Porcupine family: Difference between revisions

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<~~h2>IMPORTED REVISION FROM WIKISPACES</h2>~~

<span style="display: block; text-align: right;">[[:de:Porcupine Deutsch]]</span>

~~This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>~~

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~~: This revision was by author [[User:hearneg|hearneg]] and made on <tt>2017-05-27 13:23:04 UTC</tt>.<br>~~

__FORCETOC__

~~: The original revision id was <tt>613707509</tt>.<br>~~

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~~: The revision comment was: <tt></tt><br>~~

The 5-limit parent comma for the porcupine family is 250/243, the maximal [[diesis|diesis]] or porcupine comma. Its [[monzo|monzo]] is |1 -5 3>, and flipping that yields <<3 5 1|| for the [[wedgie|wedgie]]. This tells us the [[generator|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.

~~The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>~~

~~<h4>Original Wikitext content:</h4>~~

<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html"><span style="display: block; text-align: right;"~~>~~[[~~xenharmonie/~~Porcupine|Deutsch]]

~~<~~/span~~>~~

~~[[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.

valid range: [150.000, 171.429] (8 to 7)

nice range: [157.821, 166.015]

strict range: [157.821, 166.015]

[[~~POTE tuning~~|POTE generator]]: 163.950

[[POTE_tuning|POTE generator]]: 163.950

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

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.

[[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|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

valid range: [160.000, 163.636] (15 to 22)

nice range: [157.821, 166.015]

strict range: [160.000, 163.636]

[[~~POTE tuning~~|POTE generator]]: ~10/9 = 162.880

[[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

valid range: [160.000, 163.636] (15 to 22)

nice range: [150.637, 182.404]

strict range: [160.000, 163.636]

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

valid range: [160.000, 163.636] (15 to 22f)

nice range: [138.573, 182.404]

strict range: [160.000, 163.636]

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]]

See also: [[The_Biosphere|The Biosphere]]

Commas: 55/54, 64/63, 91/90, 100/99

valid range: [160.000, 162.162] (15 to 37)

nice range: [150.637, 182.404]

strict range: [160.000, 162.162]

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~~>~~

<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.

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|15edo]]. They can try the even sharper fifth of hystrix in [[68edo|68edo]] and see how that suits.

Commas: 36/35, 160/147

[[~~POTE tuning~~|POTE generator]]: 158.868

[[POTE_tuning|POTE generator]]: 158.868

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

Line 117:

Line 142:

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

==13-limit==

Commas: 55/54, 65/64, 91/90, 100/99

Line 146:

Line 179:

Map: [<1 2 3 5 4 3|, <0 -3 -5 -16 -4 5|]

EDOs: 22, 29, 51f, 80cdef

Badness: 0.0265

=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 <[[tel/146 232 338~~|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.

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 <[http://tel.wikispaces.com/146_232_338 146 232 338] 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

[[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

Line 198:

Line 246:

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

Line 207:

Line 257:

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

Line 216:

Line 268:

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

Line 225:

Line 279:

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.

[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

Line 237:

Line 293:

Map: [<1 2 3 3|, <0 -6 -10 -3|]

Wedgie: <<6 10 3 2 -12 -21||

EDOs: 15, [[29edo|29]], 43cd, 44d, 59d, 73cd, [[102edo|102cd]]

==11-limit==

Commas: 49/48, 55/54, 245/242

Line 246:

Line 304:

Map: [<1 2 3 3 4|, <0 -6 -10 -3 -8|]

EDOs: 14c, 15, 29, 43cde, 44d, 59d, 73cde, 102cde

==13-limit==

Commas: 49/48, 55/54, 91/90, 100/99

Line 254:

Line 313:

Map: [<1 2 3 3 4 5|, <0 -6 -10 -3 -8 -19|]

EDOs: 15f, 29, 43cde, 44d, 59df, 73cde, 102cde

Badness: 0.0223

==Belauensis==

Commas: 40/39, 49/48, 55/54, 66/65

Line 263:

Line 324:

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]]

[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

Line 273:

Line 337:

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

Line 283:

Line 350:

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

Line 292:

Line 361:

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

Line 301:

Line 372:

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

Line 311:

Line 385:

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

Line 320:

Line 396:

Map: [<1 2 3 3 4 4|, <0 -9 -15 -4 -12 -7|]

EDOs: 22

Badness: 0.0447~~</pre></div>~~

~~<h4>Original HTML content:</h4>~~

Badness: 0.0447

<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Porcupine family</title></head><body><span style="display: block; text-align: right;"><a class="wiki_link" href="http://xenharmonie.wikispaces.com/Porcupine">Deutsch</a><br />

[[Category:family]]

~~</span><br />~~

[[Category:porcupine]]

| <a href="#Porcupine">Porcupine</a> | <a href="#Hystrix">Hystrix</a> | <a href="#Porky">Porky</a> | <a href="#Coendou">Coendou</a> | <a href="#Hedgehog">Hedgehog</a> | <a href="#Nautilus">Nautilus</a> | <a href="#Ammonite">Ammonite</a> | <a href="#Ceratitid">Ceratitid</a>

[[Category:theory]]

~~<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 />~~

~~valid range:~~ [~~150.000, 171.429] (8 to 7)<br />~~

~~nice range:~~ [~~157.821, 166.015]<br />~~

~~strict range~~: ~~[157.821, 166.015]<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 />~~

<h2 id="toc0"><a name="x-Seven limit children"></a>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 />~~

~~<h1 id="toc1"><a name="Porcupine"></a>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 />~~

~~valid range: [160.000, 163.636~~] ~~(15 to 22)<br />~~

~~nice range: [157.821, 166.015~~]~~<br />~~

~~strict range:~~ [~~160.000, 163.636]<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 />~~

~~<h2 id="toc2"><a name="Porcupine-11-limit"></a>11-limit</h2>~~

~~Commas: 55/54, 64/63, 100/99<br />~~

~~<br />~~

~~valid range: [160.000, 163.636~~] ~~(15 to 22)<br />~~

~~nice range: [150.637, 182.404]<br />~~

~~strict range: [160.000, 163.636]<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 />~~

