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Porcupine family: Difference between revisions

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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 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]]'' (+21/20) → [[Very low accuracy temperaments #Oxygen|Very low accuracy temperaments]]
* ''[[Hedgehog]]'' (+50/49 or 245/243) → [[Stearnsmic clan #Hedgehog|Stearnsmic clan]]
* ''[[Jamesbond]]'' (+25/24) → [[Whitewood family #Jamesbond|Whitewood family]]


Map: [&lt;1 2 3 2 4 4|, &lt;0 -3 -5 6 -4 -2|]
The rest are considered in this page.  
EDOs: 7, 15, 22f, 37f
Badness: 0.0213


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


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


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


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


POTE generator: ~10/9 = 162.482
{{Mapping|legend=4| 1 2 3 0 4 | 0 -3 -5 0 -4 }}


Map: [&lt;1 2 3 2 4 1|, &lt;0 -3 -5 6 -4 20|]
Optimal tunings:  
EDOs: 15f, 22f, 37
* WE: ~2 = 1200.3290{{c}}, ~11/10 = 164.1227{{c}}
Badness:
* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 163.9951{{c}}


==Porkpie==
{{Optimal ET sequence|legend=0| 7, 15, 22, 73ce, 95ce }}
Commas: 55/54, 64/63, 65/63, 100/99


POTE generator: ~10/9 = 163.688
Badness (Sintel): 0.303


Map: [&lt;1 2 3 2 4 3|, &lt;0 -3 -5 6 -4 5|]
== Septimal porcupine ==
EDOs: 7, 15f, 22
{{Main| Porcupine }}
Badness: 0.0260


=Hystrix=
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.  
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
[[Subgroup]]: 2.3.5.7


[[POTE tuning|POTE generator]]: 158.868
[[Comma list]]: 64/63, 250/243


Map: [&lt;1 2 3 3|, &lt;0 -3 -5 -1|]
{{Mapping|legend=1| 1 2 3 2 | 0 -3 -5 6 }}


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


=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.
* [[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


Commas: 50/49, 245/243
[[Tuning ranges]]:  
* 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]


[[POTE tuning|POTE generator]]: ~9/7 = 435.648
{{Optimal ET sequence|legend=1| 7, 15, 22, 37, 59, 81bd }}


Map: [&lt;2 1 1 2|, &lt;0 3 5 5|]
[[Badness]] (Sintel): 1.04
Wedgie: &lt;&lt;6 10 10 2 -1 -5||
EDOs: 22, [[146edo|146]]
Badness: 0.0440


==11-limit==  
=== 11-limit ===
Commas: 50/49, 55/54, 99/98
Subgroup: 2.3.5.7.11


POTE generator: ~9/7 = 435.386
Comma list: 55/54, 64/63, 100/99


Map: [&lt;2 1 1 2 4|, &lt;0 3 5 5 4|]
{{Mapping|legend=0| 1 2 3 2 4 | 0 -3 -5 6 -4 }}
EDOs: 14c, 22, 58ce, 80ce, 102cde
Badness: 0.0231


==13-limit==
Optimal tunings:
Commas: 50/49, 55/54, 65/63, 99/98
* WE: ~2 = 1198.3250{{c}}, ~11/10 = 162.5202{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 162.8156{{c}}


POTE generator: ~9/7 = 435.861
Minimax tuning:
* 11-odd-limit: ~11/10 = {{monzo| 1/6 -1/6 0 1/12 }}
: unchanged-interval (eigenmonzo) basis: 2.9/7


Map: [&lt;2 1 1 2 4 3|, &lt;0 3 5 5 4 6|]
Tuning ranges:  
EDOs: 14cf, 22
* 11-odd-limit diamond monotone: ~11/10 = [160.000, 163.636] (2\15 to 3\22)
Badness: 0.0215
* 11-odd-limit diamond tradeoff: ~11/10 = [150.637, 182.404]


==Urchin==
{{Optimal ET sequence|legend=0| 7, 15, 22, 37, 59 }}
Commas: 40/39, 50/49, 55/54, 66/65


POTE generator: ~9/7 = 437.078
Badness (Sintel): 0.713


Map: [&lt;2 1 1 2 4 6|, &lt;0 3 5 5 4 2|]
==== Porcupinefowl ====
EDOs: 14c, 22f
This extension used to be ''tridecimal porcupine''.  
Badness: 0.0252


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


POTE generator: ~9/7 = 435.425
Comma list: 40/39, 55/54, 64/63, 66/65


Map: [&lt;2 1 1 2 12|, &lt;0 3 5 5 -7|]
{{Mapping|legend=0| 1 2 3 2 4 4 | 0 -3 -5 6 -4 -2 }}
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 = 1197.0054{{c}}, ~11/10 = 162.3022{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 162.8314{{c}}


