Porcupine family: Difference between revisions
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Wikispaces>genewardsmith **Imported revision 330734362 - Original comment: ** |
Wikispaces>phylingual **Imported revision 341882896 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User: | : This revision was by author [[User:phylingual|phylingual]] and made on <tt>2012-06-01 16:19:55 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>341882896</tt>.<br> | ||
: The revision comment was: <tt></tt><br> | : The revision comment was: <tt></tt><br> | ||
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | ||
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Badness: 0.0215 | Badness: 0.0215 | ||
==Urchin== | ==Urchin== | ||
Commas: 40/39, 50/49, 55/54, 66/65 | Commas: 40/39, 50/49, 55/54, 66/65 | ||
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Commas: 49/48, 250/243 | Commas: 49/48, 250/243 | ||
POTE generator: ~21/20 = 82.505 | |||
Map: [<1 2 3 3|, <0 -6 -10 -3|] | Map: [<1 2 3 3|, <0 -6 -10 -3|] | ||
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Badness: 0.0223 | Badness: 0.0223 | ||
==Belauensis== | ==Belauensis== | ||
Commas: 40/39, 49/48, 55/54, 66/65 | Commas: 40/39, 49/48, 55/54, 66/65 | ||
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Badness: 0.0272 | Badness: 0.0272 | ||
=Ceratitid= | =Ceratitid= | ||
Commas: 250/243, 1728/1715 | Commas: 250/243, 1728/1715 | ||
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Badness: 0.115 | Badness: 0.115 | ||
==11-limit== | ==11-limit== | ||
Commas: 55/54, 100/99, 5324/5145 | Commas: 55/54, 100/99, 5324/5145 | ||
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Badness: 0.0513 | Badness: 0.0513 | ||
==13-limit== | ==13-limit== | ||
Commas: 55/54, 65/63, 100/99, 352/343 | Commas: 55/54, 65/63, 100/99, 352/343 | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:20:&lt;h2&gt; --><h2 id="toc10"><a name="Hedgehog-Urchin"></a><!-- ws:end:WikiTextHeadingRule:20 -->Urchin</h2> | <!-- ws:start:WikiTextHeadingRule:20:&lt;h2&gt; --><h2 id="toc10"><a name="Hedgehog-Urchin"></a><!-- ws:end:WikiTextHeadingRule:20 -->Urchin</h2> | ||
Commas: 40/39, 50/49, 55/54, 66/65<br /> | Commas: 40/39, 50/49, 55/54, 66/65<br /> | ||
<br /> | <br /> | ||
POTE generator: ~9/7 = 437.078<br /> | POTE generator: ~9/7 = 437.078<br /> | ||
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Commas: 49/48, 250/243<br /> | Commas: 49/48, 250/243<br /> | ||
<br /> | <br /> | ||
POTE generator: ~21/20 = 82.505<br /> | |||
<br /> | <br /> | ||
Map: [&lt;1 2 3 3|, &lt;0 -6 -10 -3|]<br /> | Map: [&lt;1 2 3 3|, &lt;0 -6 -10 -3|]<br /> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:32:&lt;h2&gt; --><h2 id="toc16"><a name="Nautilus-Belauensis"></a><!-- ws:end:WikiTextHeadingRule:32 -->Belauensis</h2> | <!-- ws:start:WikiTextHeadingRule:32:&lt;h2&gt; --><h2 id="toc16"><a name="Nautilus-Belauensis"></a><!-- ws:end:WikiTextHeadingRule:32 -->Belauensis</h2> | ||
