Trienstonic clan
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[[toc|flat]] Adding 16/15 to the trienstonic comma of 28/27 leads to father temperament, adding 256/245 gives uncle, adding 50/49 gives octokaidecal and adding 126/125 gives opossum. Other members of the clan discussed elsewhere are sharptone, sharp, and blacksmith. =Father= Commas: 16/15, 28/27 7-limit minimax [<1 0 0 0|, <3/2 0 -1/4 1/4|, <5/2 0 1/4 -1/4|, <5/2 0 -3/4 3/4|] [[Eigenmonzo subgroup]]: 2.7/5 9-limit eigenmonzo subgroup: 2.9/5 [[POTE tuning|POTE generator]]: 742.002 Map: [<1 0 4 -2|, <0 1 -1 3|] Wedgie: <<1 -1 3 -4 2 10|| EDOs: 5, 8d, 13cd, 21bcd Badness: 0.0213 =Uncle= Commas: 28/27, 256/245 7-limit eigenmonzo subgroup: 2.5/3 9-limit eigenmonzo subgroup: 2.9/5 Map: [<1 0 12 -2|, <0 1 -6 3|] Wedgie: <<1 -6 3 -12 2 24|| EDOs: 13d, 18, 23bc, 41bcd Badness: 0.0727 =Octokaidecal= Commas: 28/27, 50/49 7-limit eigenmonzo subgroup: 2.5 9-limit eigenmonzo subgroup: 2.5 [[POTE tuning|POTE generator]]: 728.874 Map: [<2 0 -5 -4|, <0 1 3 3|] Wedgie: <<2 6 6 5 4 -2|| EDOs: 10, 18, 28b Badness: 0.0367 ==11-limit== Commas: 28/27, 50/49, 55/54 POTE generator: ~3/2 = 732.330 Map: [<2 0 -5 -4 7|, <0 1 3 3 0|] EDOs: 10, 18e Badness: 0.0302 =Opossum= Commas: 28/27, 126/125 7-limit eigenmonzo subgroup: 2.7 9-limit eigenmonzo subgroup: 2.7 [[POTE tuning|POTE generator]]: ~10/9 = 159.691 Map: [<1 2 3 4|, <0 -3 -5 -9|] Wedgie: <<3 5 9 1 6 7|| EDOs: 7d, 8d, 15 Badness: 0.0407 ==11-limit== Commas: 28/27, 55/54, 77/75 11-limit eigenmonzo subgroup: 2.7 [[POTE tuning|POTE generator]]: ~10/9 = 159.807 Map: [<1 2 3 4 4|, <0 -3 -5 -9 -4|] EDOs: 7d, 8d, 15 Badness: 0.0223 ==13-limit== Commas: 28/27, 40/39, 55/54, 66/65 13-limit eigenmonzo subgroup: 2.7 15-limit eigenmonzo subgroup: 2.7 [[POTE tuning|POTE generator]]: ~10/9 = 158.805 Map: [<1 2 3 4 4 4|, <0 -3 -5 -9 -4 -2|] EDOs: 7d, 8d, 15, 38bcef Badness: 0.0194 =Wallaby= Commas: 28/27, 35/32 POTE generator: ~3/2 = 691.351 Map: [<1 0 7 -2|, <0 1 -3 3|] Wedgie: <<1 -3 3 -7 2 15|| EDOs: 2d, 5c, 19ccdd Badness: 0.0585 =Kangaroo= Comma: 64000/59049 POTE generator: ~27/20 = 561.195 Map: [<1 0 -3|, <0 3 10|] EDOs: 15, 47b, 62b Badness: 0.2958 ==7-limit== Commas: 28/27, 1029/1000 POTE generator: ~7/5 = 560.328 Map: [<1 0 -3 -2|, <0 3 10 9|] Wedgie: <<3 10 9 9 6 -7|| EDOs: 15 Badness: 0.0779 ==11-limit== Commas: 28/27, 77/75, 245/242 POTE generator: ~7/5 = 560.155 Map: [<1 0 -3 -2 -4|, <0 3 10 9 14|] EDOs: 15 Badness: 0.0432 ==13-limit== Commas: 28/27, 40/39, 77/75, 147/143 POTE generator: ~7/5 = 559.770 Map: [<1 0 -3 -2 -4 0|, <0 3 10 9 14 7|] EDOs: 15 Badness: 0.0327
Original HTML content:
<html><head><title>Trienstonic clan</title></head><body><!-- ws:start:WikiTextTocRule:24:<img id="wikitext@@toc@@flat" class="WikiMedia WikiMediaTocFlat" title="Table of Contents" src="/site/embedthumbnail/toc/flat?w=100&h=16"/> --><!-- ws:end:WikiTextTocRule:24 --><!-- ws:start:WikiTextTocRule:25: --><a href="#Father">Father</a><!-- ws:end:WikiTextTocRule:25 --><!-- ws:start:WikiTextTocRule:26: --> | <a href="#Uncle">Uncle</a><!-- ws:end:WikiTextTocRule:26 --><!-- ws:start:WikiTextTocRule:27: --> | <a href="#Octokaidecal">Octokaidecal</a><!-- ws:end:WikiTextTocRule:27 --><!-- ws:start:WikiTextTocRule:28: --><!-- ws:end:WikiTextTocRule:28 --><!-- ws:start:WikiTextTocRule:29: --> | <a href="#Opossum">Opossum</a><!-- ws:end:WikiTextTocRule:29 --><!-- ws:start:WikiTextTocRule:30: --><!-- ws:end:WikiTextTocRule:30 --><!-- ws:start:WikiTextTocRule:31: --><!-- ws:end:WikiTextTocRule:31 --><!-- ws:start:WikiTextTocRule:32: --> | <a href="#Wallaby">Wallaby</a><!-- ws:end:WikiTextTocRule:32 --><!-- ws:start:WikiTextTocRule:33: --> | <a href="#Kangaroo">Kangaroo</a><!-- ws:end:WikiTextTocRule:33 --><!-- ws:start:WikiTextTocRule:34: --><!-- ws:end:WikiTextTocRule:34 --><!-- ws:start:WikiTextTocRule:35: --><!-- ws:end:WikiTextTocRule:35 --><!-- ws:start:WikiTextTocRule:36: --><!-- ws:end:WikiTextTocRule:36 --><!-- ws:start:WikiTextTocRule:37: --> <!-- ws:end:WikiTextTocRule:37 --><br /> Adding 16/15 to the trienstonic comma of 28/27 leads to father temperament, adding 256/245 gives uncle, adding 50/49 gives octokaidecal and adding 126/125 gives opossum. Other members of the clan discussed elsewhere are sharptone, sharp, and blacksmith.<br /> <br /> <!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="Father"></a><!-- ws:end:WikiTextHeadingRule:0 -->Father</h1> Commas: 16/15, 28/27<br /> <br /> 7-limit minimax<br /> [<1 0 0 0|, <3/2 0 -1/4 1/4|, <5/2 0 1/4 -1/4|, <5/2 0 -3/4 3/4|]<br /> <a class="wiki_link" href="/Eigenmonzo%20subgroup">Eigenmonzo subgroup</a>: 2.7/5<br /> <br /> 9-limit eigenmonzo subgroup: 2.9/5<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 742.002<br /> <br /> Map: [<1 0 4 -2|, <0 1 -1 3|]<br /> Wedgie: <<1 -1 3 -4 2 10||<br /> EDOs: 5, 8d, 13cd, 21bcd<br /> Badness: 0.0213<br /> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h1> --><h1 id="toc1"><a name="Uncle"></a><!-- ws:end:WikiTextHeadingRule:2 -->Uncle</h1> Commas: 28/27, 256/245<br /> <br /> 7-limit eigenmonzo subgroup: 2.5/3<br /> 9-limit eigenmonzo subgroup: 2.9/5<br /> <br /> Map: [<1 0 12 -2|, <0 1 -6 3|]<br /> Wedgie: <<1 -6 3 -12 2 24||<br /> EDOs: 13d, 18, 23bc, 41bcd<br /> Badness: 0.0727<br /> <br /> <!-- ws:start:WikiTextHeadingRule:4:<h1> --><h1 id="toc2"><a name="Octokaidecal"></a><!-- ws:end:WikiTextHeadingRule:4 -->Octokaidecal</h1> Commas: 28/27, 50/49<br /> <br /> 7-limit eigenmonzo subgroup: 2.5<br /> 9-limit eigenmonzo subgroup: 2.5<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 728.874<br /> <br /> Map: [<2 0 -5 -4|, <0 1 3 3|]<br /> Wedgie: <<2 6 6 5 4 -2||<br /> EDOs: 10, 18, 28b<br /> Badness: 0.0367<br /> <br /> <!-- ws:start:WikiTextHeadingRule:6:<h2> --><h2 id="toc3"><a name="Octokaidecal-11-limit"></a><!-- ws:end:WikiTextHeadingRule:6 -->11-limit</h2> Commas: 28/27, 50/49, 55/54<br /> <br /> POTE generator: ~3/2 = 732.330<br /> <br /> Map: [<2 0 -5 -4 7|, <0 1 3 3 0|]<br /> EDOs: 10, 18e<br /> Badness: 0.0302<br /> <br /> <!