Semicomma family: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>

: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2011-08-21 11:19:41 UTC</tt>.<br>

: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2011-08-21 11:20:39 UTC</tt>.<br>

: The original revision id was <tt>~~247384829~~</tt>.<br>

: The original revision id was <tt>247385041</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>

<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">[[toc]]

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.

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.

[[POTE tuning|POTE generator]]: 271.627

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<div style="margin-left: 1em;"><a href="#Music">Music</a></div>

</div>

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. <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 />

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 thirds. <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 />

<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 271.627<br />

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2011-08-21 11:19:41 UTC</tt>.<br>
+: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2011-08-21 11:20:39 UTC</tt>.<br>
-: The original revision id was <tt>247384829</tt>.<br>
+: The original revision id was <tt>247385041</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>
 <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">[[toc]]
-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 [[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.
+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 [[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.
 [[POTE tuning|POTE generator]]: 271.627
@@ Line 88: / Line 88: @@
 &lt;!-- ws:end:WikiTextTocRule:20 --&gt;&lt;!-- ws:start:WikiTextTocRule:21: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Music"&gt;Music&lt;/a&gt;&lt;/div&gt;
 &lt;!-- ws:end:WikiTextTocRule:21 --&gt;&lt;!-- ws:start:WikiTextTocRule:22: --&gt;&lt;/div&gt;
-&lt;!-- ws:end:WikiTextTocRule:22 --&gt;The 5-limit parent comma for the semicomma family is the semicomma, 2109375/2097152 = |-21 3 7&amp;gt;. This is the amount by which three pure 3/1 twelfths exceed seven pure 8/5 minor thirds. &lt;strong&gt;Orson&lt;/strong&gt;, the &lt;a class="wiki_link" href="/5-limit"&gt;5-limit&lt;/a&gt; temperament tempering it out, has a &lt;a class="wiki_link" href="/generator"&gt;generator&lt;/a&gt; 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 &lt;a class="wiki_link" href="/53edo"&gt;53edo&lt;/a&gt; or &lt;a class="wiki_link" href="/84edo"&gt;84edo&lt;/a&gt;. These give tunings to the generator which are sharp of 7/6 by less than five &lt;a class="wiki_link" href="/cent"&gt;cent&lt;/a&gt;s, making it hard to treat orson as anything other than an (at least) 7-limit system, leading to orwell.&lt;br /&gt;
+&lt;!-- ws:end:WikiTextTocRule:22 --&gt;The 5-limit parent comma for the &lt;strong&gt;semicomma family&lt;/strong&gt; is the semicomma, 2109375/2097152 = |-21 3 7&amp;gt;. This is the amount by which three pure 3/1 twelfths exceed seven pure 8/5 minor thirds. &lt;strong&gt;Orson&lt;/strong&gt;, the &lt;a class="wiki_link" href="/5-limit"&gt;5-limit&lt;/a&gt; temperament tempering it out, has a &lt;a class="wiki_link" href="/generator"&gt;generator&lt;/a&gt; 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 &lt;a class="wiki_link" href="/53edo"&gt;53edo&lt;/a&gt; or &lt;a class="wiki_link" href="/84edo"&gt;84edo&lt;/a&gt;. These give tunings to the generator which are sharp of 7/6 by less than five &lt;a class="wiki_link" href="/cent"&gt;cent&lt;/a&gt;s, making it hard to treat orson as anything other than an (at least) 7-limit system, leading to orwell.&lt;br /&gt;
 &lt;br /&gt;
 &lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 271.627&lt;br /&gt;