=Nautilus=
Minimax tuning:
Commas: 49/48, 250/243
* 13- and 15-odd-limit: ~10/9 = {{monzo| 1 0 0 0 -1/4 }}
: unchanged-interval (eigenmonzo) basis: 2.11


POTE generator: ~21/20 = 82.505
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]


Map: [&lt;1 2 3 3|, &lt;0 -6 -10 -3|]
{{Optimal ET sequence|legend=0| 7, 15, 22f }}
Wedgie: &lt;&lt;6 10 3 2 -12 -21||
EDOs: 10, 15, 19, [[29edo|29]], [[102edo|102cd]]


==11-limit==
Badness (Sintel): 0.879
Commas: 49/48, 55/54, 245/242


POTE generator: ~21/20 = 82.504
==== Porcupinefish ====
{{See also| The Biosphere }}


Map: [&lt;1 2 3 3 4|, &lt;0 -6 -10 -3 -8|]
Subgroup: 2.3.5.7.11.13
EDOs: 10e, 14c, 15, 19, 22d, 29, 102cde


==13-limit==
Comma list: 55/54, 64/63, 91/90, 100/99
Commas: 49/48, 55/54, 91/90, 100/99


POTE generator: ~21/20 = 62.530
{{Mapping|legend=0| 1 2 3 2 4 6 | 0 -3 -5 6 -4 -17 }}


Map: [&lt;1 2 3 3 4 5|, &lt;0 -6 -10 -3 -8 -19|]
Optimal tunings:  
EDOs: 10e, 15f, 17d, 19, 22d, 29, 102cde
* WE: ~2 = 1198.3206{{c}}, ~11/10 = 162.0502{{c}}
Badness: 0.0223
* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 162.3458{{c}}


==Belauensis==
Minimax tuning:
Commas: 40/39, 49/48, 55/54, 66/65
* 13- and 15-odd-limit: ~10/9 = {{monzo| 2/13 0 0 0 1/13 -1/13 }}
: unchanged-interval (eigenmonzo) basis: 2.13/11


POTE generator: ~21/20 = ~14/13 = 81.759
Tuning ranges:
* 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]


Map: [&lt;1 2 3 3 4 4|, &lt;0 -6 -10 -3 -8 -4|]
{{Optimal ET sequence|legend=0| 15, 22, 37 }}
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]]
Badness (Sintel): 1.05
=Ammonite=
Commas: 250/243, 686/675


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


Map: [&lt;1 5 8 10|, &lt;0 -9 -15 -19|]
Comma list: 55/54, 64/63, 100/99, 196/195
Wedgie: &lt;&lt;9 15 19 3 5 2||
EDOs: 29, 37, 66
Badness: 0.1077


==11-limit==
{{Mapping|legend=0| 1 2 3 2 4 1 | 0 -3 -5 6 -4 20 }}
Commas: 55/54, 100/99, 686/675


POTE generator: ~9/7 = 454.512
Optimal tunings:  
* WE: ~2 = 1198.0537{{c}}, ~11/10 = 162.2183{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 162.4665{{c}}


Map: [&lt;1 5 8 10 8|, &lt;0 -9 -15 -19 -12|]
Minimax tuning:  
EDOs: 29, 37, 66
* 13- and 15-odd-limit: ~11/10 = {{monzo| 1/14 0 0 -1/14 0 1/14 }}
Badness: 0.0457
: unchanged-interval (eigenmonzo) basis: 2.13/7


==13-limit==
{{Optimal ET sequence|legend=0| 15f, 22f, 37, 59f }}
Commas: 55/54, 91/90, 100/99, 169/168


POTE generator: ~13/10 = 454.429
Badness (Sintel): 1.45


Map: [&lt;1 5 8 10 8 9|, &lt;0 -9 -15 -19 -12 -14|]
==== Porkpie ====
EDOs: 29, 37, 66
Subgroup: 2.3.5.7.11.13
Badness: 0.0272


=Ceratitid=
Comma list: 55/54, 64/63, 65/63, 100/99
Commas: 250/243, 1728/1715


POTE generator: ~36/35 = 54.384
{{Mapping|legend=0| 1 2 3 2 4 3 | 0 -3 -5 6 -4 5 }}


Map: [&lt;1 2 3 3|, &lt;0 -9 -15 -4|]
Optimal tunings:  
Wedgie: &lt;&lt;9 15 4 3 -19 -33||
* WE: ~2 = 1200.0223{{c}}, ~11/10 = 163.6908{{c}}
EDOs: 22
* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 163.6874{{c}}
Badness: 0.115


