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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
{{Technical data page}}
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
The '''porcupine family''' of [[regular temperament|temperaments]] [[tempering out|tempers out]] the [[porcupine comma]], [[250/243]], also called the maximal diesis.  
: This revision was by author [[User:jdfreivald|jdfreivald]] and made on <tt>2012-10-08 13:40:17 UTC</tt>.<br>
: The original revision id was <tt>371174480</tt>.<br>
: The revision comment was: <tt></tt><br>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
<h4>Original Wikitext content:</h4>
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">[[toc|flat]]
----
The 5-limit parent comma for the porcupine family is 250/243, the maximal [[diesis]] or porcupine comma. Its [[monzo]] is |1 -5 3&gt;, and flipping that yields &lt;&lt;3 5 1|| for the [[wedgie]]. This tells us the [[generator]] is a minor whole tone, the [[10_9|10/9]] interval, and that three of these add up to a fourth, with two more giving the minor sixth. In fact, (10/9)^3 = 4/3 * 250/243, and (10/9)^5 = 8/5 * (250/243)^2. 3/22 is a very recommendable generator, and MOS of 7, 8 and 15 notes make for some nice scale possibilities.


[[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 [[64_63|Archytas comma]], for [[Porcupine family#Porcupine|porcupine]], [[36_35|36/35]], the [[septimal quarter tone]], for [[Porcupine family#Hystrix|hystrix]], [[50_49|50/49]], the [[jubilisma]], for [[Porcupine family#Hedgehog|hedgehog]], and [[49_48|49/48]], the [[slendro diesis]], for [[Porcupine family#Nautilus|nautilus]].


=Porcupine=
{{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.
: mapping generators: ~2, ~10/9


Commas: 250/243, 64/63
[[Optimal tuning]]s:  
* [[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 }}


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


Map: [&lt;1 2 3 2|, &lt;0 -3 -5 6|]
{{Optimal ET sequence|legend=1| 7, 15, 22, 95c }}
EDOs: 22, [[59edo|59]], [[81edo|81bd]], [[140edo|140bd]]


==11-limit==
[[Badness]] (Sintel): 0.722
Commas: 55/54, 64/63, 100/99


POTE generator: ~10/9 = 162.747
=== Overview to extensions ===
==== 7-limit extensions ====
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.  


Map: [&lt;1 2 3 2 4|, &lt;0 -3 -5 6 -4|]
Those all share the same generator with porcupine.  
EDOs: [[7edo|7]], 15, 22, [[37edo|37]], [[59edo|59]]
Badness: 0.0217


==13-limit==
[[#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.
Commas: 40/39, 55/54, 64/63, 66/65


POTE generator: ~10/9 = 162.708
Temperaments discussed elsewhere include:  
* ''[[Oxygen]]'' → [[Very low accuracy temperaments #Oxygen|Very low accuracy temperaments]]
* ''[[Jamesbond]]'' → [[Whitewood family #Jamesbond|Whitewood family]]


Map: [&lt;1 2 3 2 4 4|, &lt;0 -3 -5 6 -4 -2|]
==== Subgroup extensions ====
EDOs: 7, 15, 22f, 37f
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: 0.0213


==Porcupinefish==  
=== 2.3.5.11 subgroup (porkypine) ===
See also: [[The Biosphere]]
Subgroup: 2.3.5.11
Commas: 55/54, 64/63, 91/90, 100/99


POTE generator: ~10/9 = 162.277
Comma list: 55/54, 100/99


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


==???==
Gencom mapping: {{mapping| 1 2 3 0 4 | 0 -3 -5 0 -4 }}
Commas: 55/54, 64/63, 100/99, 196/195


POTE generator: ~10/9 = 162.482
Optimal tunings:  
* WE: ~2 = 1200.3290{{c}}, ~11/10 = 164.1227{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 163.9951{{c}}


Map: [&lt;1 2 3 2 4 1|, &lt;0 -3 -5 6 -4 20|]
{{Optimal ET sequence|legend=0| 7, 15, 22, 73ce, 95ce }}
EDOs: 15f, 22f, 37
Badness:


==Porkpie==
Badness (Sintel): 0.303
Commas: 55/54, 64/63, 65/63, 100/99


POTE generator: ~10/9 = 163.688
== Septimal porcupine ==
{{Main| Porcupine }}


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


=Hystrix=
[[Subgroup]]: 2.3.5.7
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.


Commas: 36/35, 160/147
[[Comma list]]: 64/63, 250/243


[[POTE tuning|POTE generator]]: 158.868
{{Mapping|legend=1| 1 2 3 2 | 0 -3 -5 6 }}


Map: [&lt;1 2 3 3|, &lt;0 -3 -5 -1|]
[[Optimal tuning]]s:  
* [[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 }}


EDOs: 10d, 12, 13d, 15
[[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


=Hedgehog=
[[Tuning ranges]]:
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.
* 7- and 9-odd-limit [[diamond monotone]]: ~10/9 = [160.000, 163.636] (2\15 to 3\22)
* 7-odd-limit [[diamond tradeoff]]: ~10/9 = [157.821, 166.015]
* 9-odd-limit diamond tradeoff: ~10/9 = [157.821, 182.404]


Commas: 50/49, 245/243
{{Optimal ET sequence|legend=1| 7, 15, 22, 37, 59, 81bd }}


[[POTE tuning|POTE generator]]: ~9/7 = 435.648
[[Badness]] (Sintel): 1.04


Map: [&lt;2 1 1 2|, &lt;0 3 5 5|]
=== 11-limit ===
Wedgie: &lt;&lt;6 10 10 2 -1 -5||
Subgroup: 2.3.5.7.11
EDOs: 22, [[146edo|146]]
Badness: 0.0440


==11-limit==
Comma list: 55/54, 64/63, 100/99
Commas: 50/49, 55/54, 99/98


POTE generator: ~9/7 = 435.386
Mapping: {{mapping| 1 2 3 2 4 | 0 -3 -5 6 -4 }}


Map: [&lt;2 1 1 2 4|, &lt;0 3 5 5 4|]
Optimal tunings:  
EDOs: 14c, 22, 58ce, 80ce, 102cde
* WE: ~2 = 1198.3250{{c}}, ~11/10 = 162.5202{{c}}
Badness: 0.0231
* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 162.8156{{c}}


