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→Porcupine: base the sharpness on 4/3 rather than 3/2 (see talk). Hystrix isn't actually flat of 8d
 
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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
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| en = Porcupine family
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<h4>Original Wikitext content:</h4>
{{Technical data page}}
<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">[[toc|flat]]
The '''porcupine family''' of [[regular temperament|temperaments]] [[tempering out|tempers out]] the [[porcupine comma]], [[250/243]], also called the maximal diesis.  
----
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.


[[POTE tuning|POTE generator]]: 163.950
== Porcupine ==
{{Main| Porcupine }}


Map: [&lt;1 2 3|, &lt;0 -3 -5|]
The [[generator]] of porcupine is a minor whole tone, the [[10/9]] interval, and three of these add up to a perfect fourth ([[4/3]]), with two more giving the minor sixth ([[8/5]]). In fact, {{nowrap| (10/9)<sup>3</sup> {{=}} (4/3)⋅(250/243) }}, and {{nowrap| (10/9)<sup>5</sup> {{=}} (8/5)⋅(250/243)<sup>2</sup> }}. Its [[ploidacot]] is omega-tricot. [[22edo|3\22]] is a very recommendable generator, and [[mos scale]]s of 7, 8 and 15 notes make for some nice scale possibilities.


EDOs: [[15edo|15]], [[22edo|22]], [[95edo|95c]], [[117edo|117bc]], [[139edo|139bc]], [[161edo|161bc]], [[183edo|183bc]]
[[Subgroup]]: 2.3.5


==Seven limit children==
[[Comma list]]: 250/243
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=
{{Mapping|legend=1| 1 2 3 | 0 -3 -5 }}
[[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.


Commas: 250/243, 64/63
: mapping generators: ~2, ~10/9


[[POTE tuning|POTE generator]]: ~10/9 = 162.880
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000, ~10/9 = 164.166
: [[error map]]: {{val| 0.000 +5.547 -7.143 }}
* [[POTE]]: ~2 = 1200.000, ~10/9 = 163.950
: error map: {{val| 0.000 +6.194 -6.065 }}


Map: [&lt;1 2 3 2|, &lt;0 -3 -5 6|]
[[Tuning ranges]]:  
EDOs: 22, [[59edo|59]], [[81edo|81bd]], [[140edo|140bd]]
* [[5-odd-limit]] [[diamond monotone]]: ~10/9 = [150.000, 171.429] (1\8 to 1\7)
* 5-odd-limit [[diamond tradeoff]]: ~10/9 = [157.821, 166.015]


==11-limit==
{{Optimal ET sequence|legend=1| 7, 15, 22, 95c }}
Commas: 55/54, 64/63, 100/99


POTE generator: ~10/9 = 162.747
[[Badness]] (Smith): 0.030778


Map: [&lt;1 2 3 2 4|, &lt;0 -3 -5 6 -4|]
=== Overview to extensions ===
EDOs: [[7edo|7]], 15, 22, [[37edo|37]], [[59edo|59]]
==== 7-limit extensions ====
Badness: 0.0217
The second comma defines which [[7-limit]] family member we are looking at.
* [[#Hystrix|Hystrix]] adds [[36/35]], the mint comma, for an exotemperament tuning around 8d-edo;  
* [[#Opossum|Opossum]] adds [[28/27]], the trienstonic comma, for a tuning between 8d-edo and 15edo;
* [[#Septimal porcupine|Septimal porcupine]] adds [[64/63]], the archytas comma, for a tuning between 15edo and 22edo;
* [[#Porky|Porky]] adds [[225/224]], the marvel comma, for a tuning between 22edo and 29edo;
* [[#Coendou|Coendou]] adds [[525/512]], the avicennma, for a tuning sharp of 29edo.  


==13-limit==
Those all share the same generator with porcupine.
Commas: 40/39, 55/54, 64/63, 66/65


POTE generator: ~10/9 = 162.708
[[#Nautilus|nautilus]] tempers out [[49/48]] and splits the generator in two. [[#Hedgehog|hedgehog]] tempers out [[50/49]] with a semi-octave period. Finally, [[#Ammonite|ammonite]] tempers out [[686/675]] and [[#Ceratitid|ceratitid]] tempers out [[1728/1715]]. Those split the generator in three.  


Map: [&lt;1 2 3 2 4 4|, &lt;0 -3 -5 6 -4 -2|]
Temperaments discussed elsewhere include:  
EDOs: 7, 15, 22f, 37f
* [[Oxygen]] → [[Very low accuracy temperaments #Oxygen|Very low accuracy temperaments]].
Badness: 0.0213
* [[Jamesbond]] → [[7th-octave temperaments #Jamesbond|7th-octave temperaments]].


==Porcupinefish==  
==== Subgroup extensions ====
See also: [[The Biosphere]]
Noting that {{nowrap| 250/243 {{=}} ([[55/54]])⋅([[100/99]]) {{=}} S10<sup>2</sup>⋅[[121/120|S11]] }}, the temperament thus extends naturally to the 2.3.5.11 [[subgroup]], sometimes known as ''porkypine'', given right below.
Commas: 55/54, 64/63, 91/90, 100/99


POTE generator: ~10/9 = 162.277
=== 2.3.5.11 subgroup (porkypine) ===
Subgroup: 2.3.5.11


Map: [&lt;1 2 3 2 4 6|, &lt;0 -3 -5 6 -4 -17|]
Comma list: 55/54, 100/99
EDOs: 15, 22, 37, 59, 96b
&lt;span style="background-color: #ffffff;"&gt;Badness: 0.0253&lt;/span&gt;


==Porkpie==
Sval mapping: {{mapping| 1 2 3 4 | 0 -3 -5 -4 }}
Commas: 55/54, 64/63, 65/63, 100/99


POTE generator: ~10/9 = 163.688
Gencom mapping: {{mapping| 1 2 3 0 4 | 0 -3 -5 0 -4 }}


Map: [&lt;1 2 3 2 4 3|, &lt;0 -3 -5 6 -4 5|]
: gencom: [2 10/9; 55/54, 100/99]
EDOs: 7, 15f, 22
Badness: 0.0260


=Hystrix=  
Optimal tunings:
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.
* CTE: ~2 = 1200.000, ~11/10 = 163.887
* POTE: ~2 = 1200.000, ~11/10 = 164.078


Commas: 36/35, 160/147
{{Optimal ET sequence|legend=0| 7, 15, 22, 73ce, 95ce }}


[[POTE tuning|POTE generator]]: 158.868
Badness (Smith): 0.0097


Map: [&lt;1 2 3 3|, &lt;0 -3 -5 -1|]
==== Undecimation ====
Subgroup: 2.3.5.11.13


EDOs: 10d, 12, 13d, 15
Comma list: 55/54, 100/99, 512/507


=Hedgehog=
Sval mapping: {{mapping| 1 5 8 8 2 | 0 -6 -10 -8 3 }}
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.


