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The 5-limit parent comma for the '''porcupine family''' is [[250/243]], the maximal diesis or porcupine comma. Its [[monzo]] is {{monzo| 1 -5 3 }}, and flipping that yields {{multival| 3 5 1 }} for the [[wedgie]]. This tells us the [[generator]] is a minor whole tone, the [[10/9]] interval, and that three of these add up to a fourth, with two more giving the minor sixth. In fact, (10/9)<sup>3</sup> = 4/3 × 250/243, and (10/9)<sup>5</sup> = 8/5 × (250/243)<sup>2</sup>. [[22edo|3\22]] is a very recommendable generator, and MOS of 7, 8 and 15 notes make for some nice scale possibilities.
{{Technical data page}}
 
The '''porcupine family''' of [[regular temperament|temperaments]] [[tempering out|tempers out]] the [[porcupine comma]], [[250/243]], also called the maximal diesis.  
The second comma of the [[Normal lists #Normal interval list|normal comma list]] defines which [[7-limit]] family member we are looking at. That means
* [[64/63]], the archytas comma, for [[#Septimal porcupine|septimal porcupine]],  
* [[36/35]], the septimal quarter tone, for [[#Hystrix|hystrix]],
* [[50/49]], the jubilisma, for [[#Hedgehog|hedgehog]], and
* [[49/48]], the slendro diesis, for [[#Nautilus|nautilus]].
 
All these 7-limit extensions notably share the same 2.3.5.11 subgroup, ''porkypine''.
 
Temperaments discussed elsewhere include [[opossum]], [[Septisemi temperaments #Oxygen|oxygen]], and [[Dicot family #Jamesbond|jamesbond]].


== Porcupine ==
== Porcupine ==
{{Main| 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
[[Subgroup]]: 2.3.5
Line 24: Line 17:
[[Comma list]]: 250/243
[[Comma list]]: 250/243


[[Mapping]]: [{{val| 1 2 3 }}, {{val| 0 -3 -5 }}]
{{Mapping|legend=1| 1 2 3 | 0 -3 -5 }}
: mapping generators: ~2, ~10/9


: Mapping generators: ~2, ~10/9
[[Optimal tuning]]s:  
 
* [[WE]]: ~2 = 1199.5444{{c}}, ~10/9 = 163.8881{{c}}
[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~10/9 = 164.1659
: [[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 }}


[[Tuning ranges]]:  
[[Tuning ranges]]:  
* 5-odd-limit [[diamond monotone]]: ~10/9 = [150.000, 171.429] (1\8 to 1\7)
* [[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]
* 5-odd-limit [[diamond tradeoff]]: ~10/9 = [157.821, 166.015]
* 5-odd-limit diamond monotone and tradeoff: ~10/9 = [157.821, 166.015]


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


[[Badness]]: 0.030778
[[Badness]] (Sintel): 0.722
 
=== 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]]'' → [[Whitewood family #Jamesbond|Whitewood family]]
 
==== 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) ===
=== 2.3.5.11 subgroup (porkypine) ===
Line 44: Line 59:
Comma list: 55/54, 100/99
Comma list: 55/54, 100/99


Sval mapping: [{{val| 1 2 3 4 }}, {{val| 0 -3 -5 -4 }}]
Subgroup-val mapping: {{mapping| 1 2 3 4 | 0 -3 -5 -4 }}
 
Gencom mapping: [{{val| 1 2 3 0 4 }}, {{val| 0 -3 -5 0 -4 }}]


Gencom: [2 10/9; 55/54, 100/99]
Gencom mapping: {{mapping| 1 2 3 0 4 | 0 -3 -5 0 -4 }}


Optimal tuning (CTE): ~2 = 1\1, ~11/10 = 163.8867
Optimal tunings:
* WE: ~2 = 1200.3290{{c}}, ~11/10 = 164.1227{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 163.9951{{c}}


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


Badness: 0.0097
Badness (Sintel): 0.303


==== Undecimation ====
==== Undecimation ====
Line 61: Line 76:
Comma list: 55/54, 100/99, 512/507
Comma list: 55/54, 100/99, 512/507


Sval mapping: [{{val| 1 5 8 8 2 }}, {{val| 0 -6 -10 -8 3 }}]
Subgroup-val mapping: {{mapping| 1 -1 -2 0 5 | 0 6 10 8 -3 }}


