Millioctave: Difference between revisions

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**Imported revision 239300585 - Original comment: **
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**Imported revision 509664148 - Original comment: **
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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
<h2>IMPORTED REVISION FROM WIKISPACES</h2>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2011-06-29 07:55:35 UTC</tt>.<br>
: This revision was by author [[User:spt3125|spt3125]] and made on <tt>2014-05-18 15:06:17 UTC</tt>.<br>
: The original revision id was <tt>239300585</tt>.<br>
: The original revision id was <tt>509664148</tt>.<br>
: The revision comment was: <tt></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>
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>
<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">The **millioctave** (**mO**) is a logarithmic [[interval size measure]]. Its independence from the "classical" [[12edo]] tuning makes it fit better for microtonal purposes, though it favors the work with equal divisions of the octave [[edo]].
<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">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]] values. Also the absolute size of [[comma]]s can be given in millioctave steps.
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.


== Links ==
1 millioctave may be defined as a frequency ratio of the 1000th root of 2, or 2^0.001.
http://en.wikipedia.org/wiki/Millioctave</pre></div>
 
To convert a just interval (n/d) to millioctaves (m), use the formula m = 1000 * log&lt;span style="font-size: 80%; vertical-align: sub;"&gt;2&lt;/span&gt;(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</pre></div>
<h4>Original HTML content:</h4>
<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;millioctave&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The &lt;strong&gt;millioctave&lt;/strong&gt; (&lt;strong&gt;mO&lt;/strong&gt;) is a logarithmic &lt;a class="wiki_link" href="/interval%20size%20measure"&gt;interval size measure&lt;/a&gt;. Its independence from the &amp;quot;classical&amp;quot; &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt; tuning makes it fit better for microtonal purposes, though it favors the work with equal divisions of the octave &lt;a class="wiki_link" href="/edo"&gt;edo&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;millioctave&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The &lt;strong&gt;millioctave&lt;/strong&gt; (&lt;strong&gt;mO&lt;/strong&gt;) is a logarithmic &lt;a class="wiki_link" href="/interval%20size%20measure"&gt;interval size measure&lt;/a&gt;. which divides the octave (2/1) into 1000 logarithmically equal parts. Its independence from the &amp;quot;classical&amp;quot;/&amp;quot;standard&amp;quot; &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt; tuning, and its similarity to other metric/&lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/International_System_of_Units" rel="nofollow" target="_blank"&gt;SI&lt;/a&gt; units, have led some microtonalists to prefer it over similar measures such as &lt;a class="wiki_link" href="/cents"&gt;cents&lt;/a&gt;. However, others note that it naturally favors &lt;a class="wiki_link" href="/10edo"&gt;10edo&lt;/a&gt; and its multiples, just as cents favor 12edo and its multiples.&lt;br /&gt;
&lt;br /&gt;
When comparing the approximations of &lt;a class="wiki_link" href="/just%20intervals"&gt;just intervals&lt;/a&gt; between different systems, mO values can be used equally well as &lt;a class="wiki_link" href="/Cent"&gt;cent&lt;/a&gt; values. Also the absolute size of &lt;a class="wiki_link" href="/comma"&gt;comma&lt;/a&gt;s can be given in millioctave steps.&lt;br /&gt;
&lt;br /&gt;
1 millioctave may be defined as a frequency ratio of the 1000th root of 2, or 2^0.001.&lt;br /&gt;
&lt;br /&gt;
To convert a just interval (n/d) to millioctaves (m), use the formula m = 1000 * log&lt;span style="font-size: 80%; vertical-align: sub;"&gt;2&lt;/span&gt;(n/d) .&lt;br /&gt;
Or, if your calculator or software does not have a log2 function, use m = 1000 * log(n/d) / log(2) .&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
When comparing the approximations of &lt;a class="wiki_link" href="/just%20intervals"&gt;just intervals&lt;/a&gt; between different systems, mO values can be used equally well as &lt;a class="wiki_link" href="/Cent"&gt;Cent&lt;/a&gt; values. Also the absolute size of &lt;a class="wiki_link" href="/comma"&gt;comma&lt;/a&gt;s can be given in millioctave steps.&lt;br /&gt;
1 mO is equal to exactly 1.2 cents. Conversely, 1 cent is equal to exactly 5/6 or ~0.8333 mO.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-Links"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt; Links &lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-Links"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Links&lt;/h2&gt;
&lt;!-- ws:start:WikiTextUrlRule:12:http://en.wikipedia.org/wiki/Millioctave --&gt;&lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Millioctave" rel="nofollow"&gt;http://en.wikipedia.org/wiki/Millioctave&lt;/a&gt;&lt;!-- ws:end:WikiTextUrlRule:12 --&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
&lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Millioctave" rel="nofollow" target="_blank"&gt;http://en.wikipedia.org/wiki/Millioctave&lt;/a&gt;&lt;br /&gt;
Other &lt;a class="wiki_link" href="/interval%20size%20measure"&gt;interval size measure&lt;/a&gt;s&lt;/body&gt;&lt;/html&gt;</pre></div>

Revision as of 15:06, 18 May 2014

IMPORTED REVISION FROM WIKISPACES

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

This revision was by author spt3125 and made on 2014-05-18 15:06:17 UTC.
The original revision id was 509664148.
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:

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>