~~<h2 id="toc3"><a name="Porcupine-13-limit"></a>13-limit</h2>~~

~~Commas: 40/39, 55/54, 64/63, 66/65<br />~~

~~<br />~~

~~valid range:~~ [~~160.000, 163.636] (15 to 22f)<br />~~

~~nice range:~~ [~~138.573, 182.404]<br />~~

~~strict range~~: ~~[160.000, 163.636~~]~~<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 />~~

<h2 id="toc4"><a name="Porcupine-Porcupinefish"></a>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 />~~

~~valid range: [160.000, 162.162] (15 to 37)<br />~~

~~nice range: [150.637, 182.404]<br />~~

~~strict range: [160.000, 162.162]<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 />~~

~~<h2 id="toc5"><a name="Porcupine-Pourcup"></a>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 />~~

~~<h2 id="toc6"><a name="Porcupine-Porkpie"></a>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 />~~

~~<h1 id="toc7"><a name="Hystrix"></a>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 />~~

~~<h1 id="toc8"><a name="Porky"></a>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 />~~

~~<h2 id="toc9"><a name="Porky-11-limit"></a>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 />~~

~~<h2 id="toc10"><a name="Porky-13-limit"></a>13-limit</h2>~~

~~Commas: 55/54, 65/64, 91/90, 100/99<br />~~

~~<br />~~

~~POTE generator: ~10/9 = 164.953<br />~~

~~<br />~~

~~Map: [&lt;1 2 3 5 4 3|, &lt;0 -3 -5 -16 -4 5|]<br />~~

~~EDOs: 22, 29, 51f, 80cdef<br />~~

~~Badness: 0.0265<br />~~

~~<br />~~

~~<h1 id="toc11"><a name="Coendou"></a>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 />~~

~~<h2 id="toc12"><a name="Coendou-11-limit"></a>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 />~~

~~<h2 id="toc13"><a name="Coendou-13-limit"></a>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 />~~

~~<h1 id="toc14"><a name="Hedgehog"></a>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;<a class="wiki_link" href="http://tel.wikispaces.com/146%20232%20338">146 232 338</a> 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 />~~

~~<h2 id="toc15"><a name="Hedgehog-11-limit"></a>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 />~~

~~<h2 id="toc16"><a name="Hedgehog-13-limit"></a>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 />~~

~~<h2 id="toc17"><a name="Hedgehog-Urchin"></a>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 />~~

~~<h2 id="toc18"><a name="Hedgehog-Hedgepig"></a>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 />~~

~~<h3 id="toc19"><a name="Hedgehog-Hedgepig-Music"></a>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 />~~

~~<h1 id="toc20"><a name="Nautilus"></a>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: 15, <a class="wiki_link" href="/29edo">29</a>, 43cd, 44d, 59d, 73cd, <a class="wiki_link" href="/102edo">102cd</a><br />~~

~~<br />~~

~~<h2 id="toc21"><a name="Nautilus-11-limit"></a>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: 14c, 15, 29, 43cde, 44d, 59d, 73cde, 102cde<br />~~

~~<br />~~

~~<h2 id="toc22"><a name="Nautilus-13-limit"></a>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: 15f, 29, 43cde, 44d, 59df, 73cde, 102cde<br />~~

~~Badness: 0.0223<br />~~

~~<br />~~

~~<h2 id="toc23"><a name="Nautilus-Belauensis"></a>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 />

~~<h1 id="toc24"><a name="Ammonite"></a>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 />~~

~~<h2 id="toc25"><a name="Ammonite-11-limit"></a>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 />~~

~~<h2 id="toc26"><a name="Ammonite-13-limit"></a>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 />~~

~~<h1 id="toc27"><a name="Ceratitid"></a>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 />~~

~~<h2 id="toc28"><a name="Ceratitid-11-limit"></a>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 />~~

~~<h2 id="toc29"><a name="Ceratitid-13-limit"></a>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></pre></div>~~

