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The '''porcupine family''' of [[regular temperament|temperaments]] [[tempering out|tempers out]] the [[porcupine comma]], [[250/243]], also called the maximal diesis. 

== Porcupine ==
{{Main| Porcupine }}

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.

[[Subgroup]]: 2.3.5

[[Comma list]]: 250/243

{{Mapping|legend=1| 1 2 3 | 0 -3 -5 }}

: mapping generators: ~2, ~10/9

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

[[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]

{{Optimal ET sequence|legend=1| 7, 15, 22, 95c }}

[[Badness]] (Smith): 0.030778

=== 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. 

Those all share the same generator with porcupine. 

[[#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. 

Temperaments discussed elsewhere include: 
* [[Oxygen]] → [[Very low accuracy temperaments #Oxygen|Very low accuracy temperaments]].
* [[Jamesbond]] → [[7th-octave temperaments #Jamesbond|7th-octave temperaments]].

==== Subgroup extensions ====
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.

=== 2.3.5.11 subgroup (porkypine) ===
Subgroup: 2.3.5.11

Comma list: 55/54, 100/99

Sval mapping: {{mapping| 1 2 3 4 | 0 -3 -5 -4 }}

Gencom mapping: {{mapping| 1 2 3 0 4 | 0 -3 -5 0 -4 }}

: gencom: [2 10/9; 55/54, 100/99]

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

{{Optimal ET sequence|legend=0| 7, 15, 22, 73ce, 95ce }}

Badness (Smith): 0.0097

==== Undecimation ====
Subgroup: 2.3.5.11.13

Comma list: 55/54, 100/99, 512/507

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

: sval mapping generators: ~2, ~65/44

Optimal tunings: 
* CTE: ~2 = 1200.000, ~88/65 = 518.086
* POTE: ~2 = 1200.000, ~88/65 = 518.209

{{Optimal ET sequence|legend=0| 7, 23bc, 30, 37, 44 }}

Badness (Smith): 0.0305

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

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. 

[[Subgroup]]: 2.3.5.7

[[Comma list]]: 64/63, 250/243

{{Mapping|legend=1| 1 2 3 2 | 0 -3 -5 6 }}

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

[[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

[[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]

{{Optimal ET sequence|legend=1| 7, 15, 22, 37, 59, 81bd }}

[[Badness]] (Smith): 0.041057

=== 11-limit ===
Subgroup: 2.3.5.7.11

Comma list: 55/54, 64/63, 100/99

Mapping: {{mapping| 1 2 3 2 4 | 0 -3 -5 6 -4 }}

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

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

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]

{{Optimal ET sequence|legend=0| 7, 15, 22, 37, 59 }}

Badness (Smith): 0.021562

==== Porcupinefowl ====
This extension used to be ''tridecimal porcupine''. 

Subgroup: 2.3.5.7.11.13

Comma list: 40/39, 55/54, 64/63, 66/65

Mapping: {{mapping| 1 2 3 2 4 4 | 0 -3 -5 6 -4 -2 }}

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

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

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]

{{Optimal ET sequence|legend=0| 7, 15, 22f, 37f }}

Badness (Smith): 0.021276

==== Porcupinefish ====
{{See also| The Biosphere }}

Subgroup: 2.3.5.7.11.13

Comma list: 55/54, 64/63, 91/90, 100/99

Mapping: {{mapping| 1 2 3 2 4 6 | 0 -3 -5 6 -4 -17 }}

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

Minimax tuning: 
* 13- and 15-odd-limit: ~10/9 = {{monzo| 2/13 0 0 0 1/13 -1/13 }}
: unchanged-interval (eigenmonzo) basis: 2.13/11

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

{{Optimal ET sequence|legend=0| 15, 22, 37 }}

Badness (Smith): 0.025314

==== Pourcup ====
Subgroup: 2.3.5.7.11.13

Comma list: 55/54, 64/63, 100/99, 196/195

Mapping: {{mapping| 1 2 3 2 4 1 | 0 -3 -5 6 -4 20 }}

Optimal tunings: 
* CTE: ~2 = 1200.000, ~11/10 = 163.378
* POTE: ~2 = 1200.000, ~11/10 = 162.482