Commas: 50/49, 245/243
: sval mapping generators: ~2, ~65/44


[[POTE tuning|POTE generator]]: ~9/7 = 435.648
Optimal tunings:
* CTE: ~2 = 1200.000, ~88/65 = 518.086
* POTE: ~2 = 1200.000, ~88/65 = 518.209


Map: [&lt;2 1 1 2|, &lt;0 3 5 5|]
{{Optimal ET sequence|legend=0| 7, 23bc, 30, 37, 44 }}
Wedgie: &lt;&lt;6 10 10 2 -1 -5||
EDOs: 22, [[146edo|146]]
Badness: 0.0440


==11-limit==
Badness (Smith): 0.0305
Commas: 50/49, 55/54, 99/98


POTE generator: ~9/7 = 435.386
== Septimal porcupine ==
{{Main| Porcupine }}


Map: [&lt;2 1 1 2 4|, &lt;0 3 5 5 4|]
Septimal porcupine uses six of its minor tone generator steps to get to [[7/4]]. Here, we share the same mapping of 7/4 in terms of fifths as [[archy]]. 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.  
EDOs: 14c, 22, 58ce, 80ce, 102cde
Badness: 0.0231


==13-limit==
[[Subgroup]]: 2.3.5.7
Commas: 50/49, 55/54, 65/63, 99/98


POTE generator: ~9/7 = 435.861
[[Comma list]]: 64/63, 250/243


Map: [&lt;2 1 1 2 4 3|, &lt;0 3 5 5 4 6|]
{{Mapping|legend=1| 1 2 3 2 | 0 -3 -5 6 }}
EDOs: 14cf, 22
Badness: 0.0215


==Hedgepig==  
[[Optimal tuning]]s:
Commas: 50/49, 245/243, 385/384
* [[CTE]]: ~2 = 1200.000, ~10/9 = 163.203
: [[error map]]: {{val| 0.000 +8.435 -2.330 +10.394 }}
* [[POTE]]: ~2 = 1200.000, ~10/9 = 162.880
: error map: {{val| 0.000 +9.405 -0.714 +8.455 }}


POTE generator: ~9/7 = 435.425
[[Minimax tuning]]:
* [[7-odd-limit]]: ~10/9 = {{monzo| 3/5 0 -1/5 }}
: [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.5
* [[9-odd-limit]]: ~10/9 = {{monzo| 1/6 -1/6 0 1/12 }}
: [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.9/7


Map: [&lt;2 1 1 2 12|, &lt;0 3 5 5 -7|]
[[Tuning ranges]]:  
EDOs: 22, 80c, 102cd, 124cd
* 7- and 9-odd-limit [[diamond monotone]]: ~10/9 = [160.000, 163.636] (2\15 to 3\22)
Badness: 0.0684
* 7-odd-limit [[diamond tradeoff]]: ~10/9 = [157.821, 166.015]
* 9-odd-limit diamond tradeoff: ~10/9 = [157.821, 182.404]


===Music===
{{Optimal ET sequence|legend=1| 7, 15, 22, 37, 59, 81bd }}
[[http://micro.soonlabel.com/22-ET/20120207-phobos-light-hedgehog14.mp3|Phobos Light]] by Chris Vaisvil in Hedgehog[14] [[hedgehog14|tuned]] to 22edo.


=Nautilus=
[[Badness]] (Smith): 0.041057
Commas: 49/48, 250/243


Pote generator: ~21/20 = 82.505
=== 11-limit ===
Subgroup: 2.3.5.7.11


Map: [&lt;1 2 3 3|, &lt;0 -6 -10 -3|]
Comma list: 55/54, 64/63, 100/99
Wedgie: &lt;&lt;6 10 3 2 -12 -21||
EDOs: 10, 15, 19, [[29edo|29]], [[102edo|102cd]]


==11-limit==
Mapping: {{mapping| 1 2 3 2 4 | 0 -3 -5 6 -4 }}
Commas: 49/48, 55/54, 245/242


POTE generator: ~21/20 = 82.504
Optimal tunings:
* CTE: ~2 = 1200.000, ~11/10 = 163.105
* POTE: ~2 = 1200.000, ~11/10 = 162.747


Map: [&lt;1 2 3 3 4|, &lt;0 -6 -10 -3 -8|]
Minimax tuning:  
EDOs: 10e, 14c, 15, 19, 22d, 29, 102cde
* 11-odd-limit: ~11/10 = {{monzo| 1/6 -1/6 0 1/12 }}
: unchanged-interval (eigenmonzo) basis: 2.9/7


==13-limit==
Tuning ranges:
Commas: 49/48, 55/54, 91/90, 100/99
* 11-odd-limit diamond monotone: ~11/10 = [160.000, 163.636] (2\15 to 3\22)
* 11-odd-limit diamond tradeoff: ~11/10 = [150.637, 182.404]


POTE generator: ~21/20 = 62.530
{{Optimal ET sequence|legend=0| 7, 15, 22, 37, 59 }}


Map: [&lt;1 2 3 3 4 5|, &lt;0 -6 -10 -3 -8 -19|]
Badness (Smith): 0.021562
EDOs: 10e, 15f, 17d, 19, 22d, 29, 102cde


[[http://micro.soonlabel.com/gene_ward_smith/Others/Igs/NautilusReverie.mp3|Nautilus Reverie]] by [[IgliashonJones|Igliashon Calvin Jones-Coolidge]]
==== Porcupinefowl ====
=Ammonite=  
This extension used to be ''tridecimal porcupine''.
Commas: 250/243, 686/675


POTE generator: ~9/7 = 454.448
Subgroup: 2.3.5.7.11.13


Map: [&lt;1 5 8 10|, &lt;0 -9 -15 -19|]
Comma list: 40/39, 55/54, 64/63, 66/65
Wedgie: &lt;&lt;9 15 19 3 5 2||
EDOs: 29, 37, 66
Badness: 0.1077


==11-limit==
Mapping: {{mapping| 1 2 3 2 4 4 | 0 -3 -5 6 -4 -2 }}
Commas: 55/54, 100/99, 686/675