==13-limit==
Minimax tuning:
Commas: 50/49, 55/54, 65/63, 99/98
* 11-odd-limit: ~11/10 = {{monzo| 1/6 -1/6 0 1/12 }}
: unchanged-interval (eigenmonzo) basis: 2.9/7


POTE generator: ~9/7 = 435.861
Tuning ranges:
* 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;2 1 1 2 4 3|, &lt;0 3 5 5 4 6|]
{{Optimal ET sequence|legend=0| 7, 15, 22, 37, 59 }}
EDOs: 14cf, 22
Badness: 0.0215


==Urchin==
Badness (Sintel): 0.713
Commas: 40/39, 50/49, 55/54, 66/65


POTE generator: ~9/7 = 437.078
==== Porcupinefowl ====
This extension used to be ''tridecimal porcupine''.  


Map: [&lt;2 1 1 2 4 6|, &lt;0 3 5 5 4 2|]
Subgroup: 2.3.5.7.11.13
EDOs: 14c, 22f
Badness: 0.0252


==Hedgepig==
Comma list: 40/39, 55/54, 64/63, 66/65
Commas: 50/49, 245/243, 385/384


POTE generator: ~9/7 = 435.425
Mapping: {{mapping| 1 2 3 2 4 4 | 0 -3 -5 6 -4 -2 }}


Map: [&lt;2 1 1 2 12|, &lt;0 3 5 5 -7|]
Optimal tunings:  
EDOs: 22, 80c, 102cd, 124cd
* WE: ~2 = 1197.0054{{c}}, ~11/10 = 162.3022{{c}}
Badness: 0.0684
* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 162.8314{{c}}


===Music===
Minimax tuning:
[[http://micro.soonlabel.com/22-ET/20120207-phobos-light-hedgehog14.mp3|Phobos Light]] by Chris Vaisvil in Hedgehog[14] [[hedgehog14|tuned]] to 22edo.
* 13- and 15-odd-limit: ~10/9 = {{monzo| 1 0 0 0 -1/4 }}
: unchanged-interval (eigenmonzo) basis: 2.11


=Nautilus=  
Tuning ranges:
Commas: 49/48, 250/243
* 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: ~21/20 = 82.505
{{Optimal ET sequence|legend=0| 7, 15, 22f }}


Map: [&lt;1 2 3 3|, &lt;0 -6 -10 -3|]
Badness (Sintel): 0.879
Wedgie: &lt;&lt;6 10 3 2 -12 -21||
EDOs: 10, 15, 19, [[29edo|29]], [[102edo|102cd]]


==11-limit==  
==== Porcupinefish ====
Commas: 49/48, 55/54, 245/242
{{See also| The Biosphere }}


POTE generator: ~21/20 = 82.504
Subgroup: 2.3.5.7.11.13


Map: [&lt;1 2 3 3 4|, &lt;0 -6 -10 -3 -8|]
Comma list: 55/54, 64/63, 91/90, 100/99
EDOs: 10e, 14c, 15, 19, 22d, 29, 102cde


==13-limit==
Mapping: {{mapping| 1 2 3 2 4 6 | 0 -3 -5 6 -4 -17 }}
Commas: 49/48, 55/54, 91/90, 100/99


POTE generator: ~21/20 = 62.530
Optimal tunings:  
* WE: ~2 = 1198.3206{{c}}, ~11/10 = 162.0502{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 162.3458{{c}}


Map: [&lt;1 2 3 3 4 5|, &lt;0 -6 -10 -3 -8 -19|]
Minimax tuning:  
EDOs: 10e, 15f, 17d, 19, 22d, 29, 102cde
* 13- and 15-odd-limit: ~10/9 = {{monzo| 2/13 0 0 0 1/13 -1/13 }}
Badness: 0.0223
: unchanged-interval (eigenmonzo) basis: 2.13/11


==Belauensis==
Tuning ranges:
Commas: 40/39, 49/48, 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: ~21/20 = ~14/13 = 81.759
{{Optimal ET sequence|legend=0| 15, 22, 37 }}


Map: [&lt;1 2 3 3 4 4|, &lt;0 -6 -10 -3 -8 -4|]
Badness (Sintel): 1.05
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]]
==== Pourcup ====
=Ammonite=
Subgroup: 2.3.5.7.11.13
Commas: 250/243, 686/675


POTE generator: ~9/7 = 454.448
Comma list: 55/54, 64/63, 100/99, 196/195


Map: [&lt;1 5 8 10|, &lt;0 -9 -15 -19|]
Mapping: {{mapping| 1 2 3 2 4 1 | 0 -3 -5 6 -4 20 }}
Wedgie: &lt;&lt;9 15 19 3 5 2||
EDOs: 29, 37, 66
Badness: 0.1077


==11-limit==  
Optimal tunings:
Commas: 55/54, 100/99, 686/675
* WE: ~2 = 1198.0537{{c}}, ~11/10 = 162.2183{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 162.4665{{c}}


POTE generator: ~9/7 = 454.512
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 5 8 10 8|, &lt;0 -9 -15 -19 -12|]
{{Optimal ET sequence|legend=0| 15f, 22f, 37, 59f }}
EDOs: 29, 37, 66
Badness: 0.0457


==13-limit==
Badness (Sintel): 1.45
Commas: 55/54, 91/90, 100/99, 169/168


POTE generator: ~13/10 = 454.429
==== Porkpie ====
Subgroup: 2.3.5.7.11.13


Map: [&lt;1 5 8 10 8 9|, &lt;0 -9 -15 -19 -12 -14|]
Comma list: 55/54, 64/63, 65/63, 100/99
EDOs: 29, 37, 66
Badness: 0.0272


=Ceratitid=
Mapping: {{mapping| 1 2 3 2 4 3 | 0 -3 -5 6 -4 5 }}
Commas: 250/243, 1728/1715