@@ Line 1: / Line 1: @@
-<h2>IMPORTED REVISION FROM WIKISPACES</h2>
+<span style="display: block; text-align: right;">[[:de:Porcupine Deutsch]]</span>
-This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
+|
-: This revision was by author [[User:hearneg|hearneg]] and made on <tt>2017-05-27 13:23:04 UTC</tt>.<br>
+__FORCETOC__
-: The original revision id was <tt>613707509</tt>.<br>
+-----
-: The revision comment was: <tt></tt><br>
+The 5-limit parent comma for the porcupine family is 250/243, the maximal [[diesis|diesis]] or porcupine comma. Its [[monzo|monzo]] is |1 -5 3&gt;, and flipping that yields &lt;&lt;3 5 1|| for the [[wedgie|wedgie]]. This tells us the [[generator|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.
-The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
-<h4>Original Wikitext content:</h4>
-<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">&lt;span style="display: block; text-align: right;"&gt;[[xenharmonie/Porcupine|Deutsch]]
-&lt;/span&gt;
-[[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&gt;, and flipping that yields &lt;&lt;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.
 valid range: [150.000, 171.429] (8 to 7)
 nice range: [157.821, 166.015]
 strict range: [157.821, 166.015]
-[[POTE tuning|POTE generator]]: 163.950
+[[POTE_tuning|POTE generator]]: 163.950
 Map: [&lt;1 2 3|, &lt;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]].
+The second comma of the [[Normal_lists|normal comma list]] defines which [[7-limit|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|septimal quarter tone]], for [[Porcupine_family#Hystrix|hystrix]], [[50/49|50/49]], the [[jubilisma|jubilisma]], for [[Porcupine_family#Hedgehog|hedgehog]], and [[49/48|49/48]], the [[slendro_diesis|slendro diesis]], for [[Porcupine_family#Nautilus|nautilus]].
 =Porcupine=
-[[Porcupine]], with wedgie &lt;&lt;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.
+[[Porcupine|Porcupine]], with wedgie &lt;&lt;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|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
 valid range: [160.000, 163.636] (15 to 22)
 nice range: [157.821, 166.015]
 strict range: [160.000, 163.636]
-[[POTE tuning|POTE generator]]: ~10/9 = 162.880
+[[POTE_tuning|POTE generator]]: ~10/9 = 162.880
 - and 9-limit minimax eigenmonzo: 9/7
 Map: [&lt;1 2 3 2|, &lt;0 -3 -5 6|]
 EDOs: 22, [[59edo|59]], [[81edo|81bd]], [[140edo|140bd]]
 Badness: 0.0411
 ==11-limit==
 Commas: 55/54, 64/63, 100/99
 valid range: [160.000, 163.636] (15 to 22)
 nice range: [150.637, 182.404]
 strict range: [160.000, 163.636]
 POTE generator: ~10/9 = 162.747
 -limit minimax eigenmonzo: 9/7
 Map: [&lt;1 2 3 2 4|, &lt;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
 valid range: [160.000, 163.636] (15 to 22f)
 nice range: [138.573, 182.404]
 strict range: [160.000, 163.636]
 POTE generator: ~10/9 = 162.708
 - and 15-limit minimax eigenmonzo: 11/8
 Map: [&lt;1 2 3 2 4 4|, &lt;0 -3 -5 6 -4 -2|]
 EDOs: 7, 15, 22f, 37f
 Badness: 0.0213
 ==Porcupinefish==
-See also: [[The Biosphere]]
+See also: [[The_Biosphere|The Biosphere]]
 Commas: 55/54, 64/63, 91/90, 100/99
 valid range: [160.000, 162.162] (15 to 37)
 nice range: [150.637, 182.404]
 strict range: [160.000, 162.162]
 POTE generator: ~10/9 = 162.277
 - and 15-limit minimax eigenmonzo: 13/11
 Map: [&lt;1 2 3 2 4 6|, &lt;0 -3 -5 6 -4 -17|]
 EDOs: 15, 22, 37, 59, 96b
-&lt;span style="background-color: #ffffff;"&gt;Badness: 0.0253&lt;/span&gt;
+<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
 - and 15-limit minimax eigenmonzo: 13/7
 Map: [&lt;1 2 3 2 4 1|, &lt;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
 - and 15-limit minimax eigenmonzo: 9/7
 Map: [&lt;1 2 3 2 4 3|, &lt;0 -3 -5 6 -4 5|]
 EDOs: 7, 15f, 22
 Badness: 0.0260
 =Hystrix=
-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 [[15edo]]. They can try the even sharper fifth of hystrix in [[68edo]] and see how that suits.
+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 [[15edo|15edo]]. They can try the even sharper fifth of hystrix in [[68edo|68edo]] and see how that suits.
 Commas: 36/35, 160/147
-[[POTE tuning|POTE generator]]: 158.868
+[[POTE_tuning|POTE generator]]: 158.868
 - and 9-limit minimax eigenmonzo: 5/4
@@ Line 117: / Line 142: @@
 EDOs: 10d, 12, 13d, 15
 Badness: 0.0449
 =Porky=
 Commas: 225/224, 250/243
 POTE generator: ~10/9 = 164.412
 - and 9-limit minimax eigenmonzo: 7/5
 Map: [&lt;1 2 3 5|, &lt;0 -3 -5 -16|]
 Wedgie: &lt;&lt;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
 -limit minimax eigenmonzo: 7/5
 Map: [&lt;1 2 3 5 4|, &lt;0 -3 -5 -16 -4|]
 EDOs: 7, 8, 15, 22, 29, 51, 73
 Badness: 0.0273
 ==13-limit==
 Commas: 55/54, 65/64, 91/90, 100/99
@@ Line 146: / Line 179: @@
 Map: [&lt;1 2 3 5 4 3|, &lt;0 -3 -5 -16 -4 5|]
 EDOs: 22, 29, 51f, 80cdef
 Badness: 0.0265
 =Coendou=
 Commas: 250/243, 525/512
 POTE generator: ~10/9 = 166.041
 - and 9-limit minimax eigenmonzo: 3/2
 Map: [&lt;1 2 3 1|, &lt;0 -3 -5 13|]
 Wedgie: &lt;&lt;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
 -limit minimax eigenmonzo: 3/2
 Map: [&lt;1 2 3 1 4|, &lt;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
 - and 15-limit minimax eigenmonzo: 3/2
 Map: [&lt;1 2 3 1 4 3|, &lt;0 -3 -5 13 -4 5|]
