The wedgie: Difference between revisions

Wikispaces>genewardsmith
**Imported revision 515067722 - Original comment: **
Wikispaces>clumma
**Imported revision 535153166 - 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>2014-06-26 21:25:26 UTC</tt>.<br>
: This revision was by author [[User:clumma|clumma]] and made on <tt>2014-12-14 22:40:45 UTC</tt>.<br>
: The original revision id was <tt>515067722</tt>.<br>
: The original revision id was <tt>535153166</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="left"]]
=Basics=
=Basics=
The //[[Wedgies and Multivals|wedgie]]// is a way of defining and working with an [[abstract regular temperament]]. If one takes r independent [[vals]] in a p-limit group of n primes, then the wedgie is defined by taking the [[Wedgies and Multivals|wedge product]] of the vals, and dividing out the greatest common divisior of the coefficients, to produce an r-multival. If the first non-zero coefficient of this multival is negative, it is then scalar multiplied by -1, changing the sign of the first non-zero coefficient to be positive. The result is the wedgie. Wedgies are in a one-to-one relationship with abstract regular temperaments; that is, regular temperaments where no tuning has been decided on.
The //[[Wedgies and Multivals|wedgie]]// is a way of defining and working with an [[abstract regular temperament]]. If one takes r independent [[vals]] in a p-limit group of n primes, then the wedgie is defined by taking the [[Wedgies and Multivals|wedge product]] of the vals, and dividing out the greatest common divisior of the coefficients, to produce an r-multival. If the first non-zero coefficient of this multival is negative, it is then scalar multiplied by -1, changing the sign of the first non-zero coefficient to be positive. The result is the wedgie. Wedgies are in a one-to-one relationship with abstract regular temperaments; that is, regular temperaments where no tuning has been decided on.
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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">&lt;html&gt;&lt;head&gt;&lt;title&gt;The wedgie&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:11:&amp;lt;img id=&amp;quot;wikitext@@toc@@flat&amp;quot; class=&amp;quot;WikiMedia WikiMediaTocFlat&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/flat?w=100&amp;amp;h=16&amp;quot;/&amp;gt; --&gt;&lt;!-- ws:end:WikiTextTocRule:11 --&gt;&lt;!-- ws:start:WikiTextTocRule:12: --&gt;&lt;a href="#Basics"&gt;Basics&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:12 --&gt;&lt;!-- ws:start:WikiTextTocRule:13: --&gt; | &lt;a href="#Truncation of wedgies"&gt;Truncation of wedgies&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:13 --&gt;&lt;!-- ws:start:WikiTextTocRule:14: --&gt; | &lt;a href="#Conditions on being a wedgie"&gt;Conditions on being a wedgie&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:14 --&gt;&lt;!-- ws:start:WikiTextTocRule:15: --&gt; | &lt;a href="#Constrained wedgies"&gt;Constrained wedgies&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:15 --&gt;&lt;!-- ws:start:WikiTextTocRule:16: --&gt; | &lt;a href="#Reconstituting wedgies in general"&gt;Reconstituting wedgies in general&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:16 --&gt;&lt;!-- ws:start:WikiTextTocRule:17: --&gt;
<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">&lt;html&gt;&lt;head&gt;&lt;title&gt;The wedgie&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:11:&amp;lt;img id=&amp;quot;wikitext@@toc@@flat&amp;quot; class=&amp;quot;WikiMedia WikiMediaTocFlat&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/flat?w=100&amp;amp;h=16&amp;quot;/&amp;gt; --&gt;&lt;!-- ws:end:WikiTextTocRule:11 --&gt;&lt;!-- ws:start:WikiTextTocRule:12: --&gt;&lt;a href="#Basics"&gt;Basics&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:12 --&gt;&lt;!-- ws:start:WikiTextTocRule:13: --&gt; | &lt;a href="#Truncation of wedgies"&gt;Truncation of wedgies&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:13 --&gt;&lt;!-- ws:start:WikiTextTocRule:14: --&gt; | &lt;a href="#Conditions on being a wedgie"&gt;Conditions on being a wedgie&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:14 --&gt;&lt;!-- ws:start:WikiTextTocRule:15: --&gt; | &lt;a href="#Constrained wedgies"&gt;Constrained wedgies&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:15 --&gt;&lt;!-- ws:start:WikiTextTocRule:16: --&gt; | &lt;a href="#Reconstituting wedgies in general"&gt;Reconstituting wedgies in general&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:16 --&gt;&lt;!-- ws:start:WikiTextTocRule:17: --&gt;
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&lt;!-- ws:start:WikiTextHeadingRule:1:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Basics"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:1 --&gt;Basics&lt;/h1&gt;
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The &lt;em&gt;&lt;a class="wiki_link" href="/Wedgies%20and%20Multivals"&gt;wedgie&lt;/a&gt;&lt;/em&gt; is a way of defining and working with an &lt;a class="wiki_link" href="/abstract%20regular%20temperament"&gt;abstract regular temperament&lt;/a&gt;. If one takes r independent &lt;a class="wiki_link" href="/vals"&gt;vals&lt;/a&gt; in a p-limit group of n primes, then the wedgie is defined by taking the &lt;a class="wiki_link" href="/Wedgies%20and%20Multivals"&gt;wedge product&lt;/a&gt; of the vals, and dividing out the greatest common divisior of the coefficients, to produce an r-multival. If the first non-zero coefficient of this multival is negative, it is then scalar multiplied by -1, changing the sign of the first non-zero coefficient to be positive. The result is the wedgie. Wedgies are in a one-to-one relationship with abstract regular temperaments; that is, regular temperaments where no tuning has been decided on.&lt;br /&gt;
The &lt;em&gt;&lt;a class="wiki_link" href="/Wedgies%20and%20Multivals"&gt;wedgie&lt;/a&gt;&lt;/em&gt; is a way of defining and working with an &lt;a class="wiki_link" href="/abstract%20regular%20temperament"&gt;abstract regular temperament&lt;/a&gt;. If one takes r independent &lt;a class="wiki_link" href="/vals"&gt;vals&lt;/a&gt; in a p-limit group of n primes, then the wedgie is defined by taking the &lt;a class="wiki_link" href="/Wedgies%20and%20Multivals"&gt;wedge product&lt;/a&gt; of the vals, and dividing out the greatest common divisior of the coefficients, to produce an r-multival. If the first non-zero coefficient of this multival is negative, it is then scalar multiplied by -1, changing the sign of the first non-zero coefficient to be positive. The result is the wedgie. Wedgies are in a one-to-one relationship with abstract regular temperaments; that is, regular temperaments where no tuning has been decided on.&lt;br /&gt;