==11-limit==
Minimax tuning:
Commas: 55/54, 100/99, 5324/5145
* 13- and 15-odd-limit: ~11/10 = {{monzo| 1/6 -1/6 0 1/12 }}
: unchanged-interval (eigenmonzo) basis: 2.9/7


POTE generator: ~36/35 = 54.376
{{Optimal ET sequence|legend=0| 7, 15f, 22 }}


Map: [&lt;1 2 3 3 4|, &lt;0 -9 -15 -4 -12|]
Badness (Sintel): 1.08
EDOs: 22
Badness: 0.0513


==13-limit==  
==== Undecimation ====
Commas: 55/54, 65/63, 100/99, 352/343
This weak extension is used by most patent vals that support porcupine and tune 13 well.


POTE generator: ~36/35 = 54.665
Subgroup: 2.3.5.7.11.13


Map: [&lt;1 2 3 3 4 4|, &lt;0 -9 -15 -4 -12 -7|]
Comma list: 55/54, 64/63, 100/99, 169/168
EDOs: 22
Badness: 0.0447


=Porky=
{{Mapping|legend=0| 1 -1 -2 8 0 5 | 0 6 10 -12 8 -3 }}
Commas: 225/224, 250/243
: mapping generators: ~2, ~35/26


POTE generator: ~10/9 = 164.412
Optimal tunings:
* WE: ~2 = 1198.4569{{c}}, ~35/26 = 517.9375{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~35/26 = 518.5822{{c}}


Map: [&lt;1 2 3 5|, &lt;0 -3 -5 -16|]
{{Optimal ET sequence|legend=0| 7, 30, 37, 81bd }}
Wedgie: &lt;&lt;3 5 16 1 17 23||
EDOS: 7, 8, 15, 22, 29, 51, 73
Badness: 0.0544


==11-limit==
Badness (Sintel): 1.68
Commas: 55/54, 100/99, 225/224


POTE generator: ~10/9 = 164.552
== Opossum ==
{{Main| Opossum }}


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


=Coendou=
[[Subgroup]]: 2.3.5.7
Commas: 250/243, 525/512


POTE generator: ~10/9 = 166.041
[[Comma list]]: 28/27, 126/125


Map: [&lt;1 2 3 1|, &lt;0 -3 -5 13|]
{{Mapping|legend=1| 1 2 3 4 | 0 -3 -5 -9 }}
Wedgie: &lt;&lt;3 5 -13 1 -29 -44||
EDOs: 7, 29, 65c, 94cd
Badness: 0.1183


==11-limit==  
[[Optimal tuning]]s:
Commas: 55/54, 100/99, 525/512
* [[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: ~10/9 = 165.981
[[Minimax tuning]]:  
* [[7-odd-limit|7-]] and [[9-odd-limit]] [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.7


Map: [&lt;1 2 3 1 4|, &lt;0 -3 -5 13 -4|]
{{Optimal ET sequence|legend=1| 7d, 8d, 15 }}
EDOs: 7, 29, 65ce, 94cde
Badness: 0.0497


==13-limit==
[[Badness]] (Sintel): 1.03
Commas: 55/54, 65/64, 100/99, 105/104


POTE generator: ~10/9 = 165.974
=== 11-limit ===
Subgroup: 2.3.5.7.11


Map: [&lt;1 2 3 1 4 3|, &lt;0 -3 -5 13 -4 5|]
Comma list: 28/27, 55/54, 77/75
EDOs: 7, 29, 65cef, 94cdef
 
Badness: 0.0302</pre></div>
{{Mapping|legend=0| 1 2 3 4 4 | 0 -3 -5 -9 -4 }}
<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: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;
Optimal tunings:  
&lt;!-- ws:end:WikiTextTocRule:88 --&gt;&lt;hr /&gt;
* WE: ~2 = 1196.2331{{c}}, ~11/10 = 159.3050{{c}}
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;
* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 160.4644{{c}}
&lt;br /&gt;
 
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 163.950&lt;br /&gt;
Minimax tuning:  
&lt;br /&gt;
* 11-odd-limit unchanged-interval (eigenmonzo) basis: 2.7
Map: [&amp;lt;1 2 3|, &amp;lt;0 -3 -5|]&lt;br /&gt;
 
&lt;br /&gt;
{{Optimal ET sequence|legend=0| 7d, 8d, 15 }}
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;
Badness (Sintel): 0.738
&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;
=== 13-limit ===
&lt;br /&gt;
Subgroup: 2.3.5.7.11.13
&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;
Comma list: 28/27, 40/39, 55/54, 66/65
&lt;br /&gt;
 
