Mercator's comma
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author xenjacob and made on 2011-08-28 22:36:14 UTC.
- The original revision id was 249008353.
- The revision comment was:
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.
Original Wikitext content:
|-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]].Original HTML content:
<html><head><title>Mercator's comma</title></head><body>|-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 <br />
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<!-- ws:start:WikiTextMathRule:0:
[[math]]<br/>
\frac{(\frac32)^{53}}{2^{31}}<br/>[[math]]
--><script type="math/tex">\frac{(\frac32)^{53}}{2^{31}}</script><!-- ws:end:WikiTextMathRule:0 --><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 />
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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>