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


valid range: [150.000, 171.429] (8 to 7)
== Porcupine ==
nice range: [157.821, 166.015]
{{Main| Porcupine }}
strict range: [157.821, 166.015]


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


Map: [&lt;1 2 3|, &lt;0 -3 -5|]
[[Subgroup]]: 2.3.5


EDOs: [[15edo|15]], [[22edo|22]], [[95edo|95c]], [[117edo|117bc]], [[139edo|139bc]], [[161edo|161bc]], [[183edo|183bc]]
[[Comma list]]: 250/243
Badness: 0.0308


==Seven limit children==
{{Mapping|legend=1| 1 2 3 | 0 -3 -5 }}
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]].
: mapping generators: ~2, ~10/9


=Porcupine=  
[[Optimal tuning]]s:
[[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.
* [[WE]]: ~2 = 1199.5444{{c}}, ~10/9 = 163.8881{{c}}
: [[error map]]: {{val| -0.456 +5.469 -7.121 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~10/9 = 164.0621{{c}}
: error map: {{val| 0.000 +5.859 -6.624 }}


Commas: 250/243, 64/63
[[Tuning ranges]]:  
* [[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]


valid range: [160.000, 163.636] (15 to 22)
{{Optimal ET sequence|legend=1| 7, 15, 22, 95c }}
nice range: [157.821, 166.015]
strict range: [160.000, 163.636]


[[POTE tuning|POTE generator]]: ~10/9 = 162.880
[[Badness]] (Sintel): 0.722
7- and 9-limit minimax eigenmonzo: 9/7


Map: [&lt;1 2 3 2|, &lt;0 -3 -5 6|]
=== Overview to extensions ===
EDOs: 22, [[59edo|59]], [[81edo|81bd]], [[140edo|140bd]]
==== 7-limit extensions ====
Badness: 0.0411
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.  


==11-limit==
Those all share the same generator with porcupine.
Commas: 55/54, 64/63, 100/99


valid range: [160.000, 163.636] (15 to 22)
[[#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.  
nice range: [150.637, 182.404]
strict range: [160.000, 163.636]


POTE generator: ~10/9 = 162.747
Temperaments discussed elsewhere include:  
11-limit minimax eigenmonzo: 9/7
* ''[[Oxygen]]'' → [[Very low accuracy temperaments #Oxygen|Very low accuracy temperaments]]
* ''[[Jamesbond]]'' → [[Whitewood family #Jamesbond|Whitewood family]]


Map: [&lt;1 2 3 2 4|, &lt;0 -3 -5 6 -4|]
==== Subgroup extensions ====
EDOs: [[7edo|7]], 15, 22, [[37edo|37]], [[59edo|59]]
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.
Badness: 0.0217


==13-limit==  
=== 2.3.5.11 subgroup (porkypine) ===
Commas: 40/39, 55/54, 64/63, 66/65
Subgroup: 2.3.5.11


valid range: [160.000, 163.636] (15 to 22f)
Comma list: 55/54, 100/99
nice range: [138.573, 182.404]
strict range: [160.000, 163.636]


POTE generator: ~10/9 = 162.708
Subgroup-val mapping: {{mapping| 1 2 3 4 | 0 -3 -5 -4 }}
13- and 15-limit minimax eigenmonzo: 11/8


Map: [&lt;1 2 3 2 4 4|, &lt;0 -3 -5 6 -4 -2|]
Gencom mapping: {{mapping| 1 2 3 0 4 | 0 -3 -5 0 -4 }}
EDOs: 7, 15, 22f, 37f
Badness: 0.0213


==Porcupinefish==
Optimal tunings:  
See also: [[The Biosphere]]
* WE: ~2 = 1200.3290{{c}}, ~11/10 = 164.1227{{c}}
Commas: 55/54, 64/63, 91/90, 100/99
* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 163.9951{{c}}


valid range: [160.000, 162.162] (15 to 37)
{{Optimal ET sequence|legend=0| 7, 15, 22, 73ce, 95ce }}
nice range: [150.637, 182.404]
strict range:  [160.000, 162.162]


POTE generator: ~10/9 = 162.277
Badness (Sintel): 0.303
13- and 15-limit minimax eigenmonzo: 13/11


Map: [&lt;1 2 3 2 4 6|, &lt;0 -3 -5 6 -4 -17|]
==== Undecimation ====
EDOs: 15, 22, 37, 59, 96b
Subgroup: 2.3.5.11.13
&lt;span style="background-color: #ffffff;"&gt;Badness: 0.0253&lt;/span&gt;
Badness: 0.0253


==Pourcup==
Comma list: 55/54, 100/99, 512/507
Commas: 55/54, 64/63, 100/99, 196/195


POTE generator: ~10/9 = 162.482
Subgroup-val mapping: {{mapping| 1 -1 -2 0 5 | 0 6 10 8 -3 }}
13- and 15-limit minimax eigenmonzo: 13/7


Map: [&lt;1 2 3 2 4 1|, &lt;0 -3 -5 6 -4 20|]
: mapping generators: ~2, ~88/65
EDOs: 15f, 22f, 37
Badness: 0.0351


==Porkpie==
Optimal tunings:
Commas: 55/54, 64/63, 65/63, 100/99
* WE: ~2 = 1199.4791{{c}}, ~88/65 = 517.9845{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~88/65 = 518.1740{{c}}


POTE generator: ~10/9 = 163.688
{{Optimal ET sequence|legend=0| 7, 23bc, 30, 37, 44 }}
13- and 15-limit minimax eigenmonzo: 9/7


Map: [&lt;1 2 3 2 4 3|, &lt;0 -3 -5 6 -4 5|]
Badness (Sintel): 1.21
EDOs: 7, 15f, 22
Badness: 0.0260


=Hystrix=  
== Septimal porcupine ==
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.
{{Main| Porcupine }}


Commas: 36/35, 160/147
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.