 EDOs: 7, 29, 65cef, 94cdef
 Badness: 0.0302
 =Hedgehog=
-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;[[tel/146 232 338|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.
+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;[http://tel.wikispaces.com/146_232_338 146 232 338] 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
+[[POTE_tuning|POTE generator]]: ~9/7 = 435.648
 Map: [&lt;2 1 1 2|, &lt;0 3 5 5|]
 Wedgie: &lt;&lt;6 10 10 2 -1 -5||
 EDOs: 22, [[146edo|146]]
 Badness: 0.0440
 ==11-limit==
 Commas: 50/49, 55/54, 99/98
@@ Line 198: / Line 246: @@
 Map: [&lt;2 1 1 2 4|, &lt;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
@@ Line 207: / Line 257: @@
 Map: [&lt;2 1 1 2 4 3|, &lt;0 3 5 5 4 6|]
 EDOs: 14cf, 22
 Badness: 0.0215
 ==Urchin==
 Commas: 40/39, 50/49, 55/54, 66/65
@@ Line 216: / Line 268: @@
 Map: [&lt;2 1 1 2 4 6|, &lt;0 3 5 5 4 2|]
 EDOs: 14c, 22f
 Badness: 0.0252
 ==Hedgepig==
 Commas: 50/49, 245/243, 385/384
@@ Line 225: / Line 279: @@
 Map: [&lt;2 1 1 2 12|, &lt;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.
+[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
@@ Line 237: / Line 293: @@
 Map: [&lt;1 2 3 3|, &lt;0 -6 -10 -3|]
 Wedgie: &lt;&lt;6 10 3 2 -12 -21||
 EDOs: 15, [[29edo|29]], 43cd, 44d, 59d, 73cd, [[102edo|102cd]]
 ==11-limit==
 Commas: 49/48, 55/54, 245/242
@@ Line 246: / Line 304: @@
 Map: [&lt;1 2 3 3 4|, &lt;0 -6 -10 -3 -8|]
 EDOs: 14c, 15, 29, 43cde, 44d, 59d, 73cde, 102cde
 ==13-limit==
 Commas: 49/48, 55/54, 91/90, 100/99
@@ Line 254: / Line 313: @@
 Map: [&lt;1 2 3 3 4 5|, &lt;0 -6 -10 -3 -8 -19|]
 EDOs: 15f, 29, 43cde, 44d, 59df, 73cde, 102cde
 Badness: 0.0223
 ==Belauensis==
 Commas: 40/39, 49/48, 55/54, 66/65
@@ Line 263: / Line 324: @@
 Map: [&lt;1 2 3 3 4 4|, &lt;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]]
+[http://micro.soonlabel.com/gene_ward_smith/Others/Igs/NautilusReverie.mp3 Nautilus Reverie] by [[IgliashonJones|Igliashon Calvin Jones-Coolidge]]
-=Ammonite=
+=Ammonite=
 Commas: 250/243, 686/675
@@ Line 273: / Line 337: @@
 Map: [&lt;1 5 8 10|, &lt;0 -9 -15 -19|]
 Wedgie: &lt;&lt;9 15 19 3 5 2||
 EDOs: 29, 37, 66
 Badness: 0.1077
 ==11-limit==
 Commas: 55/54, 100/99, 686/675
@@ Line 283: / Line 350: @@
 Map: [&lt;1 5 8 10 8|, &lt;0 -9 -15 -19 -12|]
 EDOs: 29, 37, 66
 Badness: 0.0457
 ==13-limit==
 Commas: 55/54, 91/90, 100/99, 169/168
@@ Line 292: / Line 361: @@
 Map: [&lt;1 5 8 10 8 9|, &lt;0 -9 -15 -19 -12 -14|]
 EDOs: 29, 37, 66
 Badness: 0.0272
 =Ceratitid=
 Commas: 250/243, 1728/1715
@@ Line 301: / Line 372: @@
 Map: [&lt;1 2 3 3|, &lt;0 -9 -15 -4|]
 Wedgie: &lt;&lt;9 15 4 3 -19 -33||
 EDOs: 22
 Badness: 0.115
 ==11-limit==
 Commas: 55/54, 100/99, 5324/5145
@@ Line 311: / Line 385: @@
 Map: [&lt;1 2 3 3 4|, &lt;0 -9 -15 -4 -12|]
 EDOs: 22
 Badness: 0.0513
 ==13-limit==
 Commas: 55/54, 65/63, 100/99, 352/343
@@ Line 320: / Line 396: @@
 Map: [&lt;1 2 3 3 4 4|, &lt;0 -9 -15 -4 -12 -7|]
 EDOs: 22
-Badness: 0.0447</pre></div>
-<h4>Original HTML content:</h4>
+Badness: 0.0447
-<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;Porcupine family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;span style="display: block; text-align: right;"&gt;&lt;a class="wiki_link" href="http://xenharmonie.wikispaces.com/Porcupine"&gt;Deutsch&lt;/a&gt;&lt;br /&gt;
+[[Category:family]]
-&lt;/span&gt;&lt;br /&gt;
+[[Category:porcupine]]
-&lt;!-- ws:start:WikiTextTocRule:60:&amp;lt;img id=&amp;quot;wikitext@@toc@@flat&amp;quot; class=&amp;quot;WikiMedia WikiMediaTocFlat&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/flat?w=100&amp;amp;h=16&amp;quot;/&amp;gt; --&gt;&lt;!-- ws:end:WikiTextTocRule:60 --&gt;&lt;!-- ws:start:WikiTextTocRule:61: --&gt;&lt;!-- ws:end:WikiTextTocRule:61 --&gt;&lt;!-- ws:start:WikiTextTocRule:62: --&gt; | &lt;a href="#Porcupine"&gt;Porcupine&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:62 --&gt;&lt;!-- ws:start:WikiTextTocRule:63: --&gt;&lt;!-- ws:end:WikiTextTocRule:63 --&gt;&lt;!-- ws:start:WikiTextTocRule:64: --&gt;&lt;!-- ws:end:WikiTextTocRule:64 --&gt;&lt;!-- ws:start:WikiTextTocRule:65: --&gt;&lt;!-- ws:end:WikiTextTocRule:65 --&gt;&lt;!-- ws:start:WikiTextTocRule:66: --&gt;&lt;!-- ws:end:WikiTextTocRule:66 --&gt;&lt;!-- ws:start:WikiTextTocRule:67: --&gt;&lt;!-- ws:end:WikiTextTocRule:67 --&gt;&lt;!-- ws:start:WikiTextTocRule:68: --&gt; | &lt;a href="#Hystrix"&gt;Hystrix&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:68 --&gt;&lt;!-- ws:start:WikiTextTocRule:69: --&gt; | &lt;a href="#Porky"&gt;Porky&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:69 --&gt;&lt;!-- ws:start:WikiTextTocRule:70: --&gt;&lt;!-- ws:end:WikiTextTocRule:70 --&gt;&lt;!-- ws:start:WikiTextTocRule:71: --&gt;&lt;!-- ws:end:WikiTextTocRule:71 --&gt;&lt;!-- ws:start:WikiTextTocRule:72: --&gt; | &lt;a href="#Coendou"&gt;Coendou&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:72 --&gt;&lt;!-- ws:start:WikiTextTocRule:73: --&gt;&lt;!-- ws:end:WikiTextTocRule:73 --&gt;&lt;!-- ws:start:WikiTextTocRule:74: --&gt;&lt;!-- ws:end:WikiTextTocRule:74 --&gt;&lt;!-- ws:start:WikiTextTocRule:75: --&gt; | &lt;a href="#Hedgehog"&gt;Hedgehog&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:75 --&gt;&lt;!