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Wikispaces>guest **Imported revision 264924162 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 264924444 - 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: | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-10-14 18:21:31 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>264924444</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">**Magic** is a linear temperament in which the ~380 cent generator represents 5/4, and five of those make a 3/1. This implies that the [[magic comma]] 3125/3072 is tempered out, making it a member of the [[Magic family]]. This article also assumes the default mapping for the prime 7, which tempers out 225/224 and makes two generators equivalent to 14/9. 7/4 can be reached by 12 generators in this mapping. (There is an alternative mapping for 7 known as [[Magic family#Muggles|muggles]], but there's basically no reason to use it unless you're using [[19edo]].) | <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">**Magic** is a linear temperament in which the ~380 cent generator represents 5/4, and five of those make a 3/1. This implies that the [[magic comma]] 3125/3072 is tempered out, making it a member of the [[Magic family]]. This article also assumes the default mapping for the prime 7, which tempers out 225/224 and makes two generators equivalent to 14/9. 7/4 can be reached by 12 generators in this mapping. (There is an alternative mapping for 7 known as [[Magic family#Muggles|muggles]], but there's basically no reason to use it unless you're using [[19edo]], in which case it's identical to magic anyway.) | ||
Because the generator is so close to 1\3 of an octave, and the interval left over (which represents both 128/125 and 25/24) is accordingly so small, all small magic MOSes consist of three large intervals alternating with three groups of this small interval. Specifically, there are the following MOSes, where s always represents the characteristic small interval of 128/125~25/24. | Because the generator is so close to 1\3 of an octave, and the interval left over (which represents both 128/125 and 25/24) is accordingly so small, all small magic MOSes consist of three large intervals alternating with three groups of this small interval. Specifically, there are the following MOSes, where s always represents the characteristic small interval of 128/125~25/24. | ||
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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>Magic</title></head><body><strong>Magic</strong> is a linear temperament in which the ~380 cent generator represents 5/4, and five of those make a 3/1. This implies that the <a class="wiki_link" href="/magic%20comma">magic comma</a> 3125/3072 is tempered out, making it a member of the <a class="wiki_link" href="/Magic%20family">Magic family</a>. This article also assumes the default mapping for the prime 7, which tempers out 225/224 and makes two generators equivalent to 14/9. 7/4 can be reached by 12 generators in this mapping. (There is an alternative mapping for 7 known as <a class="wiki_link" href="/Magic%20family#Muggles">muggles</a>, but there's basically no reason to use it unless you're using <a class="wiki_link" href="/19edo">19edo</a>.)<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>Magic</title></head><body><strong>Magic</strong> is a linear temperament in which the ~380 cent generator represents 5/4, and five of those make a 3/1. This implies that the <a class="wiki_link" href="/magic%20comma">magic comma</a> 3125/3072 is tempered out, making it a member of the <a class="wiki_link" href="/Magic%20family">Magic family</a>. This article also assumes the default mapping for the prime 7, which tempers out 225/224 and makes two generators equivalent to 14/9. 7/4 can be reached by 12 generators in this mapping. (There is an alternative mapping for 7 known as <a class="wiki_link" href="/Magic%20family#Muggles">muggles</a>, but there's basically no reason to use it unless you're using <a class="wiki_link" href="/19edo">19edo</a>, in which case it's identical to magic anyway.)<br /> | ||
<br /> | <br /> | ||
Because the generator is so close to 1\3 of an octave, and the interval left over (which represents both 128/125 and 25/24) is accordingly so small, all small magic MOSes consist of three large intervals alternating with three groups of this small interval. Specifically, there are the following MOSes, where s always represents the characteristic small interval of 128/125~25/24.<br /> | Because the generator is so close to 1\3 of an octave, and the interval left over (which represents both 128/125 and 25/24) is accordingly so small, all small magic MOSes consist of three large intervals alternating with three groups of this small interval. Specifically, there are the following MOSes, where s always represents the characteristic small interval of 128/125~25/24.<br /> | ||
Revision as of 18:21, 14 October 2011
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 2011-10-14 18:21:31 UTC.
- The original revision id was 264924444.
