Mavila family: Difference between revisions

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Wikispaces>Osmiorisbendi
**Imported revision 256356090 - Original comment: **
Wikispaces>genewardsmith
**Imported revision 274737174 - Original comment: **
Line 1: Line 1:
<h2>IMPORTED REVISION FROM WIKISPACES</h2>
<h2>IMPORTED REVISION FROM WIKISPACES</h2>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:Osmiorisbendi|Osmiorisbendi]] and made on <tt>2011-09-20 21:38:14 UTC</tt>.<br>
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-11-12 22:40:51 UTC</tt>.<br>
: The original revision id was <tt>256356090</tt>.<br>
: The original revision id was <tt>274737174</tt>.<br>
: The revision comment was: <tt></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>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
Line 17: Line 17:
[[POTE tuning|POTE generator]]: 679.806
[[POTE tuning|POTE generator]]: 679.806
Map: [[1 0 7], [0 1 -3]]
Map: [[1 0 7], [0 1 -3]]
EDOs: [[7edo|7]], [[9edo|9]], [[16edo|16]], [[23edo|23]], [[25edo|25b]], [[30edo|30b]]
EDOs: [[7edo|7]], [[9edo|9]], [[14edo|14c]], [[16edo|16]], [[23edo|23]], [[30edo|30bc]]


[[Gene Ward Smith]]
[[Gene Ward Smith]]
Line 33: Line 33:
[[POTE tuning|POTE generator]]: 677.912
[[POTE tuning|POTE generator]]: 677.912
Map: [&lt;1 0 7 20], &lt;0 1 -3 -11|]
Map: [&lt;1 0 7 20], &lt;0 1 -3 -11|]
EDOs: [[16edo|16]], [[23edo|23d]]
EDOs: [[14edo|14c]], [[16edo|16]], [[23edo|23d]]


=Pelogic=  
=Pelogic=  
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Map: [&lt;1 0 7 9|, &lt;0 1 -3 -4|]
Map: [&lt;1 0 7 9|, &lt;0 1 -3 -4|]
[[Wedgie]]: &lt;&lt;1 -3 -4 -7 -9 -1||
[[Wedgie]]: &lt;&lt;1 -3 -4 -7 -9 -1||
EDOs: [[9edo|9]], [[11edo|11]]
EDOs: [[9edo|9]], [[16edo|16d]], [[25edo|25bd]]


=Armodue=  
=Armodue=  
Line 54: Line 54:
Map: [&lt;1 0 7 -16], &lt;0 1 -3 12|]
Map: [&lt;1 0 7 -16], &lt;0 1 -3 12|]
[[Wedgie]]: &lt;&lt;1 -3 12 -7 16 36||
[[Wedgie]]: &lt;&lt;1 -3 12 -7 16 36||
EDOs: [[7edo|7]], [[23edo|23d]], [[30edo|30bc]]
EDOs: [[7edo|7]], [[9edo|9]], [[16edo|16]], [[23edo|23d]], [[41edo|41d]], [[57edo|57d]]


=Superpelog=  
=Superpelog=  
Line 61: Line 61:
Map: [&lt;1 0 7 2|, &lt;0 2 -6 1|]
Map: [&lt;1 0 7 2|, &lt;0 2 -6 1|]
[[Wedgie]]: &lt;&lt;2 -6 1 -14 -4 19||
[[Wedgie]]: &lt;&lt;2 -6 1 -14 -4 19||
EDOs: [[5edo|5]], [[9edo|9]], [[14edo|14]], [[23edo|23]], [[37edo|37]], [[60edo|60]]
EDOs: [[9edo|9]], [[14edo|14c]], [[23edo|23d]], [[37edo|37bcd]], [[60edo|60bcd]]


