Mavila family
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[[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]] ==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= [[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]]
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<html><head><title>Pelogic family</title></head><body><!-- ws:start:WikiTextTocRule:16:<img id="wikitext@@toc@@flat" class="WikiMedia WikiMediaTocFlat" title="Table of Contents" src="/site/embedthumbnail/toc/flat?w=100&h=16"/> --><!-- ws:end:WikiTextTocRule:16 --><!-- ws:start:WikiTextTocRule:17: --><a href="#Mavila">Mavila</a><!-- ws:end:WikiTextTocRule:17 --><!-- ws:start:WikiTextTocRule:18: --> | <a href="#Septimal Mavila">Septimal Mavila</a><!-- ws:end:WikiTextTocRule:18 --><!-- ws:start:WikiTextTocRule:19: --> | <a href="#Pelogic">Pelogic</a><!-- ws:end:WikiTextTocRule:19 --><!-- ws:start:WikiTextTocRule:20: --> | <a href="#Armodue">Armodue</a><!-- ws:end:WikiTextTocRule:20 --><!-- ws:start:WikiTextTocRule:21: --><!-- ws:end:WikiTextTocRule:21 --><!-- ws:start:WikiTextTocRule:22: --> | <a href="#Hornbostel">Hornbostel</a><!-- ws:end:WikiTextTocRule:22 --><!-- ws:start:WikiTextTocRule:23: --> | <a href="#Superpelog">Superpelog</a><!-- ws:end:WikiTextTocRule:23 --><!-- ws:start:WikiTextTocRule:24: --> | <a href="#Bipelog">Bipelog</a><!-- ws:end:WikiTextTocRule:24 --><!-- ws:start:WikiTextTocRule:25: --> <!-- ws:end:WikiTextTocRule:25 -->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 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 /> <br /> <!-- ws:start:WikiTextHeadingRule:0:<h1> --><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 /> <br /> <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 /> <br /> <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 /> <br /> <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 /> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h1> --><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: [<1 0 7 20], <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 /> <br /> <!-- ws:start:WikiTextHeadingRule:4:<h1> --><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: [<1 0 7 9|, <0 1 -3 -4|]<br /> <a class="wiki_link" href="/Wedgie">Wedgie</a>: <<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 /> <br /> <!-- ws:start:WikiTextHeadingRule:6:<h1> --><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: [<1 0 7 -5], <0 1 -3 5|]<br /> <a class="wiki_link" href="/Wedgie">Wedgie</a>: <<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:8:<h2> --><h2 id="toc4"><a name="Armodue-11-limit"></a><!-- ws:end:WikiTextHeadingRule:8 -->11-limit</h2> Commas: 33/32 36/35 45/44<br /> <br /> POTE generator: ~3/2 = 673.807<br /> <br /> Map: [<1 0 7 -5 5|, <0 1 -3 5 -1|]<br /> EDOs: 7, 9, 16, 41be, 57be<br /> Badness: 0.0272<br /> <br /> <!-- ws:start:WikiTextHeadingRule:10:<h1> --><h1 id="toc5"><a name="Hornbostel"></a><!-- ws:end:WikiTextHeadingRule:10 -->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: [<1 0 7 -16], <0 1 -3 12|]<br /> <a class="wiki_link" href="/Wedgie">Wedgie</a>: <<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 /> <br /> <!-- ws:start:WikiTextHeadingRule:12:<h1> --><h1 id="toc6"><a name="Superpelog"></a><!-- ws:end:WikiTextHeadingRule:12 -->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: [<1 0 7 2|, <0 2 -6 1|]<br /> <a class="wiki_link" href="/Wedgie">Wedgie</a>: <<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 /> <br /> <!-- ws:start:WikiTextHeadingRule:14:<h1> --><h1 id="toc7"><a name="Bipelog"></a><!-- ws:end:WikiTextHeadingRule:14 -->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: [<2 0 14 15|, <0 1 -3 -3|]<br /> <a class="wiki_link" href="/Wedgie">Wedgie</a>: <<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>