POTE generator: ~36/35 = 54.384
Optimal tunings:  
* WE: ~2 = 1200.0223{{c}}, ~11/10 = 163.6908{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 163.6874{{c}}


Map: [&lt;1 2 3 3|, &lt;0 -9 -15 -4|]
Minimax tuning:  
Wedgie: &lt;&lt;9 15 4 3 -19 -33||
* 13- and 15-odd-limit: ~11/10 = {{monzo| 1/6 -1/6 0 1/12 }}
EDOs: 22
: unchanged-interval (eigenmonzo) basis: 2.9/7
Badness: 0.115


==11-limit==
{{Optimal ET sequence|legend=0| 7, 15f, 22 }}
Commas: 55/54, 100/99, 5324/5145


POTE generator: ~36/35 = 54.376
Badness (Sintel): 1.08


Map: [&lt;1 2 3 3 4|, &lt;0 -9 -15 -4 -12|]
==== Undecimation ====
EDOs: 22
This weak extension is used by most patent vals that support porcupine and tune 13 well.
Badness: 0.0513


==13-limit==
Subgroup: 2.3.5.7.11.13
Commas: 55/54, 65/63, 100/99, 352/343


POTE generator: ~36/35 = 54.665
Comma list: 55/54, 64/63, 100/99, 169/168


Map: [&lt;1 2 3 3 4 4|, &lt;0 -9 -15 -4 -12 -7|]
Mapping: {{mapping| 1 -1 -2 8 0 5 | 0 6 10 -12 8 -3 }}
EDOs: 22
: mapping generators: ~2, ~35/26
Badness: 0.0447


=Porky=  
Optimal tunings:
Commas: 225/224, 250/243
* WE: ~2 = 1198.4569{{c}}, ~35/26 = 517.9375{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~35/26 = 518.5822{{c}}


POTE generator: ~10/9 = 164.412
{{Optimal ET sequence|legend=0| 7, 30, 37, 81bd }}


Map: [&lt;1 2 3 5|, &lt;0 -3 -5 -16|]
Badness (Sintel): 1.68
Wedgie: &lt;&lt;3 5 16 1 17 23||
EDOS: 7, 8, 15, 22, 29, 51, 73
Badness: 0.0544


==11-limit==  
== Opossum ==
Commas: 55/54, 100/99, 225/224
{{Main| Opossum }}


POTE generator: ~10/9 = 164.552
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.  


Map: [&lt;1 2 3 5 4|, &lt;0 -3 -5 -16 -4|]
[[Subgroup]]: 2.3.5.7
EDOs: 7, 8, 15, 22, 29, 51, 73
Badness: 0.0273


=Coendou=
[[Comma list]]: 28/27, 126/125
Commas: 250/243, 525/512


POTE generator: ~10/9 = 166.041
{{Mapping|legend=1| 1 2 3 4 | 0 -3 -5 -9 }}


Map: [&lt;1 2 3 1|, &lt;0 -3 -5 13|]
[[Optimal tuning]]s:  
Wedgie: &lt;&lt;3 5 -13 1 -29 -44||
* [[WE]]: ~2 = 1195.7927{{c}}, ~10/9 = 159.1315{{c}}
EDOs: 7, 29, 65c, 94cd
: [[error map]]: {{val| -4.207 +12.236 +5.407 -17.838 }}
Badness: 0.1183
* [[CWE]]: ~2 = 1200.0000{{c}}, ~10/9 = 160.4589{{c}}
: error map: {{val| 0.000 +16.668 +11.392 -12.956 }}


==11-limit==
[[Minimax tuning]]:
Commas: 55/54, 100/99, 525/512
* [[7-odd-limit|7-]] and [[9-odd-limit]] [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.7


POTE generator: ~10/9 = 165.981
{{Optimal ET sequence|legend=1| 7d, 8d, 15 }}


Map: [&lt;1 2 3 1 4|, &lt;0 -3 -5 13 -4|]
[[Badness]] (Sintel): 1.03
EDOs: 7, 29, 65ce, 94cde
Badness: 0.0497


==13-limit==  
=== 11-limit ===
Commas: 55/54, 65/64, 100/99, 105/104
Subgroup: 2.3.5.7.11


POTE generator: ~10/9 = 165.974
Comma list: 28/27, 55/54, 77/75


Map: [&lt;1 2 3 1 4 3|, &lt;0 -3 -5 13 -4 5|]
Mapping: {{mapping| 1 2 3 4 4 | 0 -3 -5 -9 -4 }}
EDOs: 7, 29, 65cef, 94cdef
 
Badness: 0.0302</pre></div>
Optimal tunings:  
<h4>Original HTML content:</h4>
* WE: ~2 = 1196.2331{{c}}, ~11/10 = 159.3050{{c}}
<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:58:&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:58 --&gt;&lt;!-- ws:start:WikiTextTocRule:59: --&gt;&lt;!-- ws:end:WikiTextTocRule:59 --&gt;&lt;!-- ws:start:WikiTextTocRule:60: --&gt; | &lt;a href="#Porcupine"&gt;Porcupine&lt;/a&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;!-- 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;a href="#Hystrix"&gt;Hystrix&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:66 --&gt;&lt;!-- ws:start:WikiTextTocRule:67: --&gt; | &lt;a href="#Hedgehog"&gt;Hedgehog&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;&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;!-- ws:end:WikiTextTocRule:72 --&gt;&lt;!-- ws:start:WikiTextTocRule:73: --&gt; | &lt;a href="#Nautilus"&gt;Nautilus&lt;/a&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;!-- ws:end:WikiTextTocRule:75 --&gt;&lt;!-- ws:start:WikiTextTocRule:76: --&gt;&lt;!-- ws:end:WikiTextTocRule:76 --&gt;&lt;!-- ws:start:WikiTextTocRule:77: --&gt; | &lt;a href="#Ammonite"&gt;Ammonite&lt;/a&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;a href="#Ceratitid"&gt;Ceratitid&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:80 --&gt;&lt;!-- ws:start:WikiTextTocRule:81: --&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;a href="#Porky"&gt;Porky&lt;/a&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="#Coendou"&gt;Coendou&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;
* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 160.4644{{c}}
&lt;!-- ws:end:WikiTextTocRule:88 --&gt;&lt;hr /&gt;
 