[[POTE tuning|POTE generator]]: 158.868
[[Subgroup]]: 2.3.5.7
7- and 9-limit minimax eigenmonzo: 5/4


Map: [&lt;1 2 3 3|, &lt;0 -3 -5 -1|]
[[Comma list]]: 64/63, 250/243


EDOs: 10d, 12, 13d, 15
{{Mapping|legend=1| 1 2 3 2 | 0 -3 -5 6 }}
Badness: 0.0449


=Porky=  
[[Optimal tuning]]s:
Commas: 225/224, 250/243
* [[WE]]: ~2 = 1197.8178{{c}}, ~10/9 = 162.5839{{c}}
: [[error map]]: {{val| -2.182 +5.929 -5.780 +2.313 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~10/9 = 162.9493{{c}}
: error map: {{val| 0.000 +9.197 -1.060 +8.870 }}


POTE generator: ~10/9 = 164.412
[[Minimax tuning]]:
7- and 9-limit minimax eigenmonzo: 7/5
* [[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;1 2 3 5|, &lt;0 -3 -5 -16|]
[[Tuning ranges]]:  
Wedgie: &lt;&lt;3 5 16 1 17 23||
* 7- and 9-odd-limit [[diamond monotone]]: ~10/9 = [160.000, 163.636] (2\15 to 3\22)
EDOS: 7, 8, 15, 22, 29, 51, 73
* 7-odd-limit [[diamond tradeoff]]: ~10/9 = [157.821, 166.015]
Badness: 0.0544
* 9-odd-limit diamond tradeoff: ~10/9 = [157.821, 182.404]


==11-limit==
{{Optimal ET sequence|legend=1| 7, 15, 22, 37, 59, 81bd }}
Commas: 55/54, 100/99, 225/224


POTE generator: ~10/9 = 164.552
[[Badness]] (Sintel): 1.04
11-limit minimax eigenmonzo: 7/5


Map: [&lt;1 2 3 5 4|, &lt;0 -3 -5 -16 -4|]
=== 11-limit ===
EDOs: 7, 8, 15, 22, 29, 51, 73
Subgroup: 2.3.5.7.11
Badness: 0.0273


==13-limit==
Comma list: 55/54, 64/63, 100/99
Commas: 55/54, 65/64, 91/90, 100/99  


POTE generator: ~10/9 = 164.953
Mapping: {{mapping| 1 2 3 2 4 | 0 -3 -5 6 -4 }}


Map: [&lt;1 2 3 5 4 3|, &lt;0 -3 -5 -16 -4 5|]
Optimal tunings:  
EDOs: 22, 29, 51f, 80cdef
* WE: ~2 = 1198.3250{{c}}, ~11/10 = 162.5202{{c}}
Badness: 0.0265
* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 162.8156{{c}}


=Coendou=
Minimax tuning:
Commas: 250/243, 525/512
* 11-odd-limit: ~11/10 = {{monzo| 1/6 -1/6 0 1/12 }}
: unchanged-interval (eigenmonzo) basis: 2.9/7


POTE generator: ~10/9 = 166.041
Tuning ranges:
7- and 9-limit minimax eigenmonzo: 3/2
* 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]


Map: [&lt;1 2 3 1|, &lt;0 -3 -5 13|]
{{Optimal ET sequence|legend=0| 7, 15, 22, 37, 59 }}
Wedgie: &lt;&lt;3 5 -13 1 -29 -44||
EDOs: 7, 29, 65c, 94cd
Badness: 0.1183


==11-limit==
Badness (Sintel): 0.713
Commas: 55/54, 100/99, 525/512


POTE generator: ~10/9 = 165.981
==== Porcupinefowl ====
11-limit minimax eigenmonzo: 3/2
This extension used to be ''tridecimal porcupine''.  


Map: [&lt;1 2 3 1 4|, &lt;0 -3 -5 13 -4|]
Subgroup: 2.3.5.7.11.13
EDOs: 7, 29, 65ce, 94cde
Badness: 0.0497


==13-limit==
Comma list: 40/39, 55/54, 64/63, 66/65
Commas: 55/54, 65/64, 100/99, 105/104


POTE generator: ~10/9 = 165.974
Mapping: {{mapping| 1 2 3 2 4 4 | 0 -3 -5 6 -4 -2 }}
13- and 15-limit minimax eigenmonzo: 3/2


Map: [&lt;1 2 3 1 4 3|, &lt;0 -3 -5 13 -4 5|]
Optimal tunings:  
EDOs: 7, 29, 65cef, 94cdef
* WE: ~2 = 1197.0054{{c}}, ~11/10 = 162.3022{{c}}
Badness: 0.0302
* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 162.8314{{c}}


=Hedgehog=
Minimax tuning:
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.
* 13- and 15-odd-limit: ~10/9 = {{monzo| 1 0 0 0 -1/4 }}
: unchanged-interval (eigenmonzo) basis: 2.11


Commas: 50/49, 245/243
Tuning ranges:  
* 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 tuning|POTE generator]]: ~9/7 = 435.648
{{Optimal ET sequence|legend=0| 7, 15, 22f }}


Map: [&lt;2 1 1 2|, &lt;0 3 5 5|]
Badness (Sintel): 0.879
Wedgie: &lt;&lt;6 10 10 2 -1 -5||
EDOs: 22, [[146edo|146]]
Badness: 0.0440


==11-limit==  
==== Porcupinefish ====
Commas: 50/49, 55/54, 99/98
{{See also| The Biosphere }}


POTE generator: ~9/7 = 435.386
Subgroup: 2.3.5.7.11.13


Map: [&lt;2 1 1 2 4|, &lt;0 3 5 5 4|]
Comma list: 55/54, 64/63, 91/90, 100/99
EDOs: 14c, 22, 58ce, 80ce, 102cde
Badness: 0.0231


==13-limit==
Mapping: {{mapping| 1 2 3 2 4 6 | 0 -3 -5 6 -4 -17 }}
Commas: 50/49, 55/54, 65/63, 99/98


POTE generator: ~9/7 = 435.861
Optimal tunings:  
* WE: ~2 = 1198.3206{{c}}, ~11/10 = 162.0502{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 162.3458{{c}}


Map: [&lt;2 1 1 2 4 3|, &lt;0 3 5 5 4 6|]
Minimax tuning:  
EDOs: 14cf, 22
* 13- and 15-odd-limit: ~10/9 = {{monzo| 2/13 0 0 0 1/13 -1/13 }}
Badness: 0.0215
: unchanged-interval (eigenmonzo) basis: 2.13/11