: Sval mapping generators: ~2, ~65/44
: mapping generators: ~2, ~88/65


Optimal tuning (CTE): ~2 = 1\1, ~88/65 = 518.2094
Optimal tunings:
* WE: ~2 = 1199.4791{{c}}, ~88/65 = 517.9845{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~88/65 = 518.1740{{c}}


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


Badness: 0.0305
Badness (Sintel): 1.21


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


Septimal porcupine uses six of its minor tone generator steps to get to [[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.
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
[[Subgroup]]: 2.3.5.7
Line 80: Line 97:
[[Comma list]]: 64/63, 250/243
[[Comma list]]: 64/63, 250/243


[[Mapping]]: [{{val| 1 2 3 2 }}, {{val| 0 -3 -5 6 }}]
{{Mapping|legend=1| 1 2 3 2 | 0 -3 -5 6 }}
 
{{Multival|legend=1| 3 5 -6 1 -18 -28 }}


[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~10/9 = 163.2032
[[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 }}


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


[[Tuning ranges]]:  
[[Tuning ranges]]:  
Line 96: Line 115:
* 7-odd-limit [[diamond tradeoff]]: ~10/9 = [157.821, 166.015]
* 7-odd-limit [[diamond tradeoff]]: ~10/9 = [157.821, 166.015]
* 9-odd-limit diamond tradeoff: ~10/9 = [157.821, 182.404]
* 9-odd-limit diamond tradeoff: ~10/9 = [157.821, 182.404]
* 7- and 9-odd-limit diamond monotone and tradeoff: ~10/9 = [160.000, 163.636]


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


[[Badness]]: 0.041057
[[Badness]] (Sintel): 1.04


=== 11-limit ===
=== 11-limit ===
Line 107: Line 125:
Comma list: 55/54, 64/63, 100/99
Comma list: 55/54, 64/63, 100/99


Mapping: [{{val| 1 2 3 2 4 }}, {{val| 0 -3 -5 6 -4 }}]
Mapping: {{mapping| 1 2 3 2 4 | 0 -3 -5 6 -4 }}


Optimal tuning (CTE): ~2 = 1\1, ~11/10 = 163.1055
Optimal tunings:
* WE: ~2 = 1198.3250{{c}}, ~11/10 = 162.5202{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 162.8156{{c}}


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


Tuning ranges:  
Tuning ranges:  
* 11-odd-limit diamond monotone: ~11/10 = [160.000, 163.636] (2\15 to 3\22)
* 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]
* 11-odd-limit diamond tradeoff: ~11/10 = [150.637, 182.404]
* 11-odd-limit diamond monotone and tradeoff: ~11/10 = [160.000, 163.636]


Optimal GPV sequence: {{val list| 7, 15, 22, 37, 59 }}
{{Optimal ET sequence|legend=0| 7, 15, 22, 37, 59 }}
 
Badness (Sintel): 0.713


Badness: 0.021562
==== Porcupinefowl ====
This extension used to be ''tridecimal porcupine''.  


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


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


Mapping: [{{val| 1 2 3 2 4 4 }}, {{val| 0 -3 -5 6 -4 -2 }}]
Mapping: {{mapping| 1 2 3 2 4 4 | 0 -3 -5 6 -4 -2 }}


Optimal tuning (CTE): ~2 = 1\1, ~11/10 = 163.4425
Optimal tunings:
* WE: ~2 = 1197.0054{{c}}, ~11/10 = 162.3022{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 162.8314{{c}}


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


Tuning ranges:  
Tuning ranges:  
Line 141: Line 164:
* 15-odd-limit diamond monotone: ~11/10 = 163.636 (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]
* 13- and 15-odd-limit diamond tradeoff: ~11/10 = [138.573, 182.404]
* 13-odd-limit diamond monotone and tradeoff: ~11/10 = [160.000, 163.636]
* 15-odd-limit diamond monotone and tradeoff: ~11/10 = 163.636


Optimal GPV sequence: {{val list| 7, 15, 22f, 37f }}
{{Optimal ET sequence|legend=0| 7, 15, 22f }}


Badness: 0.021276
Badness (Sintel): 0.879


==== Porcupinefish ====
==== Porcupinefish ====
Line 155: Line 176:
Comma list: 55/54, 64/63, 91/90, 100/99
Comma list: 55/54, 64/63, 91/90, 100/99


