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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>
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| : This revision was by author [[User:spt3125|spt3125]] and made on <tt>2014-05-18 15:06:17 UTC</tt>.<br>
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| : The original revision id was <tt>509664148</tt>.<br>
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| : The revision comment was: <tt></tt><br>
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| 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>
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| <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.
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| 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. |
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| 1 millioctave may be defined as a frequency ratio of the 1000th root of 2, or 2^0.001. | | 1 millioctave may be defined as a frequency ratio of the 1000th root of 2, or 2^0.001. |
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| 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) . |
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| Or, if your calculator or software does not have a log2 function, use m = 1000 * log(n/d) / log(2) . | | Or, if your calculator or software does not have a log2 function, use m = 1000 * log(n/d) / log(2) . |
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| 1 mO is equal to exactly 1.2 cents. Conversely, 1 cent is equal to exactly 5/6 or ~0.8333 mO. | | 1 mO is equal to exactly 1.2 cents. Conversely, 1 cent is equal to exactly 5/6 or ~0.8333 mO. |
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| ==Links== | | ==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>
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| <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]] |
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| | [[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]] |
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| | [[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]] |
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| 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 />
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| Or, if your calculator or software does not have a log2 function, use m = 1000 * log(n/d) / log(2) .<br />
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| <br />
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| 1 mO is equal to exactly 1.2 cents. Conversely, 1 cent is equal to exactly 5/6 or ~0.8333 mO.<br />
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| <!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Links"></a><!-- ws:end:WikiTextHeadingRule:0 -->Links</h2>
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| <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Millioctave" rel="nofollow" target="_blank">http://en.wikipedia.org/wiki/Millioctave</a><br />
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| Other <a class="wiki_link" href="/interval%20size%20measure">interval size measure</a>s</body></html></pre></div>
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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/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 commas 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 * log2(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 measures