Amity family
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[[toc|flat]] =Amity= The generator for amity temperament is the acute minor third, which means an ordinary 6/5 minor third raised by an 81/80 comma to 243/200, and from this it derives its name. Aside from the ragisma it tempers out the 5-limit amity comma, 1600000/1594323, 5120/5103 and 6144/6125. It can also be described as the 46&53 temperament, or by its wedgie, <<5 13 -17 9 -41 -76||. [[99edo]] is a good tuning for amity, with generator 28/99, and MOS of 11, 18, 25, 32, 46 or 53 notes are available. If you are looking for a different kind of neutral third this could be the temperament for you. In the 5-limit amity is a genuine microtemperament, with 58/205 being a possible tuning. Another good choice is (64/5)^(1/13), which gives pure major thirds. Comma: 1600000/1594323 POTE generator: ~243/200 = 339.519 Map: [<1 3 6|, <0 -5 -13|] EDOs: 7, 39, 46, 53, 152, 205, 463, 668, 873 Badness: 0.0220 ==7-limit== Commas: 4375/4374, 5120/5103 POTE generator: ~243/200 = 339.432 Map: [<1 3 6 -2|, <0 -5 -13 17|] Wedgie: <<5 13 -17 9 -41 -76|| EDOs: 7, 39, 46, 53, 99, 251, 350 Badness: 0.0236 ==11-limit== Commas: 540/539, 4375/4374, 5120/5103 POTE generator: ~243/200 = 339.464 Map: [<1 3 6 -2 21|, <0 -5 -13 17 -62|] EDOs: 53, 99e, 152, 555de, 707de, 859bde Badness: 0.0315 ==Hitchcock== Commas: 121/120, 176/175, 2200/2187 POTE generator: ~11/9 = 339.340 Map: [<1 3 6 -2 6|, <0 -5 -13 17 -9|] EDOs: 7, 39, 46, 53, 99 Badness: 0.0352 ==Hemiamity== Commas: 4375/4374, 5120/5103, 3025/3024 POTE generator: ~ 243/200 = 339.493 Map: [<2 1 -1 13 13|, <0 5 13 -17 -14|] EDOs: 14, 46, 106, 152, 350 =Bamity= Commas: 245/243, 64827/64000 POTE generator: ~7/6 = 260.402 Map: [<2 1 -1 3|, <0 5 13 6|] Wedgie: <<10 26 12 18 -9 -45|| EDOs: 46, 60, 106d Badness: 0.0836 ==11-limit== Commas: 121/120, 245/243, 441/440 POTE generator: ~7/6 = 260.393 Map: [<2 1 -1 3 3|, <0 5 13 6 9|] EDOs: 14c, 46, 60e, 106de Badness: 0.0355 =Hamity= Commas: 2430/2401, 4000/3969 POTE generator: ~9/7 = 430.219 Map: [<1 8 19 15|, <0 -10 -26 -19|] Wedgie: <<10 26 19 18 2 -29|| EDOs: 14c, 39d, 53 Badness: 0.0740 ==11-limit== Commas: 99/98, 121/120, 4000/3969 POTE generator: ~9/7 = 430.192 Map: [<1 8 19 15 15|, <0 -10 -26 -19 -18|] EDOs: 14c, 39d, 53 Badness: 0.0429 ==13-limit== Commas: 99/98, 121/120, 275/273, 572/567 POTE generator: ~9/7 = 430.216 Map: [<1 8 19 15 15 30|, <0 -10 -26 -19 -18 -41|] EDOs: 53 Badness: 0.0298
Original HTML content:
<html><head><title>Amity family</title></head><body><!-- ws:start:WikiTextTocRule:20:<img id="wikitext@@toc@@flat" class="WikiMedia WikiMediaTocFlat" title="Table of Contents" src="/site/embedthumbnail/toc/flat?w=100&h=16"/> --><!-- ws:end:WikiTextTocRule:20 --><!-- ws:start:WikiTextTocRule:21: --><a href="#Amity">Amity</a><!-- ws:end:WikiTextTocRule:21 --><!-- ws:start:WikiTextTocRule:22: --><!-- ws:end:WikiTextTocRule:22 --><!-- ws:start:WikiTextTocRule:23: --><!-- ws:end:WikiTextTocRule:23 --><!-- ws:start:WikiTextTocRule:24: --><!-- ws:end:WikiTextTocRule:24 --><!-- ws:start:WikiTextTocRule:25: --><!-- ws:end:WikiTextTocRule:25 --><!-- ws:start:WikiTextTocRule:26: --> | <a href="#Bamity">Bamity</a><!-- ws:end:WikiTextTocRule:26 --><!-- ws:start:WikiTextTocRule:27: --><!-- ws:end:WikiTextTocRule:27 --><!-- ws:start:WikiTextTocRule:28: --> | <a href="#Hamity">Hamity</a><!-- ws:end:WikiTextTocRule:28 --><!-- ws:start:WikiTextTocRule:29: --><!-- ws:end:WikiTextTocRule:29 --><!-- ws:start:WikiTextTocRule:30: --><!-- ws:end:WikiTextTocRule:30 --><!-- ws:start:WikiTextTocRule:31: --> <!-- ws:end:WikiTextTocRule:31 --><br /> <!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="Amity"></a><!