7-limit symmetrical lattices: 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:xenwolf|xenwolf]] and made on <tt>2010-05-11 10:47:42 UTC</tt>.<br>

: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2010-05-11 10:50:03 UTC</tt>.<br>

: The original revision id was <tt>~~141115263~~</tt>.<br>

: The original revision id was <tt>141116167</tt>.<br>

: The revision comment was: <tt>~~re-formatted hyperlinks - BTW: Interesting, but seems to be a deep copy?~~</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">The octave-equivalent note classes of 7-limit harmony can be represented in vector (odd-only monzo) form as triples of integers (a b c). We can make this into a [[http://en.wikipedia.org/wiki/Lattice_%28group%29|lattice]]

<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 following extracted from http://lumma.org/tuning/gws/sevlat.htm//

The octave-equivalent note classes of 7-limit harmony can be represented in vector (odd-only monzo) form as triples of integers (a b c). We can make this into a [[http://en.wikipedia.org/wiki/Lattice_%28group%29|lattice]]

by putting a [[http://en.wikipedia.org/wiki/Normed_vector_space|norm]] on the three dimensional real we can regard them as living in. If we define

the norm by

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temperament.</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>The Seven Limit Symmetrical Lattices</title></head><body>The octave-equivalent note classes of 7-limit harmony can be represented in vector (odd-only monzo) form as triples of integers (a b c). We can make this into a <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Lattice_%28group%29" rel="nofollow">lattice</a> <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>The Seven Limit Symmetrical Lattices</title></head><body><em>the following extracted from <a class="wiki_link_ext" href="http://lumma.org/tuning/gws/sevlat.htm" rel="nofollow">http://lumma.org/tuning/gws/sevlat.htm</a></em><br />

<br />

The octave-equivalent note classes of 7-limit harmony can be represented in vector (odd-only monzo) form as triples of integers (a b c). We can make this into a <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Lattice_%28group%29" rel="nofollow">lattice</a> <br />

by putting a <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Normed_vector_space" rel="nofollow">norm</a> on the three dimensional real we can regard them as living in. If we define <br />

the norm by<br />

@@ 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:xenwolf|xenwolf]] and made on <tt>2010-05-11 10:47:42 UTC</tt>.<br>
+: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2010-05-11 10:50:03 UTC</tt>.<br>
-: The original revision id was <tt>141115263</tt>.<br>
+: The original revision id was <tt>141116167</tt>.<br>
-: The revision comment was: <tt>re-formatted hyperlinks - BTW: Interesting, but seems to be a deep copy?</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">The octave-equivalent note classes of 7-limit harmony can be represented in vector (odd-only monzo) form as triples of integers (a b c). We can make this into a [[http://en.wikipedia.org/wiki/Lattice_%28group%29|lattice]]
+<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 following extracted from http://lumma.org/tuning/gws/sevlat.htm//
+The octave-equivalent note classes of 7-limit harmony can be represented in vector (odd-only monzo) form as triples of integers (a b c). We can make this into a [[http://en.wikipedia.org/wiki/Lattice_%28group%29|lattice]]
 by putting a [[http://en.wikipedia.org/wiki/Normed_vector_space|norm]]  on the three dimensional real we can regard them as living in. If we define
 the norm by
@@ Line 82: / Line 84: @@
 temperament.</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;The Seven Limit Symmetrical Lattices&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The octave-equivalent note classes of 7-limit harmony can be represented in vector (odd-only monzo) form as triples of integers (a b c). We can make this into a &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Lattice_%28group%29" rel="nofollow"&gt;lattice&lt;/a&gt;   &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;The Seven Limit Symmetrical Lattices&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;em&gt;the following extracted from &lt;!-- ws:start:WikiTextUrlRule:87:http://lumma.org/tuning/gws/sevlat.htm --&gt;&lt;a class="wiki_link_ext" href="http://lumma.org/tuning/gws/sevlat.htm" rel="nofollow"&gt;http://lumma.org/tuning/gws/sevlat.htm&lt;/a&gt;&lt;!-- ws:end:WikiTextUrlRule:87 --&gt;&lt;/em&gt;&lt;br /&gt;
+&lt;br /&gt;
+The octave-equivalent note classes of 7-limit harmony can be represented in vector (odd-only monzo) form as triples of integers (a b c). We can make this into a &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Lattice_%28group%29" rel="nofollow"&gt;lattice&lt;/a&gt;   &lt;br /&gt;
 by putting a &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Normed_vector_space" rel="nofollow"&gt;norm&lt;/a&gt;  on the three dimensional real we can regard them as living in. If we define &lt;br /&gt;
 the norm by&lt;br /&gt;