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

{{Optimal ET sequence|legend=0| 15f, 22f, 37, 59f }}

Badness (Smith): 0.035130

==== Porkpie ====
Subgroup: 2.3.5.7.11.13

Comma list: 55/54, 64/63, 65/63, 100/99

Mapping: {{mapping| 1 2 3 2 4 3 | 0 -3 -5 6 -4 5 }}

Optimal tunings: 
* CTE: ~2 = 1200.000, ~11/10 = 163.678
* POTE: ~2 = 1200.000, ~11/10 = 163.688

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

{{Optimal ET sequence|legend=0| 7, 15f, 22 }}

Badness (Smith): 0.026043

== Opossum ==
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. 

[[Subgroup]]: 2.3.5.7

[[Comma list]]: 28/27, 126/125

{{Mapping|legend=1| 1 2 3 4 | 0 -3 -5 -9 }}

[[Optimal tuning]]s: 
* [[CTE]]: ~2 = 1200.000, ~10/9 = 161.306
: [[error map]]: {{val| 0.000 +14.126 +7.155 -20.583 }}
* [[POTE]]: ~2 = 1200.000, ~10/9 = 159.691
: error map: {{val| 0.000 +18.971 +15.229 -6.048 }}

[[Minimax tuning]]: 
* [[7-odd-limit|7-]] and [[9-odd-limit]] [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.7

{{Optimal ET sequence|legend=1| 7d, 8d, 15 }}

[[Badness]] (Smith): 0.040650

=== 11-limit ===
Subgroup: 2.3.5.7.11

Comma list: 28/27, 55/54, 77/75

Mapping: {{mapping| 1 2 3 4 4 | 0 -3 -5 -9 -4 }}

Optimal tunings: 
* CTE: ~2 = 1200.000, ~11/10 = 161.365
* POTE: ~2 = 1200.000, ~11/10 = 159.807

Minimax tuning: 
* 11-odd-limit unchanged-interval (eigenmonzo) basis: 2.7

{{Optimal ET sequence|legend=0| 7d, 8d, 15 }}

Badness (Smith): 0.022325

=== 13-limit ===
Subgroup: 2.3.5.7.11.13

Comma list: 28/27, 40/39, 55/54, 66/65

Mapping: {{mapping| 1 2 3 4 4 4 | 0 -3 -5 -9 -4 -2 }}

Optimal tunings: 
* CTE: ~2 = 1200.000, ~11/10 = 161.631
* POTE: ~2 = 1200.000, ~11/10 = 158.805

Minimax tuning: 
* 13- and 15-odd-limit unchanged-interval (eigenmonzo) basis: 2.7

{{Optimal ET sequence|legend=0| 7d, 8d, 15, 38bceff }}

Badness (Smith): 0.019389

== Porky ==
Porky can be described as {{nowrap| 22 & 29 }}, suggesting a less sharp perfect fifth. 7\51 is a good generator. 

[[Subgroup]]: 2.3.5.7

[[Comma list]]: 225/224, 250/243

{{Mapping|legend=1| 1 2 3 5 | 0 -3 -5 -16 }}

[[Optimal tuning]]s: 
* [[CTE]]: ~2 = 1200.000, ~10/9 = 164.391
: [[error map]]: {{val| 0.000 +4.871 -8.270 +0.913 }}
* [[POTE]]: ~2 = 1200.000, ~10/9 = 164.412
: error map: {{val| 0.000 +4.809 -8.375 +0.580 }}

[[Minimax tuning]]: 
* [[7-odd-limit|7-]] and [[9-odd-limit]]: ~10/9 = {{monzo| 2/11 0 1/11 -1/11 }}
: [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.7/5

