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= Comma: 3456/3125 POTE generator: ~25/24 = 140.995 Map: [<1 1 2|, <0 5 3|] EDOs: 8, 9, 17c Badness: 0.2005 ==7-limit== 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= Comma: 6561/6250 POTE generator: ~27/25 = 100.838 Map: [<1 2 3|, <0 -5 -8|] EDOs: 12, 71b, 83b, 95b, 107bc, 119bc Badness: 0.1389 ==7-limit== 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 ==13-limit== Commas: 26/25, 36/35, 56/55, 243/242 POTE generator: ~5/4 = 423.020 Map: [<1 3 2 6 7 3|, <0 -4 1 -9 -10 2|] EDOs: 14, 17c Badness: 0.0368 =Hemismate= commas: 256/245, 392/375 POTE generator: ~8/7 = 210.452 Map: [<1 3 2 3|, <0 -8 2 -1|] Wedgie: <<8 -2 1 -22 -21 8|| EDOs: 6, 11, 17c, 40bcd Badness: 0.1543 ==11-limit== Commas: 56/55, 77/75, 256/245 POTE generator: ~8/7 = 210.481 Map: [<1 3 2 3 4|, <0 -8 2 -1 -3|] EDOs: 6, 11, 17c, 40bcde Badness: 0.0655 ==13-limit== Commas: 26/25, 56/55, 77/75, 256/245 POTE generator: ~8/7 = 210.974 Map: [<1 3 2 3 4 3|, <0 -8 2 -1 -3 4|] EDOs: 6, 11, 17c Badness: 0.0505 =Subklei= Comma: 17496/15625 POTE generator: ~6/5 = 284.293 Map: [<1 3 4|, <0 -6 -7|] EDOs: 4, 17c, 21, 38c Badness: 0.3559 ==7-limit== Commas: 36/35, 1029/1000 POTE generator: ~6/5 = 284.219 Map: [<1 3 4 4|, <0 -6 -7 -5|] Wedgie: <<6 7 5 -3 -9 -8|| EDOs: 4, 17c, 21, 38c Badness: 0.0611 ==11-limit== Commas: 36/35, 77/75, 352/343 POTE generator: ~6/5 = 283.253 Map: [<1 3 4 4 7|, <0 -6 -7 -5 -15|] EDOs: 17c, 55cd Badness: 0.0447 ==Subkla== Commas: 36/35, 56/55, 1029/1000 POTE generator: ~6/5 = 283.822 Map: [<1 3 4 4 3|, <0 -6 -7 -5 2|] EDOs: 4, 17c, 21, 38ce, 55cde Badness: 0.0472 ===13-limit=== Commas: 36/35, 56/55, 66/65, 640/637 POTE generator: ~6/5 = 283.882 Map: [<1 3 4 4 3 3|, <0 -6 -7 -5 2 3|] EDOs: 4, 17c, 21, 38ce, 55cde Badness: 0.0367 ==13-limit== Commas: 26/25, 36/35, 66/65, 352/343 POTE generator: ~6/5 = 282.856 Map: [<1 3 4 4 7 7|, <0 -6 -7 -5 -15 -14|] EDOs: 17c Badness: 0.0323 =Slurpee= Comma: 177147/156250 POTE generator: ~27/25 = 72.742 Map: [<1 2 3|, <0 -7 -11|] EDOs: 16, 17c, 33 Badness: 0.6893 ==7-limit== Commas: 36/35, 51200/50421 POTE generator: ~21/20 = 72.303 Map: [<1 2 3 3|, <0 -7 -11 -3|] Wedgie: <<7 11 3 1 -15 -24|| EDOs: 16, 17c, 33, 50cd, 83bcd Badness: 0.1149 ==11-limit== Commas: 36/35, 121/120, 352/343 POTE generator: ~21/20 = 72.297 Map: [<1 2 3 3 4|, <0 -7 -11 -3 -9|] EDOs: 16, 17c, 33, 50cd, 83bcd Badness: 0.0505 ==13-limit== Commas: 36/35. 66/65, 143/140, 352/343 POTE generator: ~21/20 = 72.409 Map: [<1 2 3 3 4 4|, <0 -7 -11 -3 -9 -5|] EDOs: 16, 17c, 33, 83bcd Badness: 0.0331
Original HTML content:
<html><head><title>Mint temperaments</title></head><body><!-- ws:start:WikiTextTocRule:50:<img id="wikitext@@toc@@flat" class="WikiMedia WikiMediaTocFlat" title="Table of Contents" src="/site/embedthumbnail/toc/flat?w=100&h=16"/> --><!-- ws:end:WikiTextTocRule:50 --><!-- ws:start:WikiTextTocRule:51: --><a href="#Progression">Progression</a><!-- ws:end:WikiTextTocRule:51 --><!-- ws:start:WikiTextTocRule:52: --><!-- ws:end:WikiTextTocRule:52 --><!-- ws:start:WikiTextTocRule:53: --><!-- ws:end:WikiTextTocRule:53 --><!-- ws:start:WikiTextTocRule:54: --><!-- ws:end:WikiTextTocRule:54 --><!-- ws:start:WikiTextTocRule:55: --><!-- ws:end:WikiTextTocRule:55 --><!-- ws:start:WikiTextTocRule:56: --><!-- ws:end:WikiTextTocRule:56 --><!-- ws:start:WikiTextTocRule:57: --> | <a href="#Ripple">Ripple</a><!-- ws:end:WikiTextTocRule:57 --><!-- ws:start:WikiTextTocRule:58: --><!-- ws:end:WikiTextTocRule:58 --><!-- ws:start:WikiTextTocRule:59: --> | <a href="#Smate">Smate</a><!-- ws:end:WikiTextTocRule:59 --><!-- ws:start:WikiTextTocRule:60: --><!-- ws:end:WikiTextTocRule:60 --><!-- ws:start:WikiTextTocRule:61: --><!-- ws:end:WikiTextTocRule:61 --><!-- ws:start:WikiTextTocRule:62: --><!-- ws:end:WikiTextTocRule:62 --><!-- ws:start:WikiTextTocRule:63: --> | <a href="#Hemismate">Hemismate</a><!-- ws:end:WikiTextTocRule:63 --><!-- ws:start:WikiTextTocRule:64: --><!-- ws:end:WikiTextTocRule:64 --><!-- ws:start:WikiTextTocRule:65: --><!-- ws:end:WikiTextTocRule:65 --><!-- ws:start:WikiTextTocRule:66: --> | <a href="#Subklei">Subklei</a><!-- ws:end:WikiTextTocRule:66 --><!-- ws:start:WikiTextTocRule:67: --><!-- ws:end:WikiTextTocRule:67 --><!-- ws:start:WikiTextTocRule:68: --><!-- ws:end:WikiTextTocRule:68 --><!-- ws:start:WikiTextTocRule:69: --><!-- ws:end:WikiTextTocRule:69 --><!-- ws:start:WikiTextTocRule:70: --><!-- ws:end:WikiTextTocRule:70 --><!-- ws:start:WikiTextTocRule:71: --><!-- ws:end:WikiTextTocRule:71 --><!-- ws:start:WikiTextTocRule:72: --> | <a href="#Slurpee">Slurpee</a><!-- ws:end:WikiTextTocRule:72 --><!-- ws:start:WikiTextTocRule:73: --><!-- ws:end:WikiTextTocRule:73 --><!-- ws:start:WikiTextTocRule:74: --><!-- ws:end:WikiTextTocRule:74 --><!-- ws:start:WikiTextTocRule:75: --><!-- ws:end:WikiTextTocRule:75 --><!-- ws:start:WikiTextTocRule:76: --> <!-- ws:end:WikiTextTocRule:76 --><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> Comma: 3456/3125<br /> <br /> POTE generator: ~25/24 = 140.995<br /> <br /> Map: [<1 1 2|, <0 5 3|]<br /> EDOs: 8, 9, 17c<br /> Badness: 0.2005<br /> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h2> --><h2 id="toc1"><a name="Progression-7-limit"></a><!-- ws:end:WikiTextHeadingRule:2 -->7-limit</h2> 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:4:<h2> --><h2 id="toc2"><a name="Progression-11-limit"></a><!-- ws:end:WikiTextHeadingRule:4 -->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:6:<h2> --><h2 id="toc3"><a name="Progression-13-limit"></a><!-- ws:end:WikiTextHeadingRule:6 -->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:8:<h2> --><h2 id="toc4"><a name="Progression-17-limit"></a><!-- ws:end:WikiTextHeadingRule:8 -->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:10:<h3> --><h3 id="toc5"><a name="Progression-17-limit-19-limit"></a><!