Porcupine family
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[[toc|flat]] ---- The 5-limit parent comma for the porcupine family is 250/243, the maximal [[diesis]] or porcupine comma. Its [[monzo]] is |1 -5 3>, and flipping that yields <<3 5 1|| for the [[wedgie]]. This tells us the [[generator]] is a minor whole tone, the [[10_9|10/9]] interval, and that three of these add up to a fourth, with two more giving the minor sixth. In fact, (10/9)^3 = 4/3 * 250/243, and (10/9)^5 = 8/5 * (250/243)^2. 3/22 is a very recommendable generator, and MOS of 7, 8 and 15 notes make for some nice scale possibilities. [[POTE tuning|POTE generator]]: 163.950 Map: [<1 2 3|, <0 -3 -5|] EDOs: [[15edo|15]], [[22edo|22]], [[161edo|161]], [[183edo|183]] ==Seven limit children== The second comma of the [[Normal lists|normal comma list]] defines which [[7-limit]] family member we are looking at. That means [[64_63|64/63]], the [[Archyta's comma]], for [[Porcupine family#Porcupine|porcupine]], [[36_35|36/35]], the [[septimal quarter tone]], for [[Porcupine family#Hystrix|hystrix]], [[50_49|50/49]], the [[jubilisma]], for [[Porcupine family#Hedgehog|hedgehog]], and [[49_48|49/48]], the [[slendro diesis]], for [[Porcupine family#Nautilus|nautilus]]. =Porcupine= Porcupine, with wedgie <<3 5 -6 1 -18 -28||, uses six of its minor tone generator steps to get to [[7_4|7/4]]. For this to work you need a small minor tone such as [[22edo]] provides, and once again 3\22 is a good tuning choice, though we might pick in preference 8\59, 11\81, or 19\140 for our generator. Commas: 250/243, 64/63 [[POTE tuning|POTE generator]]: ~10/9 = 162.880 Map: [<1 2 3 2|, <0 -3 -5 6|] EDOs: 22, [[59edo|59]], [[81edo|81]], [[140edo|140]] ==11-limit== Commas: 55/54, 64/63, 100/99 POTE generator: ~10/9 = 162.747 Map: [<1 2 3 2 4|, <0 -3 -5 6 -4|] EDOs: [[7edo|7]], 15, 22, [[37edo|37]], 59 Badness: 0.0217 =Hystrix= Hystrix, with wedgie <<3 5 1 1 -7 -12||, provides a less complex avenue to the 7-limit. Unfortunately in temperaments as in life you get what you pay for, and hystrix, for which a generator of 2\15 or 9\68 can be used, is a temperament for the adventurous souls who have probably already tried [[15edo]]. They can try the even sharper fifth of hystrix in [[68edo]] and see how that suits. Commas: 36/35, 160/147 [[POTE tuning|POTE generator]]: 158.868 Map: [<1 2 3 3|, <0 -3 -5 -1|] EDOs: 15, 68 =Hedgehog= See //[[Hedgehog]]// =Nautilus= Commas: 49/48, 250/243 Pote generator: ~21/20 = 82.505 Map: [<1 2 3 3|, <0 -6 -10 -3|] Wedgie: <<6 10 3 2 -12 -21|| EDOs: [[14edo|14]], 15, [[29edo|29]], [[44edo|44]], [[73edo|73]], [[160edo|160]] ==11-limit== Commas: 49/48, 55/54, 245/242 POTE generator: ~21/20 = 82.504 Map: [<1 2 3 3 4|, <0 -6 -10 -3 -8|] EDOs: 14, 15, 29, 44, 73, 160 ==13-limit== Commas: 49/48, 55/54, 91/90, 100/99 POTE generator: ~21/20 = 62.530 Map: [<1 2 3 3 4 5|, <0 -6 -10 -3 -8 -19|] EDOs: 14, 15, 29, 44, 73, 160 =Ammonite= Commas: 250/243, 686/675 POTE generator: ~9/7 = 454.448 Map: [<1 5 8 10|, <0 -9 -15 -19|] Wedgie: <<9 15 19 3 5 2|| EDOs: 29, 37, 66 Badness: 0.1077 11-limit Commas: 55/54, 100/99, 686/675 POTE generator: ~9/7 = 454.512 Map: [<1 5 8 10 8|, <0 -9 -15 -19 -12|] EDOs: 29, 37, 66 Badness: 0.0457 13-limit Commas: 55/54, 91/90, 100/99, 169/168 POTE generator: ~13/10 = 454.429 Map: [<1 5 8 10 8 9|, <0 -9 -15 -19 -12 -14|] EDOs: 29, 37, 66 Badness: 0.0272 =Porky= Commas: 225/224, 250/243 POTE generator: ~10/9 = 164.412 Map: [<1 2 3 5|, <0 -3 -5 -16|] Wedgie: <<3 5 16 1 17 23|| EDOS: 7, 8, 15, 22, 29, 51, 73 Badness: 0.0544 ==11-limit== Commas: 55/54, 100/99, 225/224 POTE generator: ~10/9 = 164.552 Map: [<1 2 3 5 4|, <0 -3 -5 -16 -4|] EDOs: 7, 8, 15, 22, 29, 51, 73 Badness: 0.0273
Original HTML content:
<html><head><title>Porcupine family</title></head><body><!-- ws:start:WikiTextTocRule:22:<img id="wikitext@@toc@@flat" class="WikiMedia WikiMediaTocFlat" title="Table of Contents" src="/site/embedthumbnail/toc/flat?w=100&h=16"/> --><!-- ws:end:WikiTextTocRule:22 --><!-- ws:start:WikiTextTocRule:23: --><!-- ws:end:WikiTextTocRule:23 --><!-- ws:start:WikiTextTocRule:24: --> | <a href="#Porcupine">Porcupine</a><!-- ws:end:WikiTextTocRule:24 --><!-- ws:start:WikiTextTocRule:25: --><!-- ws:end:WikiTextTocRule:25 --><!-- ws:start:WikiTextTocRule:26: --> | <a href="#Hystrix">Hystrix</a><!-- ws:end:WikiTextTocRule:26 --><!-- ws:start:WikiTextTocRule:27: --> | <a href="#Hedgehog">Hedgehog</a><!-- ws:end:WikiTextTocRule:27 --><!-- ws:start:WikiTextTocRule:28: --> | <a href="#Nautilus">Nautilus</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: --> | <a href="#Ammonite">Ammonite</a><!-- ws:end:WikiTextTocRule:31 --><!-- ws:start:WikiTextTocRule:32: --> | <a href="#Porky">Porky</a><!-- ws:end:WikiTextTocRule:32 --><!-- ws:start:WikiTextTocRule:33: --><!-- ws:end:WikiTextTocRule:33 --><!-- ws:start:WikiTextTocRule:34: --> <!-- ws:end:WikiTextTocRule:34 --><hr /> The 5-limit parent comma for the porcupine family is 250/243, the maximal <a class="wiki_link" href="/diesis">diesis</a> or porcupine comma. Its <a class="wiki_link" href="/monzo">monzo</a> is |1 -5 3>, and flipping that yields <<3 5 1|| for the <a class="wiki_link" href="/wedgie">wedgie</a>. This tells us the <a class="wiki_link" href="/generator">generator</a> is a minor whole tone, the <a class="wiki_link" href="/10_9">10/9</a> interval, and that three of these add up to a fourth, with two more giving the minor sixth. In fact, (10/9)^3 = 4/3 * 250/243, and (10/9)^5 = 8/5 * (250/243)^2. 3/22 is a very recommendable generator, and MOS of 7, 8 and 15 notes make for some nice scale possibilities.<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 163.950<br /> <br /> Map: [<1 2 3|, <0 -3 -5|]<br /> <br /> EDOs: <a class="wiki_link" href="/15edo">15</a>, <a class="wiki_link" href="/22edo">22</a>, <a class="wiki_link" href="/161edo">161</a>, <a class="wiki_link" href="/183edo">183</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:0:<h2> --><h2 id="toc0"><a name="x-Seven limit children"></a><!