Commas: 250/243, 64/63&lt;br /&gt;
{{Mapping|legend=0| 1 2 3 4 4 4 | 0 -3 -5 -9 -4 -2 }}
&lt;br /&gt;
 
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~10/9 = 162.880&lt;br /&gt;
Optimal tunings:  
&lt;br /&gt;
* WE: ~2 = 1193.5447{{c}}, ~11/10 = 157.9505{{c}}
Map: [&amp;lt;1 2 3 2|, &amp;lt;0 -3 -5 6|]&lt;br /&gt;
* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 159.7600{{c}}
EDOs: 22, &lt;a class="wiki_link" href="/59edo"&gt;59&lt;/a&gt;, &lt;a class="wiki_link" href="/81edo"&gt;81bd&lt;/a&gt;, &lt;a class="wiki_link" href="/140edo"&gt;140bd&lt;/a&gt;&lt;br /&gt;
 
&lt;br /&gt;
Minimax tuning:  
&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;
* 13- and 15-odd-limit unchanged-interval (eigenmonzo) basis: 2.7
Commas: 55/54, 64/63, 100/99&lt;br /&gt;
 
&lt;br /&gt;
{{Optimal ET sequence|legend=0| 7d, 8d, 15, 38bceff }}
POTE generator: ~10/9 = 162.747&lt;br /&gt;
 
&lt;br /&gt;
Badness (Sintel): 0.801
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;
== Porky ==
Badness: 0.0217&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;
 
&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;
[[Subgroup]]: 2.3.5.7
Commas: 40/39, 55/54, 64/63, 66/65&lt;br /&gt;
 
&lt;br /&gt;
[[Comma list]]: 225/224, 250/243
POTE generator: ~10/9 = 162.708&lt;br /&gt;
 
&lt;br /&gt;
{{Mapping|legend=1| 1 2 3 5 | 0 -3 -5 -16 }}
Map: [&amp;lt;1 2 3 2 4 4|, &amp;lt;0 -3 -5 6 -4 -2|]&lt;br /&gt;
 
EDOs: 7, 15, 22f, 37f&lt;br /&gt;
[[Optimal tuning]]s:  
Badness: 0.0213&lt;br /&gt;
* [[WE]]: ~2 = 1200.0685{{c}}, ~10/9 = 164.4215{{c}}
&lt;br /&gt;
: [[error map]]: {{val| +0.068 +4.917 -8.216 +0.772 }}
&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;
* [[CWE]]: ~2 = 1200.0000{{c}}, ~10/9 = 164.4060{{c}}
See also: &lt;a class="wiki_link" href="/The%20Biosphere"&gt;The Biosphere&lt;/a&gt;&lt;br /&gt;
: error map: {{val| 0.000 +4.827 -8.344 +0.678 }}
Commas: 55/54, 64/63, 91/90, 100/99&lt;br /&gt;
 
&lt;br /&gt;
[[Minimax tuning]]:  
POTE generator: ~10/9 = 162.277&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
Map: [&amp;lt;1 2 3 2 4 6|, &amp;lt;0 -3 -5 6 -4 -17|]&lt;br /&gt;
 
EDOs: 15, 22, 37, 59, 96b&lt;br /&gt;
{{Optimal ET sequence|legend=1| 7d, 15d, 22, 51, 73c }}
&lt;span style="background-color: #ffffff;"&gt;Badness: 0.0253&lt;/span&gt;&lt;br /&gt;
 
&lt;br /&gt;
[[Badness]] (Sintel): 1.38
&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;
 
Commas: 55/54, 64/63, 100/99, 196/195&lt;br /&gt;
=== 11-limit ===
&lt;br /&gt;
Subgroup: 2.3.5.7.11
POTE generator: ~10/9 = 162.482&lt;br /&gt;
 
&lt;br /&gt;
Comma list: 55/54, 100/99, 225/224
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;
{{Mapping|legend=0| 1 2 3 5 4 | 0 -3 -5 -16 -4 }}
Badness:&lt;br /&gt;
 
&lt;br /&gt;
Optimal tunings:  
&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;
* WE: ~2 = 1200.8706{{c}}, ~11/10 = 164.6715{{c}}
Commas: 55/54, 64/63, 65/63, 100/99&lt;br /&gt;
* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 164.4810{{c}}
&lt;br /&gt;
 
POTE generator: ~10/9 = 163.688&lt;br /&gt;
Minimax tuning:
&lt;br /&gt;
* 11-odd-limit: ~11/10 = {{monzo| 2/11 0 1/11 -1/11 }}
Map: [&amp;lt;1 2 3 2 4 3|, &amp;lt;0 -3 -5 6 -4 5|]&lt;br /&gt;
: unchanged-interval (eigenmonzo) basis: 2.7/5
EDOs: 7, 15f, 22&lt;br /&gt;
 
