Porcupine family: Difference between revisions

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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]], [[95edo|95c]], [[117edo|117bc]], [[139edo|139bc]], [[161edo|161bc]], [[183edo|183bc]]
Badness: 0.0308

==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 [[64_63|Archytas 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
7- and 9-limit minimax eigenmonzo: 9/7

Map: [<1 2 3 2|, <0 -3 -5 6|]
EDOs: 22, [[59edo|59]], [[81edo|81bd]], [[140edo|140bd]]
Badness: 0.0411

==11-limit== 
Commas: 55/54, 64/63, 100/99

POTE generator: ~10/9 = 162.747
11-limit minimax eigenmonzo: 9/7

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
13- and 15-limit minimax eigenmonzo: 11/8

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
13- and 15-limit minimax eigenmonzo: 13/11

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>
Badness: 0.0253

==Pourcup== 
Commas: 55/54, 64/63, 100/99, 196/195

POTE generator: ~10/9 = 162.482
13- and 15-limit minimax eigenmonzo: 13/7

Map: [<1 2 3 2 4 1|, <0 -3 -5 6 -4 20|]
EDOs: 15f, 22f, 37
Badness: 0.0351

==Porkpie== 
Commas: 55/54, 64/63, 65/63, 100/99

POTE generator: ~10/9 = 163.688
13- and 15-limit minimax eigenmonzo: 9/7

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
7- and 9-limit minimax eigenmonzo: 5/4

Map: [<1 2 3 3|, <0 -3 -5 -1|]

EDOs: 10d, 12, 13d, 15
Badness: 0.0449

=Porky= 
Commas: 225/224, 250/243

POTE generator: ~10/9 = 164.412
7- and 9-limit minimax eigenmonzo: 7/5

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
11-limit minimax eigenmonzo: 7/5

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
7- and 9-limit minimax eigenmonzo: 3/2

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
11-limit minimax eigenmonzo: 3/2 

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
13- and 15-limit minimax eigenmonzo: 3/2

Map: [<1 2 3 1 4 3|, <0 -3 -5 13 -4 5|]
EDOs: 7, 29, 65cef, 94cdef
Badness: 0.0302

=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

Original HTML content:

<html><head><title>Porcupine family</title></head><body><!-- ws:start:WikiTextTocRule:58:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:58 --><!-- ws:start:WikiTextTocRule:59: --><!-- ws:end:WikiTextTocRule:59 --><!-- ws:start:WikiTextTocRule:60: --> | <a href="#Porcupine">Porcupine</a><!-- ws:end:WikiTextTocRule:60 --><!-- ws:start:WikiTextTocRule:61: --><!-- ws:end:WikiTextTocRule:61 --><!-- ws:start:WikiTextTocRule:62: --><!-- ws:end:WikiTextTocRule:62 --><!-- ws:start:WikiTextTocRule:63: --><!-- ws:end:WikiTextTocRule:63 --><!-- ws:start:WikiTextTocRule:64: --><!-- ws:end:WikiTextTocRule:64 --><!-- ws:start:WikiTextTocRule:65: --><!-- ws:end:WikiTextTocRule:65 --><!-- ws:start:WikiTextTocRule:66: --> | <a href="#Hystrix">Hystrix</a><!-- ws:end:WikiTextTocRule:66 --><!-- ws:start:WikiTextTocRule:67: --> | <a href="#Porky">Porky</a><!-- ws:end:WikiTextTocRule:67 --><!-- ws:start:WikiTextTocRule:68: --><!-- ws:end:WikiTextTocRule:68 --><!-- ws:start:WikiTextTocRule:69: --> | <a href="#Coendou">Coendou</a><!-- ws:end:WikiTextTocRule:69 --><!-- ws:start:WikiTextTocRule:70: --><!-- ws:end:WikiTextTocRule:70 --><!-- ws:start:WikiTextTocRule:71: --><!-- ws:end:WikiTextTocRule:71 --><!-- ws:start:WikiTextTocRule:72: --> | <a href="#Hedgehog">Hedgehog</a><!-- ws:end:WikiTextTocRule:72 --><!-- ws:start:WikiTextTocRule:73: --><!-- ws:end:WikiTextTocRule:73 --><!-- ws:start:WikiTextTocRule:74: --><!-- ws:end:WikiTextTocRule:74 --><!-- ws:start:WikiTextTocRule:75: --><!-- ws:end:WikiTextTocRule:75 --><!-- ws:start:WikiTextTocRule:76: --><!-- ws:end:WikiTextTocRule:76 --><!-- ws:start:WikiTextTocRule:77: --><!-- ws:end:WikiTextTocRule:77 --><!-- ws:start:WikiTextTocRule:78: --> | <a href="#Nautilus">Nautilus</a><!-- ws:end:WikiTextTocRule:78 --><!-- ws:start:WikiTextTocRule:79: --><!-- ws:end:WikiTextTocRule:79 --><!-- ws:start:WikiTextTocRule:80: --><!-- ws:end:WikiTextTocRule:80 --><!-- ws:start:WikiTextTocRule:81: --><!-- ws:end:WikiTextTocRule:81 --><!-- ws:start:WikiTextTocRule:82: --> | <a href="#Ammonite">Ammonite</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: --> | <a href="#Ceratitid">Ceratitid</a><!-- ws:end:WikiTextTocRule:85 --><!-- ws:start:WikiTextTocRule:86: --><!-- ws:end:WikiTextTocRule:86 --><!-- ws:start:WikiTextTocRule:87: --><!-- ws:end:WikiTextTocRule:87 --><!-- ws:start:WikiTextTocRule:88: -->
<!-- ws:end:WikiTextTocRule:88 --><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&gt;, and flipping that yields &lt;&lt;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: [&lt;1 2 3|, &lt;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 />
Badness: 0.0308<br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><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="/64_63">Archytas 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:&lt;h1&gt; --><h1 id="toc1"><a name="Porcupine"></a><!-- ws:end:WikiTextHeadingRule:2 -->Porcupine</h1>
 <a class="wiki_link" href="/Porcupine">Porcupine</a>, with wedgie &lt;&lt;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 />
7- and 9-limit minimax eigenmonzo: 9/7<br />
<br />
Map: [&lt;1 2 3 2|, &lt;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 />
