Semicomma family: Difference between revisions
Wikispaces>genewardsmith **Imported revision 519421944 - Original comment: ** |
Wikispaces>hearneg **Imported revision 526123066 - 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:hearneg|hearneg]] and made on <tt>2014-10-12 11:26:53 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>526123066</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> | ||
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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;white-space: pre-wrap ! important" class="old-revision-html">[[toc]] | <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]] | ||
=Orson= | =Orson= | ||
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 | 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 sixths. **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. | ||
Comma: 2109375/2097152 | Comma: 2109375/2097152 | ||
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valid range: [270.968, 271.698] (31 to 53) | valid range: [270.968, 271.698] (31 to 53) | ||
nice range: [266.871, 275.659] | nice range: [266.871, 275.659] | ||
strict range: | strict range: [270.968, 271.698] | ||
[[POTE tuning|POTE generator]]: ~7/6 = 271.546 | [[POTE tuning|POTE generator]]: ~7/6 = 271.546 | ||
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valid range: [135.484, 136.364] (62 to 44) | valid range: [135.484, 136.364] (62 to 44) | ||
nice range: [128.298, 138.573] | nice range: [128.298, 138.573] | ||
strict range: | strict range: [135.484, 136.364] | ||
POTE tuning: ~13/12 = 135.723 | POTE tuning: ~13/12 = 135.723 | ||
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<!-- ws:end:WikiTextTocRule:36 --><!-- ws:start:WikiTextTocRule:37: --></div> | <!-- ws:end:WikiTextTocRule:36 --><!-- ws:start:WikiTextTocRule:37: --></div> | ||
<!-- ws:end:WikiTextTocRule:37 --><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Orson"></a><!-- ws:end:WikiTextHeadingRule:0 -->Orson</h1> | <!-- ws:end:WikiTextTocRule:37 --><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Orson"></a><!-- ws:end:WikiTextHeadingRule:0 -->Orson</h1> | ||
The 5-limit parent comma for the <strong>semicomma family</strong> 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 | The 5-limit parent comma for the <strong>semicomma family</strong> 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 sixths. <strong>Orson</strong>, 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 /> | <br /> | ||
Comma: 2109375/2097152<br /> | Comma: 2109375/2097152<br /> | ||
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valid range: [270.968, 271.698] (31 to 53)<br /> | valid range: [270.968, 271.698] (31 to 53)<br /> | ||
nice range: [266.871, 275.659]<br /> | nice range: [266.871, 275.659]<br /> | ||
strict range: | strict range: [270.968, 271.698]<br /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~7/6 = 271.546<br /> | <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~7/6 = 271.546<br /> | ||
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valid range: [135.484, 136.364] (62 to 44)<br /> | valid range: [135.484, 136.364] (62 to 44)<br /> | ||
nice range: [128.298, 138.573]<br /> | nice range: [128.298, 138.573]<br /> | ||
strict range: | strict range: [135.484, 136.364]<br /> | ||
<br /> | <br /> | ||
POTE tuning: ~13/12 = 135.723<br /> | POTE tuning: ~13/12 = 135.723<br /> | ||