Hemimean clan
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- This revision was by author genewardsmith and made on 2012-02-21 20:24:20 UTC.
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[[toc|flat]] The hemimean clan, tempering out the no-threes hemimean comma 3136/3125, contains the temperaments misty and semisept, considered below, as well as meantone, hemiwuerschmidt, parakleismic, hemithirds, clyde, hemischismic, passion, hexe and sycamore considered elsewhere. Comma: 3136/3125 No-threes [[POTE tuning|POTE generator]] (~28/25): 193.772 Map: [<1 0 0 -3|, <0 0 2 5|] EDOs: [[6edo|6]], [[12edo|12]], [[19edo|12]], [[31edo|31]], [[68edo|68]], [[80edo|80]], [[87edo|87]], [[99edo|99]], [[130edo|130]], [[217edo|217]], [[229edo|229]], [[328edo|328]], [[347edo|347]], [[446edo|446]], [[545edo|545c]], [[675edo|675]] =Misty= Commas: 3136/3125, 5120/5103 [[POTE tuning|POTE generator]]: 703.021 Map: [<3 0 26 56|, <0 1 -4 -10|] Wedgie: <<3 -12 -30 -26 -56 -36|| EDOs: [[12edo|12]], [[87edo|87]], [[99edo|99]] ==11-limit== Commas: 441/440, 3136/3125, 4375/4356 [[POTE tuning|POTE generator]]: 703.210 Map: [<3 0 26 56 77|, <0 1 -4 -10 -14|] EDOs: 12, 87, 99e, 186e ==13-limit== Commas: 196/195, 352/351, 364/363, 625/624 [[POTE tuning|POTE generator]]: 703.303 Map: [<3 0 26 56 77 92|, <0 1 -4 -10 -14 -17|] EDOs: 12, 87, 186ef, 273ef =Mystic= Commas: 325/324, 441/440, 896/891, 1001/1000 [[POTE tuning|POTE generator]]: 703.311 Map: [<3 0 26 56 77 -46|, <0 1 -4 -10 -14 12|] EDOs: 12, 87, 186e, 273e, 633bde ==17-limit== Commas: 196/195, 352/351, 364/363, 625/624 [[POTE tuning|POTE generator]]: 703.233 Map: [<3 0 26 56 77 92 -2|, <0 1 -4 -10 -14 -17 3|] EDOs: 87, 186ef, 273ef ==19-limit== Commas: 154/153, 196/195, 245/243, 273/272, 286/285, 325/324 [[POTE tuning|POTE generator]]: 703.253 Map: [<3 0 26 56 77 92 -2 8|, <0 1 -4 -10 -14 -17 3 1|] EDOs: 46, 87, 133, 326de, 413degh =Semisept= Commas: 3136/3126, 1728/1715 [[POTE tuning|POTE generator]]: (~75/49) 735.155 Map: [<1 12 6 12|, <0 -17 -6 -15|] Wedgie: <<17 6 15 -30 -24 18|| EDOs: [[18edo|18]], 31, [[80edo|80]], 111 11-limit Commas: 176/175, 540/539, 1331/1323 [[POTE tuning|POTE generator]]: (~55/36) 735.125 Map: [<1 12 6 12 20|, <0 -17 -6 -15 -27|] EDOs: 18, 31, 80, 111, 364cd, 13-limit Commas: 176/175, 351/350, 540/539, 1375/1372 [[POTE tuning|POTE generator]]: 735.126 Map: [<1 12 6 12 20 -11|, <0 -17 -6 -15 -27 24|] EDOs: 31, 80, 111 17-limit Commas: 176/175, 256/255, 351/350, 640/637, 715/714 [[POTE tuning|POTE generator]]: (~26/17) 735.125 Map: [<1 12 6 12 20 -11 -10|, <0 -17 -6 -15 -27 24 23|] EDOs: 31, 80, 111 19-limit Commas: 176/175, 286/285, 351/350, 476/475, 540/539, 1331/1323 [[POTE tuning|POTE generator]]: 735.116 Map: [<1 12 6 12 20 -11 -10 -8|, <0 -17 -6 -15 -27 24 23 20|] EDOs: 31, 80, 111 23-limit Commas: 176/175, 253/252, 286/285, 345/343, 351/350, 391/390, 460/459 [[POTE tuning|POTE generator]]: 435.106 Map: [<1 12 6 12 20 -11 -10 -8 18|, <0 -17 -6 -15 -27 24 23 20 -22|] EDOs: 31, 80, 111, 191cdh, 302cdgh =Sengagen= Commas: 3136/3125, 420175/419904 POTE generator: ~686/675 = 24.217 Map: [<1 1 2 2|, <0 29 16 40|] Wedgie: <<29 16 40 -42 -18 48|| EDOs: 49, 50, 99, 248, 347, 446 Badness: 0.0580 =Subpental= Commas: 3136/3125, 19683/19600 POTE generator: ~56/45 = 378.467 Map: [<1 6 8 17|, <0 -14 -18 -45|] Wedgie: <<14 18 45 -4 32 54|| EDOs: 19, 111, 130, 929c, 1059c, 1189bc, 1319bc Badness: 0.0543 ==11-limit== Commas: 540/539, 3136/3125, 8019/8000 POTE generator: ~56/45 = 378.440 Map: [<1 6 8 17 -6|, <0 -14 -18 -45 30|] EDOs: 19, 111, 130, 241, 371ce, 501cde, 872cde Badness: 0.0453 ==13-limit== Commas: 351/350, 540/539, 676/675, 3136/3125 POTE generator: ~56/45 = 378.437 Map: [<1 6 8 17 -6 16|, <0 -14 -18 -45 30 -39|] EDOs: 19, 111, 130, 241, 371ce Badness: 0.0239 =Arch= Commas: 3136/3125, 5250987/5242880 POTE generator: ~64/63 = 27.668 Map: [<1 2 2 2|, <0 -18 14 35|] Wedgie: <<18 -14 -35 -64 -106 -42|| EDOs: 43, 87, 130, 217, 347, 824c, 1171c, 1518cd Badness: 0.0943 ==11-limit== Commas: 441/440, 3136/3125, 4000/3993 POTE generator: ~64/63 = 27.663 Map: [<1 2 2 2 3|, <0 -18 14 35 20|] EDOs: 43, 87, 130, 217, 347e, 911cde Badness: 0.0365 ==13-limit== Commasa: 364/363, 441/440, 676/675, 3136/3125 POTE generator: ~64/63 = 27.660 Map: [<1 2 2 2 3 4|, <0 -18 14 35 20 -13|] EDOs: 43, 87, 130, 217, 347e, 564e Badness: 0.0195
Original HTML content:
<html><head><title>Hemimean clan</title></head><body><!-- ws:start:WikiTextTocRule:28:<img id="wikitext@@toc@@flat" class="WikiMedia WikiMediaTocFlat" title="Table of Contents" src="/site/embedthumbnail/toc/flat?w=100&h=16"/> --><!-- ws:end:WikiTextTocRule:28 --><!-- ws:start:WikiTextTocRule:29: --><a href="#Misty">Misty</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="#Mystic">Mystic</a><!-- ws:end:WikiTextTocRule:32 --><!-- ws:start:WikiTextTocRule:33: --><!-- ws:end:WikiTextTocRule:33 --><!-- ws:start:WikiTextTocRule:34: --><!-- ws:end:WikiTextTocRule:34 --><!-- ws:start:WikiTextTocRule:35: --> | <a href="#Semisept">Semisept</a><!-- ws:end:WikiTextTocRule:35 --><!-- ws:start:WikiTextTocRule:36: --> | <a href="#Sengagen">Sengagen</a><!-- ws:end:WikiTextTocRule:36 --><!-- ws:start:WikiTextTocRule:37: --> | <a href="#Subpental">Subpental</a><!-- ws:end:WikiTextTocRule:37 --><!-- ws:start:WikiTextTocRule:38: --><!-- ws:end:WikiTextTocRule:38 --><!-- ws:start:WikiTextTocRule:39: --><!-- ws:end:WikiTextTocRule:39 --><!-- ws:start:WikiTextTocRule:40: --> | <a href="#Arch">Arch</a><!-- ws:end:WikiTextTocRule:40 --><!-- ws:start:WikiTextTocRule:41: --><!-- ws:end:WikiTextTocRule:41 --><!-- ws:start:WikiTextTocRule:42: --><!-- ws:end:WikiTextTocRule:42 --><!-- ws:start:WikiTextTocRule:43: --> <!-- ws:end:WikiTextTocRule:43 --><br /> The hemimean clan, tempering out the no-threes hemimean comma 3136/3125, contains the temperaments misty and semisept, considered below, as well as meantone, hemiwuerschmidt, parakleismic, hemithirds, clyde, hemischismic, passion, hexe and sycamore considered elsewhere.<br /> <br /> Comma: 3136/3125<br /> <br /> No-threes <a class="wiki_link" href="/POTE%20tuning">POTE generator</a> (~28/25): 193.772<br /> <br /> Map: [<1 0 0 -3|, <0 0 2 5|]<br /> EDOs: <a class="wiki_link" href="/6edo">6</a>, <a class="wiki_link" href="/12edo">12</a>, <a class="wiki_link" href="/19edo">12</a>, <a class="wiki_link" href="/31edo">31</a>, <a class="wiki_link" href="/68edo">68</a>, <a class="wiki_link" href="/80edo">80</a>, <a class="wiki_link" href="/87edo">87</a>, <a class="wiki_link" href="/99edo">99</a>, <a class="wiki_link" href="/130edo">130</a>, <a class="wiki_link" href="/217edo">217</a>, <a class="wiki_link" href="/229edo">229</a>, <a class="wiki_link" href="/328edo">328</a>, <a class="wiki_link" href="/347edo">347</a>, <a class="wiki_link" href="/446edo">446</a>, <a class="wiki_link" href="/545edo">545c</a>, <a class="wiki_link" href="/675edo">675</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="Misty"></a><!