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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | {{Infobox Interval |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| | | Monzo = -84 53 |
| : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-08-27 21:26:05 UTC</tt>.<br>
| | | Name = Mercator's comma, 53-comma |
| : The original revision id was <tt>248845721</tt>.<br>
| | | Color name = Wa-53 comma |
| : The revision comment was: <tt></tt><br>
| | | Comma = yes |
| 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>
| | The comma with the monzo of {{monzo|-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 [[perfect fifth]]s exceed 31 [[octave]]s, in other words (3/2)<sup>53</sup>/2<sup>31</sup>. It is also the amount by which a stack of four [[Pythagorean comma]]s exceeds a [[Pythagorean limma]], the amount by which a stack of eight [[apotome]]s exceeds a [[27/16]] major sixth, and the amount by which a stack of two [[Pythagorean countercomma]]s fall short of the [[mystery comma]]. |
| <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]], [[106edo]], [[159edo]], [[212edo]], [[265edo]], [[530edo]], [[583edo]], [[689edo]], [[742edo]].</pre></div>
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| <h4>Original HTML content:</h4>
| | The comma is named for [[Nicholas Mercator]], who first took note of it as a part of his study of [[53edo]]. |
| <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="/106edo">106edo</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="/530edo">530edo</a>, <a class="wiki_link" href="/583edo">583edo</a>, <a class="wiki_link" href="/689edo">689edo</a>, <a class="wiki_link" href="/742edo">742edo</a>.</body></html></pre></div>
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| | == Temperament == |
| | Tempering out this comma leads to the [[Mercator family]] of temperaments. For edos N up to [[8745edo|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]]. |
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| | == See also == |
| | * [[Holdrian comma#Mercator's comma, Mercator’s old comma, and the Holdrian comma|Mercator's old comma]] (It is what Wikipedia calls "Mercator's comma", but it is not what most modern musicians or theorists mean by "Mercator's comma".) |
| | * [[Holdrian comma]] |
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| | [[Category:Commas named after mathematicians]] |
| | [[Category:Commas named after music theorists]] |