Structure metric

Revision as of 23:53, 17 October 2015 by Wikispaces>genewardsmith (**Imported revision 562824955 - Original comment: **)

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