Mavila family: Difference between revisions

Revision as of 13:41, 11 February 2012

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[[toc]]
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 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]])

One of the most common temperaments talked about in the pelogic family is **mavila**, the 5-limit temperament eliminating 138/125, from which higher-limit extensions are derived.

=__5-limit Parent Temperament__= 
=Mavila= 
[[Comma]]s: 135/128
[[POTE tuning|POTE generator]]: 679.806
Map: [<1 0 7|, <0 1 -3|]
EDOs: [[7edo|7]], [[9edo|9]], [[16edo|16]], [[23edo|23]], [[25edo|25b]], [[30edo|30bc]]


=__**7-limit children**__= 
=Septimal Mavila= 
[[Comma]]s: 135/128, 126/125
[[POTE tuning|POTE generator]]: 677.912
Map: [<1 0 7 20|, <0 1 -3 -11|]
EDOs: [[7edo|7]], [[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]]

==11-limit Armodue== 
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, 23p, 25b, 41be, 57be
Badness: 0.0272
----
=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]]



=Mavila Listening examples:= 
**[[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]]

Original HTML content:

<html><head><title>Pelogic family</title></head><body><!-- ws:start:WikiTextTocRule:22:&lt;img id=&quot;wikitext@@toc@@normal&quot; class=&quot;WikiMedia WikiMediaToc&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/normal?w=225&amp;h=100&quot;/&gt; --><div id="toc"><h1 class="nopad">Table of Contents</h1><!-- ws:end:WikiTextTocRule:22 --><!-- ws:start:WikiTextTocRule:23: --><div style="margin-left: 1em;"><a href="#x5-limit Parent Temperament">5-limit Parent Temperament</a></div>
<!-- ws:end:WikiTextTocRule:23 --><!-- ws:start:WikiTextTocRule:24: --><div style="margin-left: 1em;"><a href="#Mavila">Mavila</a></div>
<!-- ws:end:WikiTextTocRule:24 --><!-- ws:start:WikiTextTocRule:25: --><div style="margin-left: 1em;"><a href="#x7-limit children">7-limit children</a></div>
<!-- ws:end:WikiTextTocRule:25 --><!-- ws:start:WikiTextTocRule:26: --><div style="margin-left: 1em;"><a href="#Septimal Mavila">Septimal Mavila</a></div>
<!-- ws:end:WikiTextTocRule:26 --><!-- ws:start:WikiTextTocRule:27: --><div style="margin-left: 1em;"><a href="#Pelogic">Pelogic</a></div>
<!-- ws:end:WikiTextTocRule:27 --><!-- ws:start:WikiTextTocRule:28: --><div style="margin-left: 1em;"><a href="#Armodue">Armodue</a></div>
<!-- ws:end:WikiTextTocRule:28 --><!-- ws:start:WikiTextTocRule:29: --><div style="margin-left: 2em;"><a href="#Armodue-11-limit Armodue">11-limit Armodue</a></div>
<!-- ws:end:WikiTextTocRule:29 --><!-- ws:start:WikiTextTocRule:30: --><div style="margin-left: 1em;"><a href="#Hornbostel">Hornbostel</a></div>
<!-- ws:end:WikiTextTocRule:30 --><!-- ws:start:WikiTextTocRule:31: --><div style="margin-left: 1em;"><a href="#Superpelog">Superpelog</a></div>
<!-- ws:end:WikiTextTocRule:31 --><!-- ws:start:WikiTextTocRule:32: --><div style="margin-left: 1em;"><a href="#Bipelog">Bipelog</a></div>
<!-- ws:end:WikiTextTocRule:32 --><!-- ws:start:WikiTextTocRule:33: --><div style="margin-left: 1em;"><a href="#Mavila Listening examples:">Mavila Listening examples:</a></div>
<!-- ws:end:WikiTextTocRule:33 --><!-- ws:start:WikiTextTocRule:34: --></div>
<!-- ws:end:WikiTextTocRule:34 -->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 />
<br />
Another salient feature of pelogic temperament is the fact that 9 note MOS scales may be produced, thus giving us three different 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 />