Mapping: [{{val| 1 2 3 2 4 6 }}, {{val| 0 -3 -5 6 -4 -17 }}]
Mapping: {{mapping| 1 2 3 2 4 6 | 0 -3 -5 6 -4 -17 }}


Optimal tuning (CTE): ~2 = 1\1, ~11/10 = 162.6361
Optimal tunings:
* WE: ~2 = 1198.3206{{c}}, ~11/10 = 162.0502{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 162.3458{{c}}


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


Tuning ranges:  
Tuning ranges:  
* 13-odd-limit diamond monotone: ~10/9 = [160.000, 162.162] (2\15 to 5\37)
* 13-odd-limit diamond monotone: ~11/10 = [160.000, 162.162] (2\15 to 5\37)
* 15-odd-limit diamond monotone: ~10/9 = 162.162 (5\37)
* 15-odd-limit diamond monotone: ~11/10 = 162.162 (5\37)
* 13- and 15-odd-limit diamond tradeoff: ~10/9 = [150.637, 182.404]
* 13- and 15-odd-limit diamond tradeoff: ~11/10 = [150.637, 182.404]
* 13-odd-limit diamond monotone and tradeoff: ~10/9 = [160.000, 162.162]
* 15-odd-limit diamond monotone and tradeoff: ~10/9 = 162.162


Optimal GPV sequence: {{val list| 15, 22, 37 }}
{{Optimal ET sequence|legend=0| 15, 22, 37 }}


Badness: 0.025314
Badness (Sintel): 1.05


==== Pourcup ====
==== Pourcup ====
Line 179: Line 200:
Comma list: 55/54, 64/63, 100/99, 196/195
Comma list: 55/54, 64/63, 100/99, 196/195


Mapping: [{{val| 1 2 3 2 4 1 }}, {{val| 0 -3 -5 6 -4 20 }}]
Mapping: {{mapping| 1 2 3 2 4 1 | 0 -3 -5 6 -4 20 }}


Optimal tuning (CTE): ~2 = 1\1, ~11/10 = 163.3781
Optimal tunings:
* WE: ~2 = 1198.0537{{c}}, ~11/10 = 162.2183{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 162.4665{{c}}


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


Optimal GPV sequence: {{val list| 15f, 22f, 37, 59f }
{{Optimal ET sequence|legend=0| 15f, 22f, 37, 59f }}


Badness: 0.035130
Badness (Sintel): 1.45


==== Porkpie ====
==== Porkpie ====
Line 196: Line 219:
Comma list: 55/54, 64/63, 65/63, 100/99
Comma list: 55/54, 64/63, 65/63, 100/99


Mapping: [{{val| 1 2 3 2 4 3 }}, {{val| 0 -3 -5 6 -4 5 }}]
Mapping: {{mapping| 1 2 3 2 4 3 | 0 -3 -5 6 -4 5 }}


Optimal tuning (CTE): ~2 = 1\1, ~11/10 = 163.6778
Optimal tunings:
* WE: ~2 = 1200.0223{{c}}, ~11/10 = 163.6908{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 163.6874{{c}}


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


Optimal GPV sequence: {{val list| 7, 15f, 22 }}
{{Optimal ET sequence|legend=0| 7, 15f, 22 }}


Badness: 0.026043
Badness (Sintel): 1.08


== Hystrix ==
== Opossum ==
Hystrix 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|15EDO]]. They can try the even sharper fifth of hystrix in [[68edo|68EDO]] and see how that suits.
{{Main| Opossum }}


Subgroup: 2.3.5.7
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.  


