Least common multiple - Revision history

Fredg999: Simplify Wikipedia template

2025-04-24T21:46:45Z

Simplify Wikipedia template

← Older revision		Revision as of 21:46, 24 April 2025
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	{{~~wikipedia\|Least common multiple~~}}		{{Wikipedia}}
	The '''least common multiple''' ('''LCM''') or its logarithm (for example [[log2]]) can be used as a [[complexity]] measure for [[interval]]s and [[chord]]s.		The '''least common multiple''' ('''LCM''') or its logarithm (for example [[log2]]) can be used as a [[complexity]] measure for [[interval]]s and [[chord]]s.
	In terms of harmonic series, it represents the location of the first shared harmonic between all of the notes.		In terms of harmonic series, it represents the location of the first shared harmonic between all of the notes.

Sintel: categories

2025-04-24T10:21:06Z

Sintel: Categories

2025-04-24T10:20:46Z

Sintel: expand, give interpretation

2025-04-24T10:16:48Z

expand, give interpretation

← Older revision		Revision as of 10:16, 24 April 2025
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	The '''least common multiple''' ('''LCM''') or its logarithm (for example [[log2]]) can be used as a [[~~dissonance measure~~]] for [[interval]]s and [[chord]]s.		{{wikipedia\|Least common multiple}}
			The '''least common multiple''' ('''LCM''') or its logarithm (for example [[log2]]) can be used as a [[complexity]] measure for [[interval]]s and [[chord]]s.
			In terms of harmonic series, it represents the location of the first shared harmonic between all of the notes.
			Note that, for dyads, this is the same as [[Benedetti height]], since a ratio in lowest terms has no shared factors between its numerator and denominator.

	== Examples ==		== Examples ==
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	\| 40		\| 40
	\|-		\|-
	\| 5:6:7		\| 4:5:6
	\| ~~210~~		\| 60
			\|-
			\| 10:12:15
			\| 60
	\|-		\|-
	\| 6:7:8		\| 6:7:8
	\| 168		\| 168
			\|-
			\| 5:6:7
			\| 210
	\|}		\|}

	~~== See also ==~~
	* [[Wikipedia: Least common multiple]]

	[[Category:Consonance and dissonance]]		[[Category:Consonance and dissonance]]

BudjarnLambeth: Stub

2025-04-24T03:21:33Z

Stub

← Older revision		Revision as of 03:21, 24 April 2025
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	[[Category:Consonance and dissonance]]		[[Category:Consonance and dissonance]]
	[[Category:Harmonic entropy]]		[[Category:Harmonic entropy]]


			{{stub}}

Fredg999 category edits: Removing from Category:Dissonance using Cat-a-lot

2023-03-04T18:39:15Z

Removing from Category:Dissonance using Cat-a-lot

← Older revision		Revision as of 18:39, 4 March 2023
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	[[Category:Consonance and dissonance]]		[[Category:Consonance and dissonance]]
	~~[[Category:Dissonance]]~~
	[[Category:Harmonic entropy]]		[[Category:Harmonic entropy]]

Fredg999 category edits: Moving from Category:Consonance to Category:Consonance and dissonance using Cat-a-lot

2023-03-04T18:38:54Z

Moving from Category:Consonance to Category:Consonance and dissonance using Cat-a-lot

← Older revision		Revision as of 18:38, 4 March 2023
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	* [[Wikipedia: Least common multiple]]		* [[Wikipedia: Least common multiple]]

	[[Category:Consonance]]		[[Category:Consonance and dissonance]]
	[[Category:Dissonance]]		[[Category:Dissonance]]
	[[Category:Harmonic entropy]]		[[Category:Harmonic entropy]]

FloraC: Cleanup

2021-05-06T07:08:03Z

Cleanup

← Older revision		Revision as of 07:08, 6 May 2021
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	The '''least common multiple''' ('''~~lcm~~''') or its logarithm (for example [[log2~~\|Log2~~]]) can be used as a [[~~dissonance_measure\|~~dissonance measure]] for [[~~intervals\|intervals~~]] and [[~~Chords\|chords~~]].		The '''least common multiple''' ('''LCM''') or its logarithm (for example [[log2]]) can be used as a [[dissonance measure]] for [[interval]]s and [[chord]]s.