==Urchin==
Tuning ranges:
Commas: 40/39, 50/49, 55/54, 66/65
* 13-odd-limit diamond monotone: ~11/10 = [160.000, 162.162] (2\15 to 5\37)
* 15-odd-limit diamond monotone: ~11/10 = 162.162 (5\37)
* 13- and 15-odd-limit diamond tradeoff: ~11/10 = [150.637, 182.404]


POTE generator: ~9/7 = 437.078
{{Optimal ET sequence|legend=0| 15, 22, 37 }}


Map: [&lt;2 1 1 2 4 6|, &lt;0 3 5 5 4 2|]
Badness (Sintel): 1.05
EDOs: 14c, 22f
Badness: 0.0252


==Hedgepig==  
==== Pourcup ====
Commas: 50/49, 245/243, 385/384
Subgroup: 2.3.5.7.11.13


POTE generator: ~9/7 = 435.425
Comma list: 55/54, 64/63, 100/99, 196/195


Map: [&lt;2 1 1 2 12|, &lt;0 3 5 5 -7|]
Mapping: {{mapping| 1 2 3 2 4 1 | 0 -3 -5 6 -4 20 }}
EDOs: 22, 80c, 102cd, 124cd
Badness: 0.0684


===Music===
Optimal tunings:
[[http://micro.soonlabel.com/22-ET/20120207-phobos-light-hedgehog14.mp3|Phobos Light]] by Chris Vaisvil in Hedgehog[14] [[hedgehog14|tuned]] to 22edo.
* WE: ~2 = 1198.0537{{c}}, ~11/10 = 162.2183{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 162.4665{{c}}


=Nautilus=
Minimax tuning:
Commas: 49/48, 250/243
* 13- and 15-odd-limit: ~11/10 = {{monzo| 1/14 0 0 -1/14 0 1/14 }}
: unchanged-interval (eigenmonzo) basis: 2.13/7


POTE generator: ~21/20 = 82.505
{{Optimal ET sequence|legend=0| 15f, 22f, 37, 59f }}


Map: [&lt;1 2 3 3|, &lt;0 -6 -10 -3|]
Badness (Sintel): 1.45
Wedgie: &lt;&lt;6 10 3 2 -12 -21||
EDOs: 10, 15, 19, [[29edo|29]], [[102edo|102cd]]


==11-limit==  
==== Porkpie ====
Commas: 49/48, 55/54, 245/242
Subgroup: 2.3.5.7.11.13


POTE generator: ~21/20 = 82.504
Comma list: 55/54, 64/63, 65/63, 100/99


Map: [&lt;1 2 3 3 4|, &lt;0 -6 -10 -3 -8|]
Mapping: {{mapping| 1 2 3 2 4 3 | 0 -3 -5 6 -4 5 }}
EDOs: 10e, 14c, 15, 19, 22d, 29, 102cde


==13-limit==
Optimal tunings:
Commas: 49/48, 55/54, 91/90, 100/99
* WE: ~2 = 1200.0223{{c}}, ~11/10 = 163.6908{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 163.6874{{c}}


POTE generator: ~21/20 = 62.530
Minimax tuning:
* 13- and 15-odd-limit: ~11/10 = {{monzo| 1/6 -1/6 0 1/12 }}
: unchanged-interval (eigenmonzo) basis: 2.9/7


Map: [&lt;1 2 3 3 4 5|, &lt;0 -6 -10 -3 -8 -19|]
{{Optimal ET sequence|legend=0| 7, 15f, 22 }}
EDOs: 10e, 15f, 17d, 19, 22d, 29, 102cde
Badness: 0.0223


==Belauensis==
Badness (Sintel): 1.08
Commas: 40/39, 49/48, 55/54, 66/65


POTE generator: ~21/20 = ~14/13 = 81.759
== Opossum ==
{{Main| Opossum }}


Map: [&lt;1 2 3 3 4 4|, &lt;0 -6 -10 -3 -8 -4|]
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: 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]]
[[Subgroup]]: 2.3.5.7
=Ammonite=
Commas: 250/243, 686/675


POTE generator: ~9/7 = 454.448
[[Comma list]]: 28/27, 126/125


Map: [&lt;1 5 8 10|, &lt;0 -9 -15 -19|]
{{Mapping|legend=1| 1 2 3 4 | 0 -3 -5 -9 }}
Wedgie: &lt;&lt;9 15 19 3 5 2||
EDOs: 29, 37, 66
Badness: 0.1077


==11-limit==  
[[Optimal tuning]]s:
Commas: 55/54, 100/99, 686/675
* [[WE]]: ~2 = 1195.7927{{c}}, ~10/9 = 159.1315{{c}}
: [[error map]]: {{val| -4.207 +12.236 +5.407 -17.838 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~10/9 = 160.4589{{c}}
: error map: {{val| 0.000 +16.668 +11.392 -12.956 }}


POTE generator: ~9/7 = 454.512
[[Minimax tuning]]:  
* [[7-odd-limit|7-]] and [[9-odd-limit]] [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.7


Map: [&lt;1 5 8 10 8|, &lt;0 -9 -15 -19 -12|]
{{Optimal ET sequence|legend=1| 7d, 8d, 15 }}
EDOs: 29, 37, 66
Badness: 0.0457


==13-limit==
[[Badness]] (Sintel): 1.03
Commas: 55/54, 91/90, 100/99, 169/168


POTE generator: ~13/10 = 454.429
=== 11-limit ===
Subgroup: 2.3.5.7.11


Map: [&lt;1 5 8 10 8 9|, &lt;0 -9 -15 -19 -12 -14|]
Comma list: 28/27, 55/54, 77/75
EDOs: 29, 37, 66
Badness: 0.0272


=Ceratitid=
Mapping: {{mapping| 1 2 3 4 4 | 0 -3 -5 -9 -4 }}
Commas: 250/243, 1728/1715


POTE generator: ~36/35 = 54.384
Optimal tunings:  
* WE: ~2 = 1196.2331{{c}}, ~11/10 = 159.3050{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 160.4644{{c}}


Map: [&lt;1 2 3 3|, &lt;0 -9 -15 -4|]
Minimax tuning:  
Wedgie: &lt;&lt;9 15 4 3 -19 -33||
* 11-odd-limit unchanged-interval (eigenmonzo) basis: 2.7
EDOs: 22
Badness: 0.115