Commas: 40/39, 49/48, 55/54, 66/65<br /> | Commas: 40/39, 49/48, 55/54, 66/65<br /> | ||
<br /> | <br /> | ||
POTE generator: ~21/20 = ~14/13 = 81.759<br /> | POTE generator: ~21/20 = ~14/13 = 81.759<br /> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:40:&lt;h1&gt; --><h1 id="toc20"><a name="Ceratitid"></a><!-- ws:end:WikiTextHeadingRule:40 -->Ceratitid</h1> | <!-- ws:start:WikiTextHeadingRule:40:&lt;h1&gt; --><h1 id="toc20"><a name="Ceratitid"></a><!-- ws:end:WikiTextHeadingRule:40 -->Ceratitid</h1> | ||
Commas: 250/243, 1728/1715<br /> | Commas: 250/243, 1728/1715<br /> | ||
<br /> | <br /> | ||
POTE generator: ~36/35 = 54.384<br /> | POTE generator: ~36/35 = 54.384<br /> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:42:&lt;h2&gt; --><h2 id="toc21"><a name="Ceratitid-11-limit"></a><!-- ws:end:WikiTextHeadingRule:42 -->11-limit</h2> | <!-- ws:start:WikiTextHeadingRule:42:&lt;h2&gt; --><h2 id="toc21"><a name="Ceratitid-11-limit"></a><!-- ws:end:WikiTextHeadingRule:42 -->11-limit</h2> | ||
Commas: 55/54, 100/99, 5324/5145<br /> | Commas: 55/54, 100/99, 5324/5145<br /> | ||
<br /> | <br /> | ||
POTE generator: ~36/35 = 54.376<br /> | POTE generator: ~36/35 = 54.376<br /> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:44:&lt;h2&gt; --><h2 id="toc22"><a name="Ceratitid-13-limit"></a><!-- ws:end:WikiTextHeadingRule:44 -->13-limit</h2> | <!-- ws:start:WikiTextHeadingRule:44:&lt;h2&gt; --><h2 id="toc22"><a name="Ceratitid-13-limit"></a><!-- ws:end:WikiTextHeadingRule:44 -->13-limit</h2> | ||
Commas: 55/54, 65/63, 100/99, 352/343<br /> | Commas: 55/54, 65/63, 100/99, 352/343<br /> | ||
<br /> | <br /> | ||
POTE generator: ~36/35 = 54.665<br /> | POTE generator: ~36/35 = 54.665<br /> | ||
Revision as of 16:19, 1 June 2012
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author phylingual and made on 2012-06-01 16:19:55 UTC.
- The original revision id was 341882896.
- The revision comment was:
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.
Original Wikitext content:
[[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]], [[95edo|95c]], [[117edo|117bc]], [[139edo|139bc]], [[161edo|161bc]], [[183edo|183bc]] ==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|81bd]], [[140edo|140bd]] ==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]], [[59edo|59]] Badness: 0.0217 ==13-limit== Commas: 40/39, 55/54, 64/63, 66/65 POTE generator: ~10/9 = 162.708 Map: [<1 2 3 2 4 4|, <0 -3 -5 6 -4 -2|] EDOs: 7, 15, 22f, 37f Badness: 0.0213 ==Porcupinefish== See also: [[The Biosphere]] Commas: 55/54, 64/63, 91/90, 100/99 POTE generator: ~10/9 = 162.277 Map: [<1 2 3 2 4 6|, <0 -3 -5 6 -4 -17|] EDOs: 15, 22, 37, 59, 96b <span style="background-color: #ffffff;">Badness: 0.0253</span> ==Porkpie== Commas: 55/54, 64/63, 65/63, 100/99 POTE generator: ~10/9 = 163.688 Map: [<1 2 3 2 4 3|, <0 -3 -5 6 -4 5|] EDOs: 7, 15f, 22 Badness: 0.0260 =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: 10d, 12, 13d, 15 =Hedgehog= Hedgehog, with wedgie <<6 10 10 2 -1 -5||, has a period 1/2 octave and a generator which can be taken to be 9/7 instead of 10/9. It also tempers out 245/243, the sensamagic comma. 