Mercator's comma: 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:~~genewardsmith~~|~~genewardsmith~~]] and made on <tt>2011-08-28 01:00:33 UTC</tt>.<br>

: This revision was by author [[User:xenjacob|xenjacob]] and made on <tt>2011-08-28 22:36:14 UTC</tt>.<br>

: The original revision id was <tt>~~248862749~~</tt>.<br>

: The original revision id was <tt>249008353</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">|-84 53>, known as Mercator's comma or the 53-comma, is a small comma of 3.615 cents which is the amount by which 53 fifths exceed 31 octaves, in other words (~~3/2~~)^53/2^31. For equal divisions N up to 8745, the comma is tempered out if and only if 53 divides N. Examples of such EDOs include [[53edo]], [[159edo]], [[212edo]], [[265edo]], [[742edo]], [[954edo]] and [[1749edo]].

<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">|-84 53>, known as Mercator's comma or the 53-comma, is a small comma of 3.615 cents which is the amount by which 53 fifths exceed 31 octaves, in other words

[[math]]

\frac{(\frac32)^{53}}{2^{31}}

[[math]]

For equal divisions N up to 8745, the comma is tempered out if and only if 53 divides N. Examples of such EDOs include [[53edo]], [[159edo]], [[212edo]], [[265edo]], [[742edo]], [[954edo]] and [[1749edo]].

The comma is named for [[http://en.wikipedia.org/wiki/Nicholas_Mercator|Nicholas Mercator]], who first took note of it as a part of his study of [[53edo]].</pre></div>

<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>Mercator's comma</title></head><body>|-84 53&gt;, known as Mercator's comma or the 53-comma, is a small comma of 3.615 cents which is the amount by which 53 fifths exceed 31 octaves, in other words (3/2)^53/2^31. For equal divisions N up to 8745, the comma is tempered out if and only if 53 divides N. Examples of such EDOs include <a class="wiki_link" href="/53edo">53edo</a>, <a class="wiki_link" href="/159edo">159edo</a>, <a class="wiki_link" href="/212edo">212edo</a>, <a class="wiki_link" href="/265edo">265edo</a>, <a class="wiki_link" href="/742edo">742edo</a>, <a class="wiki_link" href="/954edo">954edo</a> and <a class="wiki_link" href="/1749edo">1749edo</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>Mercator's comma</title></head><body>|-84 53&gt;, known as Mercator's comma or the 53-comma, is a small comma of 3.615 cents which is the amount by which 53 fifths exceed 31 octaves, in other words <br />

<br />

<!-- ws:start:WikiTextMathRule:0:

[[math]]&lt;br/&gt;

\frac{(\frac32)^{53}}{2^{31}}&lt;br/&gt;[[math]]

--><script type="math/tex">\frac{(\frac32)^{53}}{2^{31}}</script><br />

<br />

For equal divisions N up to 8745, the comma is tempered out if and only if 53 divides N. Examples of such EDOs include <a class="wiki_link" href="/53edo">53edo</a>, <a class="wiki_link" href="/159edo">159edo</a>, <a class="wiki_link" href="/212edo">212edo</a>, <a class="wiki_link" href="/265edo">265edo</a>, <a class="wiki_link" href="/742edo">742edo</a>, <a class="wiki_link" href="/954edo">954edo</a> and <a class="wiki_link" href="/1749edo">1749edo</a>.<br />