==11-limit==
{{Optimal ET sequence|legend=0| 7d, 8d, 15 }}
Commas: 55/54, 100/99, 5324/5145


POTE generator: ~36/35 = 54.376
Badness (Sintel): 0.738


Map: [&lt;1 2 3 3 4|, &lt;0 -9 -15 -4 -12|]
=== 13-limit ===
EDOs: 22
Subgroup: 2.3.5.7.11.13
Badness: 0.0513


==13-limit==
Comma list: 28/27, 40/39, 55/54, 66/65
Commas: 55/54, 65/63, 100/99, 352/343


POTE generator: ~36/35 = 54.665
Mapping: {{mapping| 1 2 3 4 4 4 | 0 -3 -5 -9 -4 -2 }}


Map: [&lt;1 2 3 3 4 4|, &lt;0 -9 -15 -4 -12 -7|]
Optimal tunings:  
EDOs: 22
* WE: ~2 = 1193.5447{{c}}, ~11/10 = 157.9505{{c}}
Badness: 0.0447</pre></div>
* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 159.7600{{c}}
<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: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;
Minimax tuning:  
&lt;!-- ws:end:WikiTextTocRule:91 --&gt;&lt;hr /&gt;
* 13- and 15-odd-limit unchanged-interval (eigenmonzo) basis: 2.7
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;
{{Optimal ET sequence|legend=0| 7d, 8d, 15, 38bceff }}
valid range: [150.000, 171.429] (8 to 7)&lt;br /&gt;
 
nice range: [157.821, 166.015]&lt;br /&gt;
Badness (Sintel): 0.801
strict range: [157.821, 166.015]&lt;br /&gt;
 
&lt;br /&gt;
== Porky ==
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 163.950&lt;br /&gt;
Porky can be described as {{nowrap| 22 & 29 }}, suggesting a less sharp perfect fifth. 7\51 is a good generator.
&lt;br /&gt;
 
Map: [&amp;lt;1 2 3|, &amp;lt;0 -3 -5|]&lt;br /&gt;
[[Subgroup]]: 2.3.5.7
&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;
[[Comma list]]: 225/224, 250/243
Badness: 0.0308&lt;br /&gt;
 
&lt;br /&gt;
{{Mapping|legend=1| 1 2 3 5 | 0 -3 -5 -16 }}
&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;
[[Optimal tuning]]s:  
&lt;br /&gt;
* [[WE]]: ~2 = 1200.0685{{c}}, ~10/9 = 164.4215{{c}}
&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;
: [[error map]]: {{val| +0.068 +4.917 -8.216 +0.772 }}
&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;
* [[CWE]]: ~2 = 1200.0000{{c}}, ~10/9 = 164.4060{{c}}
&lt;br /&gt;
: error map: {{val| 0.000 +4.827 -8.344 +0.678 }}
Commas: 250/243, 64/63&lt;br /&gt;
 
&lt;br /&gt;
[[Minimax tuning]]:  
valid range: [160.000, 163.636] (15 to 22)&lt;br /&gt;
* [[7-odd-limit|7-]] and [[9-odd-limit]]: ~10/9 = {{monzo| 2/11 0 1/11 -1/11 }}
nice range: [157.821, 166.015]&lt;br /&gt;
: [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.7/5
strict range: [160.000, 163.636]&lt;br /&gt;
 
&lt;br /&gt;
{{Optimal ET sequence|legend=1| 7d, 15d, 22, 51, 73c }}
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~10/9 = 162.880&lt;br /&gt;
 
7- and 9-limit minimax eigenmonzo: 9/7&lt;br /&gt;
[[Badness]] (Sintel): 1.38
&lt;br /&gt;
 
Map: [&amp;lt;1 2 3 2|, &amp;lt;0 -3 -5 6|]&lt;br /&gt;
=== 11-limit ===
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;
Subgroup: 2.3.5.7.11
Badness: 0.0411&lt;br /&gt;
 
&lt;br /&gt;
Comma list: 55/54, 100/99, 225/224
&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;
Mapping: {{mapping| 1 2 3 5 4 | 0 -3 -5 -16 -4 }}
&lt;br /&gt;
 
valid range: [160.000, 163.636] (15 to 22)&lt;br /&gt;
Optimal tunings:  
nice range: [150.637, 182.404]&lt;br /&gt;
* WE: ~2 = 1200.8706{{c}}, ~11/10 = 164.6715{{c}}
strict range: [160.000, 163.636]&lt;br /&gt;
* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 164.4810{{c}}
&lt;br /&gt;
 
POTE generator: ~10/9 = 162.747&lt;br /&gt;
Minimax tuning:  
11-limit minimax eigenmonzo: 9/7&lt;br /&gt;
* 11-odd-limit: ~11/10 = {{monzo| 2/11 0 1/11 -1/11 }}
&lt;br /&gt;
: unchanged-interval (eigenmonzo) basis: 2.7/5
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;
{{Optimal ET sequence|legend=0| 7d, 15d, 22, 51 }}
Badness: 0.0217&lt;br /&gt;
 
&lt;br /&gt;
Badness (Sintel): 0.901
&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;
=== 13-limit ===
&lt;br /&gt;
Subgroup: 2.3.5.7.11.13
valid range: [160.000, 163.636] (15 to 22f)&lt;br /&gt;
 
nice range: [138.573, 182.404]&lt;br /&gt;
Comma list: 55/54, 65/64, 91/90, 100/99
strict range: [160.000, 163.636]&lt;br /&gt;
 
&lt;br /&gt;
Mapping: {{mapping| 1 2 3 5 4 3 | 0 -3 -5 -16 -4 5 }}
POTE generator: ~10/9 = 162.708&lt;br /&gt;
 
13- and 15-limit minimax eigenmonzo: 11/8&lt;br /&gt;
Optimal tunings:  
&lt;br /&gt;
* WE: ~2 = 1202.1557{{c}}, ~11/10 = 165.2494{{c}}
Map: [&amp;lt;1 2 3 2 4 4|, &amp;lt;0 -3 -5 6 -4 -2|]&lt;br /&gt;
* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 164.8579{{c}}
EDOs: 7, 15, 22f, 37f&lt;br /&gt;
 