The 5-limit parent comma for the porcupine family is 250/243, the maximal &lt;a class="wiki_link" href="/diesis"&gt;diesis&lt;/a&gt; or porcupine comma. Its &lt;a class="wiki_link" href="/monzo"&gt;monzo&lt;/a&gt; is |1 -5 3&amp;gt;, and flipping that yields &amp;lt;&amp;lt;3 5 1|| for the &lt;a class="wiki_link" href="/wedgie"&gt;wedgie&lt;/a&gt;. This tells us the &lt;a class="wiki_link" href="/generator"&gt;generator&lt;/a&gt; is a minor whole tone, the &lt;a class="wiki_link" href="/10_9"&gt;10/9&lt;/a&gt; interval, and that three of these add up to a fourth, with two more giving the minor sixth. In fact, (10/9)^3 = 4/3 * 250/243, and (10/9)^5 = 8/5 * (250/243)^2. 3/22 is a very recommendable generator, and MOS of 7, 8 and 15 notes make for some nice scale possibilities.&lt;br /&gt;
Minimax tuning:  
&lt;br /&gt;
* 11-odd-limit unchanged-interval (eigenmonzo) basis: 2.7
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 163.950&lt;br /&gt;
 
&lt;br /&gt;
{{Optimal ET sequence|legend=0| 7d, 8d, 15 }}
Map: [&amp;lt;1 2 3|, &amp;lt;0 -3 -5|]&lt;br /&gt;
 
&lt;br /&gt;
Badness (Sintel): 0.738
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;
 
&lt;br /&gt;
=== 13-limit ===
&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;
Subgroup: 2.3.5.7.11.13
The second comma of the &lt;a class="wiki_link" href="/Normal%20lists"&gt;normal comma list&lt;/a&gt; defines which &lt;a class="wiki_link" href="/7-limit"&gt;7-limit&lt;/a&gt; family member we are looking at. That means &lt;a class="wiki_link" href="/64_63"&gt;64/63&lt;/a&gt;, the &lt;a class="wiki_link" href="/64_63"&gt;Archytas comma&lt;/a&gt;, for &lt;a class="wiki_link" href="/Porcupine%20family#Porcupine"&gt;porcupine&lt;/a&gt;, &lt;a class="wiki_link" href="/36_35"&gt;36/35&lt;/a&gt;, the &lt;a class="wiki_link" href="/septimal%20quarter%20tone"&gt;septimal quarter tone&lt;/a&gt;, for &lt;a class="wiki_link" href="/Porcupine%20family#Hystrix"&gt;hystrix&lt;/a&gt;, &lt;a class="wiki_link" href="/50_49"&gt;50/49&lt;/a&gt;, the &lt;a class="wiki_link" href="/jubilisma"&gt;jubilisma&lt;/a&gt;, for &lt;a class="wiki_link" href="/Porcupine%20family#Hedgehog"&gt;hedgehog&lt;/a&gt;, and &lt;a class="wiki_link" href="/49_48"&gt;49/48&lt;/a&gt;, the &lt;a class="wiki_link" href="/slendro%20diesis"&gt;slendro diesis&lt;/a&gt;, for &lt;a class="wiki_link" href="/Porcupine%20family#Nautilus"&gt;nautilus&lt;/a&gt;.&lt;br /&gt;
 
&lt;br /&gt;
Comma list: 28/27, 40/39, 55/54, 66/65
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Porcupine"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Porcupine&lt;/h1&gt;
 
&lt;a class="wiki_link" href="/Porcupine"&gt;Porcupine&lt;/a&gt;, with wedgie &amp;lt;&amp;lt;3 5 -6 1 -18 -28||, uses six of its minor tone generator steps to get to &lt;a class="wiki_link" href="/7_4"&gt;7/4&lt;/a&gt;. For this to work you need a small minor tone such as &lt;a class="wiki_link" href="/22edo"&gt;22edo&lt;/a&gt; provides, and once again 3\22 is a good tuning choice, though we might pick in preference 8\59, 11\81, or 19\140 for our generator.&lt;br /&gt;
Mapping: {{mapping| 1 2 3 4 4 4 | 0 -3 -5 -9 -4 -2 }}
&lt;br /&gt;
 
Commas: 250/243, 64/63&lt;br /&gt;
Optimal tunings:  
&lt;br /&gt;
* WE: ~2 = 1193.5447{{c}}, ~11/10 = 157.9505{{c}}
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~10/9 = 162.880&lt;br /&gt;
* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 159.7600{{c}}
&lt;br /&gt;
 
Map: [&amp;lt;1 2 3 2|, &amp;lt;0 -3 -5 6|]&lt;br /&gt;
Minimax tuning:
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;
* 13- and 15-odd-limit unchanged-interval (eigenmonzo) basis: 2.7
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="Porcupine-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;11-limit&lt;/h2&gt;
{{Optimal ET sequence|legend=0| 7d, 8d, 15, 38bceff }}
Commas: 55/54, 64/63, 100/99&lt;br /&gt;
 
&lt;br /&gt;
Badness (Sintel): 0.801
POTE generator: ~10/9 = 162.747&lt;br /&gt;
 
&lt;br /&gt;
== Porky ==
Map: [&amp;lt;1 2 3 2 4|, &amp;lt;0 -3 -5 6 -4|]&lt;br /&gt;
Porky can be described as {{nowrap| 22 & 29 }}, suggesting a less sharp perfect fifth. 7\51 is a good generator.
EDOs: &lt;a class="wiki_link" href="/7edo"&gt;7&lt;/a&gt;, 15, 22, &lt;a class="wiki_link" href="/37edo"&gt;37&lt;/a&gt;, &lt;a class="wiki_link" href="/59edo"&gt;59&lt;/a&gt;&lt;br /&gt;
 
Badness: 0.0217&lt;br /&gt;
[[Subgroup]]: 2.3.5.7
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="Porcupine-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;13-limit&lt;/h2&gt;
[[Comma list]]: 225/224, 250/243
Commas: 40/39, 55/54, 64/63, 66/65&lt;br /&gt;
 
