: --><div style="margin-left: 2em;"><a href="#Rank two examples-13-limit qilin">13-limit qilin</a></div> <!-- ws:end:WikiTextTocRule:34 --><!-- ws:start:WikiTextTocRule:35: --><div style="margin-left: 2em;"><a href="#Rank two examples-13-limit sensus">13-limit sensus</a></div> <!-- ws:end:WikiTextTocRule:35 --><!-- ws:start:WikiTextTocRule:36: --><div style="margin-left: 2em;"><a href="#Rank two examples-11-limit valentine">11-limit valentine</a></div> <!-- ws:end:WikiTextTocRule:36 --><!-- ws:start:WikiTextTocRule:37: --><div style="margin-left: 1em;"><a href="#Rank three examples">Rank three examples</a></div> <!-- ws:end:WikiTextTocRule:37 --><!-- ws:start:WikiTextTocRule:38: --><div style="margin-left: 2em;"><a href="#Rank three examples-11-limit jove">11-limit jove</a></div> <!-- ws:end:WikiTextTocRule:38 --><!-- ws:start:WikiTextTocRule:39: --><div style="margin-left: 2em;"><a href="#Rank three examples-11-limit portent">11-limit portent</a></div> <!-- ws:end:WikiTextTocRule:39 --><!-- ws:start:WikiTextTocRule:40: --></div> <!-- ws:end:WikiTextTocRule:40 --><br /> <!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="Definition of elves"></a><!-- ws:end:WikiTextHeadingRule:0 -->Definition of elves</h1> 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; which is to say, the interval of least temperamental complexity with ties broken by Benedetti height. The tempering of this transversal by a tuning map for the temperament is the elf.<br /> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h1> --><h1 id="toc1"><a name="Rank two examples"></a><!-- ws:end:WikiTextHeadingRule:2 -->Rank two examples</h1> <!-- ws:start:WikiTextHeadingRule:4:<h2> --><h2 id="toc2"><a name="Rank two examples-13-limit leapday"></a><!-- ws:end:WikiTextHeadingRule:4 -->13-limit leapday</h2> <a class="wiki_link" href="/elfleapday7">elfleapday7</a><br /> <a class="wiki_link" href="/elfleapday8d">elfleapday8d</a><br /> <a class="wiki_link" href="/elfleapday9">elfleapday9</a><br /> <a class="wiki_link" href="/elfleapday10">elfleapday10</a><br /> <a class="wiki_link" href="/elfleapday12f">elfleapday12f</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:6:<h2> --><h2 id="toc3"><a name="Rank two examples-11-limit magic"></a><!-- ws:end:WikiTextHeadingRule:6 -->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><br /> <a class="wiki_link" href="/elfmagic12">elfmagic12</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:8:<h2> --><h2 id="toc4"><a name="Rank two examples-11-limit miracle"></a><!-- ws:end:WikiTextHeadingRule:8 -->11-limit miracle</h2> <a class="wiki_link" href="/elfmiracle7">elfmiracle7</a><br /> <a class="wiki_link" href="/elfmiracle8d">elfmiracle8d</a><br /> <a class="wiki_link" href="/elfmiracle9">elfmiracle9</a><br /> <a class="wiki_link" href="/elfmiracle10">elfmiracle10</a><br /> <a class="wiki_link" href="/elfmiracle12">elfmiracle12</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:10:<h2> --><h2 id="toc5"><a name="Rank two examples-13-limit myna"></a><!-- ws:end:WikiTextHeadingRule:10 -->13-limit myna</h2> <a class="wiki_link" href="/elfmyna7">elfmyna7</a><br /> <a class="wiki_link" href="/elfmyna8d">elfmyna8d</a><br /> <a class="wiki_link" href="/elfmyna9">elfmyna9</a><br /> <a class="wiki_link" href="/elfmyna10">elfmyna10</a><br /> <a class="wiki_link" href="/elfmyna12f">elfmyna12f</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:12:<h2> --><h2 id="toc6"><a name="Rank two examples-13-limit octacot"></a><!