POTE generator: ~9/7 = 454.512
Optimal tunings:
* CTE: ~2 = 1200.000, ~11/10 = 163.442
* POTE: ~2 = 1200.000, ~11/10 = 162.708


Map: [&lt;1 5 8 10 8|, &lt;0 -9 -15 -19 -12|]
Minimax tuning:  
EDOs: 29, 37, 66
* 13- and 15-odd-limit: ~10/9 = {{monzo| 1 0 0 0 -1/4 }}
Badness: 0.0457
: unchanged-interval (eigenmonzo) basis: 2.11


==13-limit==  
Tuning ranges:
Commas: 55/54, 91/90, 100/99, 169/168
* 13-odd-limit diamond monotone: ~11/10 = [160.000, 163.636] (2\15 to 3\22)
* 15-odd-limit diamond monotone: ~11/10 = 163.636 (3\22)
* 13- and 15-odd-limit diamond tradeoff: ~11/10 = [138.573, 182.404]


POTE generator: ~13/10 = 454.429
{{Optimal ET sequence|legend=0| 7, 15, 22f, 37f }}


Map: [&lt;1 5 8 10 8 9|, &lt;0 -9 -15 -19 -12 -14|]
Badness (Smith): 0.021276
EDOs: 29, 37, 66
Badness: 0.0272


=Porky=  
==== Porcupinefish ====
Commas: 225/224, 250/243
{{See also| The Biosphere }}


POTE generator: ~10/9 = 164.412
Subgroup: 2.3.5.7.11.13


Map: [&lt;1 2 3 5|, &lt;0 -3 -5 -16|]
Comma list: 55/54, 64/63, 91/90, 100/99
Wedgie: &lt;&lt;3 5 16 1 17 23||
EDOS: 7, 8, 15, 22, 29, 51, 73
Badness: 0.0544


==11-limit==
Mapping: {{mapping| 1 2 3 2 4 6 | 0 -3 -5 6 -4 -17 }}
Commas: 55/54, 100/99, 225/224


POTE generator: ~10/9 = 164.552
Optimal tunings:
* CTE: ~2 = 1200.000, ~11/10 = 162.636
* POTE: ~2 = 1200.000, ~11/10 = 162.277


Map: [&lt;1 2 3 5 4|, &lt;0 -3 -5 -16 -4|]
Minimax tuning:  
EDOs: 7, 8, 15, 22, 29, 51, 73
* 13- and 15-odd-limit: ~10/9 = {{monzo| 2/13 0 0 0 1/13 -1/13 }}
Badness: 0.0273
: unchanged-interval (eigenmonzo) basis: 2.13/11


=Coendou=  
Tuning ranges:
Commas: 250/243, 525/512
* 13-odd-limit diamond monotone: ~10/9 = [160.000, 162.162] (2\15 to 5\37)
* 15-odd-limit diamond monotone: ~10/9 = 162.162 (5\37)
* 13- and 15-odd-limit diamond tradeoff: ~10/9 = [150.637, 182.404]


POTE generator: ~10/9 = 166.041
{{Optimal ET sequence|legend=0| 15, 22, 37 }}


Map: [&lt;1 2 3 1|, &lt;0 -3 -5 13|]
Badness (Smith): 0.025314
Wedgie: &lt;&lt;3 5 -13 1 -29 -44||
EDOs: 7, 29, 65c, 94cd
Badness: 0.1183


==11-limit==  
==== Pourcup ====
Commas: 55/54, 100/99, 525/512
Subgroup: 2.3.5.7.11.13


POTE generator: ~10/9 = 165.981
Comma list: 55/54, 64/63, 100/99, 196/195


Map: [&lt;1 2 3 1 4|, &lt;0 -3 -5 13 -4|]
Mapping: {{mapping| 1 2 3 2 4 1 | 0 -3 -5 6 -4 20 }}
EDOs: 7, 29, 65ce, 94cde
Badness: 0.0497


==13-limit==
Optimal tunings:
Commas: 55/54, 65/64, 100/99, 105/104
* CTE: ~2 = 1200.000, ~11/10 = 163.378
* POTE: ~2 = 1200.000, ~11/10 = 162.482


POTE generator: ~10/9 = 165.974
Minimax tuning:
* 13- and 15-odd-limit: ~11/10 = {{monzo| 1/14 0 0 -1/14 0 1/14 }}
: unchanged-interval (eigenmonzo) basis: 2.13/7


Map: [&lt;1 2 3 1 4 3|, &lt;0 -3 -5 13 -4 5|]
{{Optimal ET sequence|legend=0| 15f, 22f, 37, 59f }}
EDOs: 7, 29, 65cef, 94cdef
 
Badness: 0.0302</pre></div>
Badness (Smith): 0.035130
<h4>Original HTML 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;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;!-- ws:start:WikiTextTocRule:46:&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:46 --&gt;&lt;!-- ws:start:WikiTextTocRule:47: --&gt;&lt;!-- ws:end:WikiTextTocRule:47 --&gt;&lt;!-- ws:start:WikiTextTocRule:48: --&gt; | &lt;a href="#Porcupine"&gt;Porcupine&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:48 --&gt;&lt;!-- ws:start:WikiTextTocRule:49: --&gt;&lt;!-- ws:end:WikiTextTocRule:49 --&gt;&lt;!-- ws:start:WikiTextTocRule:50: --&gt;&lt;!-- ws:end:WikiTextTocRule:50 --&gt;&lt;!-- ws:start:WikiTextTocRule:51: --&gt;&lt;!-- ws:end:WikiTextTocRule:51 --&gt;&lt;!-- ws:start:WikiTextTocRule:52: --&gt;&lt;!-- ws:end:WikiTextTocRule:52 --&gt;&lt;!-- ws:start:WikiTextTocRule:53: --&gt; | &lt;a href="#Hystrix"&gt;Hystrix&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:53 --&gt;&lt;!-- ws:start:WikiTextTocRule:54: --&gt; | &lt;a href="#Hedgehog"&gt;Hedgehog&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:54 --&gt;&lt;!-- ws:start:WikiTextTocRule:55: --&gt;&lt;!-- ws:end:WikiTextTocRule:55 --&gt;&lt;!-- ws:start:WikiTextTocRule:56: --&gt;&lt;!-- ws:end:WikiTextTocRule:56 --&gt;&lt;!-- ws:start:WikiTextTocRule:57: --&gt;&lt;!-- ws:end:WikiTextTocRule:57 --&gt;&lt;!-- ws:start:WikiTextTocRule:58: --&gt;&lt;!-- ws:end:WikiTextTocRule:58 --&gt;&lt;!-- ws:start:WikiTextTocRule:59: --&gt; | &lt;a href="#Nautilus"&gt;Nautilus&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:59 --&gt;&lt;!-- ws:start:WikiTextTocRule:60: --&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="#Ammonite"&gt;Ammonite&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;a href="#Porky"&gt;Porky&lt;/a&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;a href="#Coendou"&gt;Coendou&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:67 --&gt;&lt;!-- ws:start:WikiTextTocRule:68: --&gt;&lt;!-- ws:end:WikiTextTocRule:68 --&gt;&lt;!-- ws:start:WikiTextTocRule:69: --&gt;&lt;!-- ws:end:WikiTextTocRule:69 --&gt;&lt;!-- ws:start:WikiTextTocRule:70: --&gt;
==== Porkpie ====
&lt;!-- ws:end:WikiTextTocRule:70 --&gt;&lt;hr /&gt;
Subgroup: 2.3.5.7.11.13
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;
Comma list: 55/54, 64/63, 65/63, 100/99
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 163.950&lt;br /&gt;
 
