Magic family: Difference between revisions
Wikispaces>genewardsmith **Imported revision 179194027 - Original comment: ** |
Wikispaces>xenwolf **Imported revision 179391683 - Original comment: links added** |
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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:xenwolf|xenwolf]] and made on <tt>2010-11-14 16:50:27 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>179391683</tt>.<br> | ||
: The revision comment was: <tt></tt><br> | : The revision comment was: <tt>links added</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">The 5-limit parent comma for the magic family is 3125/3072, the small diesis or magic comma. Its monzo is |-10 -1 5>, and flipping that yields <<5 1 -10|| for the wedgie. This tells us the generator is a major third, and that to get to the interval class of fifths will require five of these. In fact, (5/4)^5 = 3 * 3125/3072. 13/41 is a highly recommendable generator, though 19/60 also makes sense and using [[19edo]] or [[22edo]] is always possible. | <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">The 5-limit parent comma for the magic family is 3125/3072, the small diesis or magic comma. Its monzo is |-10 -1 5>, and flipping that yields <<5 1 -10|| for the wedgie. This tells us the generator is a major third, and that to get to the interval class of fifths will require five of these. In fact, (5/4)^5 = 3 * 3125/3072. 13/41 is a highly recommendable generator, though 19/60 also makes sense and using [[19edo]] or [[22edo]] is always possible. | ||
Comma: 3125/3072 | [[Comma]]: 3125/3072 | ||
5-limit minimax | 5-limit minimax | ||
[<1 0 0|, <0 1 0|, <2 1/5 0|] | [<1 0 0|, <0 1 0|, <2 1/5 0|] | ||
Eigenmonzos: 2, 3 | [[Eigenmonzo|Eigenmonzos]]: 2, 3 | ||
Algebraic generator: Terzbirat, the positive root of 9x^2-8x-4 = (4+2*sqrt(13))/9; approximately 380.3175 cents. | Algebraic generator: Terzbirat, the positive root of 9x^2-8x-4 = (4+2*sqrt(13))/9; approximately 380.3175 [[Cent|cents]]. | ||
Map: [<1 0 2|, <0 5 1|] | Map: [<1 0 2|, <0 5 1|] | ||
Generators: 2, 5/4 | [[Generator|Generators]]: 2, 5/4 | ||
Edos: 6, 16, 19, 22, 41, 60 | [[Edo|Edos]]: [[6edo|6]], [[16edo|16]], [[19edo|19]], [[22edo|22]], [[41edo|41]], [[60edo|60]] | ||
==Seven limit children== | ==Seven limit children== | ||
| Line 34: | Line 34: | ||
7 and 9 limit minimax | 7 and 9 limit minimax | ||
[|1 0 0 0>, |0 1 0 0>, |2 1/5 0 0>, |-1 12/5 0 0>] | [|1 0 0 0>, |0 1 0 0>, |2 1/5 0 0>, |-1 12/5 0 0>] | ||
Eigenmonzos: 2, 3 | [[Eigenmonzo|Eigenmonzos]]: 2, 3 | ||
Algebraic generators: Tirzbirat or Septimage, the real root of 5x^5+4x-20, 380.7604 cents. | Algebraic generators: Tirzbirat or Septimage, the real root of 5x^5+4x-20, 380.7604 cents. | ||
Map: [<1 0 2 -1|, <0 5 1 12|] | Map: [<1 0 2 -1|, <0 5 1 12|] | ||
Generators: 2, 5/4 | [[Generator|Generators]]: 2, 5/4 | ||
===Muggles=== | ===Muggles=== | ||
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<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 family</title></head><body>The 5-limit parent comma for the magic family is 3125/3072, the small diesis or magic comma. Its monzo is |-10 -1 5&gt;, and flipping that yields &lt;&lt;5 1 -10|| for the wedgie. This tells us the generator is a major third, and that to get to the interval class of fifths will require five of these. In fact, (5/4)^5 = 3 * 3125/3072. 13/41 is a highly recommendable generator, though 19/60 also makes sense and using <a class="wiki_link" href="/19edo">19edo</a> or <a class="wiki_link" href="/22edo">22edo</a> is always possible.<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 family</title></head><body>The 5-limit parent comma for the magic family is 3125/3072, the small diesis or magic comma. Its monzo is |-10 -1 5&gt;, and flipping that yields &lt;&lt;5 1 -10|| for the wedgie. This tells us the generator is a major third, and that to get to the interval class of fifths will require five of these. In fact, (5/4)^5 = 3 * 3125/3072. 13/41 is a highly recommendable generator, though 19/60 also makes sense and using <a class="wiki_link" href="/19edo">19edo</a> or <a class="wiki_link" href="/22edo">22edo</a> is always possible.<br /> | ||
