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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | |-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 |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
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| : This revision was by author [[User:xenjacob|xenjacob]] and made on <tt>2011-08-28 22:36:14 UTC</tt>.<br>
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| : The original revision id was <tt>249008353</tt>.<br>
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| : The revision comment was: <tt></tt><br>
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| 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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| <h4>Original Wikitext content:</h4>
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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">|-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
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| [[math]]
| | <math>\frac{(\frac32)^{53}}{2^{31}}</math> |
| \frac{(\frac32)^{53}}{2^{31}} | |
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| 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]]. | | 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|53edo]], [[159edo|159edo]], [[212edo|212edo]], [[265edo|265edo]], [[742edo|742edo]], [[954edo|954edo]] and [[1749edo|1749edo]]. |
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| 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> | | 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|53edo]]. |
| <h4>Original HTML content:</h4>
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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;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 />
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| <!-- ws:start:WikiTextMathRule:0:
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| [[math]]&lt;br/&gt;
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| \frac{(\frac32)^{53}}{2^{31}}&lt;br/&gt;[[math]]
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| --><script type="math/tex">\frac{(\frac32)^{53}}{2^{31}}</script><!-- ws:end:WikiTextMathRule:0 --><br />
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| 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 />
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| 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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|-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]\displaystyle{ \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 Nicholas Mercator, who first took note of it as a part of his study of 53edo.