&lt;br /&gt;
Mapping: {{mapping| 1 2 3 2 4 3 | 0 -3 -5 6 -4 5 }}
Map: [&amp;lt;1 2 3|, &amp;lt;0 -3 -5|]&lt;br /&gt;
 
&lt;br /&gt;
Optimal tunings:  
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;
* CTE: ~2 = 1200.000, ~11/10 = 163.678
&lt;br /&gt;
* POTE: ~2 = 1200.000, ~11/10 = 163.688
&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="/Archyta%27s%20comma"&gt;Archyta's 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;
Minimax tuning:
&lt;br /&gt;
* 13- and 15-odd-limit: ~11/10 = {{monzo| 1/6 -1/6 0 1/12 }}
&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;
: unchanged-interval (eigenmonzo) basis: 2.9/7
&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;
{{Optimal ET sequence|legend=0| 7, 15f, 22 }}
Commas: 250/243, 64/63&lt;br /&gt;
 
&lt;br /&gt;
Badness (Smith): 0.026043
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~10/9 = 162.880&lt;br /&gt;
 
&lt;br /&gt;
== Opossum ==
Map: [&amp;lt;1 2 3 2|, &amp;lt;0 -3 -5 6|]&lt;br /&gt;
Opossum can be described as {{nowrap| 8d & 15 }}. Tempering out [[28/27]], the perfect fifth of three generator steps is conflated with not [[32/21]] as in porcupine but [[14/9]]. Three such fifths or nine generator steps octave reduced give a flat 7/4. 2\15 is a good generator.
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;
 
&lt;br /&gt;
[[Subgroup]]: 2.3.5.7
&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;
[[Comma list]]: 28/27, 126/125
&lt;br /&gt;
 
POTE generator: ~10/9 = 162.747&lt;br /&gt;
{{Mapping|legend=1| 1 2 3 4 | 0 -3 -5 -9 }}
&lt;br /&gt;
 
Map: [&amp;lt;1 2 3 2 4|, &amp;lt;0 -3 -5 6 -4|]&lt;br /&gt;
[[Optimal tuning]]s:  
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;
* [[CTE]]: ~2 = 1200.000, ~10/9 = 161.306
Badness: 0.0217&lt;br /&gt;
: [[error map]]: {{val| 0.000 +14.126 +7.155 -20.583 }}
&lt;br /&gt;
* [[POTE]]: ~2 = 1200.000, ~10/9 = 159.691
&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;
: error map: {{val| 0.000 +18.971 +15.229 -6.048 }}
Commas: 40/39, 55/54, 64/63, 66/65&lt;br /&gt;
 
&lt;br /&gt;
[[Minimax tuning]]:  
POTE generator: ~10/9 = 162.708&lt;br /&gt;
* [[7-odd-limit|7-]] and [[9-odd-limit]] [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.7
&lt;br /&gt;
 
Map: [&amp;lt;1 2 3 2 4 4|, &amp;lt;0 -3 -5 6 -4 -2|]&lt;br /&gt;
{{Optimal ET sequence|legend=1| 7d, 8d, 15 }}
EDOs: 7, 15, 22f, 37f&lt;br /&gt;
 
Badness: 0.0213&lt;br /&gt;
[[Badness]] (Smith): 0.040650
&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;
=== 11-limit ===
See also: &lt;a class="wiki_link" href="/The%20Biosphere"&gt;The Biosphere&lt;/a&gt;&lt;br /&gt;
Subgroup: 2.3.5.7.11
Commas: 55/54, 64/63, 91/90, 100/99&lt;br /&gt;
 
&lt;br /&gt;
Comma list: 28/27, 55/54, 77/75
POTE generator: ~10/9 = 162.277&lt;br /&gt;
 
&lt;br /&gt;
Mapping: {{mapping| 1 2 3 4 4 | 0 -3 -5 -9 -4 }}
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;
Optimal tunings:
&lt;span style="background-color: #ffffff;"&gt;Badness: 0.0253&lt;/span&gt;&lt;br /&gt;
* CTE: ~2 = 1200.000, ~11/10 = 161.365
&lt;br /&gt;
* POTE: ~2 = 1200.000, ~11/10 = 159.807
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc5"&gt;&lt;a name="Porcupine-Porkpie"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Porkpie&lt;/h2&gt;
 
Commas: 55/54, 64/63, 65/63, 100/99&lt;br /&gt;
Minimax tuning:  
&lt;br /&gt;
* 11-odd-limit unchanged-interval (eigenmonzo) basis: 2.7
POTE generator: ~10/9 = 163.688&lt;br /&gt;
 
&lt;br /&gt;
{{Optimal ET sequence|legend=0| 7d, 8d, 15 }}
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 (Smith): 0.022325
Badness: 0.0260&lt;br /&gt;
 
&lt;br /&gt;
=== 13-limit ===
&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc6"&gt;&lt;a name="Hystrix"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;Hystrix&lt;/h1&gt;
Subgroup: 2.3.5.7.11.13
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;
Comma list: 28/27, 40/39, 55/54, 66/65
Commas: 36/35, 160/147&lt;br /&gt;
 
&lt;br /&gt;
Mapping: {{mapping| 1 2 3 4 4 4 | 0 -3 -5 -9 -4 -2 }}
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 158.868&lt;br /&gt;
 
