Mint temperaments
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[[toc|flat]] These are low complexity, high error temperaments tempering out the septimal quarter-tone, [[36_35|36/35]]. 36 is both a square and a [[triangular number]], and this helps make 36/35 a septimal interval of considerable significance. Temperaments tempering it out include beep, dicot, dominant, father, diminished, august, hystrix, penta, hexadecimal, ripple and gorgo. =Progression= Commas: 36/35, 392/375 POTE generator: ~15/14 = 140.927 Map: [<1 1 2 2|, <0 5 3 7|] Wedgie: <<5 3 7 -7 -3 8|| EDOs: 9, 17c Badness: 0.0484 ==11-limit== Commas: 36/35, 56/55, 77/75 [[POTE tuning|POTE generator]]: ~15/14 = 140.747 Map: [<1 1 2 2 3|, <0 5 3 7 4|] EDOs: 8, 9, 17 Badness: 0.0261 ==13-limit== Commas: 26/25, 36/35, 56/55, 66/65 [[POTE tuning|POTE generator]]: ~15/14 = 140.751 Map: Map: [<1 1 2 2 3 3|, <0 5 3 7 4 6|] EDOs: 8, 9, 17 Badness: 0.0182 ==17-limit== Commas: 26/25, 36/35, 51/50, 56/55, 66/65 [[POTE tuning|POTE generator]]: ~15/14 = 141.404 Map: [<1 1 2 2 3 3 4|, <0 5 3 7 4 6 1|] EDOs: 8, 9, 17 Badness: 0.0167 ===19-limit=== Commas: 26/25, 36/35, 51/50, 56/55, 57/55, 66/65 [[POTE tuning|POTE generator]]: ~15/14 = 140.479 Map: [<1 1 2 2 3 3 4 4|, <0 5 3 7 4 6 1 2|] EDOs: 8, 9, 17, [[94edo|94]] Badness: 0.0168 =Ripple= Commas: 36/35, 2560/2401 [[POTE tuning|POTE generator]]: ~21/20 = 99.483 Map: [<1 2 3 3|, <0 -5 -8 -2|] Wedgie: <<5 8 2 1 -11 -18|| EDOs: [[12edo|12]], [[23edo|23]] Badness: 0.0597 =Smate= Comma: 2048/1875 POTE generator: ~5/4 = 420.855 Map: [<1 3 2|, <0 -4 1|] EDOs: 11, 14, 17c, 20c, 37c Badness: 0.179 ==7-limit== Commas: 36/35, 2048/1875 POTE generator: ~5/4 = 422.275 Map: [<1 3 2 6|, <0 -4 1 -9|] Wedgie: <<4 -1 9 -11 3 24|| EDOs: 14, 17c, 37cd Badness: 0.0779 ==11-limit== Commas: 36/35 56/55 243/242 POTE generator: ~5/4 = 422.217 Map: [<1 3 2 6 7|, <0 -4 1 -9 -10|] EDOs: 14, 17c, 37cde Badness: 0.0425
Original HTML content:
<html><head><title>Mint temperaments</title></head><body><!-- ws:start:WikiTextTocRule:18:<img id="wikitext@@toc@@flat" class="WikiMedia WikiMediaTocFlat" title="Table of Contents" src="/site/embedthumbnail/toc/flat?w=100&h=16"/> --><!-- ws:end:WikiTextTocRule:18 --><!-- ws:start:WikiTextTocRule:19: --><a href="#Progression">Progression</a><!-- ws:end:WikiTextTocRule:19 --><!-- ws:start:WikiTextTocRule:20: --><!-- ws:end:WikiTextTocRule:20 --><!-- ws:start:WikiTextTocRule:21: --><!-- ws:end:WikiTextTocRule:21 --><!-- ws:start:WikiTextTocRule:22: --><!-- ws:end:WikiTextTocRule:22 --><!-- ws:start:WikiTextTocRule:23: --><!-- ws:end:WikiTextTocRule:23 --><!-- ws:start:WikiTextTocRule:24: --> | <a href="#Ripple">Ripple</a><!-- ws:end:WikiTextTocRule:24 --><!-- ws:start:WikiTextTocRule:25: --> | <a href="#Smate">Smate</a><!-- ws:end:WikiTextTocRule:25 --><!-- ws:start:WikiTextTocRule:26: --><!-- ws:end:WikiTextTocRule:26 --><!-- ws:start:WikiTextTocRule:27: --><!-- ws:end:WikiTextTocRule:27 --><!-- ws:start:WikiTextTocRule:28: --> <!-- ws:end:WikiTextTocRule:28 --><br /> These are low complexity, high error temperaments tempering out the septimal quarter-tone, <a class="wiki_link" href="/36_35">36/35</a>. 36 is both a square and a <a class="wiki_link" href="/triangular%20number">triangular number</a>, and this helps make 36/35 a septimal interval of considerable significance. Temperaments tempering it out include beep, dicot, dominant, father, diminished, august, hystrix, penta, hexadecimal, ripple and gorgo.