=Bipelog=  
=Bipelog=  
Line 68: Line 68:
Map: [&lt;2 0 14 15|, &lt;0 1 -3 -3|]
Map: [&lt;2 0 14 15|, &lt;0 1 -3 -3|]
[[Wedgie]]: &lt;&lt;2 -6 -6 -14 -15 3||
[[Wedgie]]: &lt;&lt;2 -6 -6 -14 -15 3||
EDOs: [[14edo|14]], [[16edo|16]], [[30edo|30]], [[44edo|44]], [[74edo|74]]</pre></div>
EDOs: [[14edo|14c]], [[16edo|16]], [[23edo|23d]], [[37edo|37bcd]]</pre></div>
<h4>Original HTML content:</h4>
<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: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;
Line 81: Line 81:
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 679.806&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 679.806&lt;br /&gt;
Map: [[1 0 7], [0 1 -3]]&lt;br /&gt;
Map: [[1 0 7], [0 1 -3]]&lt;br /&gt;
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;23&lt;/a&gt;, &lt;a class="wiki_link" href="/25edo"&gt;25b&lt;/a&gt;, &lt;a class="wiki_link" href="/30edo"&gt;30b&lt;/a&gt;&lt;br /&gt;
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="/14edo"&gt;14c&lt;/a&gt;, &lt;a class="wiki_link" href="/16edo"&gt;16&lt;/a&gt;, &lt;a class="wiki_link" href="/23edo"&gt;23&lt;/a&gt;, &lt;a class="wiki_link" href="/30edo"&gt;30bc&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Gene%20Ward%20Smith"&gt;Gene Ward Smith&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/Gene%20Ward%20Smith"&gt;Gene Ward Smith&lt;/a&gt;&lt;br /&gt;
Line 97: Line 97:
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 677.912&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 677.912&lt;br /&gt;
Map: [&amp;lt;1 0 7 20], &amp;lt;0 1 -3 -11|]&lt;br /&gt;
Map: [&amp;lt;1 0 7 20], &amp;lt;0 1 -3 -11|]&lt;br /&gt;
EDOs: &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;br /&gt;
EDOs: &lt;a class="wiki_link" href="/14edo"&gt;14c&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;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc2"&gt;&lt;a name="Pelogic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Pelogic&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc2"&gt;&lt;a name="Pelogic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Pelogic&lt;/h1&gt;
Line 104: Line 104:
Map: [&amp;lt;1 0 7 9|, &amp;lt;0 1 -3 -4|]&lt;br /&gt;
Map: [&amp;lt;1 0 7 9|, &amp;lt;0 1 -3 -4|]&lt;br /&gt;
&lt;a class="wiki_link" href="/Wedgie"&gt;Wedgie&lt;/a&gt;: &amp;lt;&amp;lt;1 -3 -4 -7 -9 -1||&lt;br /&gt;
&lt;a class="wiki_link" href="/Wedgie"&gt;Wedgie&lt;/a&gt;: &amp;lt;&amp;lt;1 -3 -4 -7 -9 -1||&lt;br /&gt;
EDOs: &lt;a class="wiki_link" href="/9edo"&gt;9&lt;/a&gt;, &lt;a class="wiki_link" href="/11edo"&gt;11&lt;/a&gt;&lt;br /&gt;
EDOs: &lt;a class="wiki_link" href="/9edo"&gt;9&lt;/a&gt;, &lt;a class="wiki_link" href="/16edo"&gt;16d&lt;/a&gt;, &lt;a class="wiki_link" href="/25edo"&gt;25bd&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc3"&gt;&lt;a name="Armodue"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Armodue&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc3"&gt;&lt;a name="Armodue"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Armodue&lt;/h1&gt;
Line 118: Line 118:
Map: [&amp;lt;1 0 7 -16], &amp;lt;0 1 -3 12|]&lt;br /&gt;
Map: [&amp;lt;1 0 7 -16], &amp;lt;0 1 -3 12|]&lt;br /&gt;
&lt;a class="wiki_link" href="/Wedgie"&gt;Wedgie&lt;/a&gt;: &amp;lt;&amp;lt;1 -3 12 -7 16 36||&lt;br /&gt;
&lt;a class="wiki_link" href="/Wedgie"&gt;Wedgie&lt;/a&gt;: &amp;lt;&amp;lt;1 -3 12 -7 16 36||&lt;br /&gt;
EDOs: &lt;a class="wiki_link" href="/7edo"&gt;7&lt;/a&gt;, &lt;a class="wiki_link" href="/23edo"&gt;23d&lt;/a&gt;, &lt;a class="wiki_link" href="/30edo"&gt;30bc&lt;/a&gt;&lt;br /&gt;
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;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: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;
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Map: [&amp;lt;1 0 7 2|, &amp;lt;0 2 -6 1|]&lt;br /&gt;
Map: [&amp;lt;1 0 7 2|, &amp;lt;0 2 -6 1|]&lt;br /&gt;
&lt;a class="wiki_link" href="/Wedgie"&gt;Wedgie&lt;/a&gt;: &amp;lt;&amp;lt;2 -6 1 -14 -4 19||&lt;br /&gt;
&lt;a class="wiki_link" href="/Wedgie"&gt;Wedgie&lt;/a&gt;: &amp;lt;&amp;lt;2 -6 1 -14 -4 19||&lt;br /&gt;
EDOs: &lt;a class="wiki_link" href="/5edo"&gt;5&lt;/a&gt;, &lt;a class="wiki_link" href="/9edo"&gt;9&lt;/a&gt;, &lt;a class="wiki_link" href="/14edo"&gt;14&lt;/a&gt;, &lt;a class="wiki_link" href="/23edo"&gt;23&lt;/a&gt;, &lt;a class="wiki_link" href="/37edo"&gt;37&lt;/a&gt;, &lt;a class="wiki_link" href="/60edo"&gt;60&lt;/a&gt;&lt;br /&gt;
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;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: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;
Line 132: Line 132:
Map: [&amp;lt;2 0 14 15|, &amp;lt;0 1 -3 -3|]&lt;br /&gt;
Map: [&amp;lt;2 0 14 15|, &amp;lt;0 1 -3 -3|]&lt;br /&gt;
&lt;a class="wiki_link" href="/Wedgie"&gt;Wedgie&lt;/a&gt;: &amp;lt;&amp;lt;2 -6 -6 -14 -15 3||&lt;br /&gt;
&lt;a class="wiki_link" href="/Wedgie"&gt;Wedgie&lt;/a&gt;: &amp;lt;&amp;lt;2 -6 -6 -14 -15 3||&lt;br /&gt;
EDOs: &lt;a class="wiki_link" href="/14edo"&gt;14&lt;/a&gt;, &lt;a class="wiki_link" href="/16edo"&gt;16&lt;/a&gt;, &lt;a class="wiki_link" href="/30edo"&gt;30&lt;/a&gt;, &lt;a class="wiki_link" href="/44edo"&gt;44&lt;/a&gt;, &lt;a class="wiki_link" href="/74edo"&gt;74&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
EDOs: &lt;a class="wiki_link" href="/14edo"&gt;14c&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="/37edo"&gt;37bcd&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>

