Millioctave

Revision as of 15:06, 18 May 2014 by Wikispaces>spt3125 (**Imported revision 509664148 - Original comment: **)

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Original Wikitext content:

The **millioctave** (**mO**) is a logarithmic [[interval size measure]]. which divides the octave (2/1) into 1000 logarithmically equal parts. Its independence from the "classical"/"standard" [[12edo]] tuning, and its similarity to other metric/[[@http://en.wikipedia.org/wiki/International_System_of_Units|SI]] units, have led some microtonalists to prefer it over similar measures such as [[cents]]. However, others note that it naturally favors [[10edo]] and its multiples, just as cents favor 12edo and its multiples.

When comparing the approximations of [[just intervals]] between different systems, mO values can be used equally well as [[Cent|cent]] values. Also the absolute size of [[comma]]s can be given in millioctave steps.

1 millioctave may be defined as a frequency ratio of the 1000th root of 2, or 2^0.001.

To convert a just interval (n/d) to millioctaves (m), use the formula m = 1000 * log<span style="font-size: 80%; vertical-align: sub;">2</span>(n/d) .
Or, if your calculator or software does not have a log2 function, use m = 1000 * log(n/d) / log(2) .

1 mO is equal to exactly 1.2 cents. Conversely, 1 cent is equal to exactly 5/6 or ~0.8333 mO.

==Links== 
[[@http://en.wikipedia.org/wiki/Millioctave]]
Other [[interval size measure]]s

Original HTML content:

<html><head><title>millioctave</title></head><body>The <strong>millioctave</strong> (<strong>mO</strong>) is a logarithmic <a class="wiki_link" href="/interval%20size%20measure">interval size measure</a>. which divides the octave (2/1) into 1000 logarithmically equal parts. Its independence from the &quot;classical&quot;/&quot;standard&quot; <a class="wiki_link" href="/12edo">12edo</a> tuning, and its similarity to other metric/<a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/International_System_of_Units" rel="nofollow" target="_blank">SI</a> units, have led some microtonalists to prefer it over similar measures such as <a class="wiki_link" href="/cents">cents</a>. However, others note that it naturally favors <a class="wiki_link" href="/10edo">10edo</a> and its multiples, just as cents favor 12edo and its multiples.<br />
<br />
When comparing the approximations of <a class="wiki_link" href="/just%20intervals">just intervals</a> between different systems, mO values can be used equally well as <a class="wiki_link" href="/Cent">cent</a> values. Also the absolute size of <a class="wiki_link" href="/comma">comma</a>s can be given in millioctave steps.<br />
<br />
1 millioctave may be defined as a frequency ratio of the 1000th root of 2, or 2^0.001.<br />
<br />
To convert a just interval (n/d) to millioctaves (m), use the formula m = 1000 * log<span style="font-size: 80%; vertical-align: sub;">2</span>(n/d) .<br />
Or, if your calculator or software does not have a log2 function, use m = 1000 * log(n/d) / log(2) .<br />
<br />
1 mO is equal to exactly 1.2 cents. Conversely, 1 cent is equal to exactly 5/6 or ~0.8333 mO.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Links"></a><!-- ws:end:WikiTextHeadingRule:0 -->Links</h2>
 <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Millioctave" rel="nofollow" target="_blank">http://en.wikipedia.org/wiki/Millioctave</a><br />
Other <a class="wiki_link" href="/interval%20size%20measure">interval size measure</a>s</body></html>