Structure metric: Difference between revisions

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**Imported revision 562824909 - Original comment: **
 
Wikispaces>genewardsmith
**Imported revision 562824955 - 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>2015-10-17 23:51:03 UTC</tt>.<br>
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2015-10-17 23:53:22 UTC</tt>.<br>
: The original revision id was <tt>562824909</tt>.<br>
: The original revision id was <tt>562824955</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>
<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">The //structure metric// is a [[https://en.wikipedia.org/wiki/Metric_(mathematics)|distance function]] on the period-equivalenced notes of a [[constant structure]] [[periodic scale]] which give to it the property of being a [[https://en.wikipedia.org/wiki/Metric_space|finite metric space]]. If **s** is a periodic scale with quasiperiod **P**, and if **s[i]** is a note of **s**, then we may define the base points set base(**s[i]**) to be the set of integers {j|**s[j+i]** - **s[j]** = **s[i]**}. Reducing these modulo **P** to the range 0 ... **P**-1 gives a finite set of period-equivalenced notes.</pre></div>
<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 //structure metric// is a [[https://en.wikipedia.org/wiki/Metric_(mathematics)|distance function]] on the period-equivalenced notes of a [[constant structure]] [[periodic scale]] which give to it the property of being a [[https://en.wikipedia.org/wiki/Metric_space|finite metric space]]. If **s** is a periodic scale with quasiperiod **P**, and if **s**[i] is a note of **s**, then we may define the base points set base(**s**[i]) to be the set of integers {j|**s**[j+i] - **s**[j] = **s**[i]}. Reducing these modulo **P** to the range 0 ... **P**-1 gives a finite set of period-equivalenced notes.</pre></div>
<h4>Original HTML content:</h4>
<h4>Original HTML 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;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;Structure metric&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The &lt;em&gt;structure metric&lt;/em&gt; is a &lt;a class="wiki_link_ext" href="https://en.wikipedia.org/wiki/Metric_(mathematics)" rel="nofollow"&gt;distance function&lt;/a&gt; on the period-equivalenced notes of a &lt;a class="wiki_link" href="/constant%20structure"&gt;constant structure&lt;/a&gt; &lt;a class="wiki_link" href="/periodic%20scale"&gt;periodic scale&lt;/a&gt; which give to it the property of being a &lt;a class="wiki_link_ext" href="https://en.wikipedia.org/wiki/Metric_space" rel="nofollow"&gt;finite metric space&lt;/a&gt;. If &lt;strong&gt;s&lt;/strong&gt; is a periodic scale with quasiperiod &lt;strong&gt;P&lt;/strong&gt;, and if &lt;strong&gt;s[i]&lt;/strong&gt; is a note of &lt;strong&gt;s&lt;/strong&gt;, then we may define the base points set base(&lt;strong&gt;s[i]&lt;/strong&gt;) to be the set of integers {j|&lt;strong&gt;s[j+i]&lt;/strong&gt; - &lt;strong&gt;s[j]&lt;/strong&gt; = &lt;strong&gt;s[i]&lt;/strong&gt;}. Reducing these modulo &lt;strong&gt;P&lt;/strong&gt; to the range 0 ... &lt;strong&gt;P&lt;/strong&gt;-1 gives a finite set of period-equivalenced notes.&lt;/body&gt;&lt;/html&gt;</pre></div>
<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;Structure metric&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The &lt;em&gt;structure metric&lt;/em&gt; is a &lt;a class="wiki_link_ext" href="https://en.wikipedia.org/wiki/Metric_(mathematics)" rel="nofollow"&gt;distance function&lt;/a&gt; on the period-equivalenced notes of a &lt;a class="wiki_link" href="/constant%20structure"&gt;constant structure&lt;/a&gt; &lt;a class="wiki_link" href="/periodic%20scale"&gt;periodic scale&lt;/a&gt; which give to it the property of being a &lt;a class="wiki_link_ext" href="https://en.wikipedia.org/wiki/Metric_space" rel="nofollow"&gt;finite metric space&lt;/a&gt;. If &lt;strong&gt;s&lt;/strong&gt; is a periodic scale with quasiperiod &lt;strong&gt;P&lt;/strong&gt;, and if &lt;strong&gt;s&lt;/strong&gt;[i] is a note of &lt;strong&gt;s&lt;/strong&gt;, then we may define the base points set base(&lt;strong&gt;s&lt;/strong&gt;[i]) to be the set of integers {j|&lt;strong&gt;s&lt;/strong&gt;[j+i] - &lt;strong&gt;s&lt;/strong&gt;[j] = &lt;strong&gt;s&lt;/strong&gt;[i]}. Reducing these modulo &lt;strong&gt;P&lt;/strong&gt; to the range 0 ... &lt;strong&gt;P&lt;/strong&gt;-1 gives a finite set of period-equivalenced notes.&lt;/body&gt;&lt;/html&gt;</pre></div>

Revision as of 23:53, 17 October 2015

IMPORTED REVISION FROM WIKISPACES

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

This revision was by author genewardsmith and made on 2015-10-17 23:53:22 UTC.
The original revision id was 562824955.
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:

The //structure metric// is a [[https://en.wikipedia.org/wiki/Metric_(mathematics)|distance function]] on the period-equivalenced notes of a [[constant structure]] [[periodic scale]] which give to it the property of being a [[https://en.wikipedia.org/wiki/Metric_space|finite metric space]]. If **s** is a periodic scale with quasiperiod **P**, and if **s**[i] is a note of **s**, then we may define the base points set base(**s**[i]) to be the set of integers {j|**s**[j+i] - **s**[j] = **s**[i]}. Reducing these modulo **P** to the range 0 ... **P**-1 gives a finite set of period-equivalenced notes.

Original HTML content:

<html><head><title>Structure metric</title></head><body>The <em>structure metric</em> is a <a class="wiki_link_ext" href="https://en.wikipedia.org/wiki/Metric_(mathematics)" rel="nofollow">distance function</a> on the period-equivalenced notes of a <a class="wiki_link" href="/constant%20structure">constant structure</a> <a class="wiki_link" href="/periodic%20scale">periodic scale</a> which give to it the property of being a <a class="wiki_link_ext" href="https://en.wikipedia.org/wiki/Metric_space" rel="nofollow">finite metric space</a>. If <strong>s</strong> is a periodic scale with quasiperiod <strong>P</strong>, and if <strong>s</strong>[i] is a note of <strong>s</strong>, then we may define the base points set base(<strong>s</strong>[i]) to be the set of integers {j|<strong>s</strong>[j+i] - <strong>s</strong>[j] = <strong>s</strong>[i]}. Reducing these modulo <strong>P</strong> to the range 0 ... <strong>P</strong>-1 gives a finite set of period-equivalenced notes.</body></html>