-- ws:start:WikiTextTocRule:76: --&gt;&lt;!-- ws:end:WikiTextTocRule:76 --&gt;&lt;!-- ws:start:WikiTextTocRule:77: --&gt;&lt;!-- ws:end:WikiTextTocRule:77 --&gt;&lt;!-- ws:start:WikiTextTocRule:78: --&gt;&lt;!-- ws:end:WikiTextTocRule:78 --&gt;&lt;!-- ws:start:WikiTextTocRule:79: --&gt;&lt;!-- ws:end:WikiTextTocRule:79 --&gt;&lt;!-- ws:start:WikiTextTocRule:80: --&gt;&lt;!-- ws:end:WikiTextTocRule:80 --&gt;&lt;!-- ws:start:WikiTextTocRule:81: --&gt; | &lt;a href="#Nautilus"&gt;Nautilus&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:81 --&gt;&lt;!-- ws:start:WikiTextTocRule:82: --&gt;&lt;!-- ws:end:WikiTextTocRule:82 --&gt;&lt;!-- ws:start:WikiTextTocRule:83: --&gt;&lt;!-- ws:end:WikiTextTocRule:83 --&gt;&lt;!-- ws:start:WikiTextTocRule:84: --&gt;&lt;!-- ws:end:WikiTextTocRule:84 --&gt;&lt;!-- ws:start:WikiTextTocRule:85: --&gt; | &lt;a href="#Ammonite"&gt;Ammonite&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:85 --&gt;&lt;!-- ws:start:WikiTextTocRule:86: --&gt;&lt;!-- ws:end:WikiTextTocRule:86 --&gt;&lt;!-- ws:start:WikiTextTocRule:87: --&gt;&lt;!-- ws:end:WikiTextTocRule:87 --&gt;&lt;!-- ws:start:WikiTextTocRule:88: --&gt; | &lt;a href="#Ceratitid"&gt;Ceratitid&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:88 --&gt;&lt;!-- ws:start:WikiTextTocRule:89: --&gt;&lt;!-- ws:end:WikiTextTocRule:89 --&gt;&lt;!-- ws:start:WikiTextTocRule:90: --&gt;&lt;!-- ws:end:WikiTextTocRule:90 --&gt;&lt;!-- ws:start:WikiTextTocRule:91: --&gt;
+[[Category:theory]]
-&lt;!-- ws:end:WikiTextTocRule:91 --&gt;&lt;hr /&gt;
-The 5-limit parent comma for the porcupine family is 250/243, the maximal &lt;a class="wiki_link" href="/diesis"&gt;diesis&lt;/a&gt; or porcupine comma. Its &lt;a class="wiki_link" href="/monzo"&gt;monzo&lt;/a&gt; is |1 -5 3&amp;gt;, and flipping that yields &amp;lt;&amp;lt;3 5 1|| for the &lt;a class="wiki_link" href="/wedgie"&gt;wedgie&lt;/a&gt;. This tells us the &lt;a class="wiki_link" href="/generator"&gt;generator&lt;/a&gt; is a minor whole tone, the &lt;a class="wiki_link" href="/10_9"&gt;10/9&lt;/a&gt; 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.&lt;br /&gt;
-&lt;br /&gt;
-valid range: [150.000, 171.429] (8 to 7)&lt;br /&gt;
-nice range: [157.821, 166.015]&lt;br /&gt;
-strict range: [157.821, 166.015]&lt;br /&gt;
-&lt;br /&gt;
-&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 163.950&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 2 3|, &amp;lt;0 -3 -5|]&lt;br /&gt;
-&lt;br /&gt;
-EDOs: &lt;a class="wiki_link" href="/15edo"&gt;15&lt;/a&gt;, &lt;a class="wiki_link" href="/22edo"&gt;22&lt;/a&gt;, &lt;a class="wiki_link" href="/95edo"&gt;95c&lt;/a&gt;, &lt;a class="wiki_link" href="/117edo"&gt;117bc&lt;/a&gt;, &lt;a class="wiki_link" href="/139edo"&gt;139bc&lt;/a&gt;, &lt;a class="wiki_link" href="/161edo"&gt;161bc&lt;/a&gt;, &lt;a class="wiki_link" href="/183edo"&gt;183bc&lt;/a&gt;&lt;br /&gt;
-Badness: 0.0308&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-Seven limit children"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Seven limit children&lt;/h2&gt;
- The second comma of the &lt;a class="wiki_link" href="/Normal%20lists"&gt;normal comma list&lt;/a&gt; defines which &lt;a class="wiki_link" href="/7-limit"&gt;7-limit&lt;/a&gt; family member we are looking at. That means &lt;a class="wiki_link" href="/64_63"&gt;64/63&lt;/a&gt;, the &lt;a class="wiki_link" href="/64_63"&gt;Archytas comma&lt;/a&gt;, for &lt;a class="wiki_link" href="/Porcupine%20family#Porcupine"&gt;porcupine&lt;/a&gt;, &lt;a class="wiki_link" href="/36_35"&gt;36/35&lt;/a&gt;, the &lt;a class="wiki_link" href="/septimal%20quarter%20tone"&gt;septimal quarter tone&lt;/a&gt;, for &lt;a class="wiki_link" href="/Porcupine%20family#Hystrix"&gt;hystrix&lt;/a&gt;, &lt;a class="wiki_link" href="/50_49"&gt;50/49&lt;/a&gt;, the &lt;a class="wiki_link" href="/jubilisma"&gt;jubilisma&lt;/a&gt;, for &lt;a class="wiki_link" href="/Porcupine%20family#Hedgehog"&gt;hedgehog&lt;/a&gt;, and &lt;a class="wiki_link" href="/49_48"&gt;49/48&lt;/a&gt;, the &lt;a class="wiki_link" href="/slendro%20diesis"&gt;slendro diesis&lt;/a&gt;, for &lt;a class="wiki_link" href="/Porcupine%20family#Nautilus"&gt;nautilus&lt;/a&gt;.&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Porcupine"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Porcupine&lt;/h1&gt;
- &lt;a class="wiki_link" href="/Porcupine"&gt;Porcupine&lt;/a&gt;, with wedgie &amp;lt;&amp;lt;3 5 -6 1 -18 -28||, uses six of its minor tone generator steps to get to &lt;a class="wiki_link" href="/7_4"&gt;7/4&lt;/a&gt;. For this to work you need a small minor tone such as &lt;a class="wiki_link" href="/22edo"&gt;22edo&lt;/a&gt; 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.&lt;br /&gt;
-&lt;br /&gt;
-Commas: 250/243, 64/63&lt;br /&gt;
-&lt;br /&gt;
-valid range: [160.000, 163.636] (15 to 22)&lt;br /&gt;
-nice range: [157.821, 166.015]&lt;br /&gt;
-strict range: [160.000, 163.636]&lt;br /&gt;
-&lt;br /&gt;
-&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~10/9 = 162.880&lt;br /&gt;
-- and 9-limit minimax eigenmonzo: 9/7&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 2 3 2|, &amp;lt;0 -3 -5 6|]&lt;br /&gt;