Badness: 0.0213&lt;br /&gt;
{{Optimal ET sequence|legend=0| 7d, 22, 29, 51f, 80cdeff }}
&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;
Badness (Sintel): 1.10
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;
; Music
&lt;br /&gt;
* [https://www.youtube.com/watch?v=CN4cLOyaVGE ''Improvisation in 29edo''] (2024) by [[Budjarn Lambeth]] – in Palace scale, 29edo tuning
valid range: [160.000, 162.162] (15 to 37)&lt;br /&gt;
 
nice range: [150.637, 182.404]&lt;br /&gt;
== Coendou ==
strict range:  [160.000, 162.162]&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;br /&gt;
 
POTE generator: ~10/9 = 162.277&lt;br /&gt;
[[Subgroup]]: 2.3.5.7
13- and 15-limit minimax eigenmonzo: 13/11&lt;br /&gt;
 
&lt;br /&gt;
[[Comma list]]: 250/243, 525/512
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;
{{Mapping|legend=1| 1 2 3 1 | 0 -3 -5 13 }}
&lt;span style="background-color: #ffffff;"&gt;Badness: 0.0253&lt;/span&gt;&lt;br /&gt;
 
Badness: 0.0253&lt;br /&gt;
[[Optimal tuning]]s:  
&lt;br /&gt;
* [[WE]]: ~2 = 1202.6772{{c}}, ~10/9 = 166.4110{{c}}
&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;
: [[error map]]: {{val| +2.678 +4.166 -10.337 -2.806 }}
Commas: 55/54, 64/63, 100/99, 196/195&lt;br /&gt;
* [[CWE]]: ~2 = 1200.0000{{c}}, ~10/9 = 166.0511{{c}}
&lt;br /&gt;
: error map: {{val| 0.000 -0.108 -16.569 -10.161 }}
POTE generator: ~10/9 = 162.482&lt;br /&gt;
 
13- and 15-limit minimax eigenmonzo: 13/7&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 2 3 2 4 1|, &amp;lt;0 -3 -5 6 -4 20|]&lt;br /&gt;
: [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.3
EDOs: 15f, 22f, 37&lt;br /&gt;
 
Badness: 0.0351&lt;br /&gt;
{{Optimal ET sequence|legend=1| 7, 22d, 29, 65c }}
&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;
[[Badness]] (Sintel): 2.99
Commas: 55/54, 64/63, 65/63, 100/99&lt;br /&gt;
 
&lt;br /&gt;
=== 11-limit ===
POTE generator: ~10/9 = 163.688&lt;br /&gt;
Subgroup: 2.3.5.7.11
13- and 15-limit minimax eigenmonzo: 9/7&lt;br /&gt;
 
&lt;br /&gt;
Comma list: 55/54, 100/99, 525/512
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;
Mapping: {{mapping| 1 2 3 1 4 | 0 -3 -5 13 -4 }}
Badness: 0.0260&lt;br /&gt;
 
&lt;br /&gt;
Optimal tunings:  
&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;
* WE: ~2 = 1203.0245{{c}}, ~11/10 = 166.3991{{c}}
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;
* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 165.9714{{c}}
&lt;br /&gt;
 
Commas: 36/35, 160/147&lt;br /&gt;
Minimax tuning:
&lt;br /&gt;
* 11-odd-limit: ~11/10 = {{monzo| 2/3 -1/3 }}
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 158.868&lt;br /&gt;
: unchanged-interval (eigenmonzo) basis: 2.3
7- and 9-limit minimax eigenmonzo: 5/4&lt;br /&gt;
 
&lt;br /&gt;
{{Optimal ET sequence|legend=0| 7, 22d, 29, 65ce }}
Map: [&amp;lt;1 2 3 3|, &amp;lt;0 -3 -5 -1|]&lt;br /&gt;
 
&lt;br /&gt;
Badness (Sintel): 1.64
EDOs: 10d, 12, 13d, 15&lt;br /&gt;
 
Badness: 0.0449&lt;br /&gt;
=== 13-limit ===
&lt;br /&gt;
Subgroup: 2.3.5.7.11.13
&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;
Comma list: 55/54, 65/64, 100/99, 105/104
&lt;br /&gt;
 
POTE generator: ~10/9 = 164.412&lt;br /&gt;
Mapping: {{mapping| 1 2 3 1 4 3 | 0 -3 -5 13 -4 5 }}
7- and 9-limit minimax eigenmonzo: 7/5&lt;br /&gt;
 
&lt;br /&gt;
Optimal tunings:  
Map: [&amp;lt;1 2 3 5|, &amp;lt;0 -3 -5 -16|]&lt;br /&gt;
* WE: ~2 = 1202.9957{{c}}, ~11/10 = 166.3885{{c}}
Wedgie: &amp;lt;&amp;lt;3 5 16 1 17 23||&lt;br /&gt;
* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 165.9843{{c}}
EDOS: 7, 8, 15, 22, 29, 51, 73&lt;br /&gt;
 
Badness: 0.0544&lt;br /&gt;
Minimax tuning:  
&lt;br /&gt;
* 13- and 15-odd-limit: ~11/10 = {{monzo| 2/3 -1/3 }}
&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;
: unchanged-interval (eigenmonzo) basis: 2.3
Commas: 55/54, 100/99, 225/224&lt;br /&gt;
 
&lt;br /&gt;
{{Optimal ET sequence|legend=0| 7, 22d, 29, 65cef }}
POTE generator: ~10/9 = 164.552&lt;br /&gt;
 
11-limit minimax eigenmonzo: 7/5&lt;br /&gt;
Badness (Sintel): 1.25
&lt;br /&gt;
 
Map: [&amp;lt;1 2 3 5 4|, &amp;lt;0 -3 -5 -16 -4|]&lt;br /&gt;
== Hystrix ==
EDOs: 7, 8, 15, 22, 29, 51, 73&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.
Badness: 0.0273&lt;br /&gt;
 
&lt;br /&gt;
[[Subgroup]]: 2.3.5.7
&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;
[[Comma list]]: 36/35, 160/147
&lt;br /&gt;
 