{{Optimal ET sequence|legend=1| 7d, 15d, 22, 29, 51, 73c }}

[[Badness]] (Smith): 0.054389

=== 11-limit ===
Subgroup: 2.3.5.7.11

Comma list: 55/54, 100/99, 225/224

Mapping: {{mapping| 1 2 3 5 4 | 0 -3 -5 -16 -4 }}

Optimal tunings: 
* CTE: ~2 = 1200.000, ~11/10 = 164.321
* POTE: ~2 = 1200.000, ~11/10 = 164.552

Minimax tuning: 
* 11-odd-limit: ~11/10 = {{monzo| 2/11 0 1/11 -1/11 }}
: unchanged-interval (eigenmonzo) basis: 2.7/5

{{Optimal ET sequence|legend=0| 7d, 15d, 22, 51 }}

Badness (Smith): 0.027268

=== 13-limit ===
Subgroup: 2.3.5.7.11.13

Comma list: 55/54, 65/64, 91/90, 100/99

Mapping: {{mapping| 1 2 3 5 4 3 | 0 -3 -5 -16 -4 5 }}

Optimal tunings: 
* CTE: ~2 = 1200.000, ~11/10 = 164.478
* POTE: ~2 = 1200.000, ~11/10 = 164.953

{{Optimal ET sequence|legend=0| 7d, 22, 29, 51f, 80cdeff }}

Badness (Smith): 0.026543

; Music
* [https://www.youtube.com/watch?v=CN4cLOyaVGE ''Improvisation in 29edo''] (2024) by [[Budjarn Lambeth]] – in Palace scale, 29edo tuning

== Coendou ==
Coendou can be described as {{nowrap| 29 & 36c }}, suggesting an even less sharp or near-just perfect fifth. 9\65 is a good generator. 

[[Subgroup]]: 2.3.5.7

[[Comma list]]: 250/243, 525/512

{{Mapping|legend=1| 1 2 3 1 | 0 -3 -5 13 }}

[[Optimal tuning]]s: 
* [[CTE]]: ~2 = 1200.000, ~10/9 = 166.094
: [[error map]]: {{val| 0.000 -0.236 -16.783 -9.607 }}
* [[POTE]]: ~2 = 1200.000, ~10/9 = 166.041
: error map: {{val| 0.000 -0.077 -16.516 -10.299 }}

[[Minimax tuning]]: 
* [[7-odd-limit|7-]] and [[9-odd-limit]]: ~10/9 = {{monzo| 2/3 -1/3 }}
: [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.3

{{Optimal ET sequence|legend=1| 7, 22d, 29, 65c, 94cd }}

[[Badness]] (Smith): 0.118344

=== 11-limit ===
Subgroup: 2.3.5.7.11

Comma list: 55/54, 100/99, 525/512

Mapping: {{mapping| 1 2 3 1 4 | 0 -3 -5 13 -4 }}

Optimal tunings: 
* CTE: ~2 = 1200.000, ~11/10 = 165.925
* POTE: ~2 = 1200.000, ~11/10 = 165.981

Minimax tuning: 
* 11-odd-limit: ~11/10 = {{monzo| 2/3 -1/3 }}
: unchanged-interval (eigenmonzo) basis: 2.3

{{Optimal ET sequence|legend=0| 7, 22d, 29, 65ce }}

Badness (Smith): 0.049669

=== 13-limit ===
Subgroup: 2.3.5.7.11.13

Comma list: 55/54, 65/64, 100/99, 105/104

Mapping: {{mapping| 1 2 3 1 4 3 | 0 -3 -5 13 -4 5 }}

Optimal tunings: 
* CTE: ~2 = 1200.000, ~11/10 = 166.046
* POTE: ~2 = 1200.000, ~11/10 = 165.974

Minimax tuning: 
* 13- and 15-odd-limit: ~11/10 = {{monzo| 2/3 -1/3 }}
: unchanged-interval (eigenmonzo) basis: 2.3

{{Optimal ET sequence|legend=0| 7, 22d, 29, 65cef }}

Badness (Smith): 0.030233

== Hystrix ==
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.