Revision as of 22:40, 12 November 2011

IMPORTED REVISION FROM WIKISPACES

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

This revision was by author genewardsmith and made on 2011-11-12 22:40:51 UTC.
The original revision id was 274737174.
The revision comment was:

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

Original Wikitext content:

[[toc|flat]]
The //pelogic family// tempers out [[135_128|135/128]], the pelogic comma, also known as the major chroma or major limma. The [[5-limit]] 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.

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 [[2L 5s|2L 5s)]]

Another salient feature of pelogic temperament is the fact that 9 note MOS scales may be produced, thus giving us three different Mavila MOS scales to choose from that are not decidedly chromatic in nature; (5, 7, and 9 note scales) This is reflected in the design of the 9 + 7 layout of the Goldsmith keyboard for 16 tone equal temperament. (see[[7L 2s| 7L 2s]])

=Mavila= 
[[Comma]]s: 135/128
[[POTE tuning|POTE generator]]: 679.806
Map: [[1 0 7], [0 1 -3]]
EDOs: [[7edo|7]], [[9edo|9]], [[14edo|14c]], [[16edo|16]], [[23edo|23]], [[30edo|30bc]]

[[Gene Ward Smith]]
[[http://clones.soonlabel.com/public/micro/gene_ward_smith/mine/mushc.ogg|Mysterious Mush (spectrally mapped)]]
[[http://clones.soonlabel.com/public/micro/gene_ward_smith/mine/mush.ogg|Mysterious Mush (unmapped)]]

[[Mike Battaglia]]
[[http://soundcloud.com/mikebattagliamusic/sets/the-mavila-experiments|The Mavila Experiments]]

[[John Moriarty]]
[[http://clones.soonlabel.com/public/micro/j_l_moriat/Mavila.mp3|Mavila]]

=Septimal Mavila= 
[[Comma]]s: 135/128, 126/125
[[POTE tuning|POTE generator]]: 677.912
Map: [<1 0 7 20], <0 1 -3 -11|]
EDOs: [[14edo|14c]], [[16edo|16]], [[23edo|23d]]

