Mavila family: 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>~~2011~~-11-12 22:40:51 UTC</tt>.<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-01-02 12:37:04 UTC</tt>.<br>

: The original revision id was <tt>~~274737174~~</tt>.<br>

: The original revision id was <tt>289083607</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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[[Wedgie]]: <<11 -3 5 -7 5 20||

EDOs: [[7edo|7]], [[9edo|9]], [[16edo|16]], [[23edo|23p]], [[25edo|25b]], [[73edo|73]]

==11-limit==

Commas: 33/32 36/35 45/44

POTE generator: ~3/2 = 673.807

Map: [<1 0 7 -5 5|, <0 1 -3 5 -1|]

EDOs: 7, 9, 16, 41be, 57be

Badness: 0.0272

=Hornbostel=

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EDOs: [[14edo|14c]], [[16edo|16]], [[23edo|23d]], [[37edo|37bcd]]</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>Pelogic family</title></head><body><a href="#Mavila">Mavila</a> | <a href="#Septimal Mavila">Septimal Mavila</a> | <a href="#Pelogic">Pelogic</a> | <a href="#Armodue">Armodue</a> | <a href="#Hornbostel">Hornbostel</a> | <a href="#Superpelog">Superpelog</a> | <a href="#Bipelog">Bipelog</a>

<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>Pelogic family</title></head><body><a href="#Mavila">Mavila</a> | <a href="#Septimal Mavila">Septimal Mavila</a> | <a href="#Pelogic">Pelogic</a> | <a href="#Armodue">Armodue</a> | <a href="#Hornbostel">Hornbostel</a> | <a href="#Superpelog">Superpelog</a> | <a href="#Bipelog">Bipelog</a>

The <em>pelogic family</em> tempers out <a class="wiki_link" href="/135_128">135/128</a>, the pelogic comma, also known as the major chroma or major limma. The <a class="wiki_link" href="/5-limit">5-limit</a> temperament is (5-limit) mavila, so named after the Chopi village where it was discovered. The generator for all of these is a very flat fifth, lying on the spectrum between 7-equal and 9-equal.<br />

The <em>pelogic family</em> tempers out <a class="wiki_link" href="/135_128">135/128</a>, the pelogic comma, also known as the major chroma or major limma. The <a class="wiki_link" href="/5-limit">5-limit</a> temperament is (5-limit) mavila, so named after the Chopi village where it was discovered. The generator for all of these is a very flat fifth, lying on the spectrum between 7-equal and 9-equal.<br />

<br />

One of the most salient and characteristic features of pelogic temperament is that when you stack 4 of the tempered fifths you get to a minor third instead of the usual major third that you would get if the fifths were pure. This also means that the arrangement of small and large steps in a 7-note mavila scale is the inverse of a diatonic scale of 2 small steps and 5 large steps; Mavila has 2 large steps and 5 small steps. (see <a class="wiki_link" href="/2L%205s">2L 5s)</a><br />

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EDOs: <a class="wiki_link" href="/7edo">7</a>, <a class="wiki_link" href="/9edo">9</a>, <a class="wiki_link" href="/16edo">16</a>, <a class="wiki_link" href="/23edo">23p</a>, <a class="wiki_link" href="/25edo">25b</a>, <a class="wiki_link" href="/73edo">73</a><br />

<br />

<h1 id="~~toc4~~"><a name="Hornbostel"></a>Hornbostel</h1>

<h2 id="toc4"><a name="Armodue-11-limit"></a>11-limit</h2>

Commas: 33/32 36/35 45/44<br />

<br />

POTE generator: ~3/2 = 673.807<br />

<br />

Map: [&lt;1 0 7 -5 5|, &lt;0 1 -3 5 -1|]<br />

EDOs: 7, 9, 16, 41be, 57be<br />

Badness: 0.0272<br />

<br />

<h1 id="toc5"><a name="Hornbostel"></a>Hornbostel</h1>

<a class="wiki_link" href="/Comma">Comma</a>s: 135/128, 875/864<br />

<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 678.947<br />

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EDOs: <a class="wiki_link" href="/7edo">7</a>, <a class="wiki_link" href="/9edo">9</a>, <a class="wiki_link" href="/16edo">16</a>, <a class="wiki_link" href="/23edo">23d</a>, <a class="wiki_link" href="/41edo">41d</a>, <a class="wiki_link" href="/57edo">57d</a><br />

<br />

<h1 id="~~toc5~~"><a name="Superpelog"></a>Superpelog</h1>

<h1 id="toc6"><a name="Superpelog"></a>Superpelog</h1>

<a class="wiki_link" href="/Comma">Comma</a>s: 135/128, 49/48<br />

<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 259.952<br />

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EDOs: <a class="wiki_link" href="/9edo">9</a>, <a class="wiki_link" href="/14edo">14c</a>, <a class="wiki_link" href="/23edo">23d</a>, <a class="wiki_link" href="/37edo">37bcd</a>, <a class="wiki_link" href="/60edo">60bcd</a><br />