[[Subgroup]]: 2.3.5.7

[[Comma list]]: 36/35, 160/147

{{Mapping|legend=1| 1 2 3 3 | 0 -3 -5 -1 }}

[[Optimal tuning]]s: 
* [[CTE]]: ~2 = 1200.000, ~10/9 = 165.185
: [[error map]]: {{val| 0.000 +2.491 -12.236 +65.990 }}
* [[POTE]]: ~2 = 1200.000, ~10/9 = 158.868
: error map: {{val| 0.000 +21.442 +19.348 +72.306 }}

[[Minimax tuning]]: 
* [[7-odd-limit|7-]] and [[9-odd-limit]]: ~10/9 = {{monzo| 3/5 0 -1/5 }}
: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.5

{{Optimal ET sequence|legend=1| 7, 8d, 15d }}

[[Badness]] (Smith): 0.044944

=== 11-limit ===
Subgroup: 2.3.5.7.11

Comma list: 22/21, 36/35, 80/77

Mapping: {{mapping| 1 2 3 3 4 | 0 -3 -5 -1 -4 }}

Optimal tunings: 
* CTE: ~2 = 1200.000, ~11/10 = 164.768
* POTE: ~2 = 1200.000, ~11/10 = 158.750

{{Optimal ET sequence|legend=0| 7, 8d, 15d }}

Badness (Smith): 0.026790

== Hedgehog ==
{{See also| Sensamagic clan | Stearnsmic clan }}

Hedgehog has a period 1/2 octave and a generator which can be taken to be 9/7 instead of 10/9. It also tempers out [[245/243]], the sensamagic comma. It is a strong extension of [[BPS]] (as BPS has no 2 or sqrt(2)). Its ploidacot is diploid omega-tricot. 

22edo provides an obvious tuning, which happens to be the only [[patent val|patent-val]] tuning, but if you are looking for an alternative you could try the {{val| 146 232 338 411 }} (146bccdd) val with generator 10\73, or you could try 164 cents if you are fond of round numbers. The 14-note mos gives scope for harmony while stopping well short of 22. A related temperament is [[echidna]], which offers much more accuracy. They merge on 22edo. 

[[Subgroup]]: 2.3.5.7

[[Comma list]]: 50/49, 245/243

{{Mapping|legend=1| 2 1 1 2 | 0 3 5 5 }}

: mapping generators: ~7/5, ~9/7

[[Optimal tuning]]s: 
* [[CTE]]: ~7/5 = 600.000, ~9/7 = 435.258
: [[error map]]: {{val| 0.000 +3.819 -10.024 +7.464 }}
* [[POTE]]: ~7/5 = 600.000, ~9/7 = 435.648
: error map: {{val| 0.000 +4.989 -8.074 +9.414 }}

{{Optimal ET sequence|legend=1| 8d, 14c, 22 }}

[[Badness]] (Smith): 0.043983

=== 11-limit ===
Subgroup: 2.3.5.7.11

Comma list: 50/49, 55/54, 99/98

Mapping: {{mapping| 2 1 1 2 4 | 0 3 5 5 4 }}

Optimal tunings: 
* CTE: ~7/5 = 600.000, ~9/7 = 435.528
* POTE: ~7/5 = 600.000, ~9/7 = 435.386

{{Optimal ET sequence|legend=0| 8d, 14c, 22, 58ce }}

Badness (Smith): 0.023095

==== 13-limit ====
Subgroup: 2.3.5.7.11.13

Comma list: 50/49, 55/54, 65/63, 99/98

Mapping: {{mapping| 2 1 1 2 4 3 | 0 3 5 5 4 6 }}

Optimal tunings: 
* CTE: ~7/5 = 600.000, ~9/7 = 436.309
* POTE: ~7/5 = 600.000, ~9/7 = 435.861

{{Optimal ET sequence|legend=0| 8d, 14cf, 22 }}

Badness (Smith): 0.021516

==== Urchin ====
Subgroup: 2.3.5.7.11.13

Comma list: 40/39, 50/49, 55/54, 66/65

Mapping: {{mapping| 2 1 1 2 4 6 | 0 3 5 5 4 2 }}

Optimal tunings: 
* CTE: ~7/5 = 600.000, ~9/7 = 435.186
* POTE: ~7/5 = 600.000, ~9/7 = 437.078