-EDOs: 22, &lt;a class="wiki_link" href="/59edo"&gt;59&lt;/a&gt;, &lt;a class="wiki_link" href="/81edo"&gt;81bd&lt;/a&gt;, &lt;a class="wiki_link" href="/140edo"&gt;140bd&lt;/a&gt;&lt;br /&gt;
-Badness: 0.0411&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="Porcupine-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;11-limit&lt;/h2&gt;
- Commas: 55/54, 64/63, 100/99&lt;br /&gt;
-&lt;br /&gt;
-valid range: [160.000, 163.636] (15 to 22)&lt;br /&gt;
-nice range: [150.637, 182.404]&lt;br /&gt;
-strict range: [160.000, 163.636]&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~10/9 = 162.747&lt;br /&gt;
--limit minimax eigenmonzo: 9/7&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 2 3 2 4|, &amp;lt;0 -3 -5 6 -4|]&lt;br /&gt;
-EDOs: &lt;a class="wiki_link" href="/7edo"&gt;7&lt;/a&gt;, 15, 22, &lt;a class="wiki_link" href="/37edo"&gt;37&lt;/a&gt;, &lt;a class="wiki_link" href="/59edo"&gt;59&lt;/a&gt;&lt;br /&gt;
-Badness: 0.0217&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="Porcupine-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;13-limit&lt;/h2&gt;
- Commas: 40/39, 55/54, 64/63, 66/65&lt;br /&gt;
-&lt;br /&gt;
-valid range: [160.000, 163.636] (15 to 22f)&lt;br /&gt;
-nice range: [138.573, 182.404]&lt;br /&gt;
-strict range: [160.000, 163.636]&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~10/9 = 162.708&lt;br /&gt;
-- and 15-limit minimax eigenmonzo: 11/8&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 2 3 2 4 4|, &amp;lt;0 -3 -5 6 -4 -2|]&lt;br /&gt;
-EDOs: 7, 15, 22f, 37f&lt;br /&gt;
-Badness: 0.0213&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="Porcupine-Porcupinefish"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Porcupinefish&lt;/h2&gt;
- See also: &lt;a class="wiki_link" href="/The%20Biosphere"&gt;The Biosphere&lt;/a&gt;&lt;br /&gt;
-Commas: 55/54, 64/63, 91/90, 100/99&lt;br /&gt;
-&lt;br /&gt;
-valid range: [160.000, 162.162] (15 to 37)&lt;br /&gt;
-nice range: [150.637, 182.404]&lt;br /&gt;
-strict range: [160.000, 162.162]&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~10/9 = 162.277&lt;br /&gt;
-- and 15-limit minimax eigenmonzo: 13/11&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 2 3 2 4 6|, &amp;lt;0 -3 -5 6 -4 -17|]&lt;br /&gt;
-EDOs: 15, 22, 37, 59, 96b&lt;br /&gt;
-&lt;span style="background-color: #ffffff;"&gt;Badness: 0.0253&lt;/span&gt;&lt;br /&gt;
-Badness: 0.0253&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc5"&gt;&lt;a name="Porcupine-Pourcup"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Pourcup&lt;/h2&gt;
- Commas: 55/54, 64/63, 100/99, 196/195&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~10/9 = 162.482&lt;br /&gt;
-- and 15-limit minimax eigenmonzo: 13/7&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 2 3 2 4 1|, &amp;lt;0 -3 -5 6 -4 20|]&lt;br /&gt;
-EDOs: 15f, 22f, 37&lt;br /&gt;
-Badness: 0.0351&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc6"&gt;&lt;a name="Porcupine-Porkpie"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;Porkpie&lt;/h2&gt;
- Commas: 55/54, 64/63, 65/63, 100/99&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~10/9 = 163.688&lt;br /&gt;
-- and 15-limit minimax eigenmonzo: 9/7&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 2 3 2 4 3|, &amp;lt;0 -3 -5 6 -4 5|]&lt;br /&gt;
-EDOs: 7, 15f, 22&lt;br /&gt;
-Badness: 0.0260&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc7"&gt;&lt;a name="Hystrix"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;Hystrix&lt;/h1&gt;
- Hystrix, with wedgie &amp;lt;&amp;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 &lt;a class="wiki_link" href="/15edo"&gt;15edo&lt;/a&gt;. They can try the even sharper fifth of hystrix in &lt;a class="wiki_link" href="/68edo"&gt;68edo&lt;/a&gt; and see how that suits.&lt;br /&gt;
-&lt;br /&gt;
-Commas: 36/35, 160/147&lt;br /&gt;
-&lt;br /&gt;
-&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 158.868&lt;br /&gt;
-- and 9-limit minimax eigenmonzo: 5/4&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 2 3 3|, &amp;lt;0 -3 -5 -1|]&lt;br /&gt;
-&lt;br /&gt;
-EDOs: 10d, 12, 13d, 15&lt;br /&gt;
-Badness: 0.0449&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc8"&gt;&lt;a name="Porky"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;Porky&lt;/h1&gt;
- Commas: 225/224, 250/243&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~10/9 = 164.412&lt;br /&gt;
-- and 9-limit minimax eigenmonzo: 7/5&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 2 3 5|, &amp;lt;0 -3 -5 -16|]&lt;br /&gt;
-Wedgie: &amp;lt;&amp;lt;3 5 16 1 17 23||&lt;br /&gt;
-EDOS: 7, 8, 15, 22, 29, 51, 73&lt;br /&gt;
-Badness: 0.0544&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc9"&gt;&lt;a name="Porky-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;11-limit&lt;/h2&gt;
- Commas: 55/54, 100/99, 225/224&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~10/9 = 164.552&lt;br /&gt;
--limit minimax eigenmonzo: 7/5&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 2 3 5 4|, &amp;lt;0 -3 -5 -16 -4|]&lt;br /&gt;
-EDOs: 7, 8, 15, 22, 29, 51, 73&lt;br /&gt;
-Badness: 0.0273&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc10"&gt;&lt;a name="Porky-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;13-limit&lt;/h2&gt;
