31st-octave temperaments: Difference between revisions
Wikispaces>genewardsmith **Imported revision 281263302 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 281304484 - 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>2011-12-01 | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-12-01 18:23:43 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>281304484</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> | ||
<h4>Original Wikitext content:</h4> | <h4>Original Wikitext 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;white-space: pre-wrap ! important" class="old-revision-html">By the //31-3-comma// is meant 617673396283947/562949953421312 = <-49 31|, the amount (160.605 cents) by which 31 just (3/2) fifths exceed 18 octaves. This may not seem like much of a comma, but since 31et is such a strong 7-limit system, 11- and 13-limit temperaments based on the cycle of 31 fifths actually make sense. | <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;white-space: pre-wrap ! important" class="old-revision-html">[[toc|flat]] | ||
=31-3-comma= | |||
By the //31-3-comma// is meant 617673396283947/562949953421312 = <-49 31|, the amount (160.605 cents) by which 31 just (3/2) fifths exceed 18 octaves. This may not seem like much of a comma, but since 31et is such a strong 7-limit system, 11- and 13-limit temperaments based on the cycle of 31 fifths actually make sense. | |||
=Prajapati= | =Prajapati= | ||
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</pre></div> | </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>31 comma temperaments</title></head><body>By the <em>31-3-comma</em> is meant 617673396283947/562949953421312 = &lt;-49 31|, the amount (160.605 cents) by which 31 just (3/2) fifths exceed 18 octaves. This may not seem like much of a comma, but since 31et is such a strong 7-limit system, 11- and 13-limit temperaments based on the cycle of 31 fifths actually make sense.<br /> | <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>31 comma temperaments</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="#x31-3-comma">31-3-comma</a><!-- ws:end:WikiTextTocRule:17 --><!-- ws:start:WikiTextTocRule:18: --> | <a href="#Prajapati">Prajapati</a><!-- ws:end:WikiTextTocRule:18 --><!-- ws:start:WikiTextTocRule:19: --><!-- ws:end:WikiTextTocRule:19 --><!-- ws:start:WikiTextTocRule:20: --><!-- ws:end:WikiTextTocRule:20 --><!-- ws:start:WikiTextTocRule:21: --> | <a href="#Gallium">Gallium</a><!-- ws:end:WikiTextTocRule:21 --><!-- ws:start:WikiTextTocRule:22: --> | <a href="#Birds">Birds</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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<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x31-3-comma"></a><!-- ws:end:WikiTextHeadingRule:0 -->31-3-comma</h1> | |||
By the <em>31-3-comma</em> is meant 617673396283947/562949953421312 = &lt;-49 31|, the amount (160.605 cents) by which 31 just (3/2) fifths exceed 18 octaves. This may not seem like much of a comma, but since 31et is such a strong 7-limit system, 11- and 13-limit temperaments based on the cycle of 31 fifths actually make sense.<br /> | |||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Prajapati"></a><!-- ws:end:WikiTextHeadingRule:2 -->Prajapati</h1> | ||
The Hindu god Pradjapati is said to have created the universe by speaking aloud the odd numbers from 1 to 31. People with an interest in 31 may want to try this method themselves.<br /> | The Hindu god Pradjapati is said to have created the universe by speaking aloud the odd numbers from 1 to 31. People with an interest in 31 may want to try this method themselves.<br /> | ||
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Badness: 0.0430<br /> | Badness: 0.0430<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="Prajapati-13-limit"></a><!-- ws:end:WikiTextHeadingRule:4 -->13-limit</h2> | ||
Commas: 81/80, 126/125, 105/104, 512/507<br /> | Commas: 81/80, 126/125, 105/104, 512/507<br /> | ||
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Badness: 0.0379<br /> | Badness: 0.0379<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="Prajapati-Kumhar"></a><!-- ws:end:WikiTextHeadingRule:6 -->Kumhar</h2> | ||
Commas: 81/80, 126/125, 1029/1024, 144/143<br /> | Commas: 81/80, 126/125, 1029/1024, 144/143<br /> | ||
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Badness: 0.0486<br /> | Badness: 0.0486<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:8:&lt;h1&gt; --><h1 id="toc4"><a name="Gallium"></a><!-- ws:end:WikiTextHeadingRule:8 -->Gallium</h1> | ||
The name of gallium temperament comes from Gallium, the 31st element.<br /> | The name of gallium temperament comes from Gallium, the 31st element.<br /> | ||
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Badness: 0.0255<br /> | Badness: 0.0255<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:10:&lt;h1&gt; --><h1 id="toc5"><a name="Birds"></a><!-- ws:end:WikiTextHeadingRule:10 -->Birds</h1> | ||
The birds temperament tempers out the <em>31-5 comma</em>, |72 0 -31&gt;, which is the amount (24.275 cents) by which 31 just (5/4) major thirds fall short of ten octaves. The name comes from Isaiah 31:5 &quot;As birds flying, so wil the Lord of hostes defend Ierusalem, defending also hee will deliuer it, and passing ouer, he will preserue it.&quot; It also tempers out the 31-7 comma, but sadly, combining the two commas leads to torsion.<br /> | The birds temperament tempers out the <em>31-5 comma</em>, |72 0 -31&gt;, which is the amount (24.275 cents) by which 31 just (5/4) major thirds fall short of ten octaves. The name comes from Isaiah 31:5 &quot;As birds flying, so wil the Lord of hostes defend Ierusalem, defending also hee will deliuer it, and passing ouer, he will preserue it.&quot; It also tempers out the 31-7 comma, but sadly, combining the two commas leads to torsion.<br /> | ||
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Badness: 0.1000<br /> | Badness: 0.1000<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id="toc6"><a name="Birds-11-limit"></a><!-- ws:end:WikiTextHeadingRule:12 -->11-limit</h2> | ||
Commas: 441/440, 3136/3125, 41503/41472<br /> | Commas: 441/440, 3136/3125, 41503/41472<br /> | ||
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Badness: 0.0399<br /> | Badness: 0.0399<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc7"><a name="Birds-13-limit"></a><!-- ws:end:WikiTextHeadingRule:14 -->13-limit</h2> | ||
Commas: 441/440, 3136/3125, 1001/1000, 13720/13689<br /> | Commas: 441/440, 3136/3125, 1001/1000, 13720/13689<br /> | ||
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