POTE generator: ~10/9 = 164.953&lt;br /&gt;
{{Mapping|legend=1| 1 2 3 3 | 0 -3 -5 -1 }}
&lt;br /&gt;
 
Map: [&amp;lt;1 2 3 5 4 3|, &amp;lt;0 -3 -5 -16 -4 5|]&lt;br /&gt;
[[Optimal tuning]]s:  
EDOs: 22, 29, 51f, 80cdef&lt;br /&gt;
* [[WE]]: ~2 = 1187.8599{{c}}, ~10/9 = 157.2605{{c}}
Badness: 0.0265&lt;br /&gt;
: [[error map]]: {{val| -12.140 +1.983 -9.037 +37.493 }}
&lt;br /&gt;
* [[CWE]]: ~2 = 1200.0000{{c}}, ~10/9 = 161.2833{{c}}
&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;
: error map: {{val| 0.000 +14.195 +7.270 +69.891 }}
Commas: 250/243, 525/512&lt;br /&gt;
 
&lt;br /&gt;
[[Minimax tuning]]:  
POTE generator: ~10/9 = 166.041&lt;br /&gt;
* [[7-odd-limit|7-]] and [[9-odd-limit]]: ~10/9 = {{monzo| 3/5 0 -1/5 }}
7- and 9-limit minimax eigenmonzo: 3/2&lt;br /&gt;
: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.5
&lt;br /&gt;
 
Map: [&amp;lt;1 2 3 1|, &amp;lt;0 -3 -5 13|]&lt;br /&gt;
{{Optimal ET sequence|legend=1| 7, 8d, 15d }}
Wedgie: &amp;lt;&amp;lt;3 5 -13 1 -29 -44||&lt;br /&gt;
 
EDOs: 7, 29, 65c, 94cd&lt;br /&gt;
[[Badness]] (Sintel): 1.14
Badness: 0.1183&lt;br /&gt;
 
&lt;br /&gt;
=== 11-limit ===
&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;
Subgroup: 2.3.5.7.11
Commas: 55/54, 100/99, 525/512&lt;br /&gt;
 
&lt;br /&gt;
Comma list: 22/21, 36/35, 80/77
POTE generator: ~10/9 = 165.981&lt;br /&gt;
 
11-limit minimax eigenmonzo: 3/2 &lt;br /&gt;
Mapping: {{mapping| 1 2 3 3 4 | 0 -3 -5 -1 -4 }}
&lt;br /&gt;
 
Map: [&amp;lt;1 2 3 1 4|, &amp;lt;0 -3 -5 13 -4|]&lt;br /&gt;
Optimal tunings:  
EDOs: 7, 29, 65ce, 94cde&lt;br /&gt;
* WE: ~2 = 1189.2810{{c}}, ~11/10 = 157.3322{{c}}
Badness: 0.0497&lt;br /&gt;
* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 160.9603{{c}}
&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;
{{Optimal ET sequence|legend=0| 7, 8d, 15d }}
Commas: 55/54, 65/64, 100/99, 105/104&lt;br /&gt;
 
&lt;br /&gt;
Badness (Sintel): 0.886
POTE generator: ~10/9 = 165.974&lt;br /&gt;
 
13- and 15-limit minimax eigenmonzo: 3/2&lt;br /&gt;
== Hedgehog ==
&lt;br /&gt;
{{See also| Sensamagic clan | Stearnsmic clan }}
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;
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 alpha-tricot.
Badness: 0.0302&lt;br /&gt;
 
&lt;br /&gt;
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.
&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;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;
[[Subgroup]]: 2.3.5.7
&lt;br /&gt;
 
Commas: 50/49, 245/243&lt;br /&gt;
[[Comma list]]: 50/49, 245/243
&lt;br /&gt;
 
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~9/7 = 435.648&lt;br /&gt;
{{Mapping|legend=1| 2 1 1 2 | 0 3 5 5 }}
&lt;br /&gt;
 
Map: [&amp;lt;2 1 1 2|, &amp;lt;0 3 5 5|]&lt;br /&gt;
: mapping generators: ~7/5, ~9/7
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;
[[Optimal tuning]]s:  
Badness: 0.0440&lt;br /&gt;
* [[WE]]: ~7/5 = 599.6061{{c}}, ~9/7 = 435.3620{{c}}
&lt;br /&gt;
: [[error map]]: {{val| -0.788 +3.737 -9.897 +7.197 }}
&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;
* [[CWE]]: ~7/5 = 600.0000{{c}}, ~9/7 = 435.4483{{c}}
Commas: 50/49, 55/54, 99/98&lt;br /&gt;
: error map: {{val| 0.000 +4.390 -9.072 +8.416 }}
&lt;br /&gt;
 
POTE generator: ~9/7 = 435.386&lt;br /&gt;
{{Optimal ET sequence|legend=1| 8d, 14c, 22 }}
&lt;br /&gt;
 
Map: [&amp;lt;2 1 1 2 4|, &amp;lt;0 3 5 5 4|]&lt;br /&gt;
[[Badness]] (Sintel): 1.11
EDOs: 14c, 22, 58ce, 80ce, 102cde&lt;br /&gt;
 
Badness: 0.0231&lt;br /&gt;
=== 11-limit ===
&lt;br /&gt;
Subgroup: 2.3.5.7.11
&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;
Comma list: 50/49, 55/54, 99/98
&lt;br /&gt;
 
POTE generator: ~9/7 = 435.861&lt;br /&gt;
Mapping: {{mapping| 2 1 1 2 4 | 0 3 5 5 4 }}
&lt;br /&gt;
 
Map: [&amp;lt;2 1 1 2 4 3|, &amp;lt;0 3 5 5 4 6|]&lt;br /&gt;
Optimal tunings:  
EDOs: 14cf, 22&lt;br /&gt;
* WE: ~7/5 = 600.1133{{c}}, ~9/7 = 435.4680{{c}}
Badness: 0.0215&lt;br /&gt;
* CWE: ~7/5 = 600.0000{{c}}, ~9/7 = 435.4431{{c}}
&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;
{{Optimal ET sequence|legend=0| 8d, 14c, 22, 58ce }}
Commas: 40/39, 50/49, 55/54, 66/65&lt;br /&gt;
 