-- ws:end:WikiTextHeadingRule:0 -->Seven limit children</h2> The second comma of the <a class="wiki_link" href="/Normal%20lists">normal comma list</a> defines which <a class="wiki_link" href="/7-limit">7-limit</a> family member we are looking at. That means <a class="wiki_link" href="/64_63">64/63</a>, the <a class="wiki_link" href="/Archyta%27s%20comma">Archyta's comma</a>, for <a class="wiki_link" href="/Porcupine%20family#Porcupine">porcupine</a>, <a class="wiki_link" href="/36_35">36/35</a>, the <a class="wiki_link" href="/septimal%20quarter%20tone">septimal quarter tone</a>, for <a class="wiki_link" href="/Porcupine%20family#Hystrix">hystrix</a>, <a class="wiki_link" href="/50_49">50/49</a>, the <a class="wiki_link" href="/jubilisma">jubilisma</a>, for <a class="wiki_link" href="/Porcupine%20family#Hedgehog">hedgehog</a>, and <a class="wiki_link" href="/49_48">49/48</a>, the <a class="wiki_link" href="/slendro%20diesis">slendro diesis</a>, for <a class="wiki_link" href="/Porcupine%20family#Nautilus">nautilus</a>.<br /> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h1> --><h1 id="toc1"><a name="Porcupine"></a><!-- ws:end:WikiTextHeadingRule:2 -->Porcupine</h1> Porcupine, with wedgie <<3 5 -6 1 -18 -28||, uses six of its minor tone generator steps to get to <a class="wiki_link" href="/7_4">7/4</a>. For this to work you need a small minor tone such as <a class="wiki_link" href="/22edo">22edo</a> provides, and once again 3\22 is a good tuning choice, though we might pick in preference 8\59, 11\81, or 19\140 for our generator.<br /> <br /> Commas: 250/243, 64/63<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~10/9 = 162.880<br /> <br /> Map: [<1 2 3 2|, <0 -3 -5 6|]<br /> EDOs: 22, <a class="wiki_link" href="/59edo">59</a>, <a class="wiki_link" href="/81edo">81</a>, <a class="wiki_link" href="/140edo">140</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:4:<h2> --><h2 id="toc2"><a name="Porcupine-11-limit"></a><!-- ws:end:WikiTextHeadingRule:4 -->11-limit</h2> Commas: 55/54, 64/63, 100/99<br /> <br /> POTE generator: ~10/9 = 162.747<br /> <br /> Map: [<1 2 3 2 4|, <0 -3 -5 6 -4|]<br /> EDOs: <a class="wiki_link" href="/7edo">7</a>, 15, 22, <a class="wiki_link" href="/37edo">37</a>, 59<br /> Badness: 0.0217<br /> <br /> <!-- ws:start:WikiTextHeadingRule:6:<h1> --><h1 id="toc3"><a name="Hystrix"></a><!-- ws:end:WikiTextHeadingRule:6 -->Hystrix</h1> Hystrix, with wedgie <<3 5 1 1 -7 -12||, provides a less complex avenue to the 7-limit. Unfortunately in temperaments as in life you get what you pay for, and hystrix, for which a generator of 2\15 or 9\68 can be used, is a temperament for the adventurous souls who have probably already tried <a class="wiki_link" href="/15edo">15edo</a>. They can try the even sharper fifth of hystrix in <a class="wiki_link" href="/68edo">68edo</a> and see how that suits.