Semicomma family: Difference between revisions
Wikispaces>genewardsmith **Imported revision 186503171 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 188592707 - Original comment: ** |
||
| Line 1: | Line 1: | ||
<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>2010-12- | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-12-16 03:09:41 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>188592707</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">The 5-limit parent comma for the semicomma family is the semicomma, 2109375/2097152 = |-21 3 7>. This is the amount by which three pure 3/1 twelfths exceed seven pure 8/5 minor thirds. Orson, the [[5-limit]] temperament tempering it out, has a [[generator]] of 75/64, which is sharper than 7/6 by 225/224 when untempered, and less sharp than that in any good orson tempering, for example [[53edo]] or [[84edo]]. These give tunings to the generator which are sharp of 7/6 by less than five [[cent]]s, making it hard to treat orson as anything other than an (at least) 7-limit system, leading to orwell. | <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 semicomma family is the semicomma, 2109375/2097152 = |-21 3 7>. This is the amount by which three pure 3/1 twelfths exceed seven pure 8/5 minor thirds. Orson, the [[5-limit]] temperament tempering it out, has a [[generator]] of 75/64, which is sharper than 7/6 by 225/224 when untempered, and less sharp than that in any good orson tempering, for example [[53edo]] or [[84edo]]. These give tunings to the generator which are sharp of 7/6 by less than five [[cent]]s, making it hard to treat orson as anything other than an (at least) 7-limit system, leading to orwell. | ||
Map: [<1 0 3|, <0 7 -3|] | |||
EDOs: 22, 31, 53, 190, 253, 296 | |||
==Seven limit children== | ==Seven limit children== | ||
| Line 30: | Line 33: | ||
|42/17 -6/17 3/17 0>, |41/17 16/17 -8/17 0>] | |42/17 -6/17 3/17 0>, |41/17 16/17 -8/17 0>] | ||
[[Eigenmonzo|Eigenmonzos]]: 2, 10/9 | [[Eigenmonzo|Eigenmonzos]]: 2, 10/9 | ||
Map: [<1 0 3 1|, <0 7 -3 8|] | |||
EDOs: 22, 31, 53, 84, 137 | |||
Algebraic generators: Sabra3, the real root of 12x^3-7x-48. | Algebraic generators: Sabra3, the real root of 12x^3-7x-48. | ||
| Line 38: | Line 44: | ||
[[Minimax tuning]] | [[Minimax tuning]] | ||
[|1 0 0 0 0>, |14/11 0 -7/11 7/11 0>, |27/11 0 3/11 -3/11 0>, | |||
|27/11 0 -8/11 8/11 0>, |37/11 0 -2/11 2/11 0>] | |||
[[Eigenmonzo|Eigenmonzos]]: 2, 7/5 | [[Eigenmonzo|Eigenmonzos]]: 2, 7/5 | ||
Map: [<1 0 3 1 3|, <0 7 -3 8 2|] | Map: [<1 0 3 1 3|, <0 7 -3 8 2|] | ||
[[edo|Edos]]: [[31edo|31]], [[53edo|53]], [[84edo|84]] | [[edo|Edos]]: [[31edo|31]], [[53edo|53]], [[84edo|84]] | ||
EDOs: 22, 31, 53 | |||
==Music== | ==Music== | ||
| Line 49: | Line 57: | ||
<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>Semicomma family</title></head><body>The 5-limit parent comma for the semicomma family is the semicomma, 2109375/2097152 = |-21 3 7&gt;. This is the amount by which three pure 3/1 twelfths exceed seven pure 8/5 minor thirds. Orson, the <a class="wiki_link" href="/5-limit">5-limit</a> temperament tempering it out, has a <a class="wiki_link" href="/generator">generator</a> of 75/64, which is sharper than 7/6 by 225/224 when untempered, and less sharp than that in any good orson tempering, for example <a class="wiki_link" href="/53edo">53edo</a> or <a class="wiki_link" href="/84edo">84edo</a>. These give tunings to the generator which are sharp of 7/6 by less than five <a class="wiki_link" href="/cent">cent</a>s, making it hard to treat orson as anything other than an (at least) 7-limit system, leading to orwell.