&lt;br /&gt;
Optimal tunings:  
Map: [&amp;lt;1 2 3 3|, &amp;lt;0 -3 -5 -1|]&lt;br /&gt;
* CTE: ~2 = 1200.000, ~11/10 = 161.631
&lt;br /&gt;
* POTE: ~2 = 1200.000, ~11/10 = 158.805
EDOs: 10d, 12, 13d, 15&lt;br /&gt;
 
&lt;br /&gt;
Minimax tuning:  
&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc7"&gt;&lt;a name="Hedgehog"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;Hedgehog&lt;/h1&gt;
* 13- and 15-odd-limit unchanged-interval (eigenmonzo) basis: 2.7
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;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.&lt;br /&gt;
 
&lt;br /&gt;
{{Optimal ET sequence|legend=0| 7d, 8d, 15, 38bceff }}
Commas: 50/49, 245/243&lt;br /&gt;
 
&lt;br /&gt;
Badness (Smith): 0.019389
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~9/7 = 435.648&lt;br /&gt;
 
&lt;br /&gt;
== Porky ==
Map: [&amp;lt;2 1 1 2|, &amp;lt;0 3 5 5|]&lt;br /&gt;
Porky can be described as {{nowrap| 22 & 29 }}, suggesting a less sharp perfect fifth. 7\51 is a good generator.
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;
[[Subgroup]]: 2.3.5.7
Badness: 0.0440&lt;br /&gt;
 
&lt;br /&gt;
[[Comma list]]: 225/224, 250/243
&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc8"&gt;&lt;a name="Hedgehog-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;11-limit&lt;/h2&gt;
 
Commas: 50/49, 55/54, 99/98&lt;br /&gt;
{{Mapping|legend=1| 1 2 3 5 | 0 -3 -5 -16 }}
&lt;br /&gt;
 
POTE generator: ~9/7 = 435.386&lt;br /&gt;
[[Optimal tuning]]s:  
&lt;br /&gt;
* [[CTE]]: ~2 = 1200.000, ~10/9 = 164.391
Map: [&amp;lt;2 1 1 2 4|, &amp;lt;0 3 5 5 4|]&lt;br /&gt;
: [[error map]]: {{val| 0.000 +4.871 -8.270 +0.913 }}
EDOs: 14c, 22, 58ce, 80ce, 102cde&lt;br /&gt;
* [[POTE]]: ~2 = 1200.000, ~10/9 = 164.412
Badness: 0.0231&lt;br /&gt;
: error map: {{val| 0.000 +4.809 -8.375 +0.580 }}
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc9"&gt;&lt;a name="Hedgehog-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;13-limit&lt;/h2&gt;
[[Minimax tuning]]:
Commas: 50/49, 55/54, 65/63, 99/98&lt;br /&gt;
* [[7-odd-limit|7-]] and [[9-odd-limit]]: ~10/9 = {{monzo| 2/11 0 1/11 -1/11 }}
&lt;br /&gt;
: [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.7/5
POTE generator: ~9/7 = 435.861&lt;br /&gt;
 
&lt;br /&gt;
{{Optimal ET sequence|legend=1| 7d, 15d, 22, 29, 51, 73c }}
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]] (Smith): 0.054389
Badness: 0.0215&lt;br /&gt;
 
&lt;br /&gt;
=== 11-limit ===
&lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc10"&gt;&lt;a name="Hedgehog-Hedgepig"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;Hedgepig&lt;/h2&gt;
Subgroup: 2.3.5.7.11
Commas: 50/49, 245/243, 385/384&lt;br /&gt;
 
&lt;br /&gt;
Comma list: 55/54, 100/99, 225/224
POTE generator: ~9/7 = 435.425&lt;br /&gt;
 
&lt;br /&gt;
Mapping: {{mapping| 1 2 3 5 4 | 0 -3 -5 -16 -4 }}
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;
Optimal tunings:  
Badness: 0.0684&lt;br /&gt;
* CTE: ~2 = 1200.000, ~11/10 = 164.321
&lt;br /&gt;
* POTE: ~2 = 1200.000, ~11/10 = 164.552
&lt;!-- ws:start:WikiTextHeadingRule:22:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc11"&gt;&lt;a name="Hedgehog-Hedgepig-Music"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:22 --&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;
Minimax tuning:  
&lt;br /&gt;
* 11-odd-limit: ~11/10 = {{monzo| 2/11 0 1/11 -1/11 }}
&lt;!-- ws:start:WikiTextHeadingRule:24:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc12"&gt;&lt;a name="Nautilus"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:24 --&gt;Nautilus&lt;/h1&gt;
: unchanged-interval (eigenmonzo) basis: 2.7/5
Commas: 49/48, 250/243&lt;br /&gt;
 
&lt;br /&gt;
{{Optimal ET sequence|legend=0| 7d, 15d, 22, 51 }}
Pote generator: ~21/20 = 82.505&lt;br /&gt;
 
&lt;br /&gt;
Badness (Smith): 0.027268
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;
=== 13-limit ===
EDOs: 10, 15, 19, &lt;a class="wiki_link" href="/29edo"&gt;29&lt;/a&gt;, &lt;a class="wiki_link" href="/102edo"&gt;102cd&lt;/a&gt;&lt;br /&gt;
Subgroup: 2.3.5.7.11.13
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:26:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc13"&gt;&lt;a name="Nautilus-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:26 --&gt;11-limit&lt;/h2&gt;
Comma list: 55/54, 65/64, 91/90, 100/99
Commas: 49/48, 55/54, 245/242&lt;br /&gt;
 
&lt;br /&gt;
Mapping: {{mapping| 1 2 3 5 4 3 | 0 -3 -5 -16 -4 5 }}
POTE generator: ~21/20 = 82.504&lt;br /&gt;
 
&lt;br /&gt;
Optimal tunings:  
Map: [&amp;lt;1 2 3 3 4|, &amp;lt;0 -6 -10 -3 -8|]&lt;br /&gt;
* CTE: ~2 = 1200.000, ~11/10 = 164.478
EDOs: 10e, 14c, 15, 19, 22d, 29, 102cde&lt;br /&gt;
* POTE: ~2 = 1200.000, ~11/10 = 164.953
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:28:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc14"&gt;&lt;a name="Nautilus-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:28 --&gt;13-limit&lt;/h2&gt;
{{Optimal ET sequence|legend=0| 7d, 22, 29, 51f, 80cdeff }}
Commas: 49/48, 55/54, 91/90, 100/99&lt;br /&gt;
 