<br /> <br /> Commas: 36/35, 160/147<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 158.868<br /> <br /> Map: [<1 2 3 3|, <0 -3 -5 -1|]<br /> <br /> EDOs: 15, 68<br /> <br /> <!-- ws:start:WikiTextHeadingRule:8:<h1> --><h1 id="toc4"><a name="Hedgehog"></a><!-- ws:end:WikiTextHeadingRule:8 -->Hedgehog</h1> <br /> See <em><a class="wiki_link" href="/Hedgehog">Hedgehog</a></em><br /> <br /> <!-- ws:start:WikiTextHeadingRule:10:<h1> --><h1 id="toc5"><a name="Nautilus"></a><!-- ws:end:WikiTextHeadingRule:10 -->Nautilus</h1> Commas: 49/48, 250/243<br /> <br /> Pote generator: ~21/20 = 82.505<br /> <br /> Map: [<1 2 3 3|, <0 -6 -10 -3|]<br /> Wedgie: <<6 10 3 2 -12 -21||<br /> EDOs: <a class="wiki_link" href="/14edo">14</a>, 15, <a class="wiki_link" href="/29edo">29</a>, <a class="wiki_link" href="/44edo">44</a>, <a class="wiki_link" href="/73edo">73</a>, <a class="wiki_link" href="/160edo">160</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:12:<h2> --><h2 id="toc6"><a name="Nautilus-11-limit"></a><!-- ws:end:WikiTextHeadingRule:12 -->11-limit</h2> Commas: 49/48, 55/54, 245/242<br /> <br /> POTE generator: ~21/20 = 82.504<br /> <br /> Map: [<1 2 3 3 4|, <0 -6 -10 -3 -8|]<br /> EDOs: 14, 15, 29, 44, 73, 160<br /> <br /> <!-- ws:start:WikiTextHeadingRule:14:<h2> --><h2 id="toc7"><a name="Nautilus-13-limit"></a><!-- ws:end:WikiTextHeadingRule:14 -->13-limit</h2> Commas: 49/48, 55/54, 91/90, 100/99<br /> <br /> POTE generator: ~21/20 = 62.530<br /> <br /> Map: [<1 2 3 3 4 5|, <0 -6 -10 -3 -8 -19|]<br /> EDOs: 14, 15, 29, 44, 73, 160<br /> <br /> <!-- ws:start:WikiTextHeadingRule:16:<h1> --><h1 id="toc8"><a name="Ammonite"></a><!-- ws:end:WikiTextHeadingRule:16 -->Ammonite</h1> Commas: 250/243, 686/675<br /> <br /> POTE generator: ~9/7 = 454.448<br /> <br /> Map: [<1 5 8 10|, <0 -9 -15 -19|]<br /> Wedgie: <<9 15 19 3 5 2||<br /> EDOs: 29, 37, 66<br /> Badness: 0.1077<br /> <br /> 11-limit<br /> Commas: 55/54, 100/99, 686/675<br /> <br /> POTE generator: ~9/7 = 454.512<br /> <br /> Map: [<1 5 8 10 8|, <0 -9 -15 -19 -12|]<br /> EDOs: 29, 37, 66<br /> Badness: 0.0457<br /> <br /> 13-limit<br /> Commas: 55/54, 91/90, 100/99, 169/168<br /> <br /> POTE generator: ~13/10 = 454.429<br /> <br /> Map: [<1 5 8 10 8 9|, <0 -9 -15 -19 -12 -14|]<br /> EDOs: 29, 37, 66<br /> Badness: 0.0272 <br /> <br /> <!-- ws:start:WikiTextHeadingRule:18:<h1> --><h1 id="toc9"><a name="Porky"></a><!-- ws:end:WikiTextHeadingRule:18 -->Porky</h1> Commas: 225/224, 250/243<br /> <br /> POTE generator: ~10/9 = 164.412<br /> <br /> Map: [<1 2 3 5|, <0 -3 -5 -16|]<br /> Wedgie: <<3 5 16 1 17 23||<br /> EDOS: 7, 8, 15, 22, 29, 51, 73<br /> Badness: 0.0544<br /> <br /> <!-- ws:start:WikiTextHeadingRule:20:<h2> --><h2 id="toc10"><a name="Porky-11-limit"></a><!-- ws:end:WikiTextHeadingRule:20 -->11-limit</h2> Commas: 55/54, 100/99, 225/224<br /> <br /> POTE generator: ~10/9 = 164.552<br /> <br /> Map: [<1 2 3 5 4|, <0 -3 -5 -16 -4|]<br /> EDOs: 7, 8, 15, 22, 29, 51, 73<br /> Badness: 0.0273</body></html>