TOP tuning: Difference between revisions
Wikispaces>genewardsmith **Imported revision 509656162 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 511016592 - 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:genewardsmith|genewardsmith]] and made on <tt>2014-05- | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2014-05-24 17:08:34 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>511016592</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> | ||
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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">[[toc|flat]] | <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">[[toc|flat]] | ||
[[image:mathhazard.jpg align=" | [[image:mathhazard.jpg align="left"]] | ||
=Proportional error= | =Proportional error= | ||
A //tuning// for a regular temperament is defined by a vector T in [[Vals and Tuning Space#Vals and Monzos|Tenney tuning space]] whose entries are the size of the interval, in cents, which the k generators of the regular temperament (often the first k primes) are mapped to. T is denoted by a [[http://en.wikipedia.org/wiki/Bra-ket_notation|bra vector]], and if M is a monzo then <T|M> is the size, in cents, of the interval defined by M in the tuning T. If q is the rational number which M represents, then we may also write this quantity as T(q). | A //tuning// for a regular temperament is defined by a vector T in [[Vals and Tuning Space#Vals and Monzos|Tenney tuning space]] whose entries are the size of the interval, in cents, which the k generators of the regular temperament (often the first k primes) are mapped to. T is denoted by a [[http://en.wikipedia.org/wiki/Bra-ket_notation|bra vector]], and if M is a monzo then <T|M> is the size, in cents, of the interval defined by M in the tuning T. If q is the rational number which M represents, then we may also write this quantity as T(q). | ||
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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>TOP tuning</title></head><body><!-- ws:start:WikiTextTocRule:4:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:4 --><!-- ws:start:WikiTextTocRule:5: --><a href="#Proportional error">Proportional error</a><!-- ws:end:WikiTextTocRule:5 --><!-- ws:start:WikiTextTocRule:6: --> | <a href="#TOP tuning">TOP tuning</a><!-- ws:end:WikiTextTocRule:6 --><!-- ws:start:WikiTextTocRule:7: --> | <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>TOP tuning</title></head><body><!-- ws:start:WikiTextTocRule:4:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:4 --><!-- ws:start:WikiTextTocRule:5: --><a href="#Proportional error">Proportional error</a><!-- ws:end:WikiTextTocRule:5 --><!-- ws:start:WikiTextTocRule:6: --> | <a href="#TOP tuning">TOP tuning</a><!-- ws:end:WikiTextTocRule:6 --><!-- ws:start:WikiTextTocRule:7: --> | ||
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<!-- ws:start:WikiTextLocalImageRule:8: | <!-- ws:start:WikiTextLocalImageRule:8:&lt;img src=&quot;/file/view/mathhazard.jpg&quot; alt=&quot;&quot; title=&quot;&quot; align=&quot;left&quot; /&gt; --><img src="/file/view/mathhazard.jpg" alt="mathhazard.jpg" title="mathhazard.jpg" align="left" /><!-- ws:end:WikiTextLocalImageRule:8 --><br /> | ||
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Proportional error"></a><!-- ws:end:WikiTextHeadingRule:0 -->Proportional error</h1> | |||
A <em>tuning</em> for a regular temperament is defined by a vector T in <a class="wiki_link" href="/Vals%20and%20Tuning%20Space#Vals and Monzos">Tenney tuning space</a> whose entries are the size of the interval, in cents, which the k generators of the regular temperament (often the first k primes) are mapped to. T is denoted by a <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Bra-ket_notation" rel="nofollow">bra vector</a>, and if M is a monzo then &lt;T|M&gt; is the size, in cents, of the interval defined by M in the tuning T. If q is the rational number which M represents, then we may also write this quantity as T(q). <br /> | A <em>tuning</em> for a regular temperament is defined by a vector T in <a class="wiki_link" href="/Vals%20and%20Tuning%20Space#Vals and Monzos">Tenney tuning space</a> whose entries are the size of the interval, in cents, which the k generators of the regular temperament (often the first k primes) are mapped to. T is denoted by a <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Bra-ket_notation" rel="nofollow">bra vector</a>, and if M is a monzo then &lt;T|M&gt; is the size, in cents, of the interval defined by M in the tuning T. If q is the rational number which M represents, then we may also write this quantity as T(q). <br /> | ||
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