	==Examples==		== Examples ==

	{\| class="wikitable"		{\| class="wikitable center-all"
	\|-		\|-
	! ~~\| interval~~/		! Interval/chord
			! LCM
	chord
	! ~~\| lcm~~
	\|-		\|-
	\| \| 7:5		\| 7:5
	\| \| 35		\| 35
	\|-		\|-
	\| \| 8:5		\| 8:5
	\| \| 40		\| 40
	\|-		\|-
	\| \| 5:6:7		\| 5:6:7
	\| \| 210		\| 210
	\|-		\|-
	\| \| 6:7:8		\| 6:7:8
	\| \| 168		\| 168
	\|}		\|}

	==See also==		== See also ==
	[~~http~~:~~//en.wikipedia.org/wiki/Least_common_multiple http://en.wikipedia.org/wiki/Least_common_multiple~~] [[Category:~~consonance~~]]		* [[Wikipedia: Least common multiple]]
	[[Category:~~dissonance~~]]
	[[Category:~~harmonic_entropy~~]]		[[Category:Consonance]]
			[[Category:Dissonance]]
			[[Category:Harmonic entropy]]

Wikispaces>FREEZE at 00:00, 17 July 2018

2018-07-17T00:00:00Z

← Older revision		Revision as of 00:00, 17 July 2018
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	~~<h2>IMPORTED REVISION FROM WIKISPACES</h2>~~		The '''least common multiple''' ('''lcm''') or its logarithm (for example [[log2\|Log2]]) can be used as a [[dissonance_measure\|dissonance measure]] for [[intervals\|intervals]] and [[Chords\|chords]].
	~~This is an imported revision from Wikispaces.~~ The ~~revision metadata is included below for reference:<br>~~
	~~: This revision was by author [[User:guest\|guest]] and made on <tt>2012-05-21 18:15:04 UTC</tt>.<br>~~
	~~: The original revision id was <tt>338078884</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 least common multiple (lcm) or its logarithm (for example [[Log2]]) can be used as a [[dissonance measure]] for [[intervals]] and [[chords]].

	==Examples==		==Examples==
	~~\|\|~ interval/~~
	~~chord \|\|~ lcm \|\|~~
	~~\|\| 7:5 \|\| 35 \|\|~~
	~~\|\| 8:5 \|\| 40 \|\|~~
	~~\|\| 5:6:7 \|\| 210 \|\|~~
	~~\|\| 6:7:8 \|\| 168 \|\|~~

	~~==See also==~~		{\| class="wikitable"
	~~http://en.wikipedia.org/wiki/Least_common_multiple</pre></div>~~		\|-
	~~<h4>Original HTML content:</h4>~~		! \| interval/
	<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>Least common multiple</title></head><body>The <strong>least common multiple</strong> (<strong>lcm</strong>) or its logarithm (for example <a class="wiki_link" href="/Log2">Log2</a>) can be used as a <a class="wiki_link" href="/dissonance%20measure">dissonance measure</a> for <a class="~~wiki_link~~" ~~href="/intervals">intervals</a> and <a class="wiki_link" href="/chords">chords</a>.<br />~~
	~~<br />~~
	~~<!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Examples"></a><~~!~~-- ws:end:WikiTextHeadingRule:0 -->Examples<~~/~~h2>~~


	~~<table class="wiki_table">~~		chord
	~~<tr>~~		! \| lcm
	~~<th>interval/<br />~~		\|-
	chord~~<br />~~		\| \| 7:5
	~~</th>~~		\| \| 35
	~~<th>~~lcm~~<br />~~		\|-
	~~</th>~~		\| \| 8:5
	~~</tr>~~		\| \| 40
	~~<tr>~~		\|-
	~~<td>~~7:5~~<br />~~		\| \| 5:6:7
	~~</td>~~		\| \| 210
	~~<td>~~35~~<br />~~		\|-
	~~</td>~~		\| \| 6:7:8
	~~</tr>~~		\| \| 168
	~~<tr>~~		\|}
	~~<td>~~8:5~~<br />~~
	~~</td>~~
	~~<td>~~40~~<br />~~
	~~</td>~~
	~~</tr>~~
	~~<tr>~~
	~~<td>~~5:6:7~~<br />~~
	~~</td>~~
	~~<td>~~210~~<br />~~
	~~</td>~~
	~~</tr>~~
	~~<tr>~~
	~~<td>~~6:7:8~~<br />~~
	~~</td>~~
	~~<td>~~168~~<br />~~
	~~</td>~~
	~~</tr>~~
	~~</table>~~

	~~<br />~~		==See also==
	~~<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id~~=~~"toc1"><a name~~=~~"x-See also"></a><!-- ws:end:WikiTextHeadingRule:2 -->~~See also~~</h2>~~		[http://en.wikipedia.org/wiki/Least_common_multiple http://en.wikipedia.org/wiki/Least_common_multiple] [[Category:consonance]]
	~~<!-- ws:start:WikiTextUrlRule:54:http://en.wikipedia.org/wiki/Least_common_multiple --><a class~~=~~"wiki_link_ext" href~~="http://en.wikipedia.org/wiki/Least_common_multiple~~" rel="nofollow">~~http://en.wikipedia.org/wiki/Least_common_multiple~~</a><!-- ws~~:~~end~~:~~WikiTextUrlRule~~:~~54 --></body></html></pre></div>~~		[[Category:dissonance]]
			[[Category:harmonic_entropy]]