=Pelogic= 
[[Comma]]s: 135/128, 21/20
[[POTE tuning|POTE generator]]: 672.853
Map: [<1 0 7 9|, <0 1 -3 -4|]
[[Wedgie]]: <<1 -3 -4 -7 -9 -1||
EDOs: [[9edo|9]], [[16edo|16d]], [[25edo|25bd]]

=Armodue= 
[[Comma]]s: 135/128, 36/35
[[POTE tuning|POTE generator]]: 673.997
Map: [<1 0 7 -5], <0 1 -3 5|]
[[Wedgie]]: <<11 -3 5 -7 5 20||
EDOs: [[7edo|7]], [[9edo|9]], [[16edo|16]], [[23edo|23p]], [[25edo|25b]], [[73edo|73]]

=Hornbostel= 
[[Comma]]s: 135/128, 875/864
[[POTE tuning|POTE generator]]: 678.947
Map: [<1 0 7 -16], <0 1 -3 12|]
[[Wedgie]]: <<1 -3 12 -7 16 36||
EDOs: [[7edo|7]], [[9edo|9]], [[16edo|16]], [[23edo|23d]], [[41edo|41d]], [[57edo|57d]]

=Superpelog= 
[[Comma]]s: 135/128, 49/48
[[POTE tuning|POTE generator]]: 259.952
Map: [<1 0 7 2|, <0 2 -6 1|]
[[Wedgie]]: <<2 -6 1 -14 -4 19||
EDOs: [[9edo|9]], [[14edo|14c]], [[23edo|23d]], [[37edo|37bcd]], [[60edo|60bcd]]

=Bipelog= 
[[Comma]]s: 135/128, 50/49
[[POTE tuning|POTE generator]]: 681.195
Map: [<2 0 14 15|, <0 1 -3 -3|]
[[Wedgie]]: <<2 -6 -6 -14 -15 3||
EDOs: [[14edo|14c]], [[16edo|16]], [[23edo|23d]], [[37edo|37bcd]]

Original HTML content:

<html><head><title>Pelogic family</title></head><body><!-- ws:start:WikiTextTocRule:14:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:14 --><!-- ws:start:WikiTextTocRule:15: --><a href="#Mavila">Mavila</a><!-- ws:end:WikiTextTocRule:15 --><!-- ws:start:WikiTextTocRule:16: --> | <a href="#Septimal Mavila">Septimal Mavila</a><!-- ws:end:WikiTextTocRule:16 --><!-- ws:start:WikiTextTocRule:17: --> | <a href="#Pelogic">Pelogic</a><!-- ws:end:WikiTextTocRule:17 --><!-- ws:start:WikiTextTocRule:18: --> | <a href="#Armodue">Armodue</a><!-- ws:end:WikiTextTocRule:18 --><!-- ws:start:WikiTextTocRule:19: --> | <a href="#Hornbostel">Hornbostel</a><!-- ws:end:WikiTextTocRule:19 --><!-- ws:start:WikiTextTocRule:20: --> | <a href="#Superpelog">Superpelog</a><!-- ws:end:WikiTextTocRule:20 --><!-- ws:start:WikiTextTocRule:21: --> | <a href="#Bipelog">Bipelog</a><!-- ws:end:WikiTextTocRule:21 --><!-- ws:start:WikiTextTocRule:22: -->
<!-- ws:end:WikiTextTocRule:22 -->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 />
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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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Another salient feature of pelogic temperament is the fact that 9 note MOS scales may be produced, thus giving us three different Mavila MOS scales to choose from that are not decidedly chromatic in nature; (5, 7, and 9 note scales) This is reflected in the design of the 9 + 7 layout of the Goldsmith keyboard for 16 tone equal temperament. (see<a class="wiki_link" href="/7L%202s"> 7L 2s</a>)<br />
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<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Mavila"></a><!-- ws:end:WikiTextHeadingRule:0 -->Mavila</h1>
 <a class="wiki_link" href="/Comma">Comma</a>s: 135/128<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 679.806<br />
Map: [[1 0 7], [0 1 -3]]<br />
EDOs: <a class="wiki_link" href="/7edo">7</a>, <a class="wiki_link" href="/9edo">9</a>, <a class="wiki_link" href="/14edo">14c</a>, <a class="wiki_link" href="/16edo">16</a>, <a class="wiki_link" href="/23edo">23</a>, <a class="wiki_link" href="/30edo">30bc</a><br />
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<a class="wiki_link" href="/Gene%20Ward%20Smith">Gene Ward Smith</a><br />
<a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/mine/mushc.ogg" rel="nofollow">Mysterious Mush (spectrally mapped)</a><br />
<a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/mine/mush.ogg" rel="nofollow">Mysterious Mush (unmapped)</a><br />
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<a class="wiki_link" href="/Mike%20Battaglia">Mike Battaglia</a><br />
<a class="wiki_link_ext" href="http://soundcloud.com/mikebattagliamusic/sets/the-mavila-experiments" rel="nofollow">The Mavila Experiments</a><br />
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<a class="wiki_link" href="/John%20Moriarty">John Moriarty</a><br />
<a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/j_l_moriat/Mavila.mp3" rel="nofollow">Mavila</a><br />
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<!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Septimal Mavila"></a><!-- ws:end:WikiTextHeadingRule:2 -->Septimal Mavila</h1>
 <a class="wiki_link" href="/Comma">Comma</a>s: 135/128, 126/125<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 677.912<br />
Map: [&lt;1 0 7 20], &lt;0 1 -3 -11|]<br />
EDOs: <a class="wiki_link" href="/14edo">14c</a>, <a class="wiki_link" href="/16edo">16</a>, <a class="wiki_link" href="/23edo">23d</a><br />
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<!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="Pelogic"></a><!-- ws:end:WikiTextHeadingRule:4 -->Pelogic</h1>
 <a class="wiki_link" href="/Comma">Comma</a>s: 135/128, 21/20<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 672.853<br />
Map: [&lt;1 0 7 9|, &lt;0 1 -3 -4|]<br />
<a class="wiki_link" href="/Wedgie">Wedgie</a>: &lt;&lt;1 -3 -4 -7 -9 -1||<br />
EDOs: <a class="wiki_link" href="/9edo">9</a>, <a class="wiki_link" href="/16edo">16d</a>, <a class="wiki_link" href="/25edo">25bd</a><br />
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<!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><h1 id="toc3"><a name="Armodue"></a><!-- ws:end:WikiTextHeadingRule:6 -->Armodue</h1>
 <a class="wiki_link" href="/Comma">Comma</a>s: 135/128, 36/35<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 673.997<br />
Map: [&lt;1 0 7 -5], &lt;0 1 -3 5|]<br />
<a class="wiki_link" href="/Wedgie">Wedgie</a>: &lt;&lt;11 -3 5 -7 5 20||<br />
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 />
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<!-- ws:start:WikiTextHeadingRule:8:&lt;h1&gt; --><h1 id="toc4"><a name="Hornbostel"></a><!-- ws:end:WikiTextHeadingRule:8 -->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 />
Map: [&lt;1 0 7 -16], &lt;0 1 -3 12|]<br />
<a class="wiki_link" href="/Wedgie">Wedgie</a>: &lt;&lt;1 -3 12 -7 16 36||<br />
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 />
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<!-- ws:start:WikiTextHeadingRule:10:&lt;h1&gt; --><h1 id="toc5"><a name="Superpelog"></a><!-- ws:end:WikiTextHeadingRule:10 -->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 />
Map: [&lt;1 0 7 2|, &lt;0 2 -6 1|]<br />
<a class="wiki_link" href="/Wedgie">Wedgie</a>: &lt;&lt;2 -6 1 -14 -4 19||<br />
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 />
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<!-- ws:start:WikiTextHeadingRule:12:&lt;h1&gt; --><h1 id="toc6"><a name="Bipelog"></a><!-- ws:end:WikiTextHeadingRule:12 -->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 />
Map: [&lt;2 0 14 15|, &lt;0 1 -3 -3|]<br />
<a class="wiki_link" href="/Wedgie">Wedgie</a>: &lt;&lt;2 -6 -6 -14 -15 3||<br />
EDOs: <a class="wiki_link" href="/14edo">14c</a>, <a class="wiki_link" href="/16edo">16</a>, <a class="wiki_link" href="/23edo">23d</a>, <a class="wiki_link" href="/37edo">37bcd</a></body></html>