<br />

<h1 id="~~toc6~~"><a name="Bipelog"></a>Bipelog</h1>

<h1 id="toc7"><a name="Bipelog"></a>Bipelog</h1>

<a class="wiki_link" href="/Comma">Comma</a>s: 135/128, 50/49<br />

<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 681.195<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:genewardsmith|genewardsmith]] and made on <tt>2011-11-12 22:40:51 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-01-02 12:37:04 UTC</tt>.<br>
-: The original revision id was <tt>274737174</tt>.<br>
+: The original revision id was <tt>289083607</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 48: / Line 48: @@
 [[Wedgie]]: &lt;&lt;11 -3 5 -7 5 20||
 EDOs: [[7edo|7]], [[9edo|9]], [[16edo|16]], [[23edo|23p]], [[25edo|25b]], [[73edo|73]]
+==11-limit==
+Commas: 33/32 36/35 45/44
+POTE generator: ~3/2 = 673.807
+Map: [&lt;1 0 7 -5 5|, &lt;0 1 -3 5 -1|]
+EDOs: 7, 9, 16, 41be, 57be
+Badness: 0.0272
 =Hornbostel=
@@ Line 70: / Line 79: @@
 EDOs: [[14edo|14c]], [[16edo|16]], [[23edo|23d]], [[37edo|37bcd]]</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;Pelogic family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:14:&amp;lt;img id=&amp;quot;wikitext@@toc@@flat&amp;quot; class=&amp;quot;WikiMedia WikiMediaTocFlat&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/flat?w=100&amp;amp;h=16&amp;quot;/&amp;gt; --&gt;&lt;!-- ws:end:WikiTextTocRule:14 --&gt;&lt;!-- ws:start:WikiTextTocRule:15: --&gt;&lt;a href="#Mavila"&gt;Mavila&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:15 --&gt;&lt;!-- ws:start:WikiTextTocRule:16: --&gt; | &lt;a href="#Septimal Mavila"&gt;Septimal Mavila&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:16 --&gt;&lt;!-- ws:start:WikiTextTocRule:17: --&gt; | &lt;a href="#Pelogic"&gt;Pelogic&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:17 --&gt;&lt;!-- ws:start:WikiTextTocRule:18: --&gt; | &lt;a href="#Armodue"&gt;Armodue&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:18 --&gt;&lt;!-- ws:start:WikiTextTocRule:19: --&gt; | &lt;a href="#Hornbostel"&gt;Hornbostel&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:19 --&gt;&lt;!-- ws:start:WikiTextTocRule:20: --&gt; | &lt;a href="#Superpelog"&gt;Superpelog&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:20 --&gt;&lt;!-- ws:start:WikiTextTocRule:21: --&gt; | &lt;a href="#Bipelog"&gt;Bipelog&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:21 --&gt;&lt;!-- ws:start:WikiTextTocRule:22: --&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;Pelogic family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:16:&amp;lt;img id=&amp;quot;wikitext@@toc@@flat&amp;quot; class=&amp;quot;WikiMedia WikiMediaTocFlat&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/flat?w=100&amp;amp;h=16&amp;quot;/&amp;gt; --&gt;&lt;!-- ws:end:WikiTextTocRule:16 --&gt;&lt;!-- ws:start:WikiTextTocRule:17: --&gt;&lt;a href="#Mavila"&gt;Mavila&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:17 --&gt;&lt;!-- ws:start:WikiTextTocRule:18: --&gt; | &lt;a href="#Septimal Mavila"&gt;Septimal Mavila&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:18 --&gt;&lt;!-- ws:start:WikiTextTocRule:19: --&gt; | &lt;a href="#Pelogic"&gt;Pelogic&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:19 --&gt;&lt;!-- ws:start:WikiTextTocRule:20: --&gt; | &lt;a href="#Armodue"&gt;Armodue&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:20 --&gt;&lt;!-- ws:start:WikiTextTocRule:21: --&gt;&lt;!-- ws:end:WikiTextTocRule:21 --&gt;&lt;!-- ws:start:WikiTextTocRule:22: --&gt; | &lt;a href="#Hornbostel"&gt;Hornbostel&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:22 --&gt;&lt;!-- ws:start:WikiTextTocRule:23: --&gt; | &lt;a href="#Superpelog"&gt;Superpelog&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:23 --&gt;&lt;!-- ws:start:WikiTextTocRule:24: --&gt; | &lt;a href="#Bipelog"&gt;Bipelog&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:24 --&gt;&lt;!-- ws:start:WikiTextTocRule:25: --&gt;
