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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | {{Wikipedia}} |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| | The '''least common multiple''' ('''LCM''') or its logarithm (for example [[log2]]) can be used as a [[complexity]] measure for [[interval]]s and [[chord]]s. |
| : This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2011-06-24 05:06:44 UTC</tt>.<br>
| | In terms of harmonic series, it represents the location of the first shared harmonic between all of the notes. |
| : The original revision id was <tt>238544943</tt>.<br>
| | 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. |
| : 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>
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| <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 **least common multiple** (**lcm**) or its logarithm (for example [[Log2]]) can be used as a [[dissonance measure]] for [[intervals]] and [[chords]].
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| http://en.wikipedia.org/wiki/Least_common_multiple</pre></div>
| | == Examples == |
| <h4>Original HTML 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;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 />
| | {| class="wikitable center-all" |
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| <!-- ws:start:WikiTextUrlRule:6: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:6 --></body></html></pre></div>
| | ! Interval/chord |
| | ! LCM |
| | |- |
| | | 7:5 |
| | | 35 |
| | |- |
| | | 8:5 |
| | | 40 |
| | |- |
| | | 4:5:6 |
| | | 60 |
| | |- |
| | | 10:12:15 |
| | | 60 |
| | |- |
| | | 6:7:8 |
| | | 168 |
| | |- |
| | | 5:6:7 |
| | | 210 |
| | |} |
| | |
| | [[Category:Interval complexity measures]] |
| | [[Category:Complexity]] |
| | |
| | {{stub}} |
The least common multiple (LCM) or its logarithm (for example log2) can be used as a complexity measure for intervals and chords.
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
| Interval/chord
|
LCM
|
| 7:5
|
35
|
| 8:5
|
40
|
| 4:5:6
|
60
|
| 10:12:15
|
60
|
| 6:7:8
|
168
|
| 5:6:7
|
210
|