- Commas: 55/54, 65/64, 91/90, 100/99&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~10/9 = 164.953&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 2 3 5 4 3|, &amp;lt;0 -3 -5 -16 -4 5|]&lt;br /&gt;
-EDOs: 22, 29, 51f, 80cdef&lt;br /&gt;
-Badness: 0.0265&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:22:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc11"&gt;&lt;a name="Coendou"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:22 --&gt;Coendou&lt;/h1&gt;
- Commas: 250/243, 525/512&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~10/9 = 166.041&lt;br /&gt;
-- and 9-limit minimax eigenmonzo: 3/2&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 2 3 1|, &amp;lt;0 -3 -5 13|]&lt;br /&gt;
-Wedgie: &amp;lt;&amp;lt;3 5 -13 1 -29 -44||&lt;br /&gt;
-EDOs: 7, 29, 65c, 94cd&lt;br /&gt;
-Badness: 0.1183&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:24:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc12"&gt;&lt;a name="Coendou-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:24 --&gt;11-limit&lt;/h2&gt;
- Commas: 55/54, 100/99, 525/512&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~10/9 = 165.981&lt;br /&gt;
--limit minimax eigenmonzo: 3/2&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 2 3 1 4|, &amp;lt;0 -3 -5 13 -4|]&lt;br /&gt;
-EDOs: 7, 29, 65ce, 94cde&lt;br /&gt;
-Badness: 0.0497&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:26:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc13"&gt;&lt;a name="Coendou-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:26 --&gt;13-limit&lt;/h2&gt;
- Commas: 55/54, 65/64, 100/99, 105/104&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~10/9 = 165.974&lt;br /&gt;
-- and 15-limit minimax eigenmonzo: 3/2&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 2 3 1 4 3|, &amp;lt;0 -3 -5 13 -4 5|]&lt;br /&gt;
-EDOs: 7, 29, 65cef, 94cdef&lt;br /&gt;
-Badness: 0.0302&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:28:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc14"&gt;&lt;a name="Hedgehog"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:28 --&gt;Hedgehog&lt;/h1&gt;
- Hedgehog, with wedgie &amp;lt;&amp;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 &amp;lt;&lt;a class="wiki_link" href="http://tel.wikispaces.com/146%20232%20338"&gt;146 232 338&lt;/a&gt; 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.&lt;br /&gt;
-&lt;br /&gt;
-Commas: 50/49, 245/243&lt;br /&gt;
-&lt;br /&gt;
-&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~9/7 = 435.648&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;2 1 1 2|, &amp;lt;0 3 5 5|]&lt;br /&gt;
-Wedgie: &amp;lt;&amp;lt;6 10 10 2 -1 -5||&lt;br /&gt;
-EDOs: 22, &lt;a class="wiki_link" href="/146edo"&gt;146&lt;/a&gt;&lt;br /&gt;
-Badness: 0.0440&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:30:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc15"&gt;&lt;a name="Hedgehog-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:30 --&gt;11-limit&lt;/h2&gt;
- Commas: 50/49, 55/54, 99/98&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~9/7 = 435.386&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;2 1 1 2 4|, &amp;lt;0 3 5 5 4|]&lt;br /&gt;
-EDOs: 14c, 22, 58ce, 80ce, 102cde&lt;br /&gt;
-Badness: 0.0231&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:32:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc16"&gt;&lt;a name="Hedgehog-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:32 --&gt;13-limit&lt;/h2&gt;
- Commas: 50/49, 55/54, 65/63, 99/98&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~9/7 = 435.861&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;2 1 1 2 4 3|, &amp;lt;0 3 5 5 4 6|]&lt;br /&gt;
-EDOs: 14cf, 22&lt;br /&gt;
-Badness: 0.0215&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:34:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc17"&gt;&lt;a name="Hedgehog-Urchin"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:34 --&gt;Urchin&lt;/h2&gt;
- Commas: 40/39, 50/49, 55/54, 66/65&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~9/7 = 437.078&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;2 1 1 2 4 6|, &amp;lt;0 3 5 5 4 2|]&lt;br /&gt;
-EDOs: 14c, 22f&lt;br /&gt;
-Badness: 0.0252&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:36:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc18"&gt;&lt;a name="Hedgehog-Hedgepig"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:36 --&gt;Hedgepig&lt;/h2&gt;
- Commas: 50/49, 245/243, 385/384&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~9/7 = 435.425&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;2 1 1 2 12|, &amp;lt;0 3 5 5 -7|]&lt;br /&gt;
-EDOs: 22, 80c, 102cd, 124cd&lt;br /&gt;
-Badness: 0.0684&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:38:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc19"&gt;&lt;a name="Hedgehog-Hedgepig-Music"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:38 --&gt;Music&lt;/h3&gt;
- &lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/22-ET/20120207-phobos-light-hedgehog14.mp3" rel="nofollow"&gt;Phobos Light&lt;/a&gt; by Chris Vaisvil in Hedgehog[14] &lt;a class="wiki_link" href="/hedgehog14"&gt;tuned&lt;/a&gt; to 22edo.&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:40:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc20"&gt;&lt;a name="Nautilus"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:40 --&gt;Nautilus&lt;/h1&gt;
