Star and Nova: Difference between revisions
Wikispaces>genewardsmith **Imported revision 362253248 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 362257204 - 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 | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-09-05 13:01:23 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>362257204</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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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. Lesfipping the 5-limit transversal in the range 14 to 17 cents of tolerance leads to star; so does | 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 star== | ==Chords of star== | ||
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=Nova= | =Nova= | ||
==Nova transversal== | ==Nova transversal== | ||
Star has a twin, Nova, with very similar characteristics but without 11-limit harmonies. It too can be reached from various starting points. One is a 5-limit [[Fokker blocks|Fokker block]] [[transversal]], [[smithgw_star2]], 27/25-6/5-5/4-36/25-3/2-5/3-9/5-2/1, which consists of a chain of minor thirds 5/3-1-6/5-36/25 and that chain translated by 3/2 rather than 5/4, and which also has three major and three minor triads. | Star has a twin, [[nova|Nova]], with very similar characteristics but without 11-limit harmonies. It too can be reached from various starting points. One is a 5-limit [[Fokker blocks|Fokker block]] [[transversal]], [[smithgw_star2]], 27/25-6/5-5/4-36/25-3/2-5/3-9/5-2/1, which consists of a chain of minor thirds 5/3-1-6/5-36/25 and that chain translated by 3/2 rather than 5/4, and which also has three major and three minor triads. | ||
==Notes of Nova== | ==Notes of Nova== | ||
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 | 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> | ||
<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:16:&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:16 --><!-- ws:start:WikiTextTocRule:17: --><a href="#Star">Star</a><!-- ws:end:WikiTextTocRule:17 --><!-- ws:start:WikiTextTocRule:18: --><!-- ws:end:WikiTextTocRule:18 --><!-- ws:start:WikiTextTocRule:19: --><!-- ws:end:WikiTextTocRule:19 --><!-- ws:start:WikiTextTocRule:20: --><!-- ws:end:WikiTextTocRule:20 --><!-- ws:start:WikiTextTocRule:21: --><!-- ws:end:WikiTextTocRule:21 --><!-- ws:start:WikiTextTocRule:22: --> | <a href="#Nova">Nova</a><!-- ws:end:WikiTextTocRule:22 --><!-- ws:start:WikiTextTocRule:23: --><!-- ws:end:WikiTextTocRule:23 --><!-- ws:start:WikiTextTocRule:24: --><!-- ws:end:WikiTextTocRule:24 --><!-- ws:start:WikiTextTocRule:25: --> | <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:16:&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:16 --><!-- ws:start:WikiTextTocRule:17: --><a href="#Star">Star</a><!-- ws:end:WikiTextTocRule:17 --><!-- ws:start:WikiTextTocRule:18: --><!-- ws:end:WikiTextTocRule:18 --><!-- ws:start:WikiTextTocRule:19: --><!-- ws:end:WikiTextTocRule:19 --><!-- ws:start:WikiTextTocRule:20: --><!-- ws:end:WikiTextTocRule:20 --><!-- ws:start:WikiTextTocRule:21: --><!-- ws:end:WikiTextTocRule:21 --><!-- ws:start:WikiTextTocRule:22: --> | <a href="#Nova">Nova</a><!-- ws:end:WikiTextTocRule:22 --><!-- ws:start:WikiTextTocRule:23: --><!-- ws:end:WikiTextTocRule:23 --><!-- ws:start:WikiTextTocRule:24: --><!-- ws:end:WikiTextTocRule:24 --><!-- ws:start:WikiTextTocRule:25: --> | ||
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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. Lesfipping the 5-limit transversal in the range 14 to 17 cents of tolerance leads to star; so does | 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 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> | ||
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<!-- ws:start:WikiTextHeadingRule:10:&lt;h1&gt; --><h1 id="toc5"><a name="Nova"></a><!-- ws:end:WikiTextHeadingRule:10 -->Nova</h1> | <!-- ws:start:WikiTextHeadingRule:10:&lt;h1&gt; --><h1 id="toc5"><a name="Nova"></a><!-- ws:end:WikiTextHeadingRule:10 -->Nova</h1> | ||
<!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id="toc6"><a name="Nova-Nova transversal"></a><!-- ws:end:WikiTextHeadingRule:12 -->Nova transversal</h2> | <!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id="toc6"><a name="Nova-Nova transversal"></a><!-- ws:end:WikiTextHeadingRule:12 -->Nova transversal</h2> | ||
Star has a twin, Nova, with very similar characteristics but without 11-limit harmonies. It too can be reached from various starting points. One is a 5-limit <a class="wiki_link" href="/Fokker%20blocks">Fokker block</a> <a class="wiki_link" href="/transversal">transversal</a>, <a class="wiki_link" href="/smithgw_star2">smithgw_star2</a>, 27/25-6/5-5/4-36/25-3/2-5/3-9/5-2/1, which consists of a chain of minor thirds 5/3-1-6/5-36/25 and that chain translated by 3/2 rather than 5/4, and which also has three major and three minor triads.<br /> | Star has a twin, <a class="wiki_link" href="/nova">Nova</a>, with very similar characteristics but without 11-limit harmonies. It too can be reached from various starting points. One is a 5-limit <a class="wiki_link" href="/Fokker%20blocks">Fokker block</a> <a class="wiki_link" href="/transversal">transversal</a>, <a class="wiki_link" href="/smithgw_star2">smithgw_star2</a>, 27/25-6/5-5/4-36/25-3/2-5/3-9/5-2/1, which consists of a chain of minor thirds 5/3-1-6/5-36/25 and that chain translated by 3/2 rather than 5/4, and which also has three major and three minor triads.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc7"><a name="Nova-Notes of Nova"></a><!-- ws:end:WikiTextHeadingRule:14 -->Notes of Nova</h2> | <!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc7"><a name="Nova-Notes of Nova"></a><!-- ws:end:WikiTextHeadingRule:14 -->Notes of Nova</h2> | ||
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 | 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> | ||