22et provides the obvious tuning, but if you are looking for an alternative, you could try the <146 232 338 411| val with generator 10\73, or you could try 164 cents if you are fond of round numbers. The 14 note MOS gives scope for harmony while stopping well short of 22. Commas: 50/49, 245/243 [[POTE tuning|POTE generator]]: ~9/7 = 435.648 Map: [<2 1 1 2|, <0 3 5 5|] Wedgie: <<6 10 10 2 -1 -5|| EDOs: 22, [[146edo|146]] Badness: 0.0440 ==11-limit== Commas: 50/49, 55/54, 99/98 POTE generator: ~9/7 = 435.386 Map: [<2 1 1 2 4|, <0 3 5 5 4|] EDOs: 14c, 22, 58ce, 80ce, 102cde Badness: 0.0231 ==13-limit== Commas: 50/49, 55/54, 65/63, 99/98 POTE generator: ~9/7 = 435.861 Map: [<2 1 1 2 4 3|, <0 3 5 5 4 6|] EDOs: 14cf, 22 Badness: 0.0215 ==Urchin== Commas: 40/39, 50/49, 55/54, 66/65 POTE generator: ~9/7 = 437.078 Map: [<2 1 1 2 4 6|, <0 3 5 5 4 2|] EDOs: 14c, 22f Badness: 0.0252 ==Hedgepig== Commas: 50/49, 245/243, 385/384 POTE generator: ~9/7 = 435.425 Map: [<2 1 1 2 12|, <0 3 5 5 -7|] EDOs: 22, 80c, 102cd, 124cd Badness: 0.0684 ===Music=== [[http://micro.soonlabel.com/22-ET/20120207-phobos-light-hedgehog14.mp3|Phobos Light]] by Chris Vaisvil in Hedgehog[14] [[hedgehog14|tuned]] to 22edo. =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: 10, 15, 19, [[29edo|29]], [[102edo|102cd]] ==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: 10e, 14c, 15, 19, 22d, 29, 102cde ==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: 10e, 15f, 17d, 19, 22d, 29, 102cde Badness: 0.0223 ==Belauensis== Commas: 40/39, 49/48, 55/54, 66/65 POTE generator: ~21/20 = ~14/13 = 81.759 Map: [<1 2 3 3 4 4|, <0 -6 -10 -3 -8 -4|] EDOs: 14c, 15, 29f, 44df Badness: 0.0298 [[http://micro.soonlabel.com/gene_ward_smith/Others/Igs/NautilusReverie.mp3|Nautilus Reverie]] by [[IgliashonJones|Igliashon Calvin Jones-Coolidge]] =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 =Ceratitid= Commas: 250/243, 1728/1715 POTE generator: ~36/35 = 54.384 Map: [<1 2 3 3|, <0 -9 -15 -4|] Wedgie: <<9 15 4 3 -19 -33|| EDOs: 22 Badness: 0.115 ==11-limit== Commas: 55/54, 100/99, 5324/5145 POTE generator: ~36/35 = 54.376 Map: [<1 2 3 3 4|, <0 -9 -15 -4 -12|] EDOs: 22 Badness: 0.0513 ==13-limit== Commas: 55/54, 65/63, 100/99, 352/343 POTE generator: ~36/35 = 54.665 Map: [<1 2 3 3 4 4|, <0 -9 -15 -4 -12 -7|] EDOs: 22 Badness: 0.0447 =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 =Coendou= Commas: 250/243, 525/512 POTE