[[Comma list]]: 36/35, 160/147
[[Subgroup]]: 2.3.5.7


[[Mapping]]: [{{val| 1 2 3 3 }}, {{val| 0 -3 -5 -1 }}]
[[Comma list]]: 28/27, 126/125


{{Multival|legend=1| 3 5 1 1 -7 -12 }}
{{Mapping|legend=1| 1 2 3 4 | 0 -3 -5 -9 }}


[[POTE generator]]: ~8/7 = 158.868
[[Optimal tuning]]s:
* [[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 }}


[[Minimax tuning]]:  
[[Minimax tuning]]:  
* [[7-odd-limit|7-]] and [[9-odd-limit]]: ~8/7 = {{monzo| 3/5 0 -1/5 }}
* [[7-odd-limit|7-]] and [[9-odd-limit]] [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.7
: Eigenmonzos (unchanged intervals): 2, 5/4


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


[[Badness]]: 0.044944
[[Badness]] (Sintel): 1.03


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


Comma list: 22/21, 36/35, 80/77
Comma list: 28/27, 55/54, 77/75
 
Mapping: {{mapping| 1 2 3 4 4 | 0 -3 -5 -9 -4 }}
 
Optimal tunings:
* WE: ~2 = 1196.2331{{c}}, ~11/10 = 159.3050{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 160.4644{{c}}
 
Minimax tuning:
* 11-odd-limit unchanged-interval (eigenmonzo) basis: 2.7
 
{{Optimal ET sequence|legend=0| 7d, 8d, 15 }}
 
Badness (Sintel): 0.738
 
=== 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 }}


Mapping: [{{val| 1 2 3 3 4 }}, {{val| 0 -3 -5 -1 -4 }}]
Optimal tunings:  
* WE: ~2 = 1193.5447{{c}}, ~11/10 = 157.9505{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 159.7600{{c}}


POTE generator: ~8/7 = 158.750
Minimax tuning:  
* 13- and 15-odd-limit unchanged-interval (eigenmonzo) basis: 2.7


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


Badness: 0.026790
Badness (Sintel): 0.801


== Porky ==
== Porky ==
Subgroup: 2.3.5.7
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
[[Comma list]]: 225/224, 250/243


[[Mapping]]: [{{val| 1 2 3 5 }}, {{val| 0 -3 -5 -16 }}]
{{Mapping|legend=1| 1 2 3 5 | 0 -3 -5 -16 }}
 
{{Multival|legend=1| 3 5 16 1 17 23 }}


[[POTE generator]]: ~10/9 = 164.412
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.0685{{c}}, ~10/9 = 164.4215{{c}}
: [[error map]]: {{val| +0.068 +4.917 -8.216 +0.772 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~10/9 = 164.4060{{c}}
: error map: {{val| 0.000 +4.827 -8.344 +0.678 }}


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


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


[[Badness]]: 0.054389
[[Badness]] (Sintel): 1.38


=== 11-limit ===
=== 11-limit ===
Line 266: Line 321:
Comma list: 55/54, 100/99, 225/224
Comma list: 55/54, 100/99, 225/224


Mapping: [{{val| 1 2 3 5 4 }}, {{val| 0 -3 -5 -16 -4 }}]
Mapping: {{mapping| 1 2 3 5 4 | 0 -3 -5 -16 -4 }}


POTE generator: ~10/9 = 164.552
Optimal tunings:  
* WE: ~2 = 1200.8706{{c}}, ~11/10 = 164.6715{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 164.4810{{c}}


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


Optimal GPV sequence: {{val list| 7d, 15d, 22, 29, 51, 73ce }}
{{Optimal ET sequence|legend=0| 7d, 15d, 22, 51 }}


Badness: 0.027268
Badness (Sintel): 0.901


=== 13-limit ===
=== 13-limit ===
Line 283: Line 340:
Comma list: 55/54, 65/64, 91/90, 100/99
Comma list: 55/54, 65/64, 91/90, 100/99


Mapping: [{{val| 1 2 3 5 4 3 }}, {{val| 0 -3 -5 -16 -4 5 }}]
Mapping: {{mapping| 1 2 3 5 4 3 | 0 -3 -5 -16 -4 5 }}
 
Optimal tunings:
* WE: ~2 = 1202.1557{{c}}, ~11/10 = 165.2494{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 164.8579{{c}}


POTE generator: ~10/9 = 164.953
{{Optimal ET sequence|legend=0| 7d, 22, 29, 51f, 80cdeff }}


Optimal GPV sequence: {{val list| 7d, 22, 29, 51f, 80cdeff }}
Badness (Sintel): 1.10


Badness: 0.026543
; Music
* [https://www.youtube.com/watch?v=CN4cLOyaVGE ''Improvisation in 29edo''] (2024) by [[Budjarn Lambeth]] – in Palace scale, 29edo tuning