&lt;br /&gt;
Badness (Sintel): 0.764
POTE generator: ~9/7 = 437.078&lt;br /&gt;
 
&lt;br /&gt;
==== 13-limit ====
Map: [&amp;lt;2 1 1 2 4 6|, &amp;lt;0 3 5 5 4 2|]&lt;br /&gt;
Subgroup: 2.3.5.7.11.13
EDOs: 14c, 22f&lt;br /&gt;
 
Badness: 0.0252&lt;br /&gt;
Comma list: 50/49, 55/54, 65/63, 99/98
&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;
Mapping: {{mapping| 2 1 1 2 4 3 | 0 3 5 5 4 6 }}
Commas: 50/49, 245/243, 385/384&lt;br /&gt;
 
&lt;br /&gt;
Optimal tunings:
POTE generator: ~9/7 = 435.425&lt;br /&gt;
* WE: ~7/5 = 600.3651{{c}}, ~9/7 = 436.1258{{c}}
&lt;br /&gt;
* CWE: ~7/5 = 600.0000{{c}}, ~9/7 = 436.0483{{c}}
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 ET sequence|legend=0| 8d, 14cf, 22 }}
Badness: 0.0684&lt;br /&gt;
 
&lt;br /&gt;
Badness (Sintel): 0.889
&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;
==== Urchin ====
&lt;br /&gt;
Subgroup: 2.3.5.7.11.13
&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;
Comma list: 40/39, 50/49, 55/54, 66/65
&lt;br /&gt;
 
POTE generator: ~21/20 = 82.505&lt;br /&gt;
Mapping: {{mapping| 2 1 1 2 4 6 | 0 3 5 5 4 2 }}
&lt;br /&gt;
 
Map: [&amp;lt;1 2 3 3|, &amp;lt;0 -6 -10 -3|]&lt;br /&gt;
Optimal tunings:
Wedgie: &amp;lt;&amp;lt;6 10 3 2 -12 -21||&lt;br /&gt;
* WE: ~7/5 = 598.3303{{c}}, ~9/7 = 435.8617{{c}}
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;
* CWE: ~7/5 = 600.0000{{c}}, ~9/7 = 436.3485{{c}}
&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;
{{Optimal ET sequence|legend=0| 14c, 22f }}
Commas: 49/48, 55/54, 245/242&lt;br /&gt;
 
&lt;br /&gt;
Badness (Sintel): 1.04
POTE generator: ~21/20 = 82.504&lt;br /&gt;
 
&lt;br /&gt;
=== Hedgepig ===
Map: [&amp;lt;1 2 3 3 4|, &amp;lt;0 -6 -10 -3 -8|]&lt;br /&gt;
Subgroup: 2.3.5.7.11
EDOs: 10e, 14c, 15, 19, 22d, 29, 102cde&lt;br /&gt;
 
&lt;br /&gt;
Comma list: 50/49, 245/243, 385/384
&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;
Mapping: {{mapping| 2 1 1 2 12 | 0 3 5 5 -7 }}
&lt;br /&gt;
 
POTE generator: ~21/20 = 62.530&lt;br /&gt;
Optimal tunings:
&lt;br /&gt;
* WE: ~7/5 = 599.7917{{c}}, ~9/7 = 435.2737{{c}}
Map: [&amp;lt;1 2 3 3 4 5|, &amp;lt;0 -6 -10 -3 -8 -19|]&lt;br /&gt;
* CWE: ~7/5 = 600.0000{{c}}, ~9/7 = 435.4047{{c}}
EDOs: 10e, 15f, 17d, 19, 22d, 29, 102cde&lt;br /&gt;
 
Badness: 0.0223&lt;br /&gt;
{{Optimal ET sequence|legend=0| 22 }}
&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;
Badness (Sintel): 2.26
Commas: 40/39, 49/48, 55/54, 66/65&lt;br /&gt;
 
&lt;br /&gt;
; Music
POTE generator: ~21/20 = ~14/13 = 81.759&lt;br /&gt;
* [https://web.archive.org/web/20240624173512/http://micro.soonlabel.com/22-ET/20120207-phobos-light-hedgehog14.mp3 ''Phobos Light''] by [[Chris Vaisvil]] – in [[hedgehog14|Hedgehog[14]]], 22edo tuning.
&lt;br /&gt;
 
Map: [&amp;lt;1 2 3 3 4 4|, &amp;lt;0 -6 -10 -3 -8 -4|]&lt;br /&gt;
== Nautilus ==
EDOs: 14c, 15, 29f, 44df&lt;br /&gt;
Nautilus tempers out 49/48 and may be described as the {{nowrap| 14c & 15 }} temperament. Its ploidacot is omega-hexacot.
Badness: 0.0298&lt;br /&gt;
 
&lt;br /&gt;
[[Subgroup]]: 2.3.5.7
&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;
[[Comma list]]: 49/48, 250/243
Commas: 250/243, 686/675&lt;br /&gt;
 
&lt;br /&gt;
{{Mapping|legend=1| 1 2 3 3 | 0 -6 -10 -3 }}
POTE generator: ~9/7 = 454.448&lt;br /&gt;
 
&lt;br /&gt;
: mapping generators: ~2, ~21/20
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;
[[Optimal tuning]]s:  
EDOs: 29, 37, 66&lt;br /&gt;
* [[WE]]: ~2 = 1202.1642{{c}}, ~21/20 = 82.6542{{c}}
Badness: 0.1077&lt;br /&gt;
: [[error map]]: {{val| +2.164 +6.448 -6.364 -10.296 }}
&lt;br /&gt;
* [[CWE]]: ~2 = 1200.0000{{c}}, ~21/20 = 82.2758{{c}}
&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;
: error map: {{val| 0.000 +4.390 -9.072 -15.653 }}
Commas: 55/54, 100/99, 686/675&lt;br /&gt;
 
&lt;br /&gt;
{{Optimal ET sequence|legend=1| 14c, 15, 29 }}
POTE generator: ~9/7 = 454.512&lt;br /&gt;
 
&lt;br /&gt;
[[Badness]] (Sintel): 1.45
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;
=== 11-limit ===
Badness: 0.0457&lt;br /&gt;
Subgroup: 2.3.5.7.11
&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;
Comma list: 49/48, 55/54, 245/242
Commas: 55/54, 91/90, 100/99, 169/168&lt;br /&gt;
 