generator: ~10/9 = 166.041 Map: [<1 2 3 1|, <0 -3 -5 13|] Wedgie: <<3 5 -13 1 -29 -44|| EDOs: 7, 29, 65c, 94cd Badness: 0.1183 ==11-limit== Commas: 55/54, 100/99, 525/512 POTE generator: ~10/9 = 165.981 Map: [<1 2 3 1 4|, <0 -3 -5 13 -4|] EDOs: 7, 29, 65ce, 94cde Badness: 0.0497 ==13-limit== Commas: 55/54, 65/64, 100/99, 105/104 POTE generator: ~10/9 = 165.974 Map: [<1 2 3 1 4 3|, <0 -3 -5 13 -4 5|] EDOs: 7, 29, 65cef, 94cdef Badness: 0.0302
Original HTML content:
<html><head><title>Porcupine family</title></head><body><!-- ws:start:WikiTextTocRule:56:<img id="wikitext@@toc@@flat" class="WikiMedia WikiMediaTocFlat" title="Table of Contents" src="/site/embedthumbnail/toc/flat?w=100&h=16"/> --><!-- ws:end:WikiTextTocRule:56 --><!-- ws:start:WikiTextTocRule:57: --><!-- ws:end:WikiTextTocRule:57 --><!-- ws:start:WikiTextTocRule:58: --> | <a href="#Porcupine">Porcupine</a><!-- ws:end:WikiTextTocRule:58 --><!-- ws:start:WikiTextTocRule:59: --><!-- 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="#Hystrix">Hystrix</a><!-- ws:end:WikiTextTocRule:63 --><!-- ws:start:WikiTextTocRule:64: --> | <a href="#Hedgehog">Hedgehog</a><!-- ws:end:WikiTextTocRule:64 --><!-- ws:start:WikiTextTocRule:65: --><!-- ws:end:WikiTextTocRule:65 --><!-- ws:start:WikiTextTocRule:66: --><!-- 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: --> | <a href="#Nautilus">Nautilus</a><!-- ws:end:WikiTextTocRule:70 --><!-- ws:start:WikiTextTocRule:71: --><!-- ws:end:WikiTextTocRule:71 --><!-- ws:start:WikiTextTocRule:72: --><!-- ws:end:WikiTextTocRule:72 --><!-- ws:start:WikiTextTocRule:73: --><!-- ws:end:WikiTextTocRule:73 --><!-- ws:start:WikiTextTocRule:74: --> | <a href="#Ammonite">Ammonite</a><!-- ws:end:WikiTextTocRule:74 --><!-- ws:start:WikiTextTocRule:75: --><!-- ws:end:WikiTextTocRule:75 --><!-- ws:start:WikiTextTocRule:76: --><!-- ws:end:WikiTextTocRule:76 --><!-- ws:start:WikiTextTocRule:77: --> | <a href="#Ceratitid">Ceratitid</a><!-- ws:end:WikiTextTocRule:77 --><!-- ws:start:WikiTextTocRule:78: --><!-- ws:end:WikiTextTocRule:78 --><!-- ws:start:WikiTextTocRule:79: --><!-- ws:end:WikiTextTocRule:79 --><!-- ws:start:WikiTextTocRule:80: --> | <a href="#Porky">Porky</a><!-- ws:end:WikiTextTocRule:80 --><!-- ws:start:WikiTextTocRule:81: --><!-- ws:end:WikiTextTocRule:81 --><!-- ws:start:WikiTextTocRule:82: --> | <a href="#Coendou">Coendou</a><!-- ws:end:WikiTextTocRule:82 --><!-- ws:start:WikiTextTocRule:83: --><!-- ws:end:WikiTextTocRule:83 --><!-- ws:start:WikiTextTocRule:84: --><!-- ws:end:WikiTextTocRule:84 --><!-- ws:start:WikiTextTocRule:85: --> <!