Star and Nova: Difference between revisions
Wikispaces>genewardsmith **Imported revision 362284574 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 362354806 - 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>2012-09-05 | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-09-05 18:30:39 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>362354806</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 15: | Line 15: | ||
By tempering out 126/125, leading to [[Starling family#x7-limit starling|7-limit starling temperament]] we add the 7-limit intervals 8/7, 7/6, 7/5 and their inversions to the mix, and by tempering by 385/384 also, leading to [[Starling family#x7-limit starling-11-limit|11-limit starling]], the 11/8 interval also. There is no significant tuning advantage to 11-limit starling, a planar temperament, over the linear temperament [[Starling temperaments#Valentine temperament-11-limit|valentine]], so we may consider Star to be a scale of valentine. In valentine, with generator a tempered 21/20 of 78 cents, the notes of Star are -4, 0, 1, 4, 5, 8, 9 and 13 generators; in the ordering of the scale itself, that's 0, 1, 4, 5, 8, 9, -4, 13. | By tempering out 126/125, leading to [[Starling family#x7-limit starling|7-limit starling temperament]] we add the 7-limit intervals 8/7, 7/6, 7/5 and their inversions to the mix, and by tempering by 385/384 also, leading to [[Starling family#x7-limit starling-11-limit|11-limit starling]], the 11/8 interval also. There is no significant tuning advantage to 11-limit starling, a planar temperament, over the linear temperament [[Starling temperaments#Valentine temperament-11-limit|valentine]], so we may consider Star to be a scale of valentine. In valentine, with generator a tempered 21/20 of 78 cents, the notes of Star are -4, 0, 1, 4, 5, 8, 9 and 13 generators; in the ordering of the scale itself, that's 0, 1, 4, 5, 8, 9, -4, 13. | ||
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. | 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. Lesfiping 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 Star== | ==Chords of Star== | ||
| Line 30: | Line 30: | ||
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 | 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 lesfiping 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== | ==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 each of 1-5/4-3/2-9/5 and 1-6/5-10/7-9/5 starling tetrads, one each of 1-5/4-10/7-9/5 and 1-5/4-7/5-9/5 starling tetrads; 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> | 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 each of 1-5/4-3/2-9/5 and 1-6/5-10/7-9/5 starling tetrads, one each of 1-5/4-10/7-9/5 and 1-5/4-7/5-9/5 starling tetrads; 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. | ||
=Music= | |||
[[http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/star_1-GrimaldiA+Bmod.mp3|Star 1-GrimaldiA+Bmod]] by [[Joel Grant Taylor]] | |||
[[http://micro.soonlabel.com/star/20120830-77et-star.mid|77et Star]] | |||
[[http://micro.soonlabel.com/star/20120830_lesfip-star-11-limit.mp3|Lesfip Star]] | |||
both by [[Chris Vaisvil]]</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:20:&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:20 --><!-- ws:start:WikiTextTocRule:21: --><a href="#Star">Star</a><!-- ws:end:WikiTextTocRule:21 --><!-- ws:start:WikiTextTocRule:22: --><!-- ws:end:WikiTextTocRule:22 --><!-- ws:start:WikiTextTocRule:23: --><!-- ws:end:WikiTextTocRule:23 --><!-- ws:start:WikiTextTocRule:24: --><!-- ws:end:WikiTextTocRule:24 --><!-- ws:start:WikiTextTocRule:25: --><!-- ws:end:WikiTextTocRule:25 --><!-- ws:start:WikiTextTocRule:26: --> | <a href="#Nova">Nova</a><!-- ws:end:WikiTextTocRule:26 --><!-- ws:start:WikiTextTocRule:27: --><!-- ws:end:WikiTextTocRule:27 --><!-- ws:start:WikiTextTocRule:28: --><!-- ws:end:WikiTextTocRule:28 --><!-- ws:start:WikiTextTocRule:29: --><!-- ws:end:WikiTextTocRule:29 --><!-- ws:start:WikiTextTocRule:30: --> | <a href="#Music">Music</a><!-- ws:end:WikiTextTocRule:30 --><!-- ws:start:WikiTextTocRule:31: --> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:31 --><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> | ||
| Line 44: | Line 51: | ||
By tempering out 126/125, leading to <a class="wiki_link" href="/Starling%20family#x7-limit starling">7-limit starling temperament</a> we add the 7-limit intervals 8/7, 7/6, 7/5 and their inversions to the mix, and by tempering by 385/384 also, leading to <a class="wiki_link" href="/Starling%20family#x7-limit starling-11-limit">11-limit starling</a>, the 11/8 interval also. There is no significant tuning advantage to 11-limit starling, a planar temperament, over the linear temperament <a class="wiki_link" href="/Starling%20temperaments#Valentine temperament-11-limit">valentine</a>, so we may consider Star to be a scale of valentine. In valentine, with generator a tempered 21/20 of 78 cents, the notes of Star are -4, 0, 1, 4, 5, 8, 9 and 13 generators; in the ordering of the scale itself, that's 0, 1, 4, 5, 8, 9, -4, 13.<br /> | By tempering out 126/125, leading to <a class="wiki_link" href="/Starling%20family#x7-limit starling">7-limit starling temperament</a> we add the 7-limit intervals 8/7, 7/6, 7/5 and their inversions to the mix, and by tempering by 385/384 also, leading to <a class="wiki_link" href="/Starling%20family#x7-limit starling-11-limit">11-limit starling</a>, the 11/8 interval also. There is no significant tuning advantage to 11-limit starling, a planar temperament, over the linear temperament <a class="wiki_link" href="/Starling%20temperaments#Valentine temperament-11-limit">valentine</a>, so we may consider Star to be a scale of valentine. In valentine, with generator a tempered 21/20 of 78 cents, the notes of Star are -4, 0, 1, 4, 5, 8, 9 and 13 generators; in the ordering of the scale itself, that's 0, 1, 4, 5, 8, 9, -4, 13.<br /> | ||
<br /> | <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. | 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. Lesfiping 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 Star"></a><!-- ws:end:WikiTextHeadingRule:6 -->Chords of Star</h2> | <!-- 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> | ||
| Line 59: | Line 66: | ||
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 | 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 lesfiping 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 /> | <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> | <!-- 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 each of 1-5/4-3/2-9/5 and 1-6/5-10/7-9/5 starling tetrads, one each of 1-5/4-10/7-9/5 and 1-5/4-7/5-9/5 starling tetrads; 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> | 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 each of 1-5/4-3/2-9/5 and 1-6/5-10/7-9/5 starling tetrads, one each of 1-5/4-10/7-9/5 and 1-5/4-7/5-9/5 starling tetrads; 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. <br /> | ||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:18:&lt;h1&gt; --><h1 id="toc9"><a name="Music"></a><!-- ws:end:WikiTextHeadingRule:18 -->Music</h1> | |||
<br /> | |||
<a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/star_1-GrimaldiA+Bmod.mp3" rel="nofollow">Star 1-GrimaldiA+Bmod</a> by <a class="wiki_link" href="/Joel%20Grant%20Taylor">Joel Grant Taylor</a><br /> | |||
<a class="wiki_link_ext" href="http://micro.soonlabel.com/star/20120830-77et-star.mid" rel="nofollow">77et Star</a><br /> | |||
<a class="wiki_link_ext" href="http://micro.soonlabel.com/star/20120830_lesfip-star-11-limit.mp3" rel="nofollow">Lesfip Star</a><br /> | |||
both by <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a></body></html></pre></div> | |||