-- ws:end:WikiTextHeadingRule:10 -->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:12:<h1> --><h1 id="toc6"><a name="Ripple"></a><!-- ws:end:WikiTextHeadingRule:12 -->Ripple</h1> Comma: 6561/6250<br /> <br /> POTE generator: ~27/25 = 100.838<br /> <br /> Map: [<1 2 3|, <0 -5 -8|]<br /> EDOs: 12, 71b, 83b, 95b, 107bc, 119bc<br /> Badness: 0.1389<br /> <br /> <!-- ws:start:WikiTextHeadingRule:14:<h2> --><h2 id="toc7"><a name="Ripple-7-limit"></a><!-- ws:end:WikiTextHeadingRule:14 -->7-limit</h2> 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:16:<h1> --><h1 id="toc8"><a name="Smate"></a><!-- ws:end:WikiTextHeadingRule:16 -->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:18:<h2> --><h2 id="toc9"><a name="Smate-7-limit"></a><!-- ws:end:WikiTextHeadingRule:18 -->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:20:<h2> --><h2 id="toc10"><a name="Smate-11-limit"></a><!-- ws:end:WikiTextHeadingRule:20 -->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<br /> <br /> <!-- ws:start:WikiTextHeadingRule:22:<h2> --><h2 id="toc11"><a name="Smate-13-limit"></a><!-- ws:end:WikiTextHeadingRule:22 -->13-limit</h2> Commas: 26/25, 36/35, 56/55, 243/242 <br /> <br /> POTE generator: ~5/4 = 423.020<br /> <br /> Map: [<1 3 2 6 7 3|, <0 -4 1 -9 -10 2|]<br /> EDOs: 14, 17c<br /> Badness: 0.0368<br /> <br /> <!-- ws:start:WikiTextHeadingRule:24:<h1> --><h1 id="toc12"><a name="Hemismate"></a><!-- ws:end:WikiTextHeadingRule:24 -->Hemismate</h1> commas: 256/245, 392/375 <br /> <br /> POTE generator: ~8/7 = 210.452<br /> <br /> Map: [<1 3 2 3|, <0 -8 2 -1|]<br /> Wedgie: <<8 -2 1 -22 -21 8||<br /> EDOs: 6, 11, 17c, 40bcd<br /> Badness: 0.1543<br /> <br /> <!-- ws:start:WikiTextHeadingRule:26:<h2> --><h2 id="toc13"><a name="Hemismate-11-limit"></a><!-- ws:end:WikiTextHeadingRule:26 -->11-limit</h2> Commas: 56/55, 77/75, 256/245<br /> <br /> POTE generator: ~8/7 = 210.481<br /> <br /> Map: [<1 3 2 3 4|, <0 -8 2 -1 -3|]<br /> EDOs: 6, 11, 17c, 40bcde<br /> Badness: 0.0655<br /> <br /> <!-- ws:start:WikiTextHeadingRule:28:<h2> --><h2 id="toc14"><a name="Hemismate-13-limit"></a><!-- ws:end:WikiTextHeadingRule:28 -->13-limit</h2> Commas: 26/25, 56/55, 77/75, 256/245<br /> <br /> POTE generator: ~8/7 = 210.974<br /> <br /> Map: [<1 3 2 3 4 3|, <0 -8 2 -1 -3 4|]<br /> EDOs: 6, 11, 17c<br /> Badness: 0.0505<br /> <br /> <!-- ws:start:WikiTextHeadingRule:30:<h1> --><h1 id="toc15"><a name="Subklei"></a><!-- ws:end:WikiTextHeadingRule:30 -->Subklei</h1> Comma: 17496/15625<br /> <br /> POTE generator: ~6/5 = 284.293<br /> <br /> Map: [<1 3 4|, <0 -6 -7|]<br /> EDOs: 4, 17c, 21, 38c<br /> Badness: 0.3559<br /> <br /> <!-- ws:start:WikiTextHeadingRule:32:<h2> --><h2 id="toc16"><a name="Subklei-7-limit"></a><!