Badness: 0.0260&lt;br /&gt;
{{Optimal ET sequence|legend=0| 7d, 15d, 22, 51 }}
&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;
Badness (Sintel): 0.901
Hystrix, with wedgie &amp;lt;&amp;lt;3 5 1 1 -7 -12||, provides a less complex avenue to the 7-limit. Unfortunately in temperaments as in life you get what you pay for, and hystrix, for which a generator of 2\15 or 9\68 can be used, is a temperament for the adventurous souls who have probably already tried &lt;a class="wiki_link" href="/15edo"&gt;15edo&lt;/a&gt;. They can try the even sharper fifth of hystrix in &lt;a class="wiki_link" href="/68edo"&gt;68edo&lt;/a&gt; and see how that suits.&lt;br /&gt;
 
&lt;br /&gt;
=== 13-limit ===
Commas: 36/35, 160/147&lt;br /&gt;
Subgroup: 2.3.5.7.11.13
&lt;br /&gt;
 
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 158.868&lt;br /&gt;
Comma list: 55/54, 65/64, 91/90, 100/99
&lt;br /&gt;
 
Map: [&amp;lt;1 2 3 3|, &amp;lt;0 -3 -5 -1|]&lt;br /&gt;
{{Mapping|legend=0| 1 2 3 5 4 3 | 0 -3 -5 -16 -4 5 }}
&lt;br /&gt;
 
EDOs: 10d, 12, 13d, 15&lt;br /&gt;
Optimal tunings:  
&lt;br /&gt;
* WE: ~2 = 1202.1557{{c}}, ~11/10 = 165.2494{{c}}
&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;
* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 164.8579{{c}}
Hedgehog, with wedgie &amp;lt;&amp;lt;6 10 10 2 -1 -5||, has a period 1/2 octave and a generator which can be taken to be 9/7 instead of 10/9. It also tempers out 245/243, the sensamagic comma. 22et provides the obvious tuning, but if you are looking for an alternative, you could try the &amp;lt;146 232 338 411| val with generator 10\73, or you could try 164 cents if you are fond of round numbers. The 14 note MOS gives scope for harmony while stopping well short of 22.&lt;br /&gt;
 
&lt;br /&gt;
{{Optimal ET sequence|legend=0| 7d, 22, 29, 51f, 80cdeff }}
Commas: 50/49, 245/243&lt;br /&gt;
 
&lt;br /&gt;
Badness (Sintel): 1.10
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~9/7 = 435.648&lt;br /&gt;
 
&lt;br /&gt;
; Music
Map: [&amp;lt;2 1 1 2|, &amp;lt;0 3 5 5|]&lt;br /&gt;
* [https://www.youtube.com/watch?v=CN4cLOyaVGE ''Improvisation in 29edo''] (2024) by [[Budjarn Lambeth]] – in Palace scale, 29edo tuning
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;
== Coendou ==
Badness: 0.0440&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;
 
&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;
[[Subgroup]]: 2.3.5.7
Commas: 50/49, 55/54, 99/98&lt;br /&gt;
 
&lt;br /&gt;
[[Comma list]]: 250/243, 525/512
POTE generator: ~9/7 = 435.386&lt;br /&gt;
 
&lt;br /&gt;
{{Mapping|legend=1| 1 2 3 1 | 0 -3 -5 13 }}
Map: [&amp;lt;2 1 1 2 4|, &amp;lt;0 3 5 5 4|]&lt;br /&gt;
 
EDOs: 14c, 22, 58ce, 80ce, 102cde&lt;br /&gt;
[[Optimal tuning]]s:
Badness: 0.0231&lt;br /&gt;
* [[WE]]: ~2 = 1202.6772{{c}}, ~10/9 = 166.4110{{c}}
&lt;br /&gt;
: [[error map]]: {{val| +2.678 +4.166 -10.337 -2.806 }}
&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;
* [[CWE]]: ~2 = 1200.0000{{c}}, ~10/9 = 166.0511{{c}}
Commas: 50/49, 55/54, 65/63, 99/98&lt;br /&gt;
: error map: {{val| 0.000 -0.108 -16.569 -10.161 }}
&lt;br /&gt;
 
POTE generator: ~9/7 = 435.861&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;2 1 1 2 4 3|, &amp;lt;0 3 5 5 4 6|]&lt;br /&gt;
: [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.3
EDOs: 14cf, 22&lt;br /&gt;
 