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


[[Mapping]]: [{{val| 1 2 3 1 }}, {{val| 0 -3 -5 13 }}]
{{Mapping|legend=1| 1 2 3 1 | 0 -3 -5 13 }}


{{Multival|legend=1| 3 5 -13 1 -29 -44 }}
[[Optimal tuning]]s:
 
* [[WE]]: ~2 = 1202.6772{{c}}, ~10/9 = 166.4110{{c}}
[[POTE generator]]: ~10/9 = 166.041
: [[error map]]: {{val| +2.678 +4.166 -10.337 -2.806 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~10/9 = 166.0511{{c}}
: error map: {{val| 0.000 -0.108 -16.569 -10.161 }}


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


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


[[Badness]]: 0.118344
[[Badness]] (Sintel): 2.99


=== 11-limit ===
=== 11-limit ===
Line 315: Line 381:
Comma list: 55/54, 100/99, 525/512
Comma list: 55/54, 100/99, 525/512


Mapping: [{{val| 1 2 3 1 4 }}, {{val| 0 -3 -5 13 -4 }}]
Mapping: {{mapping| 1 2 3 1 4 | 0 -3 -5 13 -4 }}


POTE generator: ~10/9 = 165.981
Optimal tunings:  
* WE: ~2 = 1203.0245{{c}}, ~11/10 = 166.3991{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 165.9714{{c}}


Minimax tuning:  
Minimax tuning:  
* 11-odd-limit: ~10/9 = {{monzo| 2/3 -1/3 }}
* 11-odd-limit: ~11/10 = {{monzo| 2/3 -1/3 }}
: Eigenmonzos (unchanged intervals): 2, 3
: unchanged-interval (eigenmonzo) basis: 2.3


Optimal GPV sequence: {{val list| 7, 29, 65ce, 94cde }}
{{Optimal ET sequence|legend=0| 7, 22d, 29, 65ce }}


Badness: 0.049669
Badness (Sintel): 1.64


=== 13-limit ===
=== 13-limit ===
Line 332: Line 400:
Comma list: 55/54, 65/64, 100/99, 105/104
Comma list: 55/54, 65/64, 100/99, 105/104


Mapping: [{{val| 1 2 3 1 4 3 }}, {{val| 0 -3 -5 13 -4 5 }}]
Mapping: {{mapping| 1 2 3 1 4 3 | 0 -3 -5 13 -4 5 }}


POTE generator: ~10/9 = 165.974
Optimal tunings:  
* WE: ~2 = 1202.9957{{c}}, ~11/10 = 166.3885{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 165.9843{{c}}


Minimax tuning:  
Minimax tuning:  
* 13- and 15-odd-limit: ~10/9 = {{monzo| 2/3 -1/3 }}
* 13- and 15-odd-limit: ~11/10 = {{monzo| 2/3 -1/3 }}
: Eigenmonzos (unchanged intervals): 2, 3
: unchanged-interval (eigenmonzo) basis: 2.3
 
{{Optimal ET sequence|legend=0| 7, 22d, 29, 65cef }}
 
Badness (Sintel): 1.25
 
== 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:
* [[WE]]: ~2 = 1187.8599{{c}}, ~10/9 = 157.2605{{c}}
: [[error map]]: {{val| -12.140 +1.983 -9.037 +37.493 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~10/9 = 161.2833{{c}}
: error map: {{val| 0.000 +14.195 +7.270 +69.891 }}
 
[[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 }}


Optimal GPV sequence: {{val list| 7, 29, 65cef, 94cdef }}
[[Badness]] (Sintel): 1.14


Badness: 0.030233
=== 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:
* WE: ~2 = 1189.2810{{c}}, ~11/10 = 157.3322{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 160.9603{{c}}
 
{{Optimal ET sequence|legend=0| 7, 8d, 15d }}
 
Badness (Sintel): 0.886


== Hedgehog ==
== Hedgehog ==
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. 22EDO provides the obvious tuning, but if you are looking for an alternative, you could try the {{val| 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.
{{See also| Sensamagic clan | Stearnsmic clan }}


Subgroup: 2.3.5.7
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.
 