Badness: 0.0411<br />
<br />
<!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><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 />
11-limit minimax eigenmonzo: 9/7<br />
<br />
Map: [&lt;1 2 3 2 4|, &lt;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:&lt;h2&gt; --><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 />
13- and 15-limit minimax eigenmonzo: 11/8<br />
<br />
Map: [&lt;1 2 3 2 4 4|, &lt;0 -3 -5 6 -4 -2|]<br />
EDOs: 7, 15, 22f, 37f<br />
Badness: 0.0213<br />
<br />
<!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><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 />
13- and 15-limit minimax eigenmonzo: 13/11<br />
<br />
Map: [&lt;1 2 3 2 4 6|, &lt;0 -3 -5 6 -4 -17|]<br />
EDOs: 15, 22, 37, 59, 96b<br />
<span style="background-color: #ffffff;">Badness: 0.0253</span><br />
Badness: 0.0253<br />
<br />
<!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc5"><a name="Porcupine-Pourcup"></a><!-- ws:end:WikiTextHeadingRule:10 -->Pourcup</h2>
 Commas: 55/54, 64/63, 100/99, 196/195<br />
<br />
POTE generator: ~10/9 = 162.482<br />
13- and 15-limit minimax eigenmonzo: 13/7<br />
<br />
Map: [&lt;1 2 3 2 4 1|, &lt;0 -3 -5 6 -4 20|]<br />
EDOs: 15f, 22f, 37<br />
Badness: 0.0351<br />
<br />
<!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id="toc6"><a name="Porcupine-Porkpie"></a><!-- ws:end:WikiTextHeadingRule:12 -->Porkpie</h2>
 Commas: 55/54, 64/63, 65/63, 100/99<br />
<br />
POTE generator: ~10/9 = 163.688<br />
13- and 15-limit minimax eigenmonzo: 9/7<br />
<br />
Map: [&lt;1 2 3 2 4 3|, &lt;0 -3 -5 6 -4 5|]<br />
EDOs: 7, 15f, 22<br />
Badness: 0.0260<br />
<br />
<!-- ws:start:WikiTextHeadingRule:14:&lt;h1&gt; --><h1 id="toc7"><a name="Hystrix"></a><!-- ws:end:WikiTextHeadingRule:14 -->Hystrix</h1>
 Hystrix, with wedgie &lt;&lt;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 />
7- and 9-limit minimax eigenmonzo: 5/4<br />
<br />
Map: [&lt;1 2 3 3|, &lt;0 -3 -5 -1|]<br />
<br />
EDOs: 10d, 12, 13d, 15<br />
Badness: 0.0449<br />
<br />
<!-- ws:start:WikiTextHeadingRule:16:&lt;h1&gt; --><h1 id="toc8"><a name="Porky"></a><!-- ws:end:WikiTextHeadingRule:16 -->Porky</h1>
 Commas: 225/224, 250/243<br />
<br />
POTE generator: ~10/9 = 164.412<br />
7- and 9-limit minimax eigenmonzo: 7/5<br />
<br />
Map: [&lt;1 2 3 5|, &lt;0 -3 -5 -16|]<br />
Wedgie: &lt;&lt;3 5 16 1 17 23||<br />
EDOS: 7, 8, 15, 22, 29, 51, 73<br />
Badness: 0.0544<br />
<br />
<!-- ws:start:WikiTextHeadingRule:18:&lt;h2&gt; --><h2 id="toc9"><a name="Porky-11-limit"></a><!-- ws:end:WikiTextHeadingRule:18 -->11-limit</h2>
 Commas: 55/54, 100/99, 225/224<br />
<br />
POTE generator: ~10/9 = 164.552<br />
11-limit minimax eigenmonzo: 7/5<br />
<br />
Map: [&lt;1 2 3 5 4|, &lt;0 -3 -5 -16 -4|]<br />
EDOs: 7, 8, 15, 22, 29, 51, 73<br />
Badness: 0.0273<br />
<br />
<!-- ws:start:WikiTextHeadingRule:20:&lt;h1&gt; --><h1 id="toc10"><a name="Coendou"></a><!-- ws:end:WikiTextHeadingRule:20 -->Coendou</h1>
 Commas: 250/243, 525/512<br />
<br />
POTE generator: ~10/9 = 166.041<br />
7- and 9-limit minimax eigenmonzo: 3/2<br />
<br />