Badness: 0.0215&lt;br /&gt;
{{Optimal ET sequence|legend=1| 7, 22d, 29, 65c }}
&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;
[[Badness]] (Sintel): 2.99
Commas: 40/39, 50/49, 55/54, 66/65&lt;br /&gt;
 
&lt;br /&gt;
=== 11-limit ===
POTE generator: ~9/7 = 437.078&lt;br /&gt;
Subgroup: 2.3.5.7.11
&lt;br /&gt;
 
Map: [&amp;lt;2 1 1 2 4 6|, &amp;lt;0 3 5 5 4 2|]&lt;br /&gt;
Comma list: 55/54, 100/99, 525/512
EDOs: 14c, 22f&lt;br /&gt;
 
Badness: 0.0252&lt;br /&gt;
{{Mapping|legend=0| 1 2 3 1 4 | 0 -3 -5 13 -4 }}
&lt;br /&gt;
 
&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;
Optimal tunings:  
Commas: 50/49, 245/243, 385/384&lt;br /&gt;
* WE: ~2 = 1203.0245{{c}}, ~11/10 = 166.3991{{c}}
&lt;br /&gt;
* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 165.9714{{c}}
POTE generator: ~9/7 = 435.425&lt;br /&gt;
 
&lt;br /&gt;
Minimax tuning:  
Map: [&amp;lt;2 1 1 2 12|, &amp;lt;0 3 5 5 -7|]&lt;br /&gt;
* 11-odd-limit: ~11/10 = {{monzo| 2/3 -1/3 }}
EDOs: 22, 80c, 102cd, 124cd&lt;br /&gt;
: unchanged-interval (eigenmonzo) basis: 2.3
Badness: 0.0684&lt;br /&gt;
 
&lt;br /&gt;
{{Optimal ET sequence|legend=0| 7, 22d, 29, 65ce }}
&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;
Badness (Sintel): 1.64
&lt;br /&gt;
 
&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;
=== 13-limit ===
Commas: 49/48, 250/243&lt;br /&gt;
Subgroup: 2.3.5.7.11.13
&lt;br /&gt;
 
POTE generator: ~21/20 = 82.505&lt;br /&gt;
Comma list: 55/54, 65/64, 100/99, 105/104
&lt;br /&gt;
 
Map: [&amp;lt;1 2 3 3|, &amp;lt;0 -6 -10 -3|]&lt;br /&gt;
{{Mapping|legend=0| 1 2 3 1 4 3 | 0 -3 -5 13 -4 5 }}
Wedgie: &amp;lt;&amp;lt;6 10 3 2 -12 -21||&lt;br /&gt;
 
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;
Optimal tunings:  
&lt;br /&gt;
* WE: ~2 = 1202.9957{{c}}, ~11/10 = 166.3885{{c}}
&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;
* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 165.9843{{c}}
Commas: 49/48, 55/54, 245/242&lt;br /&gt;
 
&lt;br /&gt;
Minimax tuning:  
POTE generator: ~21/20 = 82.504&lt;br /&gt;
* 13- and 15-odd-limit: ~11/10 = {{monzo| 2/3 -1/3 }}
&lt;br /&gt;
: unchanged-interval (eigenmonzo) basis: 2.3
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;
{{Optimal ET sequence|legend=0| 7, 22d, 29, 65cef }}
&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;
Badness (Sintel): 1.25
Commas: 49/48, 55/54, 91/90, 100/99&lt;br /&gt;
 
&lt;br /&gt;
== Hystrix ==
POTE generator: ~21/20 = 62.530&lt;br /&gt;
Hystrix provides a less complex avenue to the 7-limit, with the generator taking on the role of approximating 8/7. Unfortunately in temperaments as in life you get what you pay for, and hystrix is very high in [[error]] due to the large disparity between typical porcupine generators and a justly-tuned 8/7, and is usually considered an [[exotemperament]]. A generator of 2\15 or 9\68 can be used for hystrix.
&lt;br /&gt;
 
Map: [&amp;lt;1 2 3 3 4 5|, &amp;lt;0 -6 -10 -3 -8 -19|]&lt;br /&gt;
[[Subgroup]]: 2.3.5.7
EDOs: 10e, 15f, 17d, 19, 22d, 29, 102cde&lt;br /&gt;
 
Badness: 0.0223&lt;br /&gt;
[[Comma list]]: 36/35, 160/147
&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;
{{Mapping|legend=1| 1 2 3 3 | 0 -3 -5 -1 }}
Commas: 40/39, 49/48, 55/54, 66/65&lt;br /&gt;
 