&lt;br /&gt;
Badness (Smith): 0.026543
POTE generator: ~21/20 = 62.530&lt;br /&gt;
 
&lt;br /&gt;
; Music
Map: [&amp;lt;1 2 3 3 4 5|, &amp;lt;0 -6 -10 -3 -8 -19|]&lt;br /&gt;
* [https://www.youtube.com/watch?v=CN4cLOyaVGE ''Improvisation in 29edo''] (2024) by [[Budjarn Lambeth]] – in Palace scale, 29edo tuning
EDOs: 10e, 15f, 17d, 19, 22d, 29, 102cde&lt;br /&gt;
 
&lt;br /&gt;
== Coendou ==
&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;
Coendou can be described as {{nowrap| 29 & 36c }}, suggesting an even less sharp or near-just perfect fifth. 9\65 is a good generator.
&lt;!-- ws:start:WikiTextHeadingRule:30:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc15"&gt;&lt;a name="Ammonite"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:30 --&gt;Ammonite&lt;/h1&gt;
 
Commas: 250/243, 686/675&lt;br /&gt;
[[Subgroup]]: 2.3.5.7
&lt;br /&gt;
 
POTE generator: ~9/7 = 454.448&lt;br /&gt;
[[Comma list]]: 250/243, 525/512
&lt;br /&gt;
 
Map: [&amp;lt;1 5 8 10|, &amp;lt;0 -9 -15 -19|]&lt;br /&gt;
{{Mapping|legend=1| 1 2 3 1 | 0 -3 -5 13 }}
Wedgie: &amp;lt;&amp;lt;9 15 19 3 5 2||&lt;br /&gt;
 
EDOs: 29, 37, 66&lt;br /&gt;
[[Optimal tuning]]s:  
Badness: 0.1077&lt;br /&gt;
* [[CTE]]: ~2 = 1200.000, ~10/9 = 166.094
&lt;br /&gt;
: [[error map]]: {{val| 0.000 -0.236 -16.783 -9.607 }}
&lt;!-- ws:start:WikiTextHeadingRule:32:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc16"&gt;&lt;a name="Ammonite-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:32 --&gt;11-limit&lt;/h2&gt;
* [[POTE]]: ~2 = 1200.000, ~10/9 = 166.041
Commas: 55/54, 100/99, 686/675&lt;br /&gt;
: error map: {{val| 0.000 -0.077 -16.516 -10.299 }}
&lt;br /&gt;
 
POTE generator: ~9/7 = 454.512&lt;br /&gt;
[[Minimax tuning]]:  
&lt;br /&gt;
* [[7-odd-limit|7-]] and [[9-odd-limit]]: ~10/9 = {{monzo| 2/3 -1/3 }}
Map: [&amp;lt;1 5 8 10 8|, &amp;lt;0 -9 -15 -19 -12|]&lt;br /&gt;
: [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.3
EDOs: 29, 37, 66&lt;br /&gt;
 
Badness: 0.0457&lt;br /&gt;
{{Optimal ET sequence|legend=1| 7, 22d, 29, 65c, 94cd }}
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:34:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc17"&gt;&lt;a name="Ammonite-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:34 --&gt;13-limit&lt;/h2&gt;
[[Badness]] (Smith): 0.118344
Commas: 55/54, 91/90, 100/99, 169/168&lt;br /&gt;
 
&lt;br /&gt;
=== 11-limit ===
POTE generator: ~13/10 = 454.429&lt;br /&gt;
Subgroup: 2.3.5.7.11
&lt;br /&gt;
 
Map: [&amp;lt;1 5 8 10 8 9|, &amp;lt;0 -9 -15 -19 -12 -14|]&lt;br /&gt;
Comma list: 55/54, 100/99, 525/512
EDOs: 29, 37, 66&lt;br /&gt;
 
Badness: 0.0272&lt;br /&gt;
Mapping: {{mapping| 1 2 3 1 4 | 0 -3 -5 13 -4 }}
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:36:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc18"&gt;&lt;a name="Porky"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:36 --&gt;Porky&lt;/h1&gt;
Optimal tunings:  
Commas: 225/224, 250/243&lt;br /&gt;
* CTE: ~2 = 1200.000, ~11/10 = 165.925
&lt;br /&gt;
* POTE: ~2 = 1200.000, ~11/10 = 165.981
POTE generator: ~10/9 = 164.412&lt;br /&gt;
 
&lt;br /&gt;
Minimax tuning:  
Map: [&amp;lt;1 2 3 5|, &amp;lt;0 -3 -5 -16|]&lt;br /&gt;
* 11-odd-limit: ~11/10 = {{monzo| 2/3 -1/3 }}
Wedgie: &amp;lt;&amp;lt;3 5 16 1 17 23||&lt;br /&gt;
: unchanged-interval (eigenmonzo) basis: 2.3
EDOS: 7, 8, 15, 22, 29, 51, 73&lt;br /&gt;
 
Badness: 0.0544&lt;br /&gt;
{{Optimal ET sequence|legend=0| 7, 22d, 29, 65ce }}
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:38:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc19"&gt;&lt;a name="Porky-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:38 --&gt;11-limit&lt;/h2&gt;
Badness (Smith): 0.049669
Commas: 55/54, 100/99, 225/224&lt;br /&gt;
 
&lt;br /&gt;
=== 13-limit ===
POTE generator: ~10/9 = 164.552&lt;br /&gt;
Subgroup: 2.3.5.7.11.13
&lt;br /&gt;
 
Map: [&amp;lt;1 2 3 5 4|, &amp;lt;0 -3 -5 -16 -4|]&lt;br /&gt;
Comma list: 55/54, 65/64, 100/99, 105/104
EDOs: 7, 8, 15, 22, 29, 51, 73&lt;br /&gt;
 
Badness: 0.0273&lt;br /&gt;
Mapping: {{mapping| 1 2 3 1 4 3 | 0 -3 -5 13 -4 5 }}
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:40:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc20"&gt;&lt;a name="Coendou"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:40 --&gt;Coendou&lt;/h1&gt;
Optimal tunings:
Commas: 250/243, 525/512&lt;br /&gt;
* CTE: ~2 = 1200.000, ~11/10 = 166.046
&lt;br /&gt;
* POTE: ~2 = 1200.000, ~11/10 = 165.974
POTE generator: ~10/9 = 166.041&lt;br /&gt;
 
