Star and Nova: Difference between revisions
Wikispaces>genewardsmith **Imported revision 362257204 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 362273344 - 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>2012-09-05 13: | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-09-05 13:50:21 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>362273344</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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Since there are a finite number of 11-limit 8-note [[lesfip scales]], we may consider the [[star-lesfip|lesfip version of Star]], star-lesfip, to be canonical. It can be reached from a variety of starting points. Lesfipping the 5-limit transversal in the range 14 to 17 cents of tolerance leads to star; so does lesfiping the 46et version in the range from 9 to 17 cents or the 77et version in the range 6 to 16 cents. Another tuning for Star, not very different, is [[star|Star in 77et]]; 77 giving the optimal patent val for both 11-limit starling and valentine. | Since there are a finite number of 11-limit 8-note [[lesfip scales]], we may consider the [[star-lesfip|lesfip version of Star]], star-lesfip, to be canonical. It can be reached from a variety of starting points. Lesfipping the 5-limit transversal in the range 14 to 17 cents of tolerance leads to star; so does lesfiping the 46et version in the range from 9 to 17 cents or the 77et version in the range 6 to 16 cents. Another tuning for Star, not very different, is [[star|Star in 77et]]; 77 giving the optimal patent val for both 11-limit starling and valentine. | ||
==Chords of | ==Chords of Star== | ||
Star has sixteen [[dyadic chord|dyadic tetrads]], of eleven different types, which are among those listed on the [[chords of valentine]] page. In terms of what's listed on that page, star has one otonal tetrad, given in the form 1-8/7-10/7-12/7 but better known as 1-5/4-3/2-7/4; one 1-6/5-3/2-12/7 utonal tetrad; and one each of the [[keenanismic chords|keenanismic tetrads]] 1-8/7-11/8-12/7, 1-6/5-11/8-12/7, 1-5/4-10/7-12/7 and 1-5/4-3/2-12/7. It also has two each of the starling tetrad, the traditional diminished seventh chord of meantone; the ambitonal [[just added sixth chord]] 1-6/5-3/2-9/5; and the three 9-limit starling tetrads 1-6/5-10/7-9/5, 1-5/4-10/7-9/5 and 1-5/4-3/2-9/5. | Star has sixteen [[dyadic chord|dyadic tetrads]], of eleven different types, which are among those listed on the [[chords of valentine]] page. In terms of what's listed on that page, star has one otonal tetrad, given in the form 1-8/7-10/7-12/7 but better known as 1-5/4-3/2-7/4; one 1-6/5-3/2-12/7 utonal tetrad; and one each of the [[keenanismic chords|keenanismic tetrads]] 1-8/7-11/8-12/7, 1-6/5-11/8-12/7, 1-5/4-10/7-12/7 and 1-5/4-3/2-12/7. It also has two each of the starling tetrad, the traditional diminished seventh chord of meantone; the ambitonal [[just added sixth chord]] 1-6/5-3/2-9/5; and the three 9-limit starling tetrads 1-6/5-10/7-9/5, 1-5/4-10/7-9/5 and 1-5/4-3/2-9/5. | ||
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The transversal of Nova, when tempered by 126/125 (starling) temperament, leads to Nova. It can also be considered a scale of 7-limit valentine, for which both 77et and 185et will serve, the latter being the optimal patent val for both 7-limit starling and 7-limit valentine. In valentine, its notes in generator terms are -4, 0, 4, 5, 8, 9, 13 and 17, which in order of size are 0, 17, 4, 5, 8, 9, -4, 13. | The transversal of Nova, when tempered by 126/125 (starling) temperament, leads to Nova. It can also be considered a scale of 7-limit valentine, for which both 77et and 185et will serve, the latter being the optimal patent val for both 7-limit starling and 7-limit valentine. In valentine, its notes in generator terms are -4, 0, 4, 5, 8, 9, 13 and 17, which in order of size are 0, 17, 4, 5, 8, 9, -4, 13. | ||