<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>Semicomma family</title></head><body>The 5-limit parent comma for the semicomma family is the semicomma, 2109375/2097152 = |-21 3 7&gt;. This is the amount by which three pure 3/1 twelfths exceed seven pure 8/5 minor thirds. Orson, the <a class="wiki_link" href="/5-limit">5-limit</a> temperament tempering it out, has a <a class="wiki_link" href="/generator">generator</a> of 75/64, which is sharper than 7/6 by 225/224 when untempered, and less sharp than that in any good orson tempering, for example <a class="wiki_link" href="/53edo">53edo</a> or <a class="wiki_link" href="/84edo">84edo</a>. These give tunings to the generator which are sharp of 7/6 by less than five <a class="wiki_link" href="/cent">cent</a>s, making it hard to treat orson as anything other than an (at least) 7-limit system, leading to orwell.<br /> | ||
<br /> | |||
Map: [&lt;1 0 3|, &lt;0 7 -3|]<br /> | |||
EDOs: 22, 31, 53, 190, 253, 296<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> | ||
| Line 72: | Line 83: | ||
|42/17 -6/17 3/17 0&gt;, |41/17 16/17 -8/17 0&gt;]<br /> | |42/17 -6/17 3/17 0&gt;, |41/17 16/17 -8/17 0&gt;]<br /> | ||
<a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 10/9<br /> | <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 10/9<br /> | ||
<br /> | |||
Map: [&lt;1 0 3 1|, &lt;0 7 -3 8|]<br /> | |||
EDOs: 22, 31, 53, 84, 137<br /> | |||
<br /> | <br /> | ||
Algebraic generators: Sabra3, the real root of 12x^3-7x-48. <br /> | Algebraic generators: Sabra3, the real root of 12x^3-7x-48. <br /> | ||
| Line 80: | Line 94: | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/Minimax%20tuning">Minimax tuning</a><br /> | <a class="wiki_link" href="/Minimax%20tuning">Minimax tuning</a><br /> | ||
<br /> | [|1 0 0 0 0&gt;, |14/11 0 -7/11 7/11 0&gt;, |27/11 0 3/11 -3/11 0&gt;,<br /> | ||
|27/11 0 -8/11 8/11 0&gt;, |37/11 0 -2/11 2/11 0&gt;]<br /> | |||
<a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 7/5<br /> | <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 7/5<br /> | ||
<br /> | <br /> | ||
Map: [&lt;1 0 3 1 3|, &lt;0 7 -3 8 2|]<br /> | Map: [&lt;1 0 3 1 3|, &lt;0 7 -3 8 2|]<br /> | ||
<a class="wiki_link" href="/edo">Edos</a>: <a class="wiki_link" href="/31edo">31</a>, <a class="wiki_link" href="/53edo">53</a>, <a class="wiki_link" href="/84edo">84</a><br /> | <a class="wiki_link" href="/edo">Edos</a>: <a class="wiki_link" href="/31edo">31</a>, <a class="wiki_link" href="/53edo">53</a>, <a class="wiki_link" href="/84edo">84</a><br /> | ||
EDOs: 22, 31, 53<br /> | |||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="x-Music"></a><!-- ws:end:WikiTextHeadingRule:6 -->Music</h2> | <!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="x-Music"></a><!-- ws:end:WikiTextHeadingRule:6 -->Music</h2> | ||
<!-- ws:start:WikiTextUrlRule: | <!-- ws:start:WikiTextUrlRule:81:http://www.archive.org/details/TrioInOrwell --><a class="wiki_link_ext" href="http://www.archive.org/details/TrioInOrwell" rel="nofollow">http://www.archive.org/details/TrioInOrwell</a><!-- ws:end:WikiTextUrlRule:81 --><br /> | ||
<a class="wiki_link_ext" href="http://soundclick.com/share?songid=9101705" rel="nofollow">one drop of rain</a>, <a class="wiki_link_ext" href="http://soundclick.com/share?songid=9101704" rel="nofollow">i've come with a bucket of roses</a>, and <a class="wiki_link_ext" href="http://soundclick.com/share?songid=8839071" rel="nofollow">my own house</a> by Andrew Heathwaite</body></html></pre></div> | <a class="wiki_link_ext" href="http://soundclick.com/share?songid=9101705" rel="nofollow">one drop of rain</a>, <a class="wiki_link_ext" href="http://soundclick.com/share?songid=9101704" rel="nofollow">i've come with a bucket of roses</a>, and <a class="wiki_link_ext" href="http://soundclick.com/share?songid=8839071" rel="nofollow">my own house</a> by Andrew Heathwaite</body></html></pre></div> | ||