Wikispaces>guest: Imported revision 338078884 - Original comment:

2012-05-21T18:15:04Z

**Imported revision 338078884 - Original comment: **

← Older revision		Revision as of 18:15, 21 May 2012
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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-~~24 05~~:10:34 UTC</tt>.<br>		: This revision was by author [[User:guest\|guest]] and made on <tt>2012-05-21 18:15:04 UTC</tt>.<br>
	: The original revision id was <tt>~~238545199~~</tt>.<br>		: The original revision id was <tt>338078884</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>
Line 8:		Line 8:
	<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 least common multiple (lcm) or its logarithm (for example [[Log2]]) can be used as a [[dissonance measure]] for [[intervals]] and [[chords]].		<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 least common multiple (lcm) or its logarithm (for example [[Log2]]) can be used as a [[dissonance measure]] for [[intervals]] and [[chords]].

	== Examples ==		==Examples==
	\|\|~ interval/		\|\|~ interval/
	chord \|\|~ lcm		chord \|\|~ lcm \|\|
	\|\| 7:5 \|\| 35 \|\|		\|\| 7:5 \|\| 35 \|\|
	\|\| 8:5 \|\| 40 \|\|		\|\| 8:5 \|\| 40 \|\|
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	\|\| 6:7:8 \|\| 168 \|\|		\|\| 6:7:8 \|\| 168 \|\|

	== See also ==		==See also==
	http://en.wikipedia.org/wiki/Least_common_multiple</pre></div>		http://en.wikipedia.org/wiki/Least_common_multiple</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"><html><head><title>Least common multiple</title></head><body>The <strong>least common multiple</strong> (<strong>lcm</strong>) or its logarithm (for example <a class="wiki_link" href="/Log2">Log2</a>) can be used as a <a class="wiki_link" href="/dissonance%20measure">dissonance measure</a> for <a class="wiki_link" href="/intervals">intervals</a> and <a class="wiki_link" href="/chords">chords</a>.<br />		<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>Least common multiple</title></head><body>The <strong>least common multiple</strong> (<strong>lcm</strong>) or its logarithm (for example <a class="wiki_link" href="/Log2">Log2</a>) can be used as a <a class="wiki_link" href="/dissonance%20measure">dissonance measure</a> for <a class="wiki_link" href="/intervals">intervals</a> and <a class="wiki_link" href="/chords">chords</a>.<br />
	<br />		<br />
	<!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Examples"></a><!-- ws:end:WikiTextHeadingRule:0 --> Examples </h2>		<!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Examples"></a><!-- ws:end:WikiTextHeadingRule:0 -->Examples</h2>


	<table class="wiki_table">		<table class="wiki_table">
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	<th>lcm<br />		<th>lcm<br />
	</th>		</th>
			</tr>
			<tr>
	<td>7:5<br />		<td>7:5<br />
	</td>		</td>
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	<br />		<br />
	<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="x-See also"></a><!-- ws:end:WikiTextHeadingRule:2 --> See also </h2>		<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="x-See also"></a><!-- ws:end:WikiTextHeadingRule:2 -->See also</h2>
	<!-- ws:start:WikiTextUrlRule:52:http://en.wikipedia.org/wiki/Least_common_multiple --><a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Least_common_multiple" rel="nofollow">http://en.wikipedia.org/wiki/Least_common_multiple</a><!-- ws:end:WikiTextUrlRule:52 --></body></html></pre></div>		<!-- ws:start:WikiTextUrlRule:54:http://en.wikipedia.org/wiki/Least_common_multiple --><a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Least_common_multiple" rel="nofollow">http://en.wikipedia.org/wiki/Least_common_multiple</a><!-- ws:end:WikiTextUrlRule:54 --></body></html></pre></div>

← Older revision		Revision as of 10:21, 24 April 2025
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	[[Category:Interval complexity measures]]		[[Category:Interval complexity measures]]
	[[Category:Complexity]]		[[Category:Complexity]]
	~~[[Category:Harmonic entropy]]~~


	{{stub}}		{{stub}}

← Older revision		Revision as of 10:20, 24 April 2025
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	\|}		\|}

	[[Category:~~Consonance and dissonance~~]]		[[Category:Interval complexity measures]]
			[[Category:Complexity]]
	[[Category:Harmonic entropy]]		[[Category:Harmonic entropy]]


	{{stub}}		{{stub}}