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
[[Comma list]]: 50/49, 245/243


[[Mapping]]: [{{val| 2 1 1 2 }}, {{val| 0 3 5 5 }}]
{{Mapping|legend=1| 2 1 1 2 | 0 3 5 5 }}


{{Multival|legend=1| 6 10 10 2 -1 -5 }}
: mapping generators: ~7/5, ~9/7


[[POTE generator]]: ~9/7 = 435.648
[[Optimal tuning]]s:  
* [[WE]]: ~7/5 = 599.6061{{c}}, ~9/7 = 435.3620{{c}}
: [[error map]]: {{val| -0.788 +3.737 -9.897 +7.197 }}
* [[CWE]]: ~7/5 = 600.0000{{c}}, ~9/7 = 435.4483{{c}}
: error map: {{val| 0.000 +4.390 -9.072 +8.416 }}


{{Val list|legend=1| 8d, 14c, 22, 146bccdd }}
{{Optimal ET sequence|legend=1| 8d, 14c, 22 }}


[[Badness]]: 0.043983
[[Badness]] (Sintel): 1.11


=== 11-limit ===
=== 11-limit ===
Line 366: Line 482:
Comma list: 50/49, 55/54, 99/98
Comma list: 50/49, 55/54, 99/98


Mapping: [{{val| 2 1 1 2 4 }}, {{val| 0 3 5 5 4 }}]
Mapping: {{mapping| 2 1 1 2 4 | 0 3 5 5 4 }}


POTE generator: ~9/7 = 435.386
Optimal tunings:  
* WE: ~7/5 = 600.1133{{c}}, ~9/7 = 435.4680{{c}}
* CWE: ~7/5 = 600.0000{{c}}, ~9/7 = 435.4431{{c}}


Optimal GPV sequence: {{val list| 8d, 14c, 22, 58ce, 80ce, 102cde }}
{{Optimal ET sequence|legend=0| 8d, 14c, 22, 58ce }}


Badness: 0.023095
Badness (Sintel): 0.764


==== 13-limit ====
==== 13-limit ====
Line 379: Line 497:
Comma list: 50/49, 55/54, 65/63, 99/98
Comma list: 50/49, 55/54, 65/63, 99/98


Mapping: [{{val| 2 1 1 2 4 3 }}, {{val| 0 3 5 5 4 6 }}]
Mapping: {{mapping| 2 1 1 2 4 3 | 0 3 5 5 4 6 }}


POTE generator: ~9/7 = 435.861
Optimal tunings:  
* WE: ~7/5 = 600.3651{{c}}, ~9/7 = 436.1258{{c}}
* CWE: ~7/5 = 600.0000{{c}}, ~9/7 = 436.0483{{c}}


Optimal GPV sequence: {{val list| 8d, 14cf, 22 }}
{{Optimal ET sequence|legend=0| 8d, 14cf, 22 }}


Badness: 0.021516
Badness (Sintel): 0.889


==== Urchin ====
==== Urchin ====
Line 392: Line 512:
Comma list: 40/39, 50/49, 55/54, 66/65
Comma list: 40/39, 50/49, 55/54, 66/65


Mapping: [{{val| 2 1 1 2 4 6 }}, {{val| 0 3 5 5 4 2 }}]
Mapping: {{mapping| 2 1 1 2 4 6 | 0 3 5 5 4 2 }}


POTE generator: ~9/7 = 437.078
Optimal tunings:  
* WE: ~7/5 = 598.3303{{c}}, ~9/7 = 435.8617{{c}}
* CWE: ~7/5 = 600.0000{{c}}, ~9/7 = 436.3485{{c}}


Optimal GPV sequence: {{val list| 14c, 22f }}
{{Optimal ET sequence|legend=0| 14c, 22f }}


Badness: 0.025233
Badness (Sintel): 1.04


=== Hedgepig ===
=== Hedgepig ===
Line 405: Line 527:
Comma list: 50/49, 245/243, 385/384
Comma list: 50/49, 245/243, 385/384


Mapping: [{{val| 2 1 1 2 12 }}, {{val| 0 3 5 5 -7 }}]
Mapping: {{mapping| 2 1 1 2 12 | 0 3 5 5 -7 }}


POTE generator: ~9/7 = 435.425
Optimal tunings:  
* WE: ~7/5 = 599.7917{{c}}, ~9/7 = 435.2737{{c}}
* CWE: ~7/5 = 600.0000{{c}}, ~9/7 = 435.4047{{c}}


