POTE tuning: 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>~~2012~~-07-~~06 12~~:41:00 UTC</tt>.<br>

: This revision was by author [[User:clumma|clumma]] and made on <tt>2016-07-27 14:07:06 UTC</tt>.<br>

: The original revision id was <tt>~~350848958~~</tt>.<br>

: The original revision id was <tt>588204701</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>

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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">**POTE tuning** is the short form of **Pure-Octaves [[Tenney-Euclidean tuning#Pure octaves TE tuning]]**, a good choice for a standard tuning enforcing just 2s as octaves.

The POTE tuning for a [[map matrix]] such as M = [<1 0 2 -1|, <0 5 1 12|] (the [[map]] for 7-limit [[Magic family|magic]], which consists of a linearly independent list of [[val]]s defining magic) can be found as follows:

The POTE tuning for a [[map matrix]] such as M = [<1 0 2 -1|, <0 5 1 12|] (the [[map]] for 7-limit [[Magic family|magic]], which consists of a linearly independent list of [[val|vals]] defining magic) can be found as follows:

#1 Form a matrix V from M by multiplying by the diagonal matrix which is zero off the diagonal and 1/log2(p) on the diagonal; in other words the diagonal is [1 1/log2(3) 1/log2(5) 1/log2(7)]. Another way to say this is that each val is "weighted" by dividing through by the logarithms, so that V = [<1 0 2/log2(5) -1/log2(7)| <5/log2(3) 1/log2(5) 12/log2(7)]

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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"><html><head><title>POTE tuning</title></head><body><strong>POTE tuning</strong> is the short form of <strong>Pure-Octaves <a class="wiki_link" href="/Tenney-Euclidean%20tuning#Pure octaves TE tuning">Tenney-Euclidean tuning</a></strong>, a good choice for a standard tuning enforcing just 2s as octaves.<br />

<br />

The POTE tuning for a <a class="wiki_link" href="/map%20matrix">map matrix</a> such as M = [&lt;1 0 2 -1|, &lt;0 5 1 12|] (the <a class="wiki_link" href="/map">map</a> for 7-limit <a class="wiki_link" href="/Magic%20family">magic</a>, which consists of a linearly independent list of <a class="wiki_link" href="/val">~~val~~</a>s defining magic) can be found as follows:<br />

The POTE tuning for a <a class="wiki_link" href="/map%20matrix">map matrix</a> such as M = [&lt;1 0 2 -1|, &lt;0 5 1 12|] (the <a class="wiki_link" href="/map">map</a> for 7-limit <a class="wiki_link" href="/Magic%20family">magic</a>, which consists of a linearly independent list of <a class="wiki_link" href="/val">vals</a> defining magic) can be found as follows:<br />

<br />

#1 Form a matrix V from M by multiplying by the diagonal matrix which is zero off the diagonal and 1/log2(p) on the diagonal; in other words the diagonal is [1 1/log2(3) 1/log2(5) 1/log2(7)]. Another way to say this is that each val is &quot;weighted&quot; by dividing through by the logarithms, so that V = [&lt;1 0 2/log2(5) -1/log2(7)| &lt;5/log2(3) 1/log2(5) 12/log2(7)]<br />

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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>2012-07-06 12:41:00 UTC</tt>.<br>
+: This revision was by author [[User:clumma|clumma]] and made on <tt>2016-07-27 14:07:06 UTC</tt>.<br>
-: The original revision id was <tt>350848958</tt>.<br>
+: The original revision id was <tt>588204701</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>
@@ Line 8: / Line 8: @@
 <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">**POTE tuning** is the short form of **Pure-Octaves [[Tenney-Euclidean tuning#Pure octaves TE tuning]]**, a good choice for a standard tuning enforcing just 2s as octaves.
-The POTE tuning for a [[map matrix]] such as M = [&lt;1 0 2 -1|, &lt;0 5 1 12|] (the [[map]] for 7-limit [[Magic family|magic]], which consists of a linearly independent list of [[val]]s defining magic) can be found as follows:
+The POTE tuning for a [[map matrix]] such as M = [&lt;1 0 2 -1|, &lt;0 5 1 12|] (the [[map]] for 7-limit [[Magic family|magic]], which consists of a linearly independent list of [[val|vals]] defining magic) can be found as follows:
 #1 Form a matrix V from M by multiplying by the diagonal matrix which is zero off the diagonal and 1/log2(p) on the diagonal; in other words the diagonal is [1 1/log2(3) 1/log2(5) 1/log2(7)]. Another way to say this is that each val is "weighted" by dividing through by the logarithms, so that V = [&lt;1 0 2/log2(5) -1/log2(7)| &lt;5/log2(3) 1/log2(5) 12/log2(7)]
@@ Line 30: / Line 30: @@
 <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;POTE tuning&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;strong&gt;POTE tuning&lt;/strong&gt; is the short form of &lt;strong&gt;Pure-Octaves &lt;a class="wiki_link" href="/Tenney-Euclidean%20tuning#Pure octaves TE tuning"&gt;Tenney-Euclidean tuning&lt;/a&gt;&lt;/strong&gt;, a good choice for a standard tuning enforcing just 2s as octaves.&lt;br /&gt;
 &lt;br /&gt;
-The POTE tuning for a &lt;a class="wiki_link" href="/map%20matrix"&gt;map matrix&lt;/a&gt; such as M = [&amp;lt;1 0 2 -1|, &amp;lt;0 5 1 12|] (the &lt;a class="wiki_link" href="/map"&gt;map&lt;/a&gt; for 7-limit &lt;a class="wiki_link" href="/Magic%20family"&gt;magic&lt;/a&gt;, which consists of a linearly independent list of &lt;a class="wiki_link" href="/val"&gt;val&lt;/a&gt;s defining magic) can be found as follows:&lt;br /&gt;
+The POTE tuning for a &lt;a class="wiki_link" href="/map%20matrix"&gt;map matrix&lt;/a&gt; such as M = [&amp;lt;1 0 2 -1|, &amp;lt;0 5 1 12|] (the &lt;a class="wiki_link" href="/map"&gt;map&lt;/a&gt; for 7-limit &lt;a class="wiki_link" href="/Magic%20family"&gt;magic&lt;/a&gt;, which consists of a linearly independent list of &lt;a class="wiki_link" href="/val"&gt;vals&lt;/a&gt; defining magic) can be found as follows:&lt;br /&gt;
 &lt;br /&gt;
 #1 Form a matrix V from M by multiplying by the diagonal matrix which is zero off the diagonal and 1/log2(p) on the diagonal; in other words the diagonal is [1 1/log2(3) 1/log2(5) 1/log2(7)]. Another way to say this is that each val is &amp;quot;weighted&amp;quot; by dividing through by the logarithms, so that V = [&amp;lt;1 0 2/log2(5) -1/log2(7)| &amp;lt;5/log2(3) 1/log2(5) 12/log2(7)]&lt;br /&gt;