<br />
One of the most common temperaments talked about in the pelogic family is <strong>mavila</strong>, the 5-limit temperament eliminating 138/125, from which higher-limit extensions are derived.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x5-limit Parent Temperament"></a><!-- ws:end:WikiTextHeadingRule:0 --><u>5-limit Parent Temperament</u></h1>
 <!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Mavila"></a><!-- ws:end:WikiTextHeadingRule:2 -->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: [&lt;1 0 7|, &lt;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="/16edo">16</a>, <a class="wiki_link" href="/23edo">23</a>, <a class="wiki_link" href="/25edo">25b</a>, <a class="wiki_link" href="/30edo">30bc</a><br />
<br />
<br />
<!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="x7-limit children"></a><!-- ws:end:WikiTextHeadingRule:4 --><u><strong>7-limit children</strong></u></h1>
 <!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><h1 id="toc3"><a name="Septimal Mavila"></a><!-- ws:end:WikiTextHeadingRule:6 -->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="/7edo">7</a>, <a class="wiki_link" href="/16edo">16</a>, <a class="wiki_link" href="/23edo">23d</a><br />
<hr />
<!-- ws:start:WikiTextHeadingRule:8:&lt;h1&gt; --><h1 id="toc4"><a name="Pelogic"></a><!-- ws:end:WikiTextHeadingRule:8 -->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 />
<hr />
<!-- ws:start:WikiTextHeadingRule:10:&lt;h1&gt; --><h1 id="toc5"><a name="Armodue"></a><!-- ws:end:WikiTextHeadingRule:10 -->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 />
<br />
<!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id="toc6"><a name="Armodue-11-limit Armodue"></a><!-- ws:end:WikiTextHeadingRule:12 -->11-limit Armodue</h2>
 Commas: 33/32 36/35 45/44<br />
POTE generator: ~3/2 = 673.807<br />
Map: [&lt;1 0 7 -5 5|, &lt;0 1 -3 5 -1|]<br />
EDOs: 7, 9, 16, 23p, 25b, 41be, 57be<br />
Badness: 0.0272<br />
<hr />
<!-- ws:start:WikiTextHeadingRule:14:&lt;h1&gt; --><h1 id="toc7"><a name="Hornbostel"></a><!-- ws:end:WikiTextHeadingRule:14 -->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 />
<hr />
<!-- ws:start:WikiTextHeadingRule:16:&lt;h1&gt; --><h1 id="toc8"><a name="Superpelog"></a><!-- ws:end:WikiTextHeadingRule:16 -->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 />
<hr />
<!-- ws:start:WikiTextHeadingRule:18:&lt;h1&gt; --><h1 id="toc9"><a name="Bipelog"></a><!-- ws:end:WikiTextHeadingRule:18 -->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><br />
<br />
<br />
<br />
<!-- ws:start:WikiTextHeadingRule:20:&lt;h1&gt; --><h1 id="toc10"><a name="Mavila Listening examples:"></a><!-- ws:end:WikiTextHeadingRule:20 -->Mavila Listening examples:</h1>
 <strong><a class="wiki_link" href="/Gene%20Ward%20Smith">Gene Ward Smith</a>:</strong><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 />
<br />
<strong><a class="wiki_link" href="/Mike%20Battaglia">Mike Battaglia</a></strong><br />
<a class="wiki_link_ext" href="http://soundcloud.com/mikebattagliamusic/sets/the-mavila-experiments" rel="nofollow">The Mavila Experiments</a><br />
<br />
<strong><a class="wiki_link" href="/John%20Moriarty">John Moriarty</a>:</strong><br />
<a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/j_l_moriat/Mavila.mp3" rel="nofollow">Mavila</a></body></html>

Mavila family: Difference between revisions

Revision as of 13:41, 11 February 2012

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