&lt;br /&gt;
{{Mapping|legend=1| 1 2 3 5 | 0 -3 -5 -16 }}
POTE generator: ~10/9 = 162.708&lt;br /&gt;
 
&lt;br /&gt;
[[Optimal tuning]]s:  
Map: [&amp;lt;1 2 3 2 4 4|, &amp;lt;0 -3 -5 6 -4 -2|]&lt;br /&gt;
* [[WE]]: ~2 = 1200.0685{{c}}, ~10/9 = 164.4215{{c}}
EDOs: 7, 15, 22f, 37f&lt;br /&gt;
: [[error map]]: {{val| +0.068 +4.917 -8.216 +0.772 }}
Badness: 0.0213&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 }}
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="Porcupine-Porcupinefish"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Porcupinefish&lt;/h2&gt;
 
See also: &lt;a class="wiki_link" href="/The%20Biosphere"&gt;The Biosphere&lt;/a&gt;&lt;br /&gt;
[[Minimax tuning]]:  
Commas: 55/54, 64/63, 91/90, 100/99&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: ~10/9 = 162.277&lt;br /&gt;
 
&lt;br /&gt;
{{Optimal ET sequence|legend=1| 7d, 15d, 22, 51, 73c }}
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;
[[Badness]] (Sintel): 1.38
&lt;span style="background-color: #ffffff;"&gt;Badness: 0.0253&lt;/span&gt;&lt;br /&gt;
 
&lt;br /&gt;
=== 11-limit ===
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc5"&gt;&lt;a name="Porcupine-???"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;???&lt;/h2&gt;
Subgroup: 2.3.5.7.11
Commas: 55/54, 64/63, 100/99, 196/195&lt;br /&gt;
 
&lt;br /&gt;
Comma list: 55/54, 100/99, 225/224
POTE generator: ~10/9 = 162.482&lt;br /&gt;
 
&lt;br /&gt;
Mapping: {{mapping| 1 2 3 5 4 | 0 -3 -5 -16 -4 }}
Map: [&amp;lt;1 2 3 2 4 1|, &amp;lt;0 -3 -5 6 -4 20|]&lt;br /&gt;
 
EDOs: 15f, 22f, 37&lt;br /&gt;
Optimal tunings:  
Badness:&lt;br /&gt;
* WE: ~2 = 1200.8706{{c}}, ~11/10 = 164.6715{{c}}
&lt;br /&gt;
* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 164.4810{{c}}
&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc6"&gt;&lt;a name="Porcupine-Porkpie"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;Porkpie&lt;/h2&gt;
 
Commas: 55/54, 64/63, 65/63, 100/99&lt;br /&gt;
Minimax tuning:  
&lt;br /&gt;
* 11-odd-limit: ~11/10 = {{monzo| 2/11 0 1/11 -1/11 }}
POTE generator: ~10/9 = 163.688&lt;br /&gt;
: unchanged-interval (eigenmonzo) basis: 2.7/5
&lt;br /&gt;
 
Map: [&amp;lt;1 2 3 2 4 3|, &amp;lt;0 -3 -5 6 -4 5|]&lt;br /&gt;
{{Optimal ET sequence|legend=0| 7d, 15d, 22, 51 }}
EDOs: 7, 15f, 22&lt;br /&gt;
 
Badness: 0.0260&lt;br /&gt;
Badness (Sintel): 0.901
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc7"&gt;&lt;a name="Hystrix"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;Hystrix&lt;/h1&gt;
=== 13-limit ===
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;
Subgroup: 2.3.5.7.11.13
&lt;br /&gt;
 
Commas: 36/35, 160/147&lt;br /&gt;
Comma list: 55/54, 65/64, 91/90, 100/99
&lt;br /&gt;
 
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 158.868&lt;br /&gt;
Mapping: {{mapping| 1 2 3 5 4 3 | 0 -3 -5 -16 -4 5 }}
&lt;br /&gt;
 
Map: [&amp;lt;1 2 3 3|, &amp;lt;0 -3 -5 -1|]&lt;br /&gt;
Optimal tunings:  
&lt;br /&gt;
* WE: ~2 = 1202.1557{{c}}, ~11/10 = 165.2494{{c}}
EDOs: 10d, 12, 13d, 15&lt;br /&gt;
* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 164.8579{{c}}
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc8"&gt;&lt;a name="Hedgehog"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;Hedgehog&lt;/h1&gt;
{{Optimal ET sequence|legend=0| 7d, 22, 29, 51f, 80cdeff }}
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;
Badness (Sintel): 1.10
Commas: 50/49, 245/243&lt;br /&gt;
 
&lt;br /&gt;
; Music
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~9/7 = 435.648&lt;br /&gt;
* [https://www.youtube.com/watch?v=CN4cLOyaVGE ''Improvisation in 29edo''] (2024) by [[Budjarn Lambeth]] – in Palace scale, 29edo tuning
&lt;br /&gt;
 
Map: [&amp;lt;2 1 1 2|, &amp;lt;0 3 5 5|]&lt;br /&gt;
== Coendou ==
Wedgie: &amp;lt;&amp;lt;6 10 10 2 -1 -5||&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.
EDOs: 22, &lt;a class="wiki_link" href="/146edo"&gt;146&lt;/a&gt;&lt;br /&gt;
 
Badness: 0.0440&lt;br /&gt;
[[Subgroup]]: 2.3.5.7
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc9"&gt;&lt;a name="Hedgehog-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;11-limit&lt;/h2&gt;
[[Comma list]]: 250/243, 525/512
Commas: 50/49, 55/54, 99/98&lt;br /&gt;
 
&lt;br /&gt;
{{Mapping|legend=1| 1 2 3 1 | 0 -3 -5 13 }}
POTE generator: ~9/7 = 435.386&lt;br /&gt;
 