The lesfip version of Nova, [[nova-lesfip]], can be reached by lesfiping the transversal in the tolerance range 14 to 21 cents. It can also be reached from the 46et, 77et, or 185et tunings. The tolerance ranges are a little broader than those for Star since the lesfipping is done with respect to tbe 9-limit diamond; it also works from the 11-limit diamond, with narrower limits like those of Star, since then the 100/99 equivalencies must be avoided.</pre></div> | The lesfip version of Nova, [[nova-lesfip]], can be reached by lesfiping the transversal in the tolerance range 14 to 21 cents. It can also be reached from the 46et, 77et, or 185et tunings. The tolerance ranges are a little broader than those for Star since the lesfipping is done with respect to tbe 9-limit diamond; it also works from the 11-limit diamond, with narrower limits like those of Star, since then the 100/99 equivalencies must be avoided. | ||
==Chords of Nova== | |||
Like Star, Nova has sixteen [[dyadic chord|dyadic tetrads]], of eleven different types, which are among those listed on the [[chords of valentine]] page. These are one major and one minor tetrad, two starling tetrads (diminished seventh), three 1-6/5-3/2-9/5 added sixth tetrads, two 1-5/4-3/2-9/5 starling tetrads, one each of the starling tetrads 1-6/5-10/7-9/5, 1-5/4-10/7-9/5 and 1-5/4-7/5-9/5; one 1-7/6-3/2-9/5 subminor tetrad, one 1-9/7-3/2-9/5 supermajor tetrad, and one 1-7/6-3/2-7/4 swiss tetrad. </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>Star and Nova</title></head><body><!-- ws:start:WikiTextTocRule: | <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>Star and Nova</title></head><body><!-- ws:start:WikiTextTocRule:18:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:18 --><!-- ws:start:WikiTextTocRule:19: --><a href="#Star">Star</a><!-- ws:end:WikiTextTocRule:19 --><!-- ws:start:WikiTextTocRule:20: --><!-- ws:end:WikiTextTocRule:20 --><!-- ws:start:WikiTextTocRule:21: --><!-- ws:end:WikiTextTocRule:21 --><!-- ws:start:WikiTextTocRule:22: --><!-- ws:end:WikiTextTocRule:22 --><!-- ws:start:WikiTextTocRule:23: --><!-- ws:end:WikiTextTocRule:23 --><!-- ws:start:WikiTextTocRule:24: --> | <a href="#Nova">Nova</a><!-- ws:end:WikiTextTocRule:24 --><!-- ws:start:WikiTextTocRule:25: --><!-- ws:end:WikiTextTocRule:25 --><!-- ws:start:WikiTextTocRule:26: --><!-- ws:end:WikiTextTocRule:26 --><!-- ws:start:WikiTextTocRule:27: --><!-- ws:end:WikiTextTocRule:27 --><!-- ws:start:WikiTextTocRule:28: --> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:28 --><br /> | ||
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Star"></a><!-- ws:end:WikiTextHeadingRule:0 -->Star</h1> | <!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Star"></a><!-- ws:end:WikiTextHeadingRule:0 -->Star</h1> | ||
<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="Star-Star transversal"></a><!-- ws:end:WikiTextHeadingRule:2 -->Star transversal</h2> | <!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="Star-Star transversal"></a><!-- ws:end:WikiTextHeadingRule:2 -->Star transversal</h2> | ||
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Since there are a finite number of 11-limit 8-note <a class="wiki_link" href="/lesfip%20scales">lesfip scales</a>, we may consider the <a class="wiki_link" href="/star-lesfip">lesfip version of Star</a>, star-lesfip, to be canonical. It can be reached from a variety of starting points. Lesfipping the 5-limit transversal in the range 14 to 17 cents of tolerance leads to star; so does lesfiping the 46et version in the range from 9 to 17 cents or the 77et version in the range 6 to 16 cents. Another tuning for Star, not very different, is <a class="wiki_link" href="/star">Star in 77et</a>; 77 giving the optimal patent val for both 11-limit starling and valentine.<br /> | Since there are a finite number of 11-limit 8-note <a class="wiki_link" href="/lesfip%20scales">lesfip scales</a>, we may consider the <a class="wiki_link" href="/star-lesfip">lesfip version of Star</a>, star-lesfip, to be canonical. It can be reached from a variety of starting points. Lesfipping the 5-limit transversal in the range 14 to 17 cents of tolerance leads to star; so does lesfiping the 46et version in the range from 9 to 17 cents or the 77et version in the range 6 to 16 cents. Another tuning for Star, not very different, is <a class="wiki_link" href="/star">Star in 77et</a>; 77 giving the optimal patent val for both 11-limit starling and valentine.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="Star-Chords of | <!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="Star-Chords of Star"></a><!-- ws:end:WikiTextHeadingRule:6 -->Chords of Star</h2> | ||