-- ws:end:WikiTextHeadingRule:0 -->Misty</h1> Commas: 3136/3125, 5120/5103<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 703.021<br /> <br /> Map: [<3 0 26 56|, <0 1 -4 -10|]<br /> Wedgie: <<3 -12 -30 -26 -56 -36||<br /> EDOs: <a class="wiki_link" href="/12edo">12</a>, <a class="wiki_link" href="/87edo">87</a>, <a class="wiki_link" href="/99edo">99</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h2> --><h2 id="toc1"><a name="Misty-11-limit"></a><!-- ws:end:WikiTextHeadingRule:2 -->11-limit</h2> Commas: 441/440, 3136/3125, 4375/4356<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 703.210<br /> <br /> Map: [<3 0 26 56 77|, <0 1 -4 -10 -14|]<br /> EDOs: 12, 87, 99e, 186e<br /> <br /> <!-- ws:start:WikiTextHeadingRule:4:<h2> --><h2 id="toc2"><a name="Misty-13-limit"></a><!-- ws:end:WikiTextHeadingRule:4 -->13-limit</h2> Commas: 196/195, 352/351, 364/363, 625/624<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 703.303<br /> <br /> Map: [<3 0 26 56 77 92|, <0 1 -4 -10 -14 -17|]<br /> EDOs: 12, 87, 186ef, 273ef<br /> <br /> <!-- ws:start:WikiTextHeadingRule:6:<h1> --><h1 id="toc3"><a name="Mystic"></a><!-- ws:end:WikiTextHeadingRule:6 -->Mystic</h1> Commas: 325/324, 441/440, 896/891, 1001/1000<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 703.311<br /> <br /> Map: [<3 0 26 56 77 -46|, <0 1 -4 -10 -14 12|]<br /> EDOs: 12, 87, 186e, 273e, 633bde<br /> <br /> <!-- ws:start:WikiTextHeadingRule:8:<h2> --><h2 id="toc4"><a name="Mystic-17-limit"></a><!-- ws:end:WikiTextHeadingRule:8 -->17-limit</h2> Commas: 196/195, 352/351, 364/363, 625/624<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 703.233<br /> <br /> Map: [<3 0 26 56 77 92 -2|, <0 1 -4 -10 -14 -17 3|]<br /> EDOs: 87, 186ef, 273ef<br /> <br /> <!-- ws:start:WikiTextHeadingRule:10:<h2> --><h2 id="toc5"><a name="Mystic-19-limit"></a><!-- ws:end:WikiTextHeadingRule:10 -->19-limit</h2> Commas: 154/153, 196/195, 245/243, 273/272, 286/285, 325/324<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 703.253<br /> <br /> Map: [<3 0 26 56 77 92 -2 8|, <0 1 -4 -10 -14 -17 3 1|]<br /> EDOs: 46, 87, 133, 326de, 413degh<br /> <br /> <!-- ws:start:WikiTextHeadingRule:12:<h1> --><h1 id="toc6"><a name="Semisept"></a><!-- ws:end:WikiTextHeadingRule:12 -->Semisept</h1> Commas: 3136/3126, 1728/1715<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: (~75/49) 735.155<br /> <br /> Map: [<1 12 6 12|, <0 -17 -6 -15|]<br /> Wedgie: <<17 6 15 -30 -24 18||<br /> EDOs: <a class="wiki_link" href="/18edo">18</a>, 31, <a class="wiki_link" href="/80edo">80</a>, 111<br /> <br /> 11-limit<br /> Commas: 176/175, 540/539, 1331/1323<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: (~55/36) 735.125<br /> <br /> Map: [<1 12 6 12 20|, <0 -17 -6 -15 -27|]<br /> EDOs: 18, 31, 80, 111, 364cd, <br /> <br /> 13-limit<br /> Commas: 176/175, 351/350, 540/539, 1375/1372<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 735.126<br /> <br /> Map: [<1 12 6 12 20 -11|, <0 -17 -6 -15 -27 24|]<br /> EDOs: 31, 80, 111<br /> <br /> 17-limit<br /> Commas: 176/175, 256/255, 