Optimal GPV sequence: {{val list| 22, 80c, 102cd, 124cd }}
{{Optimal ET sequence|legend=0| 22 }}


Badness: 0.068406
Badness (Sintel): 2.26


; Music
; Music
[http://micro.soonlabel.com/22-ET/20120207-phobos-light-hedgehog14.mp3 Phobos Light] by [[Chris Vaisvil]] in Hedgehog[14] [[hedgehog14|tuned]] to 22EDO.
* [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 ==
Subgroup: 2.3.5.7
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
[[Comma list]]: 49/48, 250/243


[[Mapping]]: [{{val| 1 2 3 3 }}, {{val| 0 -6 -10 -3 }}]
{{Mapping|legend=1| 1 2 3 3 | 0 -6 -10 -3 }}


{{Multival|legend=1| 6 10 3 2 -12 -21 }}
: mapping generators: ~2, ~21/20


[[POTE generator]]: ~21/20 = 82.505
[[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 }}


{{Val list|legend=1| 14c, 15, 29, 44d, 59d, 73cd, 102cd }}
{{Optimal ET sequence|legend=1| 14c, 15, 29 }}


[[Badness]]: 0.057420
[[Badness]] (Sintel): 1.45


=== 11-limit ===
=== 11-limit ===
Line 436: Line 566:
Comma list: 49/48, 55/54, 245/242
Comma list: 49/48, 55/54, 245/242


Mapping: [{{val| 1 2 3 3 4 }}, {{val| 0 -6 -10 -3 -8 }}]
Mapping: {{mapping| 1 2 3 3 4 | 0 -6 -10 -3 -8 }}


POTE generator: ~21/20 = 82.504
Optimal tunings:  
* WE: ~2 = 1202.3781{{c}}, ~21/20 = 82.6673{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~21/20 = 82.2434{{c}}


Optimal GPV sequence: {{val list| 14c, 15, 29, 44d, 59d, 73cde, 102cde }}
{{Optimal ET sequence|legend=0| 14c, 15, 29 }}


Badness: 0.026023
Badness (Sintel): 0.860


==== 13-limit ====
==== 13-limit ====
Line 449: Line 581:
Comma list: 49/48, 55/54, 91/90, 100/99
Comma list: 49/48, 55/54, 91/90, 100/99


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


POTE generator: ~21/20 = 82.530
Optimal tunings:  
* WE: ~2 = 1202.4145{{c}}, ~21/20 = 82.6963{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~21/20 = 82.3130{{c}}


Optimal GPV sequence: {{val list| 14cf, 15, 29, 44d, 59df, 73cde, 102cde }}
{{Optimal ET sequence|legend=0| 14cf, 15, 29 }}


Badness: 0.022285
Badness (Sintel): 0.921


==== Belauensis ====
==== Belauensis ====
Line 462: Line 596:
Comma list: 40/39, 49/48, 55/54, 66/65
Comma list: 40/39, 49/48, 55/54, 66/65


Mapping: [{{val| 1 2 3 3 4 4 }}, {{val| 0 -6 -10 -3 -8 -4 }}]
Mapping: {{mapping| 1 2 3 3 4 4 | 0 -6 -10 -3 -8 -4 }}


POTE generator: ~21/20 = 81.759
Optimal tunings:  
* WE: ~2 = 1199.0072{{c}}, ~21/20 = 81.6911{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~21/20 = 81.8576{{c}}


Optimal GPV sequence: {{val list| 14c, 15, 29f, 44df }}
{{Optimal ET sequence|legend=0| 14c, 15 }}


Badness: 0.029816
Badness (Sintel): 1.23


; Music
; Music
[http://micro.soonlabel.com/gene_ward_smith/Others/Igs/NautilusReverie.mp3 Nautilus Reverie] by [[Igliashon Jones|Igliashon Calvin Jones-Coolidge]]
* [https://web.archive.org/web/20201127013840/http://micro.soonlabel.com/gene_ward_smith/Others/Igs/NautilusReverie.mp3 ''Nautilus Reverie''] by [[Igliashon Jones]]


== Ammonite ==
== Ammonite ==
Subgroup: 2.3.5.7
{{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
[[Comma list]]: 250/243, 686/675