-- ws:end:WikiTextHeadingRule:12 -->13-limit octacot</h2> <a class="wiki_link" href="/elfoctacot7">elfoctacot7</a><br /> <a class="wiki_link" href="/elfoctacot8d">elfoctacot8d</a><br /> <a class="wiki_link" href="/elfoctacot9">elfoctacot9</a><br /> <a class="wiki_link" href="/elfoctacot10">elfoctacot10</a><br /> <a class="wiki_link" href="/elfoctacot12f">elfoctacot12f</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:14:<h2> --><h2 id="toc7"><a name="Rank two examples-13-limit qilin"></a><!-- ws:end:WikiTextHeadingRule:14 -->13-limit qilin</h2> <a class="wiki_link" href="/elfqilin7">elfqilin7</a><br /> <a class="wiki_link" href="/elfqilin8d">elfqilin8d</a><br /> <a class="wiki_link" href="/elfqilin9">elfqilin9</a><br /> <a class="wiki_link" href="/elfqilin10">elfqilin10</a><br /> <a class="wiki_link" href="/elfqilin12f">elfqilin12f</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:16:<h2> --><h2 id="toc8"><a name="Rank two examples-13-limit sensus"></a><!-- ws:end:WikiTextHeadingRule:16 -->13-limit sensus</h2> <a class="wiki_link" href="/elfsensus7">elfsensus7</a><br /> <a class="wiki_link" href="/elfsensus8d">elfsensus8d</a><br /> <a class="wiki_link" href="/elfsensus9">elfsensus9</a><br /> <a class="wiki_link" href="/elfsensus10">elfsensus10</a><br /> <a class="wiki_link" href="/elfsensus12">elfsensus12</a><br /> <a class="wiki_link" href="/elfsensus12f">elfsensus12f</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:18:<h2> --><h2 id="toc9"><a name="Rank two examples-11-limit valentine"></a><!-- ws:end:WikiTextHeadingRule:18 -->11-limit valentine</h2> <a class="wiki_link" href="/elfvalentine7">elfvalentine7</a><br /> <a class="wiki_link" href="/elfvalentine8d">elfvalentine8d</a><br /> <a class="wiki_link" href="/elfvalentine9">elfvalentine9</a><br /> <a class="wiki_link" href="/elfvalentine10">elfvalentine10</a><br /> <a class="wiki_link" href="/elfvalentine12">elfvalentine12</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:20:<h1> --><h1 id="toc10"><a name="Rank three examples"></a><!-- ws:end:WikiTextHeadingRule:20 -->Rank three examples</h1> <!-- ws:start:WikiTextHeadingRule:22:<h2> --><h2 id="toc11"><a name="Rank three examples-11-limit jove"></a><!-- ws:end:WikiTextHeadingRule:22 -->11-limit jove</h2> <a class="wiki_link" href="/elfjove7">elfjove7</a><br /> <a class="wiki_link" href="/elfjove8d">elfjove8d</a><br /> <a class="wiki_link" href="/elfjove9">elfjove9</a><br /> <a class="wiki_link" href="/elfjove10">elfjove10</a><br /> <a class="wiki_link" href="/elfjove11c">elfjove11c</a><br /> <a class="wiki_link" href="/elfjove12">elfjove12</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:24:<h2> --><h2 id="toc12"><a name="Rank three examples-11-limit portent"></a><!-- ws:end:WikiTextHeadingRule:24 -->11-limit portent</h2> <a class="wiki_link" href="/elfportent9">elfportent9</a><br /> <a class="wiki_link" href="/elfportent10">elfportent10</a><br /> <a class="wiki_link" href="/elfportent11c">elfportent11c</a><br /> <a class="wiki_link" href="/elfportent12">elfportent12</a><br /> <a class="wiki_link" href="/elfportent15">elfportent15</a></body></html>