351/350, 640/637, 715/714<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: (~26/17) 735.125<br /> <br /> Map: [<1 12 6 12 20 -11 -10|, <0 -17 -6 -15 -27 24 23|]<br /> EDOs: 31, 80, 111<br /> <br /> 19-limit<br /> Commas: 176/175, 286/285, 351/350, 476/475, 540/539, 1331/1323<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 735.116<br /> <br /> Map: [<1 12 6 12 20 -11 -10 -8|, <0 -17 -6 -15 -27 24 23 20|]<br /> EDOs: 31, 80, 111<br /> <br /> 23-limit<br /> Commas: 176/175, 253/252, 286/285, 345/343, 351/350, 391/390, 460/459<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 435.106<br /> <br /> Map: [<1 12 6 12 20 -11 -10 -8 18|, <br /> <0 -17 -6 -15 -27 24 23 20 -22|]<br /> EDOs: 31, 80, 111, 191cdh, 302cdgh<br /> <br /> <!-- ws:start:WikiTextHeadingRule:14:<h1> --><h1 id="toc7"><a name="Sengagen"></a><!-- ws:end:WikiTextHeadingRule:14 -->Sengagen</h1> Commas: 3136/3125, 420175/419904<br /> <br /> POTE generator: ~686/675 = 24.217<br /> <br /> Map: [<1 1 2 2|, <0 29 16 40|]<br /> Wedgie: <<29 16 40 -42 -18 48||<br /> EDOs: 49, 50, 99, 248, 347, 446<br /> Badness: 0.0580<br /> <br /> <!-- ws:start:WikiTextHeadingRule:16:<h1> --><h1 id="toc8"><a name="Subpental"></a><!-- ws:end:WikiTextHeadingRule:16 -->Subpental</h1> Commas: 3136/3125, 19683/19600<br /> <br /> POTE generator: ~56/45 = 378.467<br /> <br /> Map: [<1 6 8 17|, <0 -14 -18 -45|]<br /> Wedgie: <<14 18 45 -4 32 54||<br /> EDOs: 19, 111, 130, 929c, 1059c, 1189bc, 1319bc<br /> Badness: 0.0543<br /> <br /> <!-- ws:start:WikiTextHeadingRule:18:<h2> --><h2 id="toc9"><a name="Subpental-11-limit"></a><!-- ws:end:WikiTextHeadingRule:18 -->11-limit</h2> Commas: 540/539, 3136/3125, 8019/8000<br /> <br /> POTE generator: ~56/45 = 378.440<br /> <br /> Map: [<1 6 8 17 -6|, <0 -14 -18 -45 30|]<br /> EDOs: 19, 111, 130, 241, 371ce, 501cde, 872cde<br /> Badness: 0.0453<br /> <br /> <!-- ws:start:WikiTextHeadingRule:20:<h2> --><h2 id="toc10"><a name="Subpental-13-limit"></a><!-- ws:end:WikiTextHeadingRule:20 -->13-limit</h2> Commas: 351/350, 540/539, 676/675, 3136/3125<br /> <br /> POTE generator: ~56/45 = 378.437<br /> <br /> Map: [<1 6 8 17 -6 16|, <0 -14 -18 -45 30 -39|]<br /> EDOs: 19, 111, 130, 241, 371ce<br /> Badness: 0.0239<br /> <br /> <!-- ws:start:WikiTextHeadingRule:22:<h1> --><h1 id="toc11"><a name="Arch"></a><!-- ws:end:WikiTextHeadingRule:22 -->Arch</h1> Commas: 3136/3125, 5250987/5242880<br /> <br /> POTE generator: ~64/63 = 27.668<br /> <br /> Map: [<1 2 2 2|, <0 -18 14 35|]<br /> Wedgie: <<18 -14 -35 -64 -106 -42||<br /> EDOs: 43, 87, 130, 217, 347, 824c, 1171c, 1518cd<br /> Badness: 0.0943<br /> <br /> <!-- ws:start:WikiTextHeadingRule:24:<h2> --><h2 id="toc12"><a name="Arch-11-limit"></a><!-- ws:end:WikiTextHeadingRule:24 -->11-limit</h2> Commas: 441/440, 3136/3125, 4000/3993<br /> <br /> POTE generator: ~64/63 = 27.663<br /> <br /> Map: [<1 2 2 2 3|, <0 -18 14 35 20|]<br /> EDOs: 43, 87, 130, 217, 347e, 911cde<br /> Badness: 0.0365<br /> <br /> <!-- ws:start:WikiTextHeadingRule:26:<h2> --><h2 id="toc13"><a name="Arch-13-limit"></a><!-- ws:end:WikiTextHeadingRule:26 -->13-limit</h2> Commasa: 364/363, 441/440, 676/675, 3136/3125<br /> <br /> POTE generator: ~64/63 = 27.660<br /> <br /> Map: [<1 2 2 2 3 4|, <0 -18 14 35 20 -13|]<br /> EDOs: 43, 87, 130, 217, 347e, 564e<br /> Badness: 0.0195</body></html>