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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | :''This page is about the root of a chord. For the ''n''-th root of an interval, see [[Radical interval]]. For the tonic of a scale, occasionally called its 'root', see [[Tonic]].'' |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | | {{Wikipedia|Root (chord)}} |
| : This revision was by author [[User:xenjacob|xenjacob]] and made on <tt>2008-08-29 00:20:05 UTC</tt>.<br>
| | The '''root''' is a specific note that names and characterizes a given chord. Chords are often spoken about in terms of their root, their quality, and their extensions. The root of the chord often appears in the bass, although this is not always the case. When the chord is voiced such that the root is the lowest note, it is said to be in ''root position''. |
| : The original revision id was <tt>36370601</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>
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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 arithmetical concept of //[[http://en.wikipedia.org/wiki/Nth_root|roots]]// is often encountered in discussions about tuning.
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| ==How are roots related to equal divisions?== | | == In tertian harmony == |
| | If the chord can be voiced as a stack of thirds, then the root is typically the lowest note in the stack. |
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| To divide an interval //a// into //b// equal parts, that is, to calculate the size of the interval that, when repeated //b// times, would add up to //a//, calculate the //bth root of a//. The equivalent expression is to take //a// to the //(1/b)th power//.
| | == In other types types of harmony == |
| | If a chord is not composed of thirds, the root can be ambiguous. The chord may still be given a root, although there is no established procedure for doing so. |
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| Why roots and powers? Because intervals are proportions, which you must multiply in order to "add".
| | == See also == |
| | * [[Rooted interval]] |
| | * [[Uprooted interval]] |
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| Take a simple example: what's half of an octave? Well, an octave means "twice the frequency" or "2 times whatever you have" or "2 to 1" or simply "2". (The 2 itself has no units, because they cancel out: to calculate that octave between A-220 and A-440, we divide 440 Hertz by 220 Hertz and get... plain ol' 2.) If an octave means "twice", then what's half of "twice"?
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| | | {{Todo| add examples }} |
| It isn't once...because two onces is just another once!
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| It's the square //root// of 2! Try it: The √2 *multiplied* twice is √2*√2 = 2. (Note that √2 *added* twice would be 2√2.)
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| </pre></div>
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| <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>roots</title></head><body> The arithmetical concept of <em><a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Nth_root" rel="nofollow">roots</a></em> is often encountered in discussions about tuning.<br />
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| <!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-How are roots related to equal divisions?"></a><!-- ws:end:WikiTextHeadingRule:0 -->How are roots related to equal divisions?</h2>
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| To divide an interval <em>a</em> into <em>b</em> equal parts, that is, to calculate the size of the interval that, when repeated <em>b</em> times, would add up to <em>a</em>, calculate the <em>bth root of a</em>. The equivalent expression is to take <em>a</em> to the <em>(1/b)th power</em>.<br />
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| <br />
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| Why roots and powers? Because intervals are proportions, which you must multiply in order to &quot;add&quot;.<br />
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| <br />
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| Take a simple example: what's half of an octave? Well, an octave means &quot;twice the frequency&quot; or &quot;2 times whatever you have&quot; or &quot;2 to 1&quot; or simply &quot;2&quot;. (The 2 itself has no units, because they cancel out: to calculate that octave between A-220 and A-440, we divide 440 Hertz by 220 Hertz and get... plain ol' 2.) If an octave means &quot;twice&quot;, then what's half of &quot;twice&quot;? <br />
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| <br />
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| It isn't once...because two onces is just another once!<br />
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| It's the square <em>root</em> of 2! Try it: The √2 *multiplied* twice is √2*√2 = 2. (Note that √2 *added* twice would be 2√2.)</body></html></pre></div>
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