&lt;br /&gt;
[[Optimal tuning]]s:  
POTE generator: ~21/20 = ~14/13 = 81.759&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 }}
Map: [&amp;lt;1 2 3 3 4 4|, &amp;lt;0 -6 -10 -3 -8 -4|]&lt;br /&gt;
* [[CWE]]: ~2 = 1200.0000{{c}}, ~10/9 = 161.2833{{c}}
EDOs: 14c, 15, 29f, 44df&lt;br /&gt;
: error map: {{val| 0.000 +14.195 +7.270 +69.891 }}
Badness: 0.0298&lt;br /&gt;
 
&lt;br /&gt;
[[Minimax tuning]]:
&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;
* [[7-odd-limit|7-]] and [[9-odd-limit]]: ~10/9 = {{monzo| 3/5 0 -1/5 }}
&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;
: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.5
Commas: 250/243, 686/675&lt;br /&gt;
 
&lt;br /&gt;
{{Optimal ET sequence|legend=1| 7, 8d, 15d }}
POTE generator: ~9/7 = 454.448&lt;br /&gt;
 
&lt;br /&gt;
[[Badness]] (Sintel): 1.14
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;
=== 11-limit ===
EDOs: 29, 37, 66&lt;br /&gt;
Subgroup: 2.3.5.7.11
Badness: 0.1077&lt;br /&gt;
 
&lt;br /&gt;
Comma list: 22/21, 36/35, 80/77
&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;
{{Mapping|legend=0| 1 2 3 3 4 | 0 -3 -5 -1 -4 }}
&lt;br /&gt;
 
POTE generator: ~9/7 = 454.512&lt;br /&gt;
Optimal tunings:  
&lt;br /&gt;
* WE: ~2 = 1189.2810{{c}}, ~11/10 = 157.3322{{c}}
Map: [&amp;lt;1 5 8 10 8|, &amp;lt;0 -9 -15 -19 -12|]&lt;br /&gt;
* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 160.9603{{c}}
EDOs: 29, 37, 66&lt;br /&gt;
 
Badness: 0.0457&lt;br /&gt;
{{Optimal ET sequence|legend=0| 7, 8d, 15d }}
&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;
Badness (Sintel): 0.886
Commas: 55/54, 91/90, 100/99, 169/168&lt;br /&gt;
 
&lt;br /&gt;
== Nautilus ==
POTE generator: ~13/10 = 454.429&lt;br /&gt;
Nautilus tempers out 49/48 and may be described as the {{nowrap| 14c & 15 }} temperament. Its ploidacot is omega-hexacot.
&lt;br /&gt;
 
Map: [&amp;lt;1 5 8 10 8 9|, &amp;lt;0 -9 -15 -19 -12 -14|]&lt;br /&gt;
[[Subgroup]]: 2.3.5.7
EDOs: 29, 37, 66&lt;br /&gt;
 
Badness: 0.0272&lt;br /&gt;
[[Comma list]]: 49/48, 250/243
&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;
{{Mapping|legend=1| 1 2 3 3 | 0 -6 -10 -3 }}
Commas: 250/243, 1728/1715&lt;br /&gt;
 
&lt;br /&gt;
: mapping generators: ~2, ~21/20
POTE generator: ~36/35 = 54.384&lt;br /&gt;
 
&lt;br /&gt;
[[Optimal tuning]]s:  
Map: [&amp;lt;1 2 3 3|, &amp;lt;0 -9 -15 -4|]&lt;br /&gt;
* [[WE]]: ~2 = 1202.1642{{c}}, ~21/20 = 82.6542{{c}}
Wedgie: &amp;lt;&amp;lt;9 15 4 3 -19 -33||&lt;br /&gt;
: [[error map]]: {{val| +2.164 +6.448 -6.364 -10.296 }}
EDOs: 22&lt;br /&gt;
* [[CWE]]: ~2 = 1200.0000{{c}}, ~21/20 = 82.2758{{c}}
Badness: 0.115&lt;br /&gt;
: error map: {{val| 0.000 +4.390 -9.072 -15.653 }}
&lt;br /&gt;
 
&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;
{{Optimal ET sequence|legend=1| 14c, 15, 29 }}
Commas: 55/54, 100/99, 5324/5145&lt;br /&gt;
 
&lt;br /&gt;
[[Badness]] (Sintel): 1.45
POTE generator: ~36/35 = 54.376&lt;br /&gt;
 
&lt;br /&gt;
=== 11-limit ===
Map: [&amp;lt;1 2 3 3 4|, &amp;lt;0 -9 -15 -4 -12|]&lt;br /&gt;
Subgroup: 2.3.5.7.11
EDOs: 22&lt;br /&gt;
 