-&lt;!-- ws:end:WikiTextTocRule:22 --&gt;The &lt;em&gt;pelogic family&lt;/em&gt; tempers out &lt;a class="wiki_link" href="/135_128"&gt;135/128&lt;/a&gt;, the pelogic comma, also known as the major chroma or major limma. The &lt;a class="wiki_link" href="/5-limit"&gt;5-limit&lt;/a&gt; temperament is (5-limit) mavila, so named after the Chopi village where it was discovered. The generator for all of these is a very flat fifth, lying on the spectrum between 7-equal and 9-equal.&lt;br /&gt;
+&lt;!-- ws:end:WikiTextTocRule:25 --&gt;The &lt;em&gt;pelogic family&lt;/em&gt; tempers out &lt;a class="wiki_link" href="/135_128"&gt;135/128&lt;/a&gt;, the pelogic comma, also known as the major chroma or major limma. The &lt;a class="wiki_link" href="/5-limit"&gt;5-limit&lt;/a&gt; temperament is (5-limit) mavila, so named after the Chopi village where it was discovered. The generator for all of these is a very flat fifth, lying on the spectrum between 7-equal and 9-equal.&lt;br /&gt;
 &lt;br /&gt;
 One of the most salient and characteristic features of pelogic temperament is that when you stack 4 of the tempered fifths you get to a minor third instead of the usual major third that you would get if the fifths were pure. This also means that the arrangement of small and large steps in a 7-note mavila scale is the inverse of a diatonic scale of 2 small steps and 5 large steps; Mavila has 2 large steps and 5 small steps. (see &lt;a class="wiki_link" href="/2L%205s"&gt;2L 5s)&lt;/a&gt;&lt;br /&gt;
@@ Line 113: / Line 122: @@
 EDOs: &lt;a class="wiki_link" href="/7edo"&gt;7&lt;/a&gt;, &lt;a class="wiki_link" href="/9edo"&gt;9&lt;/a&gt;, &lt;a class="wiki_link" href="/16edo"&gt;16&lt;/a&gt;, &lt;a class="wiki_link" href="/23edo"&gt;23p&lt;/a&gt;, &lt;a class="wiki_link" href="/25edo"&gt;25b&lt;/a&gt;, &lt;a class="wiki_link" href="/73edo"&gt;73&lt;/a&gt;&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc4"&gt;&lt;a name="Hornbostel"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Hornbostel&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="Armodue-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;11-limit&lt;/h2&gt;
+Commas: 33/32 36/35 45/44&lt;br /&gt;
+&lt;br /&gt;
+POTE generator: ~3/2 = 673.807&lt;br /&gt;
+&lt;br /&gt;
+Map: [&amp;lt;1 0 7 -5 5|, &amp;lt;0 1 -3 5 -1|]&lt;br /&gt;
+EDOs: 7, 9, 16, 41be, 57be&lt;br /&gt;
+Badness: 0.0272&lt;br /&gt;
+&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc5"&gt;&lt;a name="Hornbostel"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Hornbostel&lt;/h1&gt;
   &lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 135/128, 875/864&lt;br /&gt;
 &lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 678.947&lt;br /&gt;
@@ Line 120: / Line 138: @@
 EDOs: &lt;a class="wiki_link" href="/7edo"&gt;7&lt;/a&gt;, &lt;a class="wiki_link" href="/9edo"&gt;9&lt;/a&gt;, &lt;a class="wiki_link" href="/16edo"&gt;16&lt;/a&gt;, &lt;a class="wiki_link" href="/23edo"&gt;23d&lt;/a&gt;, &lt;a class="wiki_link" href="/41edo"&gt;41d&lt;/a&gt;, &lt;a class="wiki_link" href="/57edo"&gt;57d&lt;/a&gt;&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc5"&gt;&lt;a name="Superpelog"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Superpelog&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc6"&gt;&lt;a name="Superpelog"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;Superpelog&lt;/h1&gt;
   &lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 135/128, 49/48&lt;br /&gt;
 &lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 259.952&lt;br /&gt;
@@ Line 127: / Line 145: @@
 EDOs: &lt;a class="wiki_link" href="/9edo"&gt;9&lt;/a&gt;, &lt;a class="wiki_link" href="/14edo"&gt;14c&lt;/a&gt;, &lt;a class="wiki_link" href="/23edo"&gt;23d&lt;/a&gt;, &lt;a class="wiki_link" href="/37edo"&gt;37bcd&lt;/a&gt;, &lt;a class="wiki_link" href="/60edo"&gt;60bcd&lt;/a&gt;&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc6"&gt;&lt;a name="Bipelog"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;Bipelog&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc7"&gt;&lt;a name="Bipelog"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;Bipelog&lt;/h1&gt;
   &lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 135/128, 50/49&lt;br /&gt;
 &lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 681.195&lt;br /&gt;