-- ws:end:WikiTextTocRule:85 --><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="/95edo">95c</a>, <a class="wiki_link" href="/117edo">117bc</a>, <a class="wiki_link" href="/139edo">139bc</a>, <a class="wiki_link" href="/161edo">161bc</a>, <a class="wiki_link" href="/183edo">183bc</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> <a class="wiki_link" href="/Porcupine">Porcupine</a>, 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">81bd</a>, <a class="wiki_link" href="/140edo">140bd</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>, <a class="wiki_link" href="/59edo">59</a><br /> Badness: 0.0217<br /> <br /> <!-- ws:start:WikiTextHeadingRule:6:<h2> --><h2 id="toc3"><a name="Porcupine-13-limit"></a><!-- ws:end:WikiTextHeadingRule:6 -->13-limit</h2> Commas: 40/39, 55/54, 64/63, 66/65<br /> <br /> POTE generator: ~10/9 = 162.708<br /> <br /> Map: [<1 2 3 2 4 4|, <0 -3 -5 6 -4 -2|]<br /> EDOs: 7, 15, 22f, 37f<br /> Badness: 0.0213<br /> <br /> <!-- ws:start:WikiTextHeadingRule:8:<h2> --><h2 id="toc4"><a name="Porcupine-Porcupinefish"></a><!-- ws:end:WikiTextHeadingRule:8 -->Porcupinefish</h2> See also: <a class="wiki_link" href="/The%20Biosphere">The Biosphere</a><br /> Commas: 55/54, 64/63, 91/90, 100/99<br /> <br /> POTE generator: ~10/9 = 162.277<br /> <br /> Map: [<1 2 3 2 4 6|, <0 -3 -5 6 -4 -17|]<br /> EDOs: 15, 22, 37, 59, 96b<br /> <span style="background-color: #ffffff;">Badness: 0.0253</span><br /> <br /> <!-- ws:start:WikiTextHeadingRule:10:<h2> --><h2 id="toc5"><a name="Porcupine-Porkpie"></a><!-- ws:end:WikiTextHeadingRule:10 -->Porkpie</h2> Commas: 55/54, 64/63, 65/63, 100/99<br /> <br /> POTE generator: ~10/9 = 163.688<br /> <br /> Map: [<1 2 3 2 4 3|, <0 -3 -5 6 -4 5|]<br /> EDOs: 7, 15f, 22<br /> Badness: 0.0260<br /> <br /> <!-- ws:start:WikiTextHeadingRule:12:<h1> --><h1 id="toc6"><a name="Hystrix"></a><!-- ws:end:WikiTextHeadingRule:12 -->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: 10d, 12, 13d, 15<br /> <br /> <!-- ws:start:WikiTextHeadingRule:14:<h1> --><h1 id="toc7"><a name="Hedgehog"></a><!-- ws:end:WikiTextHeadingRule:14 -->Hedgehog</h1> Hedgehog, with wedgie <<6 10 10 2 -1 -5||, has a period 1/2 octave and a generator which can be taken to be 9/7 instead of 10/9. It also tempers out 245/243, the sensamagic comma. 22et provides the obvious tuning, but if you are looking for an alternative, you could try the <146 232 338 411| val with generator 10\73, or you could try 164 cents if you are fond of round numbers. The 14 note MOS gives scope for harmony while stopping well short of 22.<br /> <br /> Commas: 50/49, 245/243<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~9/7 = 435.648<br /> <br /> Map: [<2 1 1 2|, <0 3 5 5|]<br /> Wedgie: <<6 10 10 2 -1 -5||<br /> EDOs: 22, <a class="wiki_link" href="/146edo">146</a><br /> Badness: 0.0440<br /> <br /> <!-- ws:start:WikiTextHeadingRule:16:<h2> --><h2 id="toc8"><a name="Hedgehog-11-limit"></a><!-- ws:end:WikiTextHeadingRule:16 -->11-limit</h2> Commas: 50/49, 55/54, 99/98<br /> <br /> POTE generator: ~9/7 = 435.386<br /> <br /> Map: [<2 1 1 2 4|, <0 3 5 5 4|]<br /> EDOs: 14c, 22, 58ce, 80ce, 102cde<br /> Badness: 0.0231<br /> <br /> <!