&lt;br /&gt;
[[Optimal tuning]]s:
Map: [&amp;lt;2 1 1 2 4|, &amp;lt;0 3 5 5 4|]&lt;br /&gt;
* [[WE]]: ~2 = 1202.6772{{c}}, ~10/9 = 166.4110{{c}}
EDOs: 14c, 22, 58ce, 80ce, 102cde&lt;br /&gt;
: [[error map]]: {{val| +2.678 +4.166 -10.337 -2.806 }}
Badness: 0.0231&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 }}
&lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc10"&gt;&lt;a name="Hedgehog-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;13-limit&lt;/h2&gt;
 
Commas: 50/49, 55/54, 65/63, 99/98&lt;br /&gt;
[[Minimax tuning]]:  
&lt;br /&gt;
* [[7-odd-limit|7-]] and [[9-odd-limit]]: ~10/9 = {{monzo| 2/3 -1/3 }}
POTE generator: ~9/7 = 435.861&lt;br /&gt;
: [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.3
&lt;br /&gt;
 
Map: [&amp;lt;2 1 1 2 4 3|, &amp;lt;0 3 5 5 4 6|]&lt;br /&gt;
{{Optimal ET sequence|legend=1| 7, 22d, 29, 65c }}
EDOs: 14cf, 22&lt;br /&gt;
 
Badness: 0.0215&lt;br /&gt;
[[Badness]] (Sintel): 2.99
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:22:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc11"&gt;&lt;a name="Hedgehog-Urchin"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:22 --&gt;Urchin&lt;/h2&gt;
=== 11-limit ===
Commas: 40/39, 50/49, 55/54, 66/65&lt;br /&gt;
Subgroup: 2.3.5.7.11
&lt;br /&gt;
 
POTE generator: ~9/7 = 437.078&lt;br /&gt;
Comma list: 55/54, 100/99, 525/512
&lt;br /&gt;
 
Map: [&amp;lt;2 1 1 2 4 6|, &amp;lt;0 3 5 5 4 2|]&lt;br /&gt;
Mapping: {{mapping| 1 2 3 1 4 | 0 -3 -5 13 -4 }}
EDOs: 14c, 22f&lt;br /&gt;
 
Badness: 0.0252&lt;br /&gt;
Optimal tunings:
&lt;br /&gt;
* WE: ~2 = 1203.0245{{c}}, ~11/10 = 166.3991{{c}}
&lt;!-- ws:start:WikiTextHeadingRule:24:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc12"&gt;&lt;a name="Hedgehog-Hedgepig"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:24 --&gt;Hedgepig&lt;/h2&gt;
* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 165.9714{{c}}
Commas: 50/49, 245/243, 385/384&lt;br /&gt;
 
&lt;br /&gt;
Minimax tuning:  
POTE generator: ~9/7 = 435.425&lt;br /&gt;
* 11-odd-limit: ~11/10 = {{monzo| 2/3 -1/3 }}
&lt;br /&gt;
: unchanged-interval (eigenmonzo) basis: 2.3
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| 7, 22d, 29, 65ce }}
Badness: 0.0684&lt;br /&gt;
 
&lt;br /&gt;
Badness (Sintel): 1.64
&lt;!-- ws:start:WikiTextHeadingRule:26:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc13"&gt;&lt;a name="Hedgehog-Hedgepig-Music"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:26 --&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;
=== 13-limit ===
&lt;br /&gt;
Subgroup: 2.3.5.7.11.13
&lt;!-- ws:start:WikiTextHeadingRule:28:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc14"&gt;&lt;a name="Nautilus"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:28 --&gt;Nautilus&lt;/h1&gt;
 
Commas: 49/48, 250/243&lt;br /&gt;
Comma list: 55/54, 65/64, 100/99, 105/104
&lt;br /&gt;
 
POTE generator: ~21/20 = 82.505&lt;br /&gt;
Mapping: {{mapping| 1 2 3 1 4 3 | 0 -3 -5 13 -4 5 }}
&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: ~2 = 1202.9957{{c}}, ~11/10 = 166.3885{{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: ~2 = 1200.0000{{c}}, ~11/10 = 165.9843{{c}}
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:30:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc15"&gt;&lt;a name="Nautilus-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:30 --&gt;11-limit&lt;/h2&gt;
Minimax tuning:  
Commas: 49/48, 55/54, 245/242&lt;br /&gt;
* 13- and 15-odd-limit: ~11/10 = {{monzo| 2/3 -1/3 }}
&lt;br /&gt;
: unchanged-interval (eigenmonzo) basis: 2.3
POTE generator: ~21/20 = 82.504&lt;br /&gt;
 
&lt;br /&gt;
{{Optimal ET sequence|legend=0| 7, 22d, 29, 65cef }}
Map: [&amp;lt;1 2 3 3 4|, &amp;lt;0 -6 -10 -3 -8|]&lt;br /&gt;
 
EDOs: 10e, 14c, 15, 19, 22d, 29, 102cde&lt;br /&gt;
Badness (Sintel): 1.25
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:32:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc16"&gt;&lt;a name="Nautilus-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:32 --&gt;13-limit&lt;/h2&gt;
== Hystrix ==
Commas: 49/48, 55/54, 91/90, 100/99&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;
 
POTE generator: ~21/20 = 62.530&lt;br /&gt;
[[Subgroup]]: 2.3.5.7
&lt;br /&gt;
 
Map: [&amp;lt;1 2 3 3 4 5|, &amp;lt;0 -6 -10 -3 -8 -19|]&lt;br /&gt;
[[Comma list]]: 36/35, 160/147
EDOs: 10e, 15f, 17d, 19, 22d, 29, 102cde&lt;br /&gt;
 
Badness: 0.0223&lt;br /&gt;
{{Mapping|legend=1| 1 2 3 3 | 0 -3 -5 -1 }}
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:34:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc17"&gt;&lt;a name="Nautilus-Belauensis"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:34 --&gt;Belauensis&lt;/h2&gt;
[[Optimal tuning]]s:  
Commas: 40/39, 49/48, 55/54, 66/65&lt;br /&gt;
* [[WE]]: ~2 = 1187.8599{{c}}, ~10/9 = 157.2605{{c}}
&lt;br /&gt;
: [[error map]]: {{val| -12.140 +1.983 -9.037 +37.493 }}
POTE generator: ~21/20 = ~14/13 = 81.759&lt;br /&gt;
* [[CWE]]: ~2 = 1200.0000{{c}}, ~10/9 = 161.2833{{c}}
&lt;br /&gt;
: error map: {{val| 0.000 +14.195 +7.270 +69.891 }}
Map: [&amp;lt;1 2 3 3 4 4|, &amp;lt;0 -6 -10 -3 -8 -4|]&lt;br /&gt;
 