{{Optimal ET sequence|legend=0| 14c, 22f }}

Badness (Smith): 0.025233

=== Hedgepig ===
Subgroup: 2.3.5.7.11

Comma list: 50/49, 245/243, 385/384

Mapping: {{mapping| 2 1 1 2 12 | 0 3 5 5 -7 }}

Optimal tunings: 
* CTE: ~7/5 = 600.000, ~9/7 = 435.329
* POTE: ~7/5 = 600.000, ~9/7 = 435.425

{{Optimal ET sequence|legend=0| 22 }}

Badness (Smith): 0.068406

; Music
* [http://micro.soonlabel.com/22-ET/20120207-phobos-light-hedgehog14.mp3 ''Phobos Light''] by [[Chris Vaisvil]] – in [[hedgehog14|hedgehog[14]]], 22edo tuning.

== Nautilus ==
Nautilus tempers out 49/48 and may be described as the {{nowrap| 14c & 15 }} temperament. Its ploidacot is omega-hexacot. 

[[Subgroup]]: 2.3.5.7

[[Comma list]]: 49/48, 250/243

{{Mapping|legend=1| 1 2 3 3 | 0 -6 -10 -3 }}

: mapping generators: ~2, ~21/20

[[Optimal tuning]]s: 
* [[CTE]]: ~2 = 1200.000, ~21/20 = 81.914
: [[error map]]: {{val| 0.000 +6.559 -5.457 -14.569 }}
* [[POTE]]: ~2 = 1200.000, ~21/20 = 82.505
: error map: {{val| 0.000 +3.012 -11.368 -16.342 }}

{{Optimal ET sequence|legend=1| 14c, 15, 29, 44d }}

[[Badness]] (Smith): 0.057420

=== 11-limit ===
Subgroup: 2.3.5.7.11

Comma list: 49/48, 55/54, 245/242

Mapping: {{mapping| 1 2 3 3 4 | 0 -6 -10 -3 -8 }}

Optimal tunings: 
* CTE: ~2 = 1200.000, ~21/20 = 81.802
* POTE: ~2 = 1200.000, ~21/20 = 82.504

{{Optimal ET sequence|legend=0| 14c, 15, 29, 44d }}

Badness (Smith): 0.026023

==== 13-limit ====
Subgroup: 2.3.5.7.11.13

Comma list: 49/48, 55/54, 91/90, 100/99

Mapping: {{mapping| 1 2 3 3 4 5 | 0 -6 -10 -3 -8 -19 }}

Optimal tunings: 
* CTE: ~2 = 1200.000, ~21/20 = 81.912
* POTE: ~2 = 1200.000, ~21/20 = 82.530

{{Optimal ET sequence|legend=0| 14cf, 15, 29, 44d }}

Badness (Smith): 0.022285

==== Belauensis ====
Subgroup: 2.3.5.7.11.13

Comma list: 40/39, 49/48, 55/54, 66/65

Mapping: {{mapping| 1 2 3 3 4 4 | 0 -6 -10 -3 -8 -4 }}

Optimal tunings: 
* CTE: ~2 = 1200.000, ~21/20 = 82.034
* POTE: ~2 = 1200.000, ~21/20 = 81.759

{{Optimal ET sequence|legend=0| 14c, 15, 29f, 44dff }}

Badness (Smith): 0.029816

; Music
* [http://micro.soonlabel.com/gene_ward_smith/Others/Igs/NautilusReverie.mp3 ''Nautilus Reverie''] by [[Igliashon Jones|Igliashon Calvin Jones-Coolidge]]

== Ammonite ==
Ammonite adds 686/675 to the comma list and may be described as the {{nowrap| 8d & 29 }} temperament. Its ploidacot is epsilon-enneacot. [[37edo]] provides an obvious tuning. 