-- ws:start:WikiTextHeadingRule:18:<h2> --><h2 id="toc9"><a name="Hedgehog-13-limit"></a><!-- ws:end:WikiTextHeadingRule:18 -->13-limit</h2> Commas: 50/49, 55/54, 65/63, 99/98<br /> <br /> POTE generator: ~9/7 = 435.861<br /> <br /> Map: [<2 1 1 2 4 3|, <0 3 5 5 4 6|]<br /> EDOs: 14cf, 22<br /> Badness: 0.0215<br /> <br /> <!-- ws:start:WikiTextHeadingRule:20:<h2> --><h2 id="toc10"><a name="Hedgehog-Urchin"></a><!-- ws:end:WikiTextHeadingRule:20 -->Urchin</h2> Commas: 40/39, 50/49, 55/54, 66/65<br /> <br /> POTE generator: ~9/7 = 437.078<br /> <br /> Map: [<2 1 1 2 4 6|, <0 3 5 5 4 2|]<br /> EDOs: 14c, 22f<br /> Badness: 0.0252<br /> <br /> <!-- ws:start:WikiTextHeadingRule:22:<h2> --><h2 id="toc11"><a name="Hedgehog-Hedgepig"></a><!-- ws:end:WikiTextHeadingRule:22 -->Hedgepig</h2> Commas: 50/49, 245/243, 385/384<br /> <br /> POTE generator: ~9/7 = 435.425<br /> <br /> Map: [<2 1 1 2 12|, <0 3 5 5 -7|]<br /> EDOs: 22, 80c, 102cd, 124cd<br /> Badness: 0.0684<br /> <br /> <!-- ws:start:WikiTextHeadingRule:24:<h3> --><h3 id="toc12"><a name="Hedgehog-Hedgepig-Music"></a><!-- ws:end:WikiTextHeadingRule:24 -->Music</h3> <a class="wiki_link_ext" href="http://micro.soonlabel.com/22-ET/20120207-phobos-light-hedgehog14.mp3" rel="nofollow">Phobos Light</a> by Chris Vaisvil in Hedgehog[14] <a class="wiki_link" href="/hedgehog14">tuned</a> to 22edo.<br /> <br /> <!-- ws:start:WikiTextHeadingRule:26:<h1> --><h1 id="toc13"><a name="Nautilus"></a><!-- ws:end:WikiTextHeadingRule:26 -->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: 10, 15, 19, <a class="wiki_link" href="/29edo">29</a>, <a class="wiki_link" href="/102edo">102cd</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:28:<h2> --><h2 id="toc14"><a name="Nautilus-11-limit"></a><!-- ws:end:WikiTextHeadingRule:28 -->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: 10e, 14c, 15, 19, 22d, 29, 102cde<br /> <br /> <!-- ws:start:WikiTextHeadingRule:30:<h2> --><h2 id="toc15"><a name="Nautilus-13-limit"></a><!-- ws:end:WikiTextHeadingRule:30 -->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: 10e, 15f, 17d, 19, 22d, 29, 102cde<br /> Badness: 0.0223<br /> <br /> <!-- ws:start:WikiTextHeadingRule:32:<h2> --><h2 id="toc16"><a name="Nautilus-Belauensis"></a><!-- ws:end:WikiTextHeadingRule:32 -->Belauensis</h2> Commas: 40/39, 49/48, 55/54, 66/65<br /> <br /> POTE generator: ~21/20 = ~14/13 = 81.759<br /> <br /> Map: [<1 2 3 3 4 4|, <0 -6 -10 -3 -8 -4|]<br /> EDOs: 14c, 15, 29f, 44df<br /> Badness: 0.0298<br /> <br /> <a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Igs/NautilusReverie.mp3" rel="nofollow">Nautilus Reverie</a> by <a class="wiki_link" href="/IgliashonJones">Igliashon Calvin Jones-Coolidge</a><br /> <!-- ws:start:WikiTextHeadingRule:34:<h1> --><h1 id="toc17"><a name="Ammonite"></a><!