Superpartient ratio: 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:~~Sarzadoce~~|~~Sarzadoce~~]] and made on <tt>2012-09-10 00:06:45 UTC</tt>.<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-09-10 11:46:47 UTC</tt>.<br>

: The original revision id was <tt>~~363309982~~</tt>.<br>

: The original revision id was <tt>363440596</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>

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[[math]]

When considering ratios, and particularly when they are ratios for [[comma|commas]], it can be useful to introduce the notion of the **degree of ~~epimericity~~** (not to be confused with ~~plain~~ //epimericity// - see link below). In terms of p/q reduced to lowest terms it is p - q. An epimoric ratio has degree 1, the 7-limit comma 245/243 degree 2, the 5-limit comma 128/125 degree 3, and so forth. [[http://en.wikipedia.org/wiki/St%C3%B8rmer's_theorem|Størmer's theorem]] can be extended to the claim that for each prime limit p and each degree of epimoricity n, there are only finitely many p-limit ratios with degree of epimoricity less than or equal to n.

When considering ratios, and particularly when they are ratios for [[comma|commas]], it can be useful to introduce the notion of the **degree of epimoricity** (not to be confused with //epimericity// - see link below). In terms of p/q reduced to lowest terms it is p - q. An epimoric ratio has degree 1, the 7-limit comma 245/243 degree 2, the 5-limit comma 128/125 degree 3, and so forth. [[http://en.wikipedia.org/wiki/St%C3%B8rmer's_theorem|Størmer's theorem]] can be extended to the claim that for each prime limit p and each degree of epimoricity n, there are only finitely many p-limit ratios with degree of epimoricity less than or equal to n.

See Also: [[ABC, High Quality Commas, and Epimericity]]</pre></div>

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--><script type="math/tex">\displaystyle \prod_{i \mathop = 1}^{P \mathop - 1} \dfrac {i + 1} {i} = P</script><br />

<br />

When considering ratios, and particularly when they are ratios for <a class="wiki_link" href="/comma">commas</a>, it can be useful to introduce the notion of the <strong>degree of ~~epimericity~~</strong> (not to be confused with ~~plain~~ <em>epimericity</em> - see link below). In terms of p/q reduced to lowest terms it is p - q. An epimoric ratio has degree 1, the 7-limit comma 245/243 degree 2, the 5-limit comma 128/125 degree 3, and so forth. <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/St%C3%B8rmer's_theorem" rel="nofollow">Størmer's theorem</a> can be extended to the claim that for each prime limit p and each degree of epimoricity n, there are only finitely many p-limit ratios with degree of epimoricity less than or equal to n.<br />

When considering ratios, and particularly when they are ratios for <a class="wiki_link" href="/comma">commas</a>, it can be useful to introduce the notion of the <strong>degree of epimoricity</strong> (not to be confused with <em>epimericity</em> - see link below). In terms of p/q reduced to lowest terms it is p - q. An epimoric ratio has degree 1, the 7-limit comma 245/243 degree 2, the 5-limit comma 128/125 degree 3, and so forth. <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/St%C3%B8rmer's_theorem" rel="nofollow">Størmer's theorem</a> can be extended to the claim that for each prime limit p and each degree of epimoricity n, there are only finitely many p-limit ratios with degree of epimoricity less than or equal to n.<br />

<br />

See Also: <a class="wiki_link" href="/ABC%2C%20High%20Quality%20Commas%2C%20and%20Epimericity">ABC, High Quality Commas, and Epimericity</a></body></html></pre></div>

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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:Sarzadoce|Sarzadoce]] and made on <tt>2012-09-10 00:06:45 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-09-10 11:46:47 UTC</tt>.<br>
-: The original revision id was <tt>363309982</tt>.<br>
+: The original revision id was <tt>363440596</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>
@@ Line 13: / Line 13: @@
 [[math]]
-When considering ratios, and particularly when they are ratios for [[comma|commas]], it can be useful to introduce the notion of the **degree of epimericity** (not to be confused with plain //epimericity// - see link below). In terms of p/q reduced to lowest terms it is p - q. An epimoric ratio has degree 1, the 7-limit comma 245/243 degree 2, the 5-limit comma 128/125 degree 3, and so forth. [[http://en.wikipedia.org/wiki/St%C3%B8rmer's_theorem|Størmer's theorem]] can be extended to the claim that for each prime limit p and each degree of epimoricity n, there are only finitely many p-limit ratios with degree of epimoricity less than or equal to n.
+When considering ratios, and particularly when they are ratios for [[comma|commas]], it can be useful to introduce the notion of the **degree of epimoricity** (not to be confused with //epimericity// - see link below). In terms of p/q reduced to lowest terms it is p - q. An epimoric ratio has degree 1, the 7-limit comma 245/243 degree 2, the 5-limit comma 128/125 degree 3, and so forth. [[http://en.wikipedia.org/wiki/St%C3%B8rmer's_theorem|Størmer's theorem]] can be extended to the claim that for each prime limit p and each degree of epimoricity n, there are only finitely many p-limit ratios with degree of epimoricity less than or equal to n.
 See Also: [[ABC, High Quality Commas, and Epimericity]]</pre></div>
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   --&gt;&lt;script type="math/tex"&gt;\displaystyle \prod_{i \mathop = 1}^{P \mathop - 1} \dfrac {i + 1} {i} = P&lt;/script&gt;&lt;!-- ws:end:WikiTextMathRule:0 --&gt;&lt;br /&gt;
 &lt;br /&gt;
-When considering ratios, and particularly when they are ratios for &lt;a class="wiki_link" href="/comma"&gt;commas&lt;/a&gt;, it can be useful to introduce the notion of the &lt;strong&gt;degree of epimericity&lt;/strong&gt; (not to be confused with plain &lt;em&gt;epimericity&lt;/em&gt; - see link below). In terms of p/q reduced to lowest terms it is p - q. An epimoric ratio has degree 1, the 7-limit comma 245/243 degree 2, the 5-limit comma 128/125 degree 3, and so forth. &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/St%C3%B8rmer's_theorem" rel="nofollow"&gt;Størmer's theorem&lt;/a&gt; can be extended to the claim that for each prime limit p and each degree of epimoricity n, there are only finitely many p-limit ratios with degree of epimoricity less than or equal to n.&lt;br /&gt;
+When considering ratios, and particularly when they are ratios for &lt;a class="wiki_link" href="/comma"&gt;commas&lt;/a&gt;, it can be useful to introduce the notion of the &lt;strong&gt;degree of epimoricity&lt;/strong&gt; (not to be confused with &lt;em&gt;epimericity&lt;/em&gt; - see link below). In terms of p/q reduced to lowest terms it is p - q. An epimoric ratio has degree 1, the 7-limit comma 245/243 degree 2, the 5-limit comma 128/125 degree 3, and so forth. &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/St%C3%B8rmer's_theorem" rel="nofollow"&gt;Størmer's theorem&lt;/a&gt; can be extended to the claim that for each prime limit p and each degree of epimoricity n, there are only finitely many p-limit ratios with degree of epimoricity less than or equal to n.&lt;br /&gt;
 &lt;br /&gt;
 See Also: &lt;a class="wiki_link" href="/ABC%2C%20High%20Quality%20Commas%2C%20and%20Epimericity"&gt;ABC, High Quality Commas, and Epimericity&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>