Tenney norm: Difference between revisions
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Wikispaces>xenwolf **Imported revision 146157150 - Original comment: definition from monzo page copied here** |
Wikispaces>xenwolf **Imported revision 146157510 - Original comment: ** |
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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>2010-06-01 03: | : This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2010-06-01 03:07:44 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>146157510</tt>.<br> | ||
: The revision comment was: <tt> | : 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> | ||
<h4>Original Wikitext content:</h4> | <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">If p/q is a positive rational number reduced to its lowest terms, then the **Tenney height**, named for [[James Tenney]] who proposed it, is the integer pq. Often it is more convenient instead to take the logarithm (usually base 2) of the height. In either form it is widely used as a measure of inharmonicity and/or complexity for intervals. | <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">If p/q is a positive rational number reduced to its lowest terms, then the **Tenney height**, named for [[James Tenney]] who proposed it, is the integer pq. Often it is more convenient instead to take the logarithm (usually base 2) of the height. In either form it is widely used as a measure of inharmonicity and/or complexity for intervals. | ||
The [[Tenney Height|Tenney height]] of | The [[Tenney Height|Tenney height]] of a [[monzo]] is given by | ||
|| |e2 e3 ... ep> || = |e2| + log2(3)|e3| + ... + log2(p) |ep| | || |e2 e3 ... ep> || = |e2| + log2(3)|e3| + ... + log2(p) |ep| | ||
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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>Tenney Height</title></head><body>If p/q is a positive rational number reduced to its lowest terms, then the <strong>Tenney height</strong>, named for <a class="wiki_link" href="/James%20Tenney">James Tenney</a> who proposed it, is the integer pq. Often it is more convenient instead to take the logarithm (usually base 2) of the height. In either form it is widely used as a measure of inharmonicity and/or complexity for intervals.<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>Tenney Height</title></head><body>If p/q is a positive rational number reduced to its lowest terms, then the <strong>Tenney height</strong>, named for <a class="wiki_link" href="/James%20Tenney">James Tenney</a> who proposed it, is the integer pq. Often it is more convenient instead to take the logarithm (usually base 2) of the height. In either form it is widely used as a measure of inharmonicity and/or complexity for intervals.<br /> | ||
<br /> | <br /> | ||
The <a class="wiki_link" href="/Tenney%20Height">Tenney height</a> of | The <a class="wiki_link" href="/Tenney%20Height">Tenney height</a> of a <a class="wiki_link" href="/monzo">monzo</a> is given by<br /> | ||
<br /> | <br /> | ||
|| |e2 e3 ... ep&gt; || = |e2| + log2(3)|e3| + ... + log2(p) |ep|<br /> | || |e2 e3 ... ep&gt; || = |e2| + log2(3)|e3| + ... + log2(p) |ep|<br /> | ||
Revision as of 03:07, 1 June 2010
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author xenwolf and made on 2010-06-01 03:07:44 UTC.
- The original revision id was 146157510.
- The revision comment was:
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.
Original Wikitext content:
If p/q is a positive rational number reduced to its lowest terms, then the **Tenney height**, named for [[James Tenney]] who proposed it, is the integer pq. Often it is more convenient instead to take the logarithm (usually base 2) of the height. In either form it is widely used as a measure of inharmonicity and/or complexity for intervals. The [[Tenney Height|Tenney height]] of a [[monzo]] is given by || |e2 e3 ... ep> || = |e2| + log2(3)|e3| + ... + log2(p) |ep| //see also discussion on http://lumma.org/music/theory/TuningFAQ.txt section CONSONANCE AND DISSONANCE//
Original HTML content:
<html><head><title>Tenney Height</title></head><body>If p/q is a positive rational number reduced to its lowest terms, then the <strong>Tenney height</strong>, named for <a class="wiki_link" href="/James%20Tenney">James Tenney</a> who proposed it, is the integer pq. Often it is more convenient instead to take the logarithm (usually base 2) of the height. In either form it is widely used as a measure of inharmonicity and/or complexity for intervals.<br /> <br /> The <a class="wiki_link" href="/Tenney%20Height">Tenney height</a> of a <a class="wiki_link" href="/monzo">monzo</a> is given by<br /> <br /> || |e2 e3 ... ep> || = |e2| + log2(3)|e3| + ... + log2(p) |ep|<br /> <br /> <br /> <em>see also discussion on <!-- ws:start:WikiTextUrlRule:10:http://lumma.org/music/theory/TuningFAQ.txt --><a class="wiki_link_ext" href="http://lumma.org/music/theory/TuningFAQ.txt" rel="nofollow">http://lumma.org/music/theory/TuningFAQ.txt</a><!-- ws:end:WikiTextUrlRule:10 --> section CONSONANCE AND DISSONANCE</em></body></html>