[[Subgroup]]: 2.3.5.7

[[Comma list]]: 250/243, 686/675

{{Mapping|legend=1| 1 5 8 10 | 0 -9 -15 -19 }}

: mapping generators: ~2, ~9/7

[[Optimal tuning]]s: 
* [[CTE]]: ~2 = 1200.000, ~9/7 = 454.550
: [[error map]]: {{val| 0.000 +7.095 -4.564 -5.276 }}
* [[POTE]]: ~2 = 1200.000, ~9/7 = 454.448
: error map: {{val| 0.000 +8.009 -3.040 -3.346 }}

{{Optimal ET sequence|legend=1| 8d, 21cd, 29, 37, 66 }}

[[Badness]] (Smith): 0.107686

=== 11-limit ===
Subgroup: 2.3.5.7.11

Comma list: 55/54, 100/99, 686/675

Mapping: {{mapping| 1 5 8 10 8 | 0 -9 -15 -19 -12 }}

Optimal tunings: 
* CTE: ~2 = 1200.000, ~9/7 = 454.505
* POTE: ~2 = 1200.000, ~9/7 = 454.512

{{Optimal ET sequence|legend=0| 8d, 21cde, 29, 37, 66 }}

Badness (Smith): 0.045694

=== 13-limit ===
Subgroup: 2.3.5.7.11.13

Comma list: 55/54, 91/90, 100/99, 169/168

Mapping: {{mapping| 1 5 8 10 8 9 | 0 -9 -15 -19 -12 -14 }}

Optimal tunings: 
* CTE: ~2 = 1200.000, ~13/10 = 454.480
* POTE: ~2 = 1200.000, ~13/10 = 454.529

{{Optimal ET sequence|legend=0| 8d, 21cdef, 29, 37, 66 }}

Badness (Smith): 0.027168

== Ceratitid ==
Ceratitid adds 1728/1715 to the comma list and may be described as the {{nowrap| 21c & 22 }} temperament. Its ploidacot is omega-enneacot. [[22edo]] provides an obvious tuning. 

[[Subgroup]]: 2.3.5.7

[[Comma list]]: 250/243, 1728/1715

{{Mapping|legend=1| 1 2 3 3 | 0 -9 -15 -4 }}

: mapping generators: ~2, ~36/35

[[Optimal tuning]]s: 
* [[CTE]]: ~2 = 1200.000, ~36/35 = 54.804
: [[error map]]: {{val| 0.000 +4.809 -8.374 +11.958 }}
* [[POTE]]: ~2 = 1200.000, ~36/35 = 54.384
: error map: {{val| 0.000 +8.585 -2.081 +13.636 }}

{{Optimal ET sequence|legend=1| 1c, 21c, 22 }}

[[Badness]] (Smith): 0.115304

=== 11-limit ===
Subgroup: 2.3.5.7.11

Comma list: 55/54, 100/99, 352/343

Mapping: {{mapping| 1 2 3 3 4 | 0 -9 -15 -4 -12 }}

Optimal tunings: 
* CTE: ~2 = 1200.000, ~36/35 = 54.702
* POTE: ~2 = 1200.000, ~36/35 = 54.376

{{Optimal ET sequence|legend=0| 1ce, 21ce, 22 }}

Badness (Smith): 0.051319

=== 13-limit ===
Subgroup: 2.3.5.7.11.13

Comma list: 55/54, 65/63, 100/99, 352/343

Mapping: {{mapping| 1 2 3 3 4 4 | 0 -9 -15 -4 -12 -7 }}

Optimal tunings: 
* CTE: ~2 = 1200.000, ~36/35 = 54.575
* POTE: ~2 = 1200.000, ~36/35 = 54.665

{{Optimal ET sequence|legend=0| 1ce, 21cef, 22 }}

Badness (Smith): 0.044739

[[Category:Temperament families]]
[[Category:Pages with mostly numerical content]]
[[Category:Porcupine family| ]] <!-- main article -->
[[Category:Porcupine| ]] <!-- key article -->
[[Category:Rank 2]]