- Commas: 49/48, 250/243&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~21/20 = 82.505&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 2 3 3|, &amp;lt;0 -6 -10 -3|]&lt;br /&gt;
-Wedgie: &amp;lt;&amp;lt;6 10 3 2 -12 -21||&lt;br /&gt;
-EDOs: 15, &lt;a class="wiki_link" href="/29edo"&gt;29&lt;/a&gt;, 43cd, 44d, 59d, 73cd, &lt;a class="wiki_link" href="/102edo"&gt;102cd&lt;/a&gt;&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:42:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc21"&gt;&lt;a name="Nautilus-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:42 --&gt;11-limit&lt;/h2&gt;
- Commas: 49/48, 55/54, 245/242&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~21/20 = 82.504&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 2 3 3 4|, &amp;lt;0 -6 -10 -3 -8|]&lt;br /&gt;
-EDOs: 14c, 15, 29, 43cde, 44d, 59d, 73cde, 102cde&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:44:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc22"&gt;&lt;a name="Nautilus-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:44 --&gt;13-limit&lt;/h2&gt;
- Commas: 49/48, 55/54, 91/90, 100/99&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~21/20 = 62.530&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 2 3 3 4 5|, &amp;lt;0 -6 -10 -3 -8 -19|]&lt;br /&gt;
-EDOs: 15f, 29, 43cde, 44d, 59df, 73cde, 102cde&lt;br /&gt;
-Badness: 0.0223&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:46:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc23"&gt;&lt;a name="Nautilus-Belauensis"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:46 --&gt;Belauensis&lt;/h2&gt;
- Commas: 40/39, 49/48, 55/54, 66/65&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~21/20 = ~14/13 = 81.759&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 2 3 3 4 4|, &amp;lt;0 -6 -10 -3 -8 -4|]&lt;br /&gt;
-EDOs: 14c, 15, 29f, 44df&lt;br /&gt;
-Badness: 0.0298&lt;br /&gt;
-&lt;br /&gt;
-&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Igs/NautilusReverie.mp3" rel="nofollow"&gt;Nautilus Reverie&lt;/a&gt; by &lt;a class="wiki_link" href="/IgliashonJones"&gt;Igliashon Calvin Jones-Coolidge&lt;/a&gt;&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:48:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc24"&gt;&lt;a name="Ammonite"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:48 --&gt;Ammonite&lt;/h1&gt;
- Commas: 250/243, 686/675&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~9/7 = 454.448&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 5 8 10|, &amp;lt;0 -9 -15 -19|]&lt;br /&gt;
-Wedgie: &amp;lt;&amp;lt;9 15 19 3 5 2||&lt;br /&gt;
-EDOs: 29, 37, 66&lt;br /&gt;
-Badness: 0.1077&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:50:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc25"&gt;&lt;a name="Ammonite-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:50 --&gt;11-limit&lt;/h2&gt;
- Commas: 55/54, 100/99, 686/675&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~9/7 = 454.512&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 5 8 10 8|, &amp;lt;0 -9 -15 -19 -12|]&lt;br /&gt;
-EDOs: 29, 37, 66&lt;br /&gt;
-Badness: 0.0457&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:52:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc26"&gt;&lt;a name="Ammonite-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:52 --&gt;13-limit&lt;/h2&gt;
- Commas: 55/54, 91/90, 100/99, 169/168&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~13/10 = 454.429&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 5 8 10 8 9|, &amp;lt;0 -9 -15 -19 -12 -14|]&lt;br /&gt;
-EDOs: 29, 37, 66&lt;br /&gt;
-Badness: 0.0272&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:54:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc27"&gt;&lt;a name="Ceratitid"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:54 --&gt;Ceratitid&lt;/h1&gt;
- Commas: 250/243, 1728/1715&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~36/35 = 54.384&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 2 3 3|, &amp;lt;0 -9 -15 -4|]&lt;br /&gt;
-Wedgie: &amp;lt;&amp;lt;9 15 4 3 -19 -33||&lt;br /&gt;
-EDOs: 22&lt;br /&gt;
-Badness: 0.115&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:56:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc28"&gt;&lt;a name="Ceratitid-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:56 --&gt;11-limit&lt;/h2&gt;
- Commas: 55/54, 100/99, 5324/5145&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~36/35 = 54.376&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 2 3 3 4|, &amp;lt;0 -9 -15 -4 -12|]&lt;br /&gt;
-EDOs: 22&lt;br /&gt;
-Badness: 0.0513&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:58:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc29"&gt;&lt;a name="Ceratitid-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:58 --&gt;13-limit&lt;/h2&gt;
- Commas: 55/54, 65/63, 100/99, 352/343&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~36/35 = 54.665&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 2 3 3 4 4|, &amp;lt;0 -9 -15 -4 -12 -7|]&lt;br /&gt;
-EDOs: 22&lt;br /&gt;
-Badness: 0.0447&lt;/body&gt;&lt;/html&gt;</pre></div>