Star has sixteen <a class="wiki_link" href="/dyadic%20chord">dyadic tetrads</a>, of eleven different types, which are among those listed on the <a class="wiki_link" href="/chords%20of%20valentine">chords of valentine</a> page. In terms of what's listed on that page, star has one otonal tetrad, given in the form 1-8/7-10/7-12/7 but better known as 1-5/4-3/2-7/4; one 1-6/5-3/2-12/7 utonal tetrad; and one each of the <a class="wiki_link" href="/keenanismic%20chords">keenanismic tetrads</a> 1-8/7-11/8-12/7, 1-6/5-11/8-12/7, 1-5/4-10/7-12/7 and 1-5/4-3/2-12/7. It also has two each of the starling tetrad, the traditional diminished seventh chord of meantone; the ambitonal <a class="wiki_link" href="/just%20added%20sixth%20chord">just added sixth chord</a> 1-6/5-3/2-9/5; and the three 9-limit starling tetrads 1-6/5-10/7-9/5, 1-5/4-10/7-9/5 and 1-5/4-3/2-9/5.<br /> | Star has sixteen <a class="wiki_link" href="/dyadic%20chord">dyadic tetrads</a>, of eleven different types, which are among those listed on the <a class="wiki_link" href="/chords%20of%20valentine">chords of valentine</a> page. In terms of what's listed on that page, star has one otonal tetrad, given in the form 1-8/7-10/7-12/7 but better known as 1-5/4-3/2-7/4; one 1-6/5-3/2-12/7 utonal tetrad; and one each of the <a class="wiki_link" href="/keenanismic%20chords">keenanismic tetrads</a> 1-8/7-11/8-12/7, 1-6/5-11/8-12/7, 1-5/4-10/7-12/7 and 1-5/4-3/2-12/7. It also has two each of the starling tetrad, the traditional diminished seventh chord of meantone; the ambitonal <a class="wiki_link" href="/just%20added%20sixth%20chord">just added sixth chord</a> 1-6/5-3/2-9/5; and the three 9-limit starling tetrads 1-6/5-10/7-9/5, 1-5/4-10/7-9/5 and 1-5/4-3/2-9/5.<br /> | ||
<br /> | <br /> | ||
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The transversal of Nova, when tempered by 126/125 (starling) temperament, leads to Nova. It can also be considered a scale of 7-limit valentine, for which both 77et and 185et will serve, the latter being the optimal patent val for both 7-limit starling and 7-limit valentine. In valentine, its notes in generator terms are -4, 0, 4, 5, 8, 9, 13 and 17, which in order of size are 0, 17, 4, 5, 8, 9, -4, 13.<br /> | The transversal of Nova, when tempered by 126/125 (starling) temperament, leads to Nova. It can also be considered a scale of 7-limit valentine, for which both 77et and 185et will serve, the latter being the optimal patent val for both 7-limit starling and 7-limit valentine. In valentine, its notes in generator terms are -4, 0, 4, 5, 8, 9, 13 and 17, which in order of size are 0, 17, 4, 5, 8, 9, -4, 13.<br /> | ||
<br /> | <br /> | ||
The lesfip version of Nova, <a class="wiki_link" href="/nova-lesfip">nova-lesfip</a>, can be reached by lesfiping the transversal in the tolerance range 14 to 21 cents. It can also be reached from the 46et, 77et, or 185et tunings. The tolerance ranges are a little broader than those for Star since the lesfipping is done with respect to tbe 9-limit diamond; it also works from the 11-limit diamond, with narrower limits like those of Star, since then the 100/99 equivalencies must be avoided.</body></html></pre></div> | The lesfip version of Nova, <a class="wiki_link" href="/nova-lesfip">nova-lesfip</a>, can be reached by lesfiping the transversal in the tolerance range 14 to 21 cents. It can also be reached from the 46et, 77et, or 185et tunings. The tolerance ranges are a little broader than those for Star since the lesfipping is done with respect to tbe 9-limit diamond; it also works from the 11-limit diamond, with narrower limits like those of Star, since then the 100/99 equivalencies must be avoided.<br /> | ||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:16:&lt;h2&gt; --><h2 id="toc8"><a name="Nova-Chords of Nova"></a><!-- ws:end:WikiTextHeadingRule:16 -->Chords of Nova</h2> | |||
Like Star, Nova has sixteen <a class="wiki_link" href="/dyadic%20chord">dyadic tetrads</a>, of eleven different types, which are among those listed on the <a class="wiki_link" href="/chords%20of%20valentine">chords of valentine</a> page. These are one major and one minor tetrad, two starling tetrads (diminished seventh), three 1-6/5-3/2-9/5 added sixth tetrads, two 1-5/4-3/2-9/5 starling tetrads, one each of the starling tetrads 1-6/5-10/7-9/5, 1-5/4-10/7-9/5 and 1-5/4-7/5-9/5; one 1-7/6-3/2-9/5 subminor tetrad, one 1-9/7-3/2-9/5 supermajor tetrad, and one 1-7/6-3/2-7/4 swiss tetrad.</body></html></pre></div> | |||