Millioctave: Difference between revisions

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~~<h2>IMPORTED REVISION FROM WIKISPACES</h2>~~

The '''millioctave''' ('''mO''') is a logarithmic [[Interval_size_measure|interval size measure]]. which divides the octave (2/1) into 1000 logarithmically equal parts. Its independence from the "classical"/"standard" [[12edo|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|cents]]. However, others note that it naturally favors [[10edo|10edo]] and its multiples, just as cents favor 12edo and its multiples.

~~This is an imported revision from Wikispaces. The revision metadata is included below for reference:<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>509664148</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>~~

~~<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]]. 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.

When comparing the approximations of [[just_intervals|just intervals]] between different systems, mO values can be used equally well as [[cent|cent]] values. Also the absolute size of [[Comma|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) .

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]]

[http://en.wikipedia.org/wiki/Millioctave http://en.wikipedia.org/wiki/Millioctave]

~~Other [[interval size measure]]s</pre></div>~~

~~<h4>Original HTML content:</h4>~~

Other [[Interval_size_measure|interval size measure]]s

<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>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 />

[[Category:absolute_measure]]

~~<br />~~

[[Category:interval]]

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 />~~

[[Category:interval_measure]]

~~<br />~~

[[Category:logarithmic_measure]]

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

[[Category:measure]]

~~<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 />~~

~~<h2 id="toc0"><a name="x-Links"></a>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></pre></div>~~

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-<h2>IMPORTED REVISION FROM WIKISPACES</h2>
+The '''millioctave''' ('''mO''') is a logarithmic [[Interval_size_measure|interval size measure]]. which divides the octave (2/1) into 1000 logarithmically equal parts. Its independence from the "classical"/"standard" [[12edo|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|cents]]. However, others note that it naturally favors [[10edo|10edo]] and its multiples, just as cents favor 12edo and its multiples.
-This is an imported revision from Wikispaces. The revision metadata is included below for reference:<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>509664148</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>
-<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]]. 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.
+When comparing the approximations of [[just_intervals|just intervals]] between different systems, mO values can be used equally well as [[cent|cent]] values. Also the absolute size of [[Comma|comma]]s can be given in millioctave steps.
 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&lt;span style="font-size: 80%; vertical-align: sub;"&gt;2&lt;/span&gt;(n/d) .
+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) .
 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]]
+[http://en.wikipedia.org/wiki/Millioctave http://en.wikipedia.org/wiki/Millioctave]
-Other [[interval size measure]]s</pre></div>
-<h4>Original HTML content:</h4>
+Other [[Interval_size_measure|interval size measure]]s
-<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;
+[[Category:absolute_measure]]
-&lt;br /&gt;
+[[Category:interval]]
-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;
+[[Category:interval_measure]]
-&lt;br /&gt;
+[[Category:logarithmic_measure]]
-millioctave may be defined as a frequency ratio of the 1000th root of 2, or 2^0.001.&lt;br /&gt;
+[[Category:measure]]
-&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;
-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;!-- 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;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>

Millioctave: Difference between revisions

Wikispaces>FREEZE