EDOs: 14c, 15, 29f, 44df&lt;br /&gt;
[[Minimax tuning]]:  
Badness: 0.0298&lt;br /&gt;
* [[7-odd-limit|7-]] and [[9-odd-limit]]: ~10/9 = {{monzo| 3/5 0 -1/5 }}
&lt;br /&gt;
: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.5
&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:36:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc18"&gt;&lt;a name="Ammonite"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:36 --&gt;Ammonite&lt;/h1&gt;
{{Optimal ET sequence|legend=1| 7, 8d, 15d }}
Commas: 250/243, 686/675&lt;br /&gt;
 
&lt;br /&gt;
[[Badness]] (Sintel): 1.14
POTE generator: ~9/7 = 454.448&lt;br /&gt;
 
&lt;br /&gt;
=== 11-limit ===
Map: [&amp;lt;1 5 8 10|, &amp;lt;0 -9 -15 -19|]&lt;br /&gt;
Subgroup: 2.3.5.7.11
Wedgie: &amp;lt;&amp;lt;9 15 19 3 5 2||&lt;br /&gt;
 
EDOs: 29, 37, 66&lt;br /&gt;
Comma list: 22/21, 36/35, 80/77
Badness: 0.1077&lt;br /&gt;
 
&lt;br /&gt;
Mapping: {{mapping| 1 2 3 3 4 | 0 -3 -5 -1 -4 }}
&lt;!-- ws:start:WikiTextHeadingRule:38:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc19"&gt;&lt;a name="Ammonite-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:38 --&gt;11-limit&lt;/h2&gt;
 
Commas: 55/54, 100/99, 686/675&lt;br /&gt;
Optimal tunings:  
&lt;br /&gt;
* WE: ~2 = 1189.2810{{c}}, ~11/10 = 157.3322{{c}}
POTE generator: ~9/7 = 454.512&lt;br /&gt;
* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 160.9603{{c}}
&lt;br /&gt;
 
Map: [&amp;lt;1 5 8 10 8|, &amp;lt;0 -9 -15 -19 -12|]&lt;br /&gt;
{{Optimal ET sequence|legend=0| 7, 8d, 15d }}
EDOs: 29, 37, 66&lt;br /&gt;
 
Badness: 0.0457&lt;br /&gt;
Badness (Sintel): 0.886
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:40:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc20"&gt;&lt;a name="Ammonite-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:40 --&gt;13-limit&lt;/h2&gt;
== Hedgehog ==
Commas: 55/54, 91/90, 100/99, 169/168&lt;br /&gt;
{{See also| Sensamagic clan | Stearnsmic clan }}
&lt;br /&gt;
 
POTE generator: ~13/10 = 454.429&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.
&lt;br /&gt;
 
Map: [&amp;lt;1 5 8 10 8 9|, &amp;lt;0 -9 -15 -19 -12 -14|]&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.
EDOs: 29, 37, 66&lt;br /&gt;
 
Badness: 0.0272&lt;br /&gt;
[[Subgroup]]: 2.3.5.7
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:42:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc21"&gt;&lt;a name="Ceratitid"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:42 --&gt;Ceratitid&lt;/h1&gt;
[[Comma list]]: 50/49, 245/243
Commas: 250/243, 1728/1715&lt;br /&gt;
 
&lt;br /&gt;
{{Mapping|legend=1| 2 1 1 2 | 0 3 5 5 }}
POTE generator: ~36/35 = 54.384&lt;br /&gt;
 
&lt;br /&gt;
: mapping generators: ~7/5, ~9/7
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;
[[Optimal tuning]]s:  
EDOs: 22&lt;br /&gt;
* [[WE]]: ~7/5 = 599.6061{{c}}, ~9/7 = 435.3620{{c}}
Badness: 0.115&lt;br /&gt;
: [[error map]]: {{val| -0.788 +3.737 -9.897 +7.197 }}
&lt;br /&gt;
* [[CWE]]: ~7/5 = 600.0000{{c}}, ~9/7 = 435.4483{{c}}
&lt;!-- ws:start:WikiTextHeadingRule:44:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc22"&gt;&lt;a name="Ceratitid-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:44 --&gt;11-limit&lt;/h2&gt;
: error map: {{val| 0.000 +4.390 -9.072 +8.416 }}
Commas: 55/54, 100/99, 5324/5145&lt;br /&gt;
 
&lt;br /&gt;
{{Optimal ET sequence|legend=1| 8d, 14c, 22 }}
POTE generator: ~36/35 = 54.376&lt;br /&gt;
 
&lt;br /&gt;
[[Badness]] (Sintel): 1.11
Map: [&amp;lt;1 2 3 3 4|, &amp;lt;0 -9 -15 -4 -12|]&lt;br /&gt;
 
EDOs: 22&lt;br /&gt;
=== 11-limit ===
Badness: 0.0513&lt;br /&gt;
Subgroup: 2.3.5.7.11
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:46:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc23"&gt;&lt;a name="Ceratitid-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:46 --&gt;13-limit&lt;/h2&gt;
Comma list: 50/49, 55/54, 99/98
Commas: 55/54, 65/63, 100/99, 352/343&lt;br /&gt;
 
&lt;br /&gt;
Mapping: {{mapping| 2 1 1 2 4 | 0 3 5 5 4 }}
POTE generator: ~36/35 = 54.665&lt;br /&gt;
 
&lt;br /&gt;
Optimal tunings:
Map: [&amp;lt;1 2 3 3 4 4|, &amp;lt;0 -9 -15 -4 -12 -7|]&lt;br /&gt;
* WE: ~7/5 = 600.1133{{c}}, ~9/7 = 435.4680{{c}}
EDOs: 22&lt;br /&gt;
* CWE: ~7/5 = 600.0000{{c}}, ~9/7 = 435.4431{{c}}
Badness: 0.0447&lt;br /&gt;
 