Map: [&lt;1 2 3 1|, &lt;0 -3 -5 13|]<br />
Wedgie: &lt;&lt;3 5 -13 1 -29 -44||<br />
EDOs: 7, 29, 65c, 94cd<br />
Badness: 0.1183<br />
<br />
<!-- ws:start:WikiTextHeadingRule:22:&lt;h2&gt; --><h2 id="toc11"><a name="Coendou-11-limit"></a><!-- ws:end:WikiTextHeadingRule:22 -->11-limit</h2>
 Commas: 55/54, 100/99, 525/512<br />
<br />
POTE generator: ~10/9 = 165.981<br />
11-limit minimax eigenmonzo: 3/2 <br />
<br />
Map: [&lt;1 2 3 1 4|, &lt;0 -3 -5 13 -4|]<br />
EDOs: 7, 29, 65ce, 94cde<br />
Badness: 0.0497<br />
<br />
<!-- ws:start:WikiTextHeadingRule:24:&lt;h2&gt; --><h2 id="toc12"><a name="Coendou-13-limit"></a><!-- ws:end:WikiTextHeadingRule:24 -->13-limit</h2>
 Commas: 55/54, 65/64, 100/99, 105/104<br />
<br />
POTE generator: ~10/9 = 165.974<br />
13- and 15-limit minimax eigenmonzo: 3/2<br />
<br />
Map: [&lt;1 2 3 1 4 3|, &lt;0 -3 -5 13 -4 5|]<br />
EDOs: 7, 29, 65cef, 94cdef<br />
Badness: 0.0302<br />
<br />
<!-- ws:start:WikiTextHeadingRule:26:&lt;h1&gt; --><h1 id="toc13"><a name="Hedgehog"></a><!-- ws:end:WikiTextHeadingRule:26 -->Hedgehog</h1>
 Hedgehog, with wedgie &lt;&lt;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 &lt;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: [&lt;2 1 1 2|, &lt;0 3 5 5|]<br />
Wedgie: &lt;&lt;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:28:&lt;h2&gt; --><h2 id="toc14"><a name="Hedgehog-11-limit"></a><!-- ws:end:WikiTextHeadingRule:28 -->11-limit</h2>
 Commas: 50/49, 55/54, 99/98<br />
<br />
POTE generator: ~9/7 = 435.386<br />
<br />
Map: [&lt;2 1 1 2 4|, &lt;0 3 5 5 4|]<br />
EDOs: 14c, 22, 58ce, 80ce, 102cde<br />
Badness: 0.0231<br />
<br />
<!-- ws:start:WikiTextHeadingRule:30:&lt;h2&gt; --><h2 id="toc15"><a name="Hedgehog-13-limit"></a><!-- ws:end:WikiTextHeadingRule:30 -->13-limit</h2>
 Commas: 50/49, 55/54, 65/63, 99/98<br />
<br />
POTE generator: ~9/7 = 435.861<br />
<br />
Map: [&lt;2 1 1 2 4 3|, &lt;0 3 5 5 4 6|]<br />
EDOs: 14cf, 22<br />
Badness: 0.0215<br />
<br />
<!-- ws:start:WikiTextHeadingRule:32:&lt;h2&gt; --><h2 id="toc16"><a name="Hedgehog-Urchin"></a><!-- ws:end:WikiTextHeadingRule:32 -->Urchin</h2>
 Commas: 40/39, 50/49, 55/54, 66/65<br />
<br />
POTE generator: ~9/7 = 437.078<br />
<br />
Map: [&lt;2 1 1 2 4 6|, &lt;0 3 5 5 4 2|]<br />
EDOs: 14c, 22f<br />
Badness: 0.0252<br />
<br />
<!-- ws:start:WikiTextHeadingRule:34:&lt;h2&gt; --><h2 id="toc17"><a name="Hedgehog-Hedgepig"></a><!-- ws:end:WikiTextHeadingRule:34 -->Hedgepig</h2>
 Commas: 50/49, 245/243, 385/384<br />
<br />
POTE generator: ~9/7 = 435.425<br />
<br />
Map: [&lt;2 1 1 2 12|, &lt;0 3 5 5 -7|]<br />
EDOs: 22, 80c, 102cd, 124cd<br />
Badness: 0.0684<br />
<br />
<!-- ws:start:WikiTextHeadingRule:36:&lt;h3&gt; --><h3 id="toc18"><a name="Hedgehog-Hedgepig-Music"></a><!-- ws:end:WikiTextHeadingRule:36 -->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:38:&lt;h1&gt; --><h1 id="toc19"><a name="Nautilus"></a><!-- ws:end:WikiTextHeadingRule:38 -->Nautilus</h1>
 Commas: 49/48, 250/243<br />
<br />
POTE generator: ~21/20 = 82.505<br />
<br />
Map: [&lt;1 2 3 3|, &lt;0 -6 -10 -3|]<br />