-- ws:start:WikiTextHeadingRule:8:<h1> --><h1 id="toc4"><a name="Opossum"></a><!-- ws:end:WikiTextHeadingRule:8 -->Opossum</h1> Commas: 28/27, 126/125<br /> <br /> 7-limit eigenmonzo subgroup: 2.7<br /> 9-limit eigenmonzo subgroup: 2.7<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~10/9 = 159.691<br /> <br /> Map: [<1 2 3 4|, <0 -3 -5 -9|]<br /> Wedgie: <<3 5 9 1 6 7||<br /> EDOs: 7d, 8d, 15<br /> Badness: 0.0407<br /> <br /> <!-- ws:start:WikiTextHeadingRule:10:<h2> --><h2 id="toc5"><a name="Opossum-11-limit"></a><!-- ws:end:WikiTextHeadingRule:10 -->11-limit</h2> Commas: 28/27, 55/54, 77/75<br /> <br /> 11-limit eigenmonzo subgroup: 2.7<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~10/9 = 159.807<br /> <br /> Map: [<1 2 3 4 4|, <0 -3 -5 -9 -4|]<br /> EDOs: 7d, 8d, 15<br /> Badness: 0.0223<br /> <br /> <!-- ws:start:WikiTextHeadingRule:12:<h2> --><h2 id="toc6"><a name="Opossum-13-limit"></a><!-- ws:end:WikiTextHeadingRule:12 -->13-limit</h2> Commas: 28/27, 40/39, 55/54, 66/65<br /> <br /> 13-limit eigenmonzo subgroup: 2.7<br /> 15-limit eigenmonzo subgroup: 2.7<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~10/9 = 158.805<br /> <br /> Map: [<1 2 3 4 4 4|, <0 -3 -5 -9 -4 -2|]<br /> EDOs: 7d, 8d, 15, 38bcef<br /> Badness: 0.0194<br /> <br /> <!-- ws:start:WikiTextHeadingRule:14:<h1> --><h1 id="toc7"><a name="Wallaby"></a><!-- ws:end:WikiTextHeadingRule:14 -->Wallaby</h1> Commas: 28/27, 35/32<br /> <br /> POTE generator: ~3/2 = 691.351<br /> <br /> Map: [<1 0 7 -2|, <0 1 -3 3|]<br /> Wedgie: <<1 -3 3 -7 2 15||<br /> EDOs: 2d, 5c, 19ccdd<br /> Badness: 0.0585<br /> <br /> <!-- ws:start:WikiTextHeadingRule:16:<h1> --><h1 id="toc8"><a name="Kangaroo"></a><!-- ws:end:WikiTextHeadingRule:16 -->Kangaroo</h1> Comma: 64000/59049<br /> <br /> POTE generator: ~27/20 = 561.195<br /> <br /> Map: [<1 0 -3|, <0 3 10|]<br /> EDOs: 15, 47b, 62b<br /> Badness: 0.2958<br /> <br /> <!-- ws:start:WikiTextHeadingRule:18:<h2> --><h2 id="toc9"><a name="Kangaroo-7-limit"></a><!-- ws:end:WikiTextHeadingRule:18 -->7-limit</h2> Commas: 28/27, 1029/1000<br /> <br /> POTE generator: ~7/5 = 560.328<br /> <br /> Map: [<1 0 -3 -2|, <0 3 10 9|]<br /> Wedgie: <<3 10 9 9 6 -7||<br /> EDOs: 15<br /> Badness: 0.0779<br /> <br /> <!-- ws:start:WikiTextHeadingRule:20:<h2> --><h2 id="toc10"><a name="Kangaroo-11-limit"></a><!-- ws:end:WikiTextHeadingRule:20 -->11-limit</h2> Commas: 28/27, 77/75, 245/242<br /> <br /> POTE generator: ~7/5 = 560.155<br /> <br /> Map: [<1 0 -3 -2 -4|, <0 3 10 9 14|]<br /> EDOs: 15<br /> Badness: 0.0432<br /> <br /> <!-- ws:start:WikiTextHeadingRule:22:<h2> --><h2 id="toc11"><a name="Kangaroo-13-limit"></a><!-- ws:end:WikiTextHeadingRule:22 -->13-limit</h2> Commas: 28/27, 40/39, 77/75, 147/143<br /> <br /> POTE generator: ~7/5 = 559.770<br /> <br /> Map: [<1 0 -3 -2 -4 0|, <0 3 10 9 14 7|]<br /> EDOs: 15<br /> Badness: 0.0327</body></html>