&lt;br /&gt;
{{Optimal ET sequence|legend=0| 8d, 14c, 22, 58ce }}
&lt;!-- ws:start:WikiTextHeadingRule:48:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc24"&gt;&lt;a name="Porky"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:48 --&gt;Porky&lt;/h1&gt;
 
Commas: 225/224, 250/243&lt;br /&gt;
Badness (Sintel): 0.764
&lt;br /&gt;
 
POTE generator: ~10/9 = 164.412&lt;br /&gt;
==== 13-limit ====
&lt;br /&gt;
Subgroup: 2.3.5.7.11.13
Map: [&amp;lt;1 2 3 5|, &amp;lt;0 -3 -5 -16|]&lt;br /&gt;
 
Wedgie: &amp;lt;&amp;lt;3 5 16 1 17 23||&lt;br /&gt;
Comma list: 50/49, 55/54, 65/63, 99/98
EDOS: 7, 8, 15, 22, 29, 51, 73&lt;br /&gt;
 
Badness: 0.0544&lt;br /&gt;
Mapping: {{mapping| 2 1 1 2 4 3 | 0 3 5 5 4 6 }}
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:50:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc25"&gt;&lt;a name="Porky-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:50 --&gt;11-limit&lt;/h2&gt;
Optimal tunings:
Commas: 55/54, 100/99, 225/224&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}}
POTE generator: ~10/9 = 164.552&lt;br /&gt;
 
&lt;br /&gt;
{{Optimal ET sequence|legend=0| 8d, 14cf, 22 }}
Map: [&amp;lt;1 2 3 5 4|, &amp;lt;0 -3 -5 -16 -4|]&lt;br /&gt;
 
EDOs: 7, 8, 15, 22, 29, 51, 73&lt;br /&gt;
Badness (Sintel): 0.889
Badness: 0.0273&lt;br /&gt;
 
&lt;br /&gt;
==== Urchin ====
&lt;!-- ws:start:WikiTextHeadingRule:52:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc26"&gt;&lt;a name="Coendou"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:52 --&gt;Coendou&lt;/h1&gt;
Subgroup: 2.3.5.7.11.13
Commas: 250/243, 525/512&lt;br /&gt;
 
&lt;br /&gt;
Comma list: 40/39, 50/49, 55/54, 66/65
POTE generator: ~10/9 = 166.041&lt;br /&gt;
 
&lt;br /&gt;
Mapping: {{mapping| 2 1 1 2 4 6 | 0 3 5 5 4 2 }}
Map: [&amp;lt;1 2 3 1|, &amp;lt;0 -3 -5 13|]&lt;br /&gt;
 
Wedgie: &amp;lt;&amp;lt;3 5 -13 1 -29 -44||&lt;br /&gt;
Optimal tunings:
EDOs: 7, 29, 65c, 94cd&lt;br /&gt;
* WE: ~7/5 = 598.3303{{c}}, ~9/7 = 435.8617{{c}}
Badness: 0.1183&lt;br /&gt;
* CWE: ~7/5 = 600.0000{{c}}, ~9/7 = 436.3485{{c}}
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:54:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc27"&gt;&lt;a name="Coendou-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:54 --&gt;11-limit&lt;/h2&gt;
{{Optimal ET sequence|legend=0| 14c, 22f }}
Commas: 55/54, 100/99, 525/512&lt;br /&gt;
 
&lt;br /&gt;
Badness (Sintel): 1.04
POTE generator: ~10/9 = 165.981&lt;br /&gt;
 
&lt;br /&gt;
=== Hedgepig ===
Map: [&amp;lt;1 2 3 1 4|, &amp;lt;0 -3 -5 13 -4|]&lt;br /&gt;
Subgroup: 2.3.5.7.11
EDOs: 7, 29, 65ce, 94cde&lt;br /&gt;
 
Badness: 0.0497&lt;br /&gt;
Comma list: 50/49, 245/243, 385/384
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:56:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc28"&gt;&lt;a name="Coendou-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:56 --&gt;13-limit&lt;/h2&gt;
Mapping: {{mapping| 2 1 1 2 12 | 0 3 5 5 -7 }}
Commas: 55/54, 65/64, 100/99, 105/104&lt;br /&gt;
 
&lt;br /&gt;
Optimal tunings:
POTE generator: ~10/9 = 165.974&lt;br /&gt;
* WE: ~7/5 = 599.7917{{c}}, ~9/7 = 435.2737{{c}}
&lt;br /&gt;
* CWE: ~7/5 = 600.0000{{c}}, ~9/7 = 435.4047{{c}}
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;
{{Optimal ET sequence|legend=0| 22 }}
Badness: 0.0302&lt;/body&gt;&lt;/html&gt;</pre></div>
 
Badness (Sintel): 2.26
 
; Music
* [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.
 
== 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:
* [[WE]]: ~2 = 1202.1642{{c}}, ~21/20 = 82.6542{{c}}
: [[error map]]: {{val| +2.164 +6.448 -6.364 -10.296 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~21/20 = 82.2758{{c}}
: error map: {{val| 0.000 +4.390 -9.072 -15.653 }}
 
{{Optimal ET sequence|legend=1| 14c, 15, 29 }}
 
[[Badness]] (Sintel): 1.45
 
=== 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:
* WE: ~2 = 1202.3781{{c}}, ~21/20 = 82.6673{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~21/20 = 82.2434{{c}}
 
{{Optimal ET sequence|legend=0| 14c, 15, 29 }}
 
Badness (Sintel): 0.860
 
==== 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:  
* WE: ~2 = 1202.4145{{c}}, ~21/20 = 82.6963{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~21/20 = 82.3130{{c}}
 
{{Optimal ET sequence|legend=0| 14cf, 15, 29 }}
 
Badness (Sintel): 0.921
 
==== 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:
* 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:Porcupine family| ]] <!-- main article -->
[[Category:Temperament families]]
[[Category:Catalogs of rank-2 temperaments]]
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