- 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:
**Magic** is a linear temperament in which the ~380 cent generator represents 5/4, and five of those make a 3/1. This implies that the [[magic comma]] 3125/3072 is tempered out, making it a member of the [[Magic family]]. This article also assumes the default mapping for the prime 7, which tempers out 225/224 and makes two generators equivalent to 14/9. 7/4 can be reached by 12 generators in this mapping. (There is an alternative mapping for 7 known as [[Magic family#Muggles|muggles]], but there's basically no reason to use it unless you're using [[19edo]], in which case it's identical to magic anyway.) Because the generator is so close to 1\3 of an octave, and the interval left over (which represents both 128/125 and 25/24) is accordingly so small, all small magic MOSes consist of three large intervals alternating with three groups of this small interval. Specifically, there are the following MOSes, where s always represents the characteristic small interval of 128/125~25/24. * [[3L 4s]]: LsLsLss where L = 6/5 * [[3L 7s]]: LssLssLsss where L = 7/6 * [[3L 10s]]: LsssLsssLssss where L = 9/8 * [[3L 13s]]: LssssLssssLsssss where L is a neutral second, which can be taken to represent 12/11 ==Interval chain== || 0. || 380.352 || 760.704 || 1141.056 || 321.408 || 701.76 || 1082.112 || 262.464 || 642.816 || 1023.168 || 203.52 || 583.872 || 964.224 || 144.576 || || 1/1 || 5/4 || 14/9 || 48/25~125/64 || 6/5 || 3/2 || 15/8 || 7/6 || || 9/5 || 9/8 || 7/5 || 7/4 || ||
Original HTML content:
<html><head><title>Magic</title></head><body><strong>Magic</strong> is a linear temperament in which the ~380 cent generator represents 5/4, and five of those make a 3/1. This implies that the <a class="wiki_link" href="/magic%20comma">magic comma</a> 3125/3072 is tempered out, making it a member of the <a class="wiki_link" href="/Magic%20family">Magic family</a>. This article also assumes the default mapping for the prime 7, which tempers out 225/224 and makes two generators equivalent to 14/9. 7/4 can be reached by 12 generators in this mapping. (There is an alternative mapping for 7 known as <a class="wiki_link" href="/Magic%20family#Muggles">muggles</a>, but there's basically no reason to use it unless you're using <a class="wiki_link" href="/19edo">19edo</a>, in which case it's identical to magic anyway.)<br />
<br />
Because the generator is so close to 1\3 of an octave, and the interval left over (which represents both 128/125 and 25/24) is accordingly so small, all small magic MOSes consist of three large intervals alternating with three groups of this small interval. Specifically, there are the following MOSes, where s always represents the characteristic small interval of 128/125~25/24.<br />
<ul><li><a class="wiki_link" href="/3L%204s">3L 4s</a>: LsLsLss where L = 6/5</li><li><a class="wiki_link" href="/3L%207s">3L 7s</a>: LssLssLsss where L = 7/6</li><li><a class="wiki_link" href="/3L%2010s">3L 10s</a>: LsssLsssLssss where L = 9/8</li><li><a class="wiki_link" href="/3L%2013s">3L 13s</a>: LssssLssssLsssss where L is a neutral second, which can be taken to represent 12/11</li></ul><br />
<!-- ws:start:WikiTextHeadingRule:0:<h2> --><h2 id="toc0"><a name="x-Interval chain"></a><!-- ws:end:WikiTextHeadingRule:0 -->Interval chain</h2>
<table class="wiki_table">
<tr>
<td>0.<br />
</td>
<td>380.352<br />
</td>
<td>760.704<br />
</td>
<td>1141.056<br />
</td>
<td>321.408<br />
</td>
<td>701.76<br />
</td>
<td>1082.112<br />
</td>
<td>262.464<br />
</td>
<td>642.816<br />
</td>
<td>1023.168<br />
</td>
<td>203.52<br />
</td>
<td>583.872<br />
</td>
<td>964.224<br />
</td>
<td>144.576<br />
</td>
</tr>
<tr>
<td>1/1<br />
</td>
<td>5/4<br />
</td>
<td>14/9<br />
</td>
<td>48/25~125/64<br />
</td>
<td>6/5<br />
</td>
<td>3/2<br />
</td>
<td>15/8<br />
</td>
<td>7/6<br />
</td>
<td><br />
</td>
<td>9/5<br />
</td>
<td>9/8<br />
</td>
<td>7/5<br />
</td>
<td>7/4<br />
</td>
<td><br />
</td>
</tr>
</table>
</body></html>