&lt;br /&gt;
Minimax tuning:
Map: [&amp;lt;1 2 3 1|, &amp;lt;0 -3 -5 13|]&lt;br /&gt;
* 13- and 15-odd-limit: ~11/10 = {{monzo| 2/3 -1/3 }}
Wedgie: &amp;lt;&amp;lt;3 5 -13 1 -29 -44||&lt;br /&gt;
: unchanged-interval (eigenmonzo) basis: 2.3
EDOs: 7, 29, 65c, 94cd&lt;br /&gt;
 
Badness: 0.1183&lt;br /&gt;
{{Optimal ET sequence|legend=0| 7, 22d, 29, 65cef }}
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:42:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc21"&gt;&lt;a name="Coendou-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:42 --&gt;11-limit&lt;/h2&gt;
Badness (Smith): 0.030233
Commas: 55/54, 100/99, 525/512&lt;br /&gt;
 
&lt;br /&gt;
== Hystrix ==
POTE generator: ~10/9 = 165.981&lt;br /&gt;
Hystrix provides a less complex avenue to the 7-limit, with the generator taking on the role of approximating 8/7. Unfortunately in temperaments as in life you get what you pay for, and hystrix is very high in [[error]] due to the large disparity between typical porcupine generators and a justly-tuned 8/7, and is usually considered an [[exotemperament]]. A generator of 2\15 or 9\68 can be used for hystrix.
&lt;br /&gt;
 
Map: [&amp;lt;1 2 3 1 4|, &amp;lt;0 -3 -5 13 -4|]&lt;br /&gt;
[[Subgroup]]: 2.3.5.7
EDOs: 7, 29, 65ce, 94cde&lt;br /&gt;
 
Badness: 0.0497&lt;br /&gt;
[[Comma list]]: 36/35, 160/147
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:44:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc22"&gt;&lt;a name="Coendou-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:44 --&gt;13-limit&lt;/h2&gt;
{{Mapping|legend=1| 1 2 3 3 | 0 -3 -5 -1 }}
Commas: 55/54, 65/64, 100/99, 105/104&lt;br /&gt;
 
&lt;br /&gt;
[[Optimal tuning]]s:
POTE generator: ~10/9 = 165.974&lt;br /&gt;
* [[CTE]]: ~2 = 1200.000, ~10/9 = 165.185
&lt;br /&gt;
: [[error map]]: {{val| 0.000 +2.491 -12.236 +65.990 }}
Map: [&amp;lt;1 2 3 1 4 3|, &amp;lt;0 -3 -5 13 -4 5|]&lt;br /&gt;
* [[POTE]]: ~2 = 1200.000, ~10/9 = 158.868
EDOs: 7, 29, 65cef, 94cdef&lt;br /&gt;
: error map: {{val| 0.000 +21.442 +19.348 +72.306 }}
Badness: 0.0302&lt;/body&gt;&lt;/html&gt;</pre></div>
 
[[Minimax tuning]]:  
* [[7-odd-limit|7-]] and [[9-odd-limit]]: ~10/9 = {{monzo| 3/5 0 -1/5 }}
: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.5
 
{{Optimal ET sequence|legend=1| 7, 8d, 15d }}
 
[[Badness]] (Smith): 0.044944
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 22/21, 36/35, 80/77
 
Mapping: {{mapping| 1 2 3 3 4 | 0 -3 -5 -1 -4 }}
 
Optimal tunings:
* CTE: ~2 = 1200.000, ~11/10 = 164.768
* POTE: ~2 = 1200.000, ~11/10 = 158.750
 
{{Optimal ET sequence|legend=0| 7, 8d, 15d }}
 
Badness (Smith): 0.026790
 
== Hedgehog ==
{{See also| Sensamagic clan | Stearnsmic clan }}
 
Hedgehog 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. It is a strong extension of [[BPS]] (as BPS has no 2 or sqrt(2)). Its ploidacot is diploid omega-tricot.
 
22edo provides an obvious tuning, which happens to be the only [[patent val|patent-val]] tuning, but if you are looking for an alternative you could try the {{val| 146 232 338 411 }} (146bccdd) 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. A related temperament is [[echidna]], which offers much more accuracy. They merge on 22edo.  
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 50/49, 245/243
 
{{Mapping|legend=1| 2 1 1 2 | 0 3 5 5 }}
 
: mapping generators: ~7/5, ~9/7
 
[[Optimal tuning]]s:
* [[CTE]]: ~7/5 = 600.000, ~9/7 = 435.258
: [[error map]]: {{val| 0.000 +3.819 -10.024 +7.464 }}
* [[POTE]]: ~7/5 = 600.000, ~9/7 = 435.648
: error map: {{val| 0.000 +4.989 -8.074 +9.414 }}
 
{{Optimal ET sequence|legend=1| 8d, 14c, 22 }}
 
[[Badness]] (Smith): 0.043983
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 50/49, 55/54, 99/98
 
Mapping: {{mapping| 2 1 1 2 4 | 0 3 5 5 4 }}
 
Optimal tunings:
* CTE: ~7/5 = 600.000, ~9/7 = 435.528
* POTE: ~7/5 = 600.000, ~9/7 = 435.386
 
{{Optimal ET sequence|legend=0| 8d, 14c, 22, 58ce }}
 
Badness (Smith): 0.023095
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 50/49, 55/54, 65/63, 99/98
 
Mapping: {{mapping| 2 1 1 2 4 3 | 0 3 5 5 4 6 }}
 
Optimal tunings:  
* CTE: ~7/5 = 600.000, ~9/7 = 436.309
* POTE: ~7/5 = 600.000, ~9/7 = 435.861
 
{{Optimal ET sequence|legend=0| 8d, 14cf, 22 }}
 
Badness (Smith): 0.021516
 
==== Urchin ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 40/39, 50/49, 55/54, 66/65
 
Mapping: {{mapping| 2 1 1 2 4 6 | 0 3 5 5 4 2 }}
 
Optimal tunings:
* CTE: ~7/5 = 600.000, ~9/7 = 435.186
* POTE: ~7/5 = 600.000, ~9/7 = 437.078
 
{{Optimal ET sequence|legend=0| 14c, 22f }}
 
Badness (Smith): 0.025233
 
=== Hedgepig ===
Subgroup: 2.3.5.7.11
 
Comma list: 50/49, 245/243, 385/384
 
Mapping: {{mapping| 2 1 1 2 12 | 0 3 5 5 -7 }}
 
Optimal tunings:
* CTE: ~7/5 = 600.000, ~9/7 = 435.329
* POTE: ~7/5 = 600.000, ~9/7 = 435.425
 
{{Optimal ET sequence|legend=0| 22 }}
 
Badness (Smith): 0.068406
 
; Music
* [http://micro.soonlabel.com/22-ET/20120207-phobos-light-hedgehog14.mp3 ''Phobos Light''] by [[Chris Vaisvil]] – in [[hedgehog14|hedgehog[14]]], 22edo tuning.
 