<br />

The comma is named for <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Nicholas_Mercator" rel="nofollow">Nicholas Mercator</a>, who first took note of it as a part of his study of <a class="wiki_link" href="/53edo">53edo</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:genewardsmith|genewardsmith]] and made on <tt>2011-08-28 01:00:33 UTC</tt>.<br>
+: This revision was by author [[User:xenjacob|xenjacob]] and made on <tt>2011-08-28 22:36:14 UTC</tt>.<br>
-: The original revision id was <tt>248862749</tt>.<br>
+: The original revision id was <tt>249008353</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">|-84 53&gt;, known as Mercator's comma or the 53-comma, is a small comma of 3.615 cents which is the amount by which 53 fifths exceed 31 octaves, in other words (3/2)^53/2^31. For equal divisions N up to 8745, the comma is tempered out if and only if 53 divides N. Examples of such EDOs include [[53edo]], [[159edo]], [[212edo]], [[265edo]], [[742edo]], [[954edo]] and [[1749edo]].
+<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">|-84 53&gt;, known as Mercator's comma or the 53-comma, is a small comma of 3.615 cents which is the amount by which 53 fifths exceed 31 octaves, in other words
+[[math]]
+\frac{(\frac32)^{53}}{2^{31}}
+[[math]]
+For equal divisions N up to 8745, the comma is tempered out if and only if 53 divides N. Examples of such EDOs include [[53edo]], [[159edo]], [[212edo]], [[265edo]], [[742edo]], [[954edo]] and [[1749edo]].
 The comma is named for [[http://en.wikipedia.org/wiki/Nicholas_Mercator|Nicholas Mercator]], who first took note of it as a part of his study of [[53edo]].</pre></div>
 <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">&lt;html&gt;&lt;head&gt;&lt;title&gt;Mercator's comma&lt;/title&gt;&lt;/head&gt;&lt;body&gt;|-84 53&amp;gt;, known as Mercator's comma or the 53-comma, is a small comma of 3.615 cents which is the amount by which 53 fifths exceed 31 octaves, in other words (3/2)^53/2^31. For equal divisions N up to 8745, the comma is tempered out if and only if 53 divides N. Examples of such EDOs include &lt;a class="wiki_link" href="/53edo"&gt;53edo&lt;/a&gt;, &lt;a class="wiki_link" href="/159edo"&gt;159edo&lt;/a&gt;, &lt;a class="wiki_link" href="/212edo"&gt;212edo&lt;/a&gt;, &lt;a class="wiki_link" href="/265edo"&gt;265edo&lt;/a&gt;, &lt;a class="wiki_link" href="/742edo"&gt;742edo&lt;/a&gt;, &lt;a class="wiki_link" href="/954edo"&gt;954edo&lt;/a&gt; and &lt;a class="wiki_link" href="/1749edo"&gt;1749edo&lt;/a&gt;.&lt;br /&gt;
+<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">&lt;html&gt;&lt;head&gt;&lt;title&gt;Mercator's comma&lt;/title&gt;&lt;/head&gt;&lt;body&gt;|-84 53&amp;gt;, known as Mercator's comma or the 53-comma, is a small comma of 3.615 cents which is the amount by which 53 fifths exceed 31 octaves, in other words &lt;br /&gt;
+&lt;br /&gt;
+&lt;!-- ws:start:WikiTextMathRule:0:
+[[math]]&amp;lt;br/&amp;gt;
+\frac{(\frac32)^{53}}{2^{31}}&amp;lt;br/&amp;gt;[[math]]
+ --&gt;&lt;script type="math/tex"&gt;\frac{(\frac32)^{53}}{2^{31}}&lt;/script&gt;&lt;!-- ws:end:WikiTextMathRule:0 --&gt;&lt;br /&gt;
+&lt;br /&gt;
+For equal divisions N up to 8745, the comma is tempered out if and only if 53 divides N. Examples of such EDOs include &lt;a class="wiki_link" href="/53edo"&gt;53edo&lt;/a&gt;, &lt;a class="wiki_link" href="/159edo"&gt;159edo&lt;/a&gt;, &lt;a class="wiki_link" href="/212edo"&gt;212edo&lt;/a&gt;, &lt;a class="wiki_link" href="/265edo"&gt;265edo&lt;/a&gt;, &lt;a class="wiki_link" href="/742edo"&gt;742edo&lt;/a&gt;, &lt;a class="wiki_link" href="/954edo"&gt;954edo&lt;/a&gt; and &lt;a class="wiki_link" href="/1749edo"&gt;1749edo&lt;/a&gt;.&lt;br /&gt;
 &lt;br /&gt;
 The comma is named for &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Nicholas_Mercator" rel="nofollow"&gt;Nicholas Mercator&lt;/a&gt;, who first took note of it as a part of his study of &lt;a class="wiki_link" href="/53edo"&gt;53edo&lt;/a&gt;.&lt;/body&gt;&lt;/html&gt;</pre></div>