Wedgie: &lt;&lt;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:40:&lt;h2&gt; --><h2 id="toc20"><a name="Nautilus-11-limit"></a><!-- ws:end:WikiTextHeadingRule:40 -->11-limit</h2>
 Commas: 49/48, 55/54, 245/242<br />
<br />
POTE generator: ~21/20 = 82.504<br />
<br />
Map: [&lt;1 2 3 3 4|, &lt;0 -6 -10 -3 -8|]<br />
EDOs: 10e, 14c, 15, 19, 22d, 29, 102cde<br />
<br />
<!-- ws:start:WikiTextHeadingRule:42:&lt;h2&gt; --><h2 id="toc21"><a name="Nautilus-13-limit"></a><!-- ws:end:WikiTextHeadingRule:42 -->13-limit</h2>
 Commas: 49/48, 55/54, 91/90, 100/99<br />
<br />
POTE generator: ~21/20 = 62.530<br />
<br />
Map: [&lt;1 2 3 3 4 5|, &lt;0 -6 -10 -3 -8 -19|]<br />
EDOs: 10e, 15f, 17d, 19, 22d, 29, 102cde<br />
Badness: 0.0223<br />
<br />
<!-- ws:start:WikiTextHeadingRule:44:&lt;h2&gt; --><h2 id="toc22"><a name="Nautilus-Belauensis"></a><!-- ws:end:WikiTextHeadingRule:44 -->Belauensis</h2>
 Commas: 40/39, 49/48, 55/54, 66/65<br />
<br />
POTE generator: ~21/20 = ~14/13 = 81.759<br />
<br />
Map: [&lt;1 2 3 3 4 4|, &lt;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:46:&lt;h1&gt; --><h1 id="toc23"><a name="Ammonite"></a><!-- ws:end:WikiTextHeadingRule:46 -->Ammonite</h1>
 Commas: 250/243, 686/675<br />
<br />
POTE generator: ~9/7 = 454.448<br />
<br />
Map: [&lt;1 5 8 10|, &lt;0 -9 -15 -19|]<br />
Wedgie: &lt;&lt;9 15 19 3 5 2||<br />
EDOs: 29, 37, 66<br />
Badness: 0.1077<br />
<br />
<!-- ws:start:WikiTextHeadingRule:48:&lt;h2&gt; --><h2 id="toc24"><a name="Ammonite-11-limit"></a><!-- ws:end:WikiTextHeadingRule:48 -->11-limit</h2>
 Commas: 55/54, 100/99, 686/675<br />
<br />
POTE generator: ~9/7 = 454.512<br />
<br />
Map: [&lt;1 5 8 10 8|, &lt;0 -9 -15 -19 -12|]<br />
EDOs: 29, 37, 66<br />
Badness: 0.0457<br />
<br />
<!-- ws:start:WikiTextHeadingRule:50:&lt;h2&gt; --><h2 id="toc25"><a name="Ammonite-13-limit"></a><!-- ws:end:WikiTextHeadingRule:50 -->13-limit</h2>
 Commas: 55/54, 91/90, 100/99, 169/168<br />
<br />
POTE generator: ~13/10 = 454.429<br />
<br />
Map: [&lt;1 5 8 10 8 9|, &lt;0 -9 -15 -19 -12 -14|]<br />
EDOs: 29, 37, 66<br />
Badness: 0.0272<br />
<br />
<!-- ws:start:WikiTextHeadingRule:52:&lt;h1&gt; --><h1 id="toc26"><a name="Ceratitid"></a><!-- ws:end:WikiTextHeadingRule:52 -->Ceratitid</h1>
 Commas: 250/243, 1728/1715<br />
<br />
POTE generator: ~36/35 = 54.384<br />
<br />
Map: [&lt;1 2 3 3|, &lt;0 -9 -15 -4|]<br />
Wedgie: &lt;&lt;9 15 4 3 -19 -33||<br />
EDOs: 22<br />
Badness: 0.115<br />
<br />
<!-- ws:start:WikiTextHeadingRule:54:&lt;h2&gt; --><h2 id="toc27"><a name="Ceratitid-11-limit"></a><!-- ws:end:WikiTextHeadingRule:54 -->11-limit</h2>
 Commas: 55/54, 100/99, 5324/5145<br />
<br />
POTE generator: ~36/35 = 54.376<br />
<br />
Map: [&lt;1 2 3 3 4|, &lt;0 -9 -15 -4 -12|]<br />
EDOs: 22<br />
Badness: 0.0513<br />
<br />
<!-- ws:start:WikiTextHeadingRule:56:&lt;h2&gt; --><h2 id="toc28"><a name="Ceratitid-13-limit"></a><!-- ws:end:WikiTextHeadingRule:56 -->13-limit</h2>
 Commas: 55/54, 65/63, 100/99, 352/343<br />
<br />
POTE generator: ~36/35 = 54.665<br />
<br />
Map: [&lt;1 2 3 3 4 4|, &lt;0 -9 -15 -4 -12 -7|]<br />
EDOs: 22<br />
Badness: 0.0447</body></html>

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