Kleismic family: Difference between revisions
Wikispaces>genewardsmith **Imported revision 179179319 - Original comment: ** |
Wikispaces>xenwolf **Imported revision 179390487 - Original comment: some 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 16:45:41 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>179390487</tt>.<br> | ||
: The revision comment was: <tt></tt><br> | : The revision comment was: <tt>some 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> | ||
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===Clyde=== | ===Clyde=== | ||
Commas: 245/243, 3136/3125 | [[Comma|Commas]]: 245/243, 3136/3125 | ||
7 and 9 limit minimax | 7 and 9 limit minimax | ||
[|1 0 0 0>, |6/25 0 0 12/25>, |6/5 0 0 2/5>, |0 0 0 1>] | [|1 0 0 0>, |6/25 0 0 12/25>, |6/5 0 0 2/5>, |0 0 0 1>] | ||
Eigenmonzos: 2, 7 | [[Eigenmonzo|Eigenmonzos]]: 2, 7 | ||
Algebraic generator: real root of 5x^3-6x-3, the Poussami generator. Approximately 441.309 cents. Associated recurrence relationship quickly converges. | Algebraic generator: real root of 5x^3-6x-3, the Poussami generator. Approximately 441.309 [[Cent|cents]]. Associated recurrence relationship quickly converges. | ||
Map: [<1 6 6 12|, <0 -12 -10 -25|] | Map: [<1 6 6 12|, <0 -12 -10 -25|] | ||
Generators: 2, 9/7 | [[Generator|Generators]]: 2, 9/7 | ||
Edos: 19, 49, 68, 87, 155</pre></div> | [[Edo|Edos]]: [[19edo|19]], [[49edo|49]], [[68edo|68]], [[87edo|87]], [[155edo|155]]</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>Kleismic family</title></head><body>The 5-limit parent comma for the kleismic family is 15625/15552, the kleisma. Its monzo is |-6 -5 6&gt;, and flipping that yields &lt;&lt;6 5 -6|| for the wedgie. This tells us the generator is a minor third, and that to get to the interval class of major thirds will require five of these, and so to get to fifths will require six. In fact, (6/5)^5 = 5/2 * 15625/15552. 14/53 is about perfect as a generator, though 9/34 also makes sense and using <a class="wiki_link" href="/19edo">19edo</a> is possible. Other tunings include <a class="wiki_link" href="/72edo">72edo</a>, <a class="wiki_link" href="/87edo">87edo</a> and <a class="wiki_link" href="/140edo">140edo</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>Kleismic family</title></head><body>The 5-limit parent comma for the kleismic family is 15625/15552, the kleisma. Its monzo is |-6 -5 6&gt;, and flipping that yields &lt;&lt;6 5 -6|| for the wedgie. This tells us the generator is a minor third, and that to get to the interval class of major thirds will require five of these, and so to get to fifths will require six. In fact, (6/5)^5 = 5/2 * 15625/15552. 14/53 is about perfect as a generator, though 9/34 also makes sense and using <a class="wiki_link" href="/19edo">19edo</a> is possible. Other tunings include <a class="wiki_link" href="/72edo">72edo</a>, <a class="wiki_link" href="/87edo">87edo</a> and <a class="wiki_link" href="/140edo">140edo</a>.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:2:&lt;h3&gt; --><h3 id="toc1"><a name="x-Seven limit children-Clyde"></a><!-- ws:end:WikiTextHeadingRule:2 -->Clyde</h3> | <!-- ws:start:WikiTextHeadingRule:2:&lt;h3&gt; --><h3 id="toc1"><a name="x-Seven limit children-Clyde"></a><!-- ws:end:WikiTextHeadingRule:2 -->Clyde</h3> | ||
Commas: 245/243, 3136/3125<br /> | <a class="wiki_link" href="/Comma">Commas</a>: 245/243, 3136/3125<br /> | ||
<br /> | <br /> | ||
7 and 9 limit minimax<br /> | 7 and 9 limit minimax<br /> | ||
[|1 0 0 0&gt;, |6/25 0 0 12/25&gt;, |6/5 0 0 2/5&gt;, |0 0 0 1&gt;]<br /> | [|1 0 0 0&gt;, |6/25 0 0 12/25&gt;, |6/5 0 0 2/5&gt;, |0 0 0 1&gt;]<br /> | ||
Eigenmonzos: 2, 7<br /> | <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 7<br /> | ||
<br /> | <br /> | ||
Algebraic generator: real root of 5x^3-6x-3, the Poussami generator. Approximately 441.309 cents. Associated recurrence relationship quickly converges.<br /> | Algebraic generator: real root of 5x^3-6x-3, the Poussami generator. Approximately 441.309 <a class="wiki_link" href="/Cent">cents</a>. Associated recurrence relationship quickly converges.<br /> | ||
<br /> | <br /> | ||
Map: [&lt;1 6 6 12|, &lt;0 -12 -10 -25|]<br /> | Map: [&lt;1 6 6 12|, &lt;0 -12 -10 -25|]<br /> | ||
Generators: 2, 9/7<br /> | <a class="wiki_link" href="/Generator">Generators</a>: 2, 9/7<br /> | ||
Edos: 19, 49, 68, 87, 155</body></html></pre></div> | <a class="wiki_link" href="/Edo">Edos</a>: <a class="wiki_link" href="/19edo">19</a>, <a class="wiki_link" href="/49edo">49</a>, <a class="wiki_link" href="/68edo">68</a>, <a class="wiki_link" href="/87edo">87</a>, <a class="wiki_link" href="/155edo">155</a></body></html></pre></div> | ||