<br /> | <br /> | ||
Comma: 3125/3072<br /> | <a class="wiki_link" href="/Comma">Comma</a>: 3125/3072<br /> | ||
<br /> | <br /> | ||
5-limit minimax<br /> | 5-limit minimax<br /> | ||
[&lt;1 0 0|, &lt;0 1 0|, &lt;2 1/5 0|]<br /> | [&lt;1 0 0|, &lt;0 1 0|, &lt;2 1/5 0|]<br /> | ||
Eigenmonzos: 2, 3<br /> | <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 3<br /> | ||
<br /> | <br /> | ||
Algebraic generator: Terzbirat, the positive root of 9x^2-8x-4 = (4+2*sqrt(13))/9; approximately 380.3175 cents.<br /> | Algebraic generator: Terzbirat, the positive root of 9x^2-8x-4 = (4+2*sqrt(13))/9; approximately 380.3175 <a class="wiki_link" href="/Cent">cents</a>.<br /> | ||
<br /> | <br /> | ||
Map: [&lt;1 0 2|, &lt;0 5 1|]<br /> | Map: [&lt;1 0 2|, &lt;0 5 1|]<br /> | ||
Generators: 2, 5/4<br /> | <a class="wiki_link" href="/Generator">Generators</a>: 2, 5/4<br /> | ||
Edos: 6, 16, 19, 22, 41, 60<br /> | <a class="wiki_link" href="/Edo">Edos</a>: <a class="wiki_link" href="/6edo">6</a>, <a class="wiki_link" href="/16edo">16</a>, <a class="wiki_link" href="/19edo">19</a>, <a class="wiki_link" href="/22edo">22</a>, <a class="wiki_link" href="/41edo">41</a>, <a class="wiki_link" href="/60edo">60</a><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Seven limit children"></a><!-- ws:end:WikiTextHeadingRule:0 -->Seven limit children</h2> | <!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Seven limit children"></a><!-- ws:end:WikiTextHeadingRule:0 -->Seven limit children</h2> | ||
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7 and 9 limit minimax<br /> | 7 and 9 limit minimax<br /> | ||
[|1 0 0 0&gt;, |0 1 0 0&gt;, |2 1/5 0 0&gt;, |-1 12/5 0 0&gt;]<br /> | [|1 0 0 0&gt;, |0 1 0 0&gt;, |2 1/5 0 0&gt;, |-1 12/5 0 0&gt;]<br /> | ||
Eigenmonzos: 2, 3<br /> | <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 3<br /> | ||
<br /> | <br /> | ||
Algebraic generators: Tirzbirat or Septimage, the real root of 5x^5+4x-20, 380.7604 cents.<br /> | Algebraic generators: Tirzbirat or Septimage, the real root of 5x^5+4x-20, 380.7604 cents.<br /> | ||
<br /> | <br /> | ||
Map: [&lt;1 0 2 -1|, &lt;0 5 1 12|]<br /> | Map: [&lt;1 0 2 -1|, &lt;0 5 1 12|]<br /> | ||
Generators: 2, 5/4<br /> | <a class="wiki_link" href="/Generator">Generators</a>: 2, 5/4<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:4:&lt;h3&gt; --><h3 id="toc2"><a name="x-Seven limit children-Muggles"></a><!-- ws:end:WikiTextHeadingRule:4 -->Muggles</h3> | <!-- ws:start:WikiTextHeadingRule:4:&lt;h3&gt; --><h3 id="toc2"><a name="x-Seven limit children-Muggles"></a><!-- ws:end:WikiTextHeadingRule:4 -->Muggles</h3> | ||
Aside from 3125/3072 and 525/512 muggles also tempers out 126/125 and 1323/1280. A good muggles tuning is <a class="wiki_link" href="/19edo">19edo</a>, in which tuning it's the same thing as magic. Muggles works better for small scales than magic in the sense that 7 or 10 note MOS are reasonable choices. The muggles wedgie is &lt;&lt;5 1 -7 -10 -25 -19||.</body></html></pre></div> | Aside from 3125/3072 and 525/512 muggles also tempers out 126/125 and 1323/1280. A good muggles tuning is <a class="wiki_link" href="/19edo">19edo</a>, in which tuning it's the same thing as magic. Muggles works better for small scales than magic in the sense that 7 or 10 note MOS are reasonable choices. The muggles wedgie is &lt;&lt;5 1 -7 -10 -25 -19||.</body></html></pre></div> | ||