== Nautilus ==
Nautilus tempers out 49/48 and may be described as the {{nowrap| 14c & 15 }} temperament. Its ploidacot is omega-hexacot.
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 49/48, 250/243
 
{{Mapping|legend=1| 1 2 3 3 | 0 -6 -10 -3 }}
 
: mapping generators: ~2, ~21/20
 
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000, ~21/20 = 81.914
: [[error map]]: {{val| 0.000 +6.559 -5.457 -14.569 }}
* [[POTE]]: ~2 = 1200.000, ~21/20 = 82.505
: error map: {{val| 0.000 +3.012 -11.368 -16.342 }}
 
{{Optimal ET sequence|legend=1| 14c, 15, 29, 44d }}
 
[[Badness]] (Smith): 0.057420
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 49/48, 55/54, 245/242
 
Mapping: {{mapping| 1 2 3 3 4 | 0 -6 -10 -3 -8 }}
 
Optimal tunings:
* CTE: ~2 = 1200.000, ~21/20 = 81.802
* POTE: ~2 = 1200.000, ~21/20 = 82.504
 
{{Optimal ET sequence|legend=0| 14c, 15, 29, 44d }}
 
Badness (Smith): 0.026023
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 49/48, 55/54, 91/90, 100/99
 
Mapping: {{mapping| 1 2 3 3 4 5 | 0 -6 -10 -3 -8 -19 }}
 
Optimal tunings:  
* CTE: ~2 = 1200.000, ~21/20 = 81.912
* POTE: ~2 = 1200.000, ~21/20 = 82.530
 
{{Optimal ET sequence|legend=0| 14cf, 15, 29, 44d }}
 
Badness (Smith): 0.022285
 
==== Belauensis ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 40/39, 49/48, 55/54, 66/65
 
Mapping: {{mapping| 1 2 3 3 4 4 | 0 -6 -10 -3 -8 -4 }}
 
Optimal tunings:  
* CTE: ~2 = 1200.000, ~21/20 = 82.034
* POTE: ~2 = 1200.000, ~21/20 = 81.759
 
{{Optimal ET sequence|legend=0| 14c, 15, 29f, 44dff }}
 
Badness (Smith): 0.029816
 
; Music
* [http://micro.soonlabel.com/gene_ward_smith/Others/Igs/NautilusReverie.mp3 ''Nautilus Reverie''] by [[Igliashon Jones|Igliashon Calvin Jones-Coolidge]]
 
== Ammonite ==
Ammonite adds 686/675 to the comma list and may be described as the {{nowrap| 8d & 29 }} temperament. Its ploidacot is epsilon-enneacot. [[37edo]] provides an obvious tuning.
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 250/243, 686/675
 
{{Mapping|legend=1| 1 5 8 10 | 0 -9 -15 -19 }}
 
: mapping generators: ~2, ~9/7
 
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000, ~9/7 = 454.550
: [[error map]]: {{val| 0.000 +7.095 -4.564 -5.276 }}
* [[POTE]]: ~2 = 1200.000, ~9/7 = 454.448
: error map: {{val| 0.000 +8.009 -3.040 -3.346 }}
 
{{Optimal ET sequence|legend=1| 8d, 21cd, 29, 37, 66 }}
 
[[Badness]] (Smith): 0.107686
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 55/54, 100/99, 686/675
 
Mapping: {{mapping| 1 5 8 10 8 | 0 -9 -15 -19 -12 }}
 
Optimal tunings:
* CTE: ~2 = 1200.000, ~9/7 = 454.505
* POTE: ~2 = 1200.000, ~9/7 = 454.512
 
{{Optimal ET sequence|legend=0| 8d, 21cde, 29, 37, 66 }}
 
Badness (Smith): 0.045694
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 55/54, 91/90, 100/99, 169/168
 
Mapping: {{mapping| 1 5 8 10 8 9 | 0 -9 -15 -19 -12 -14 }}
 
Optimal tunings:
* CTE: ~2 = 1200.000, ~13/10 = 454.480
* POTE: ~2 = 1200.000, ~13/10 = 454.529
 
{{Optimal ET sequence|legend=0| 8d, 21cdef, 29, 37, 66 }}
 
Badness (Smith): 0.027168
 
== Ceratitid ==
Ceratitid adds 1728/1715 to the comma list and may be described as the {{nowrap| 21c & 22 }} temperament. Its ploidacot is omega-enneacot. [[22edo]] provides an obvious tuning.
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 250/243, 1728/1715
 
{{Mapping|legend=1| 1 2 3 3 | 0 -9 -15 -4 }}
 
: mapping generators: ~2, ~36/35
 
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000, ~36/35 = 54.804
: [[error map]]: {{val| 0.000 +4.809 -8.374 +11.958 }}
* [[POTE]]: ~2 = 1200.000, ~36/35 = 54.384
: error map: {{val| 0.000 +8.585 -2.081 +13.636 }}
 
{{Optimal ET sequence|legend=1| 1c, 21c, 22 }}
 
[[Badness]] (Smith): 0.115304
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 55/54, 100/99, 352/343
 
Mapping: {{mapping| 1 2 3 3 4 | 0 -9 -15 -4 -12 }}
 
Optimal tunings:  
* CTE: ~2 = 1200.000, ~36/35 = 54.702
* POTE: ~2 = 1200.000, ~36/35 = 54.376
 
{{Optimal ET sequence|legend=0| 1ce, 21ce, 22 }}
 
Badness (Smith): 0.051319
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 55/54, 65/63, 100/99, 352/343
 
Mapping: {{mapping| 1 2 3 3 4 4 | 0 -9 -15 -4 -12 -7 }}
 
Optimal tunings:  
* CTE: ~2 = 1200.000, ~36/35 = 54.575
* POTE: ~2 = 1200.000, ~36/35 = 54.665
 
{{Optimal ET sequence|legend=0| 1ce, 21cef, 22 }}
 
Badness (Smith): 0.044739
 
[[Category:Temperament families]]
[[Category:Pages with mostly numerical content]]
[[Category:Porcupine family| ]] <!-- main article -->
[[Category:Porcupine| ]] <!-- key article -->
[[Category:Rank 2]]
Retrieved from "https://en.xen.wiki/w/Porcupine_family"