Projective tuning space: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

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>2014-09-~~13 11~~:16:13 UTC</tt>.<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2014-09-28 20:03:20 UTC</tt>.<br>

: The original revision id was <tt>~~522055556~~</tt>.<br>

: The original revision id was <tt>524164486</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>

<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">Projective tuning space is the [[http://en.wikipedia.org/wiki/Projectiavization|projectivization]] of ordinary [[Vals and tuning space|tuning space]]. If a point in tuning space does not map octaves to zero, we can divide by the value to which "2" is mapped and obtain a pure-octaves tuning which serves to represent the point in projective tuning space. If the dimension of tuning space is n, the ~~dimesion~~ of the ~~correponding~~ projective space is n-1. In ~~particullar~~, 5-limit projective tuning space is two-dimensional, making it easy to depict it graphically.

<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">Projective tuning space is the [[http://en.wikipedia.org/wiki/Projectiavization|projectivization]] of ordinary [[Vals and tuning space|tuning space]]. If a point in tuning space does not map octaves to zero, we can divide by the value to which "2" is mapped and obtain a pure-octaves tuning which serves to represent the point in projective tuning space. If the dimension of tuning space is n, the dimension of the corresponding projective space is n-1. In particular, 5-limit projective tuning space is two-dimensional, making it easy to depict it graphically.

=Quotes=

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[[Gallery of projective tuning space images]]</pre></div>

<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"><html><head><title>Projective tuning space</title></head><body>Projective tuning space is the <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Projectiavization" rel="nofollow">projectivization</a> of ordinary <a class="wiki_link" href="/Vals%20and%20tuning%20space">tuning space</a>. If a point in tuning space does not map octaves to zero, we can divide by the value to which &quot;2&quot; is mapped and obtain a pure-octaves tuning which serves to represent the point in projective tuning space. If the dimension of tuning space is n, the ~~dimesion~~ of the ~~correponding~~ projective space is n-1. In ~~particullar~~, 5-limit projective tuning space is two-dimensional, making it easy to depict it graphically.<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>Projective tuning space</title></head><body>Projective tuning space is the <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Projectiavization" rel="nofollow">projectivization</a> of ordinary <a class="wiki_link" href="/Vals%20and%20tuning%20space">tuning space</a>. If a point in tuning space does not map octaves to zero, we can divide by the value to which &quot;2&quot; is mapped and obtain a pure-octaves tuning which serves to represent the point in projective tuning space. If the dimension of tuning space is n, the dimension of the corresponding projective space is n-1. In particular, 5-limit projective tuning space is two-dimensional, making it easy to depict it graphically.<br />

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<h1 id="toc0"><a name="Quotes"></a>Quotes</h1>

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 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>2014-09-13 11:16:13 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2014-09-28 20:03:20 UTC</tt>.<br>
-: The original revision id was <tt>522055556</tt>.<br>
+: The original revision id was <tt>524164486</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>
 <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">Projective tuning space is the [[http://en.wikipedia.org/wiki/Projectiavization|projectivization]] of ordinary [[Vals and tuning space|tuning space]]. If a point in tuning space does not map octaves to zero, we can divide by the value to which "2" is mapped and obtain a pure-octaves tuning which serves to represent the point in projective tuning space. If the dimension of tuning space is n, the dimesion of the correponding projective space is n-1. In particullar, 5-limit projective tuning space is two-dimensional, making it easy to depict it graphically.
+<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">Projective tuning space is the [[http://en.wikipedia.org/wiki/Projectiavization|projectivization]] of ordinary [[Vals and tuning space|tuning space]]. If a point in tuning space does not map octaves to zero, we can divide by the value to which "2" is mapped and obtain a pure-octaves tuning which serves to represent the point in projective tuning space. If the dimension of tuning space is n, the dimension of the corresponding projective space is n-1. In particular, 5-limit projective tuning space is two-dimensional, making it easy to depict it graphically.
 =Quotes=
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 [[Gallery of projective tuning space images]]</pre></div>
 <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;Projective tuning space&lt;/title&gt;&lt;/head&gt;&lt;body&gt;Projective tuning space is the &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Projectiavization" rel="nofollow"&gt;projectivization&lt;/a&gt; of ordinary &lt;a class="wiki_link" href="/Vals%20and%20tuning%20space"&gt;tuning space&lt;/a&gt;. If a point in tuning space does not map octaves to zero, we can divide by the value to which &amp;quot;2&amp;quot; is mapped and obtain a pure-octaves tuning which serves to represent the point in projective tuning space. If the dimension of tuning space is n, the dimesion of the correponding projective space is n-1. In particullar, 5-limit projective tuning space is two-dimensional, making it easy to depict it graphically.&lt;br /&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;Projective tuning space&lt;/title&gt;&lt;/head&gt;&lt;body&gt;Projective tuning space is the &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Projectiavization" rel="nofollow"&gt;projectivization&lt;/a&gt; of ordinary &lt;a class="wiki_link" href="/Vals%20and%20tuning%20space"&gt;tuning space&lt;/a&gt;. If a point in tuning space does not map octaves to zero, we can divide by the value to which &amp;quot;2&amp;quot; is mapped and obtain a pure-octaves tuning which serves to represent the point in projective tuning space. If the dimension of tuning space is n, the dimension of the corresponding projective space is n-1. In particular, 5-limit projective tuning space is two-dimensional, making it easy to depict it graphically.&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Quotes"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Quotes&lt;/h1&gt;