[[Mapping]]: [{{val| 1 5 8 10 }}, {{val| 0 -9 -15 -19 }}]
{{Mapping|legend=1| 1 -4 -7 -9 | 0 9 15 19 }}


{{Multival|legend=1| 9 15 19 3 5 2 }}
: mapping generators: ~2, ~14/9


[[POTE generator]]: ~9/7 = 454.448
[[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 }}


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


[[Badness]]: 0.107686
[[Badness]] (Sintel): 2.73


=== 11-limit ===
=== 11-limit ===
Line 493: Line 636:
Comma list: 55/54, 100/99, 686/675
Comma list: 55/54, 100/99, 686/675


Mapping: [{{val| 1 5 8 10 8 }}, {{val| 0 -9 -15 -19 -12 }}]
Mapping: {{mapping| 1 -4 -7 -9 -4 | 0 9 15 19 12 }}


POTE generator: ~9/7 = 454.512
Optimal tunings:  
* WE: ~2 = 1200.0141{{c}}, ~14/9 = 745.4971{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~14/9 = 745.4894{{c}}


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


Badness: 0.045694
Badness (Sintel): 1.51


=== 13-limit ===
=== 13-limit ===
Line 506: Line 651:
Comma list: 55/54, 91/90, 100/99, 169/168
Comma list: 55/54, 91/90, 100/99, 169/168


Mapping: [{{val| 1 5 8 10 8 9 }}, {{val| 0 -9 -15 -19 -12 -14 }}]
Mapping: {{mapping| 1 -4 -7 -9 -4 -5 | 0 9 15 19 12 14 }}


POTE generator: ~13/10 = 454.529
Optimal tunings:  
* WE: ~2 = 1200.2478{{c}}, ~14/9 = 745.6252{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~14/9 = 745.4904{{c}}


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


Badness: 0.027168
Badness (Sintel): 1.12


== Ceratitid ==
== Ceratitid ==
Subgroup: 2.3.5.7
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
[[Comma list]]: 250/243, 1728/1715


[[Mapping]]: [{{val| 1 2 3 3 }}, {{val| 0 -9 -15 -4 }}]
{{Mapping|legend=1| 1 2 3 3 | 0 -9 -15 -4 }}


{{Multival|legend=1| 9 15 4 3 -19 -33 }}
: mapping generators: ~2, ~36/35


[[POTE generator]]: ~36/35 = 54.384
[[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 }}


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


[[Badness]]: 0.115304
[[Badness]] (Sintel): 2.92


=== 11-limit ===
=== 11-limit ===
Line 534: Line 687:
Comma list: 55/54, 100/99, 352/343
Comma list: 55/54, 100/99, 352/343


Mapping: [{{val| 1 2 3 3 4 }}, {{val| 0 -9 -15 -4 -12 }}]
Mapping: {{mapping| 1 2 3 3 4 | 0 -9 -15 -4 -12 }}


POTE generator: ~36/35 = 54.376
Optimal tunings:  
* WE: ~2 = 1198.2851{{c}}, ~36/35 = 54.2986{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~36/35 = 54.4992{{c}}


Optimal GPV sequence: {{val list| 1ce, 21ce, 22 }}
{{Optimal ET sequence|legend=0| 1ce, 21ce, 22 }}


Badness: 0.051319
Badness (Sintel): 1.70


=== 13-limit ===
=== 13-limit ===
Line 547: Line 702:
Comma list: 55/54, 65/63, 100/99, 352/343
Comma list: 55/54, 65/63, 100/99, 352/343


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


POTE generator: ~36/35 = 54.665
Optimal tunings:  
* WE: ~2 = 1200.3864{{c}}, ~36/35 = 54.6830{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~36/35 = 54.6396{{c}}


Optimal GPV sequence: {{val list| 1ce, 21cef, 22 }}
{{Optimal ET sequence|legend=0| 1ce, 21cef, 22 }}


Badness: 0.044739
Badness (Sintel): 1.85


[[Category:Temperament families]]
[[Category:Temperament families]]
[[Category:Porcupine family| ]] <!-- main article -->
[[Category:Porcupine family| ]] <!-- main article -->
[[Category:Porcupine]]
[[Category:Porcupine| ]] <!-- key article -->
[[Category:Rank 2]]
[[Category:Rank 2]]
Retrieved from "https://en.xen.wiki/w/Porcupine_family"