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Porcupine family: Difference between revisions

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Update keys; POTE -> CTE; review comma lists and GPV sequences (1/2)
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== Porcupine ==
== Porcupine ==
Subgroup: 2.3.5
{{Main| Porcupine }}
 
[[Subgroup]]: 2.3.5


[[Comma list]]: 250/243
[[Comma list]]: 250/243
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[[Mapping]]: [{{val| 1 2 3 }}, {{val| 0 -3 -5 }}]
[[Mapping]]: [{{val| 1 2 3 }}, {{val| 0 -3 -5 }}]


[[POTE generator]]: ~10/9 = 163.950
: Mapping generators: ~2, ~10/9
 
[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~10/9 = 164.1659


[[Tuning ranges]]:  
[[Tuning ranges]]:  
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[[Badness]]: 0.030778
[[Badness]]: 0.030778


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


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


POTE generator: ~11/10 = 164.0777
Optimal tuning (CTE): ~2 = 1\1, ~11/10 = 163.8867


Optimal GPV sequence: {{val list| 7, 15, 22, 37, 73ce, 95ce }}
Optimal GPV sequence: {{val list| 7, 15, 22, 73ce, 95ce }}
 
Badness: 0.0097


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


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


POTE generator: ~88/65 = 518.2094
: Sval mapping generators: ~2, ~65/44
 
Optimal tuning (CTE): ~2 = 1\1, ~88/65 = 518.2094


Optimal GPV sequence: {{val list| 7, 23bc, 30, 37, 44 }}
Optimal GPV sequence: {{val list| 7, 23bc, 30, 37, 44 }}
Badness: 0.0305


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


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|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]]. 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


[[Comma list]]: 64/63, 250/243
[[Comma list]]: 64/63, 250/243
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{{Multival|legend=1| 3 5 -6 1 -18 -28 }}
{{Multival|legend=1| 3 5 -6 1 -18 -28 }}


[[POTE generator]]: ~10/9 = 162.880
[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~10/9 = 163.2032


[[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 }}
: Eigenmonzos (unchanged intervals): 2, 5/4
: [[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 }}
: Eigenmonzos (unchanged intervals): 2, 9/7
: [[Eigenmonzo basis]]: 2.9/7


[[Tuning ranges]]:  
[[Tuning ranges]]:  
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* 7- and 9-odd-limit diamond monotone and tradeoff: ~10/9 = [160.000, 163.636]
* 7- and 9-odd-limit diamond monotone and tradeoff: ~10/9 = [160.000, 163.636]


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


[[Badness]]: 0.041057
[[Badness]]: 0.041057
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Mapping: [{{val| 1 2 3 2 4 }}, {{val| 0 -3 -5 6 -4 }}]
Mapping: [{{val| 1 2 3 2 4 }}, {{val| 0 -3 -5 6 -4 }}]


POTE generator: ~10/9 = 162.747
Optimal tuning (CTE): ~2 = 1\1, ~11/10 = 163.1055


Minimax tuning:  
Minimax tuning:  
* 11-odd-limit: ~10/9 = {{monzo| 1/6 -1/6 0 1/12 }}
* 11-odd-limit: ~11/10 = {{monzo| 1/6 -1/6 0 1/12 }}
: Eigenmonzos (unchanged intervals): 2, 9/7
: Eigenmonzo basis: 2.9/7


Tuning ranges:  
Tuning ranges:  
* 11-odd-limit diamond monotone: ~10/9 = [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: ~10/9 = [150.637, 182.404]
* 11-odd-limit diamond tradeoff: ~11/10 = [150.637, 182.404]
* 11-odd-limit diamond monotone and tradeoff: ~10/9 = [160.000, 163.636]
* 11-odd-limit diamond monotone and tradeoff: ~11/10 = [160.000, 163.636]


Optimal GPV sequence: {{val list| 7, 15, 22, 37, 59 }}
Optimal GPV sequence: {{val list| 7, 15, 22, 37, 59 }}
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Mapping: [{{val| 1 2 3 2 4 4 }}, {{val| 0 -3 -5 6 -4 -2 }}]
Mapping: [{{val| 1 2 3 2 4 4 }}, {{val| 0 -3 -5 6 -4 -2 }}]


POTE generator: ~10/9 = 162.708
Optimal tuning (CTE): ~2 = 1\1, ~11/10 = 163.4425


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 (unchanged intervals): 2, 11/8
: Eigenmonzo basis: 2.11


Tuning ranges:  
Tuning ranges:  
* 13-odd-limit diamond monotone: ~10/9 = [160.000, 163.636] (2\15 to 3\22)
* 13-odd-limit diamond monotone: ~11/10 = [160.000, 163.636] (2\15 to 3\22)
* 15-odd-limit diamond monotone: ~10/9 = 163.636 (3\22)
* 15-odd-limit diamond monotone: ~11/10 = 163.636 (3\22)
* 13- and 15-odd-limit diamond tradeoff: ~10/9 = [138.573, 182.404]
* 13- and 15-odd-limit diamond tradeoff: ~11/10 = [138.573, 182.404]
* 13-odd-limit diamond monotone and tradeoff: ~10/9 = [160.000, 163.636]
* 13-odd-limit diamond monotone and tradeoff: ~11/10 = [160.000, 163.636]
* 15-odd-limit diamond monotone and tradeoff: ~10/9 = 163.636
* 15-odd-limit diamond monotone and tradeoff: ~11/10 = 163.636


Optimal GPV sequence: {{val list| 7, 15, 22f, 37f }}
Optimal GPV sequence: {{val list| 7, 15, 22f, 37f }}
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==== Porcupinefish ====
==== Porcupinefish ====
{{see also| The Biosphere }}
{{See also| The Biosphere }}


Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13
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Mapping: [{{val| 1 2 3 2 4 6 }}, {{val| 0 -3 -5 6 -4 -17 }}]
Mapping: [{{val| 1 2 3 2 4 6 }}, {{val| 0 -3 -5 6 -4 -17 }}]


POTE generator: ~10/9 = 162.277
Optimal tuning (CTE): ~2 = 1\1, ~11/10 = 162.6361


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 }}
: Eigenmonzos (unchanged intervals): 2, 13/11
: Eigenmonzo basis: 2.13/11


Tuning ranges:  
Tuning ranges:  
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* 15-odd-limit diamond monotone and tradeoff: ~10/9 = 162.162
* 15-odd-limit diamond monotone and tradeoff: ~10/9 = 162.162


Optimal GPV sequence: {{val list| 15, 22, 37, 59, 96b }}
Optimal GPV sequence: {{val list| 15, 22, 37 }}


Badness: 0.025314
Badness: 0.025314
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Mapping: [{{val| 1 2 3 2 4 1 }}, {{val| 0 -3 -5 6 -4 20 }}]
Mapping: [{{val| 1 2 3 2 4 1 }}, {{val| 0 -3 -5 6 -4 20 }}]


POTE generator: ~10/9 = 162.482
Optimal tuning (CTE): ~2 = 1\1, ~11/10 = 163.3781


Minimax tuning:  
Minimax tuning:  
* 13- and 15-odd-limit: ~10/9 = {{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 }}
: Eigenmonzos (unchanged intervals): 2, 14/13
: Eigenmonzo basis: 2.13/7


Optimal GPV sequence: {{val list| 15f, 22f, 37 }}
Optimal GPV sequence: {{val list| 15f, 22f, 37, 59f }


Badness: 0.035130
Badness: 0.035130
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Mapping: [{{val| 1 2 