-- ws:end:WikiTextHeadingRule:32 -->7-limit</h2> Commas: 36/35, 1029/1000<br /> <br /> POTE generator: ~6/5 = 284.219<br /> <br /> Map: [<1 3 4 4|, <0 -6 -7 -5|]<br /> Wedgie: <<6 7 5 -3 -9 -8||<br /> EDOs: 4, 17c, 21, 38c<br /> Badness: 0.0611<br /> <br /> <!-- ws:start:WikiTextHeadingRule:34:<h2> --><h2 id="toc17"><a name="Subklei-11-limit"></a><!-- ws:end:WikiTextHeadingRule:34 -->11-limit</h2> Commas: 36/35, 77/75, 352/343<br /> <br /> POTE generator: ~6/5 = 283.253<br /> <br /> Map: [<1 3 4 4 7|, <0 -6 -7 -5 -15|]<br /> EDOs: 17c, 55cd<br /> Badness: 0.0447<br /> <br /> <!-- ws:start:WikiTextHeadingRule:36:<h2> --><h2 id="toc18"><a name="Subklei-Subkla"></a><!-- ws:end:WikiTextHeadingRule:36 -->Subkla</h2> Commas: 36/35, 56/55, 1029/1000<br /> <br /> POTE generator: ~6/5 = 283.822<br /> <br /> Map: [<1 3 4 4 3|, <0 -6 -7 -5 2|]<br /> EDOs: 4, 17c, 21, 38ce, 55cde<br /> Badness: 0.0472<br /> <br /> <!-- ws:start:WikiTextHeadingRule:38:<h3> --><h3 id="toc19"><a name="Subklei-Subkla-13-limit"></a><!-- ws:end:WikiTextHeadingRule:38 -->13-limit</h3> Commas: 36/35, 56/55, 66/65, 640/637<br /> <br /> POTE generator: ~6/5 = 283.882<br /> <br /> Map: [<1 3 4 4 3 3|, <0 -6 -7 -5 2 3|]<br /> EDOs: 4, 17c, 21, 38ce, 55cde<br /> Badness: 0.0367<br /> <br /> <!-- ws:start:WikiTextHeadingRule:40:<h2> --><h2 id="toc20"><a name="Subklei-13-limit"></a><!-- ws:end:WikiTextHeadingRule:40 -->13-limit</h2> Commas: 26/25, 36/35, 66/65, 352/343 <br /> <br /> POTE generator: ~6/5 = 282.856<br /> <br /> Map: [<1 3 4 4 7 7|, <0 -6 -7 -5 -15 -14|]<br /> EDOs: 17c<br /> Badness: 0.0323<br /> <br /> <!-- ws:start:WikiTextHeadingRule:42:<h1> --><h1 id="toc21"><a name="Slurpee"></a><!-- ws:end:WikiTextHeadingRule:42 -->Slurpee</h1> Comma: 177147/156250 <br /> <br /> POTE generator: ~27/25 = 72.742<br /> <br /> Map: [<1 2 3|, <0 -7 -11|]<br /> EDOs: 16, 17c, 33<br /> Badness: 0.6893<br /> <br /> <!-- ws:start:WikiTextHeadingRule:44:<h2> --><h2 id="toc22"><a name="Slurpee-7-limit"></a><!-- ws:end:WikiTextHeadingRule:44 -->7-limit</h2> Commas: 36/35, 51200/50421<br /> <br /> POTE generator: ~21/20 = 72.303<br /> <br /> Map: [<1 2 3 3|, <0 -7 -11 -3|]<br /> Wedgie: <<7 11 3 1 -15 -24||<br /> EDOs: 16, 17c, 33, 50cd, 83bcd<br /> Badness: 0.1149<br /> <br /> <!-- ws:start:WikiTextHeadingRule:46:<h2> --><h2 id="toc23"><a name="Slurpee-11-limit"></a><!-- ws:end:WikiTextHeadingRule:46 -->11-limit</h2> Commas: 36/35, 121/120, 352/343 <br /> <br /> POTE generator: ~21/20 = 72.297<br /> <br /> Map: [<1 2 3 3 4|, <0 -7 -11 -3 -9|]<br /> EDOs: 16, 17c, 33, 50cd, 83bcd<br /> Badness: 0.0505<br /> <br /> <!-- ws:start:WikiTextHeadingRule:48:<h2> --><h2 id="toc24"><a name="Slurpee-13-limit"></a><!-- ws:end:WikiTextHeadingRule:48 -->13-limit</h2> Commas: 36/35. 66/65, 143/140, 352/343<br /> <br /> POTE generator: ~21/20 = 72.409<br /> <br /> Map: [<1 2 3 3 4 4|, <0 -7 -11 -3 -9 -5|]<br /> EDOs: 16, 17c, 33, 83bcd<br /> Badness: 0.0331</body></html>