-- ws:end:WikiTextHeadingRule:34 -->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 /> <!-- ws:start:WikiTextHeadingRule:36:<h2> --><h2 id="toc18"><a name="Ammonite-11-limit"></a><!-- ws:end:WikiTextHeadingRule:36 -->11-limit</h2> 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 /> <!-- ws:start:WikiTextHeadingRule:38:<h2> --><h2 id="toc19"><a name="Ammonite-13-limit"></a><!-- ws:end:WikiTextHeadingRule:38 -->13-limit</h2> 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:40:<h1> --><h1 id="toc20"><a name="Ceratitid"></a><!-- ws:end:WikiTextHeadingRule:40 -->Ceratitid</h1> Commas: 250/243, 1728/1715<br /> <br /> POTE generator: ~36/35 = 54.384<br /> <br /> Map: [<1 2 3 3|, <0 -9 -15 -4|]<br /> Wedgie: <<9 15 4 3 -19 -33||<br /> EDOs: 22<br /> Badness: 0.115<br /> <br /> <!-- ws:start:WikiTextHeadingRule:42:<h2> --><h2 id="toc21"><a name="Ceratitid-11-limit"></a><!-- ws:end:WikiTextHeadingRule:42 -->11-limit</h2> Commas: 55/54, 100/99, 5324/5145<br /> <br /> POTE generator: ~36/35 = 54.376<br /> <br /> Map: [<1 2 3 3 4|, <0 -9 -15 -4 -12|]<br /> EDOs: 22<br /> Badness: 0.0513<br /> <br /> <!-- ws:start:WikiTextHeadingRule:44:<h2> --><h2 id="toc22"><a name="Ceratitid-13-limit"></a><!-- ws:end:WikiTextHeadingRule:44 -->13-limit</h2> Commas: 55/54, 65/63, 100/99, 352/343<br /> <br /> POTE generator: ~36/35 = 54.665<br /> <br /> Map: [<1 2 3 3 4 4|, <0 -9 -15 -4 -12 -7|]<br /> EDOs: 22<br /> Badness: 0.0447<br /> <br /> <!-- ws:start:WikiTextHeadingRule:46:<h1> --><h1 id="toc23"><a name="Porky"></a><!-- ws:end:WikiTextHeadingRule:46 -->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:48:<h2> --><h2 id="toc24"><a name="Porky-11-limit"></a><!-- ws:end:WikiTextHeadingRule:48 -->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<br /> <br /> <!-- ws:start:WikiTextHeadingRule:50:<h1> --><h1 id="toc25"><a name="Coendou"></a><!-- ws:end:WikiTextHeadingRule:50 -->Coendou</h1> Commas: 250/243, 525/512<br /> <br /> POTE generator: ~10/9 = 166.041<br /> <br /> Map: [<1 2 3 1|, <0 -3 -5 13|]<br /> Wedgie: <<3 5 -13 1 -29 -44||<br /> EDOs: 7, 29, 65c, 94cd<br /> Badness: 0.1183<br /> <br /> <!-- ws:start:WikiTextHeadingRule:52:<h2> --><h2 id="toc26"><a name="Coendou-11-limit"></a><!-- ws:end:WikiTextHeadingRule:52 -->11-limit</h2> Commas: 55/54, 100/99, 525/512<br /> <br /> POTE generator: ~10/9 = 165.981<br /> <br /> Map: [<1 2 3 1 4|, <0 -3 -5 13 -4|]<br /> EDOs: 7, 29, 65ce, 94cde<br /> Badness: 0.0497<br /> <br /> <!-- ws:start:WikiTextHeadingRule:54:<h2> --><h2 id="toc27"><a name="Coendou-13-limit"></a><!-- ws:end:WikiTextHeadingRule:54 -->13-limit</h2> Commas: 55/54, 65/64, 100/99, 105/104<br /> <br /> POTE generator: ~10/9 = 165.974<br /> <br /> Map: [<1 2 3 1 4 3|, <0 -3 -5 13 -4 5|]<br /> EDOs: 7, 29, 65cef, 94cdef<br /> Badness: 0.0302</body></html>