Badness: 0.0513&lt;br /&gt;
Comma list: 49/48, 55/54, 245/242
&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;
{{Mapping|legend=0| 1 2 3 3 4 | 0 -6 -10 -3 -8 }}
Commas: 55/54, 65/63, 100/99, 352/343&lt;br /&gt;
 
&lt;br /&gt;
Optimal tunings:
POTE generator: ~36/35 = 54.665&lt;br /&gt;
* WE: ~2 = 1202.3781{{c}}, ~21/20 = 82.6673{{c}}
&lt;br /&gt;
* CWE: ~2 = 1200.0000{{c}}, ~21/20 = 82.2434{{c}}
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 ET sequence|legend=0| 14c, 15, 29 }}
Badness: 0.0447&lt;br /&gt;
 
&lt;br /&gt;
Badness (Sintel): 0.860
&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;
==== 13-limit ====
&lt;br /&gt;
Subgroup: 2.3.5.7.11.13
POTE generator: ~10/9 = 164.412&lt;br /&gt;
 
&lt;br /&gt;
Comma list: 49/48, 55/54, 91/90, 100/99
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;
{{Mapping|legend=0| 1 2 3 3 4 5 | 0 -6 -10 -3 -8 -19 }}
EDOS: 7, 8, 15, 22, 29, 51, 73&lt;br /&gt;
 
Badness: 0.0544&lt;br /&gt;
Optimal tunings:
&lt;br /&gt;
* WE: ~2 = 1202.4145{{c}}, ~21/20 = 82.6963{{c}}
&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;
* CWE: ~2 = 1200.0000{{c}}, ~21/20 = 82.3130{{c}}
Commas: 55/54, 100/99, 225/224&lt;br /&gt;
 
&lt;br /&gt;
{{Optimal ET sequence|legend=0| 14cf, 15, 29 }}
POTE generator: ~10/9 = 164.552&lt;br /&gt;
 
&lt;br /&gt;
Badness (Sintel): 0.921
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;
==== Belauensis ====
Badness: 0.0273&lt;br /&gt;
Subgroup: 2.3.5.7.11.13
&lt;br /&gt;
 
&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;
Comma list: 40/39, 49/48, 55/54, 66/65
Commas: 250/243, 525/512&lt;br /&gt;
 
&lt;br /&gt;
{{Mapping|legend=0| 1 2 3 3 4 4 | 0 -6 -10 -3 -8 -4 }}
POTE generator: ~10/9 = 166.041&lt;br /&gt;
 
&lt;br /&gt;
Optimal tunings:  
Map: [&amp;lt;1 2 3 1|, &amp;lt;0 -3 -5 13|]&lt;br /&gt;
* WE: ~2 = 1199.0072{{c}}, ~21/20 = 81.6911{{c}}
Wedgie: &amp;lt;&amp;lt;3 5 -13 1 -29 -44||&lt;br /&gt;
* CWE: ~2 = 1200.0000{{c}}, ~21/20 = 81.8576{{c}}
EDOs: 7, 29, 65c, 94cd&lt;br /&gt;
 
Badness: 0.1183&lt;br /&gt;
{{Optimal ET sequence|legend=0| 14c, 15 }}
&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;
Badness (Sintel): 1.23
Commas: 55/54, 100/99, 525/512&lt;br /&gt;
 
&lt;br /&gt;
; Music
POTE generator: ~10/9 = 165.981&lt;br /&gt;
* [https://web.archive.org/web/20201127013840/http://micro.soonlabel.com/gene_ward_smith/Others/Igs/NautilusReverie.mp3 ''Nautilus Reverie''] by [[Igliashon Jones]]
&lt;br /&gt;
 
Map: [&amp;lt;1 2 3 1 4|, &amp;lt;0 -3 -5 13 -4|]&lt;br /&gt;
== Ammonite ==
EDOs: 7, 29, 65ce, 94cde&lt;br /&gt;
{{See also|Subgroup temperaments #Ammon}}
Badness: 0.0497&lt;br /&gt;
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.
&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;
[[Subgroup]]: 2.3.5.7
Commas: 55/54, 65/64, 100/99, 105/104&lt;br /&gt;
 
&lt;br /&gt;
[[Comma list]]: 250/243, 686/675
POTE generator: ~10/9 = 165.974&lt;br /&gt;
 
&lt;br /&gt;
{{Mapping|legend=1| 1 -4 -7 -9 | 0 9 15 19 }}
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;
: mapping generators: ~2, ~14/9
Badness: 0.0302&lt;/body&gt;&lt;/html&gt;</pre></div>
 
[[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|legend=0| 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|legend=0| 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|legend=0| 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|legend=0| 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]]
Retrieved from "https://en.xen.wiki/w/Porcupine_family"