&lt;br /&gt;
Mapping: {{mapping| 1 2 3 3 4 | 0 -6 -10 -3 -8 }}
POTE generator: ~13/10 = 454.429&lt;br /&gt;
 
&lt;br /&gt;
Optimal tunings:
Map: [&amp;lt;1 5 8 10 8 9|, &amp;lt;0 -9 -15 -19 -12 -14|]&lt;br /&gt;
* WE: ~2 = 1202.3781{{c}}, ~21/20 = 82.6673{{c}}
EDOs: 29, 37, 66&lt;br /&gt;
* CWE: ~2 = 1200.0000{{c}}, ~21/20 = 82.2434{{c}}
Badness: 0.0272&lt;br /&gt;
 
&lt;br /&gt;
{{Optimal ET sequence|legend=0| 14c, 15, 29 }}
&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;
Badness (Sintel): 0.860
&lt;br /&gt;
 
POTE generator: ~36/35 = 54.384&lt;br /&gt;
==== 13-limit ====
&lt;br /&gt;
Subgroup: 2.3.5.7.11.13
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;
Comma list: 49/48, 55/54, 91/90, 100/99
EDOs: 22&lt;br /&gt;
 
Badness: 0.115&lt;br /&gt;
Mapping: {{mapping| 1 2 3 3 4 5 | 0 -6 -10 -3 -8 -19 }}
&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;
Optimal tunings:
Commas: 55/54, 100/99, 5324/5145&lt;br /&gt;
* WE: ~2 = 1202.4145{{c}}, ~21/20 = 82.6963{{c}}
&lt;br /&gt;
* CWE: ~2 = 1200.0000{{c}}, ~21/20 = 82.3130{{c}}
POTE generator: ~36/35 = 54.376&lt;br /&gt;
 
&lt;br /&gt;
{{Optimal ET sequence|legend=0| 14cf, 15, 29 }}
Map: [&amp;lt;1 2 3 3 4|, &amp;lt;0 -9 -15 -4 -12|]&lt;br /&gt;
 
EDOs: 22&lt;br /&gt;
Badness (Sintel): 0.921
Badness: 0.0513&lt;br /&gt;
 
&lt;br /&gt;
==== Belauensis ====
&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;
Subgroup: 2.3.5.7.11.13
Commas: 55/54, 65/63, 100/99, 352/343&lt;br /&gt;
 
&lt;br /&gt;
Comma list: 40/39, 49/48, 55/54, 66/65
POTE generator: ~36/35 = 54.665&lt;br /&gt;
 
&lt;br /&gt;
Mapping: {{mapping| 1 2 3 3 4 4 | 0 -6 -10 -3 -8 -4 }}
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;
Optimal tunings:  
Badness: 0.0447&lt;/body&gt;&lt;/html&gt;</pre></div>
* WE: ~2 = 1199.0072{{c}}, ~21/20 = 81.6911{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~21/20 = 81.8576{{c}}
 
{{Optimal ET sequence|legend=0| 14c, 15 }}
 
Badness (Sintel): 1.23
 
; Music
* [https://web.archive.org/web/20201127013840/http://micro.soonlabel.com/gene_ward_smith/Others/Igs/NautilusReverie.mp3 ''Nautilus Reverie''] by [[Igliashon Jones]]
 
== Ammonite ==
{{See also|Subgroup temperaments #Ammon}}
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 -4 -7 -9 | 0 9 15 19 }}
 
: mapping generators: ~2, ~14/9
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.3342{{c}}, ~14/9 = 745.1379{{c}}
: [[error map]]: {{val| -0.666 +6.949 -4.584 -5.213 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~14/9 = 745.4994{{c}}
: error map: {{val| 0.000 +7.540 -3.823 -4.337 }}
 
{{Optimal ET sequence|legend=1| 8d, 21cd, 29, 37, 66 }}
 
[[Badness]] (Sintel): 2.73
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 55/54, 100/99, 686/675
 
Mapping: {{mapping| 1 -4 -7 -9 -4 | 0 9 15 19 12 }}
 
Optimal tunings:
* WE: ~2 = 1200.0141{{c}}, ~14/9 = 745.4971{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~14/9 = 745.4894{{c}}
 
{{Optimal ET sequence|legend=0| 8d, 21cde, 29, 37, 66 }}
 
Badness (Sintel): 1.51
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 55/54, 91/90, 100/99, 169/168
 
Mapping: {{mapping| 1 -4 -7 -9 -4 -5 | 0 9 15 19 12 14 }}
 
Optimal tunings:
* WE: ~2 = 1200.2478{{c}}, ~14/9 = 745.6252{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~14/9 = 745.4904{{c}}
 
{{Optimal ET sequence|legend=0| 8d, 21cdef, 29, 37, 66 }}
 
Badness (Sintel): 1.12
 
== 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:  
* [[WE]]: ~2 = 1197.6274{{c}}, ~36/35 = 54.2770{{c}}
: [[error map]]: {{val| -2.373 +4.807 -7.586 +6.948 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~36/35 = 54.5489{{c}}
: error map: {{val| 0.000 +7.105 -4.548 +12.978 }}
 
{{Optimal ET sequence|legend=1| 1c, 21c, 22 }}
 
[[Badness]] (Sintel): 2.92
 
=== 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:  
* WE: ~2 = 1198.2851{{c}}, ~36/35 = 54.2986{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~36/35 = 54.4992{{c}}
 
{{Optimal ET sequence|legend=0| 1ce, 21ce, 22 }}
 
Badness (Sintel): 1.70
 
=== 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:
* WE: ~2 = 1200.3864{{c}}, ~36/35 = 54.6830{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~36/35 = 54.6396{{c}}
 
{{Optimal ET sequence|legend=0| 1ce, 21cef, 22 }}
 
Badness (Sintel): 1.85
 
[[Category:Temperament families]]
[[Category:Porcupine family| ]] <!-- main article -->
[[Category:Porcupine| ]] <!-- key article -->
[[Category:Rank 2]]
Retrieved from "https://en.xen.wiki/w/Porcupine_family"