-- ws:end:WikiTextHeadingRule:0 -->Amity</h1> The generator for amity temperament is the acute minor third, which means an ordinary 6/5 minor third raised by an 81/80 comma to 243/200, and from this it derives its name. Aside from the ragisma it tempers out the 5-limit amity comma, 1600000/1594323, 5120/5103 and 6144/6125. It can also be described as the 46&53 temperament, or by its wedgie, <<5 13 -17 9 -41 -76||. <a class="wiki_link" href="/99edo">99edo</a> is a good tuning for amity, with generator 28/99, and MOS of 11, 18, 25, 32, 46 or 53 notes are available. If you are looking for a different kind of neutral third this could be the temperament for you.<br /> <br /> In the 5-limit amity is a genuine microtemperament, with 58/205 being a possible tuning. Another good choice is (64/5)^(1/13), which gives pure major thirds.<br /> <br /> Comma: 1600000/1594323<br /> <br /> POTE generator: ~243/200 = 339.519<br /> <br /> Map: [<1 3 6|, <0 -5 -13|]<br /> EDOs: 7, 39, 46, 53, 152, 205, 463, 668, 873<br /> Badness: 0.0220<br /> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h2> --><h2 id="toc1"><a name="Amity-7-limit"></a><!-- ws:end:WikiTextHeadingRule:2 -->7-limit</h2> Commas: 4375/4374, 5120/5103<br /> <br /> POTE generator: ~243/200 = 339.432<br /> <br /> Map: [<1 3 6 -2|, <0 -5 -13 17|]<br /> Wedgie: <<5 13 -17 9 -41 -76||<br /> EDOs: 7, 39, 46, 53, 99, 251, 350<br /> Badness: 0.0236<br /> <br /> <!-- ws:start:WikiTextHeadingRule:4:<h2> --><h2 id="toc2"><a name="Amity-11-limit"></a><!-- ws:end:WikiTextHeadingRule:4 -->11-limit</h2> Commas: 540/539, 4375/4374, 5120/5103<br /> <br /> POTE generator: ~243/200 = 339.464<br /> <br /> Map: [<1 3 6 -2 21|, <0 -5 -13 17 -62|]<br /> EDOs: 53, 99e, 152, 555de, 707de, 859bde<br /> Badness: 0.0315<br /> <br /> <!-- ws:start:WikiTextHeadingRule:6:<h2> --><h2 id="toc3"><a name="Amity-Hitchcock"></a><!-- ws:end:WikiTextHeadingRule:6 -->Hitchcock</h2> Commas: 121/120, 176/175, 2200/2187<br /> <br /> POTE generator: ~11/9 = 339.340<br /> <br /> Map: [<1 3 6 -2 6|, <0 -5 -13 17 -9|]<br /> EDOs: 7, 39, 46, 53, 99<br /> Badness: 0.0352<br /> <br /> <!-- ws:start:WikiTextHeadingRule:8:<h2> --><h2 id="toc4"><a name="Amity-Hemiamity"></a><!-- ws:end:WikiTextHeadingRule:8 -->Hemiamity</h2> Commas: 4375/4374, 5120/5103, 3025/3024<br /> <br /> POTE generator: ~ 243/200 = 339.493<br /> <br /> Map: [<2 1 -1 13 13|, <0 5 13 -17 -14|]<br /> EDOs: 14, 46, 106, 152, 350<br /> <br /> <!-- ws:start:WikiTextHeadingRule:10:<h1> --><h1 id="toc5"><a name="Bamity"></a><!-- ws:end:WikiTextHeadingRule:10 -->Bamity</h1> Commas: 245/243, 64827/64000<br /> <br /> POTE generator: ~7/6 = 260.402<br /> <br /> Map: [<2 1 -1 3|, <0 5 13 6|]<br /> Wedgie: <<10 26 12 18 -9 -45||<br /> EDOs: 46, 60, 106d<br /> Badness: 0.0836<br /> <br /> <!-- ws:start:WikiTextHeadingRule:12:<h2> --><h2 id="toc6"><a name="Bamity-11-limit"></a><!-- ws:end:WikiTextHeadingRule:12 -->11-limit</h2> Commas: 121/120, 245/243, 441/440<br /> <br /> POTE generator: ~7/6 = 260.393<br /> <br /> Map: [<2 1 -1 3 3|, <0 5 13 6 9|]<br /> EDOs: 14c, 46, 60e, 106de<br /> Badness: 0.0355<br /> <br /> <!-- ws:start:WikiTextHeadingRule:14:<h1> --><h1 id="toc7"><a name="Hamity"></a><!-- ws:end:WikiTextHeadingRule:14 -->Hamity</h1> Commas: 2430/2401, 4000/3969 <br /> <br /> POTE generator: ~9/7 = 430.219<br /> <br /> Map: [<1 8 19 15|, <0 -10 -26 -19|]<br /> Wedgie: <<10 26 19 18 2 -29||<br /> EDOs: 14c, 39d, 53<br /> Badness: 0.0740<br /> <br /> <!-- ws:start:WikiTextHeadingRule:16:<h2> --><h2 id="toc8"><a name="Hamity-11-limit"></a><!-- ws:end:WikiTextHeadingRule:16 -->11-limit</h2> Commas: 99/98, 121/120, 4000/3969<br /> <br /> POTE generator: ~9/7 = 430.192<br /> <br /> Map: [<1 8 19 15 15|, <0 -10 -26 -19 -18|]<br /> EDOs: 14c, 39d, 53<br /> Badness: 0.0429<br /> <br /> <!-- ws:start:WikiTextHeadingRule:18:<h2> --><h2 id="toc9"><a name="Hamity-13-limit"></a><!-- ws:end:WikiTextHeadingRule:18 -->13-limit</h2> Commas: 99/98, 121/120, 275/273, 572/567<br /> <br /> POTE generator: ~9/7 = 430.216<br /> <br /> Map: [<1 8 19 15 15 30|, <0 -10 -26 -19 -18 -41|]<br /> EDOs: 53<br /> Badness: 0.0298</body></html>