<br /> <br /> <!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="Progression"></a><!-- ws:end:WikiTextHeadingRule:0 -->Progression</h1> Commas: 36/35, 392/375<br /> <br /> POTE generator: ~15/14 = 140.927<br /> <br /> Map: [<1 1 2 2|, <0 5 3 7|]<br /> Wedgie: <<5 3 7 -7 -3 8||<br /> EDOs: 9, 17c<br /> Badness: 0.0484<br /> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h2> --><h2 id="toc1"><a name="Progression-11-limit"></a><!-- ws:end:WikiTextHeadingRule:2 -->11-limit</h2> Commas: 36/35, 56/55, 77/75<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~15/14 = 140.747<br /> <br /> Map: [<1 1 2 2 3|, <0 5 3 7 4|]<br /> EDOs: 8, 9, 17<br /> Badness: 0.0261<br /> <br /> <!-- ws:start:WikiTextHeadingRule:4:<h2> --><h2 id="toc2"><a name="Progression-13-limit"></a><!-- ws:end:WikiTextHeadingRule:4 -->13-limit</h2> Commas: 26/25, 36/35, 56/55, 66/65<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~15/14 = 140.751<br /> <br /> Map: Map: [<1 1 2 2 3 3|, <0 5 3 7 4 6|]<br /> EDOs: 8, 9, 17<br /> Badness: 0.0182<br /> <br /> <!-- ws:start:WikiTextHeadingRule:6:<h2> --><h2 id="toc3"><a name="Progression-17-limit"></a><!-- ws:end:WikiTextHeadingRule:6 -->17-limit</h2> Commas: 26/25, 36/35, 51/50, 56/55, 66/65<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~15/14 = 141.404<br /> <br /> Map: [<1 1 2 2 3 3 4|, <0 5 3 7 4 6 1|]<br /> EDOs: 8, 9, 17<br /> Badness: 0.0167<br /> <br /> <!-- ws:start:WikiTextHeadingRule:8:<h3> --><h3 id="toc4"><a name="Progression-17-limit-19-limit"></a><!-- ws:end:WikiTextHeadingRule:8 -->19-limit</h3> Commas: 26/25, 36/35, 51/50, 56/55, 57/55, 66/65<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~15/14 = 140.479<br /> <br /> Map: [<1 1 2 2 3 3 4 4|, <0 5 3 7 4 6 1 2|]<br /> EDOs: 8, 9, 17, <a class="wiki_link" href="/94edo">94</a><br /> Badness: 0.0168<br /> <br /> <!-- ws:start:WikiTextHeadingRule:10:<h1> --><h1 id="toc5"><a name="Ripple"></a><!-- ws:end:WikiTextHeadingRule:10 -->Ripple</h1> Commas: 36/35, 2560/2401<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~21/20 = 99.483<br /> <br /> Map: [<1 2 3 3|, <0 -5 -8 -2|]<br /> Wedgie: <<5 8 2 1 -11 -18||<br /> EDOs: <a class="wiki_link" href="/12edo">12</a>, <a class="wiki_link" href="/23edo">23</a><br /> Badness: 0.0597<br /> <br /> <!-- ws:start:WikiTextHeadingRule:12:<h1> --><h1 id="toc6"><a name="Smate"></a><!-- ws:end:WikiTextHeadingRule:12 -->Smate</h1> Comma: 2048/1875<br /> <br /> POTE generator: ~5/4 = 420.855<br /> <br /> Map: [<1 3 2|, <0 -4 1|]<br /> EDOs: 11, 14, 17c, 20c, 37c<br /> Badness: 0.179<br /> <br /> <!-- ws:start:WikiTextHeadingRule:14:<h2> --><h2 id="toc7"><a name="Smate-7-limit"></a><!-- ws:end:WikiTextHeadingRule:14 -->7-limit</h2> Commas: 36/35, 2048/1875<br /> <br /> POTE generator: ~5/4 = 422.275<br /> <br /> Map: [<1 3 2 6|, <0 -4 1 -9|]<br /> Wedgie: <<4 -1 9 -11 3 24||<br /> EDOs: 14, 17c, 37cd<br /> Badness: 0.0779<br /> <br /> <!-- ws:start:WikiTextHeadingRule:16:<h2> --><h2 id="toc8"><a name="Smate-11-limit"></a><!-- ws:end:WikiTextHeadingRule:16 -->11-limit</h2> Commas: 36/35 56/55 243/242<br /> <br /> POTE generator: ~5/4 = 422.217<br /> <br /> Map: [<1 3 2 6 7|, <0 -4 1 -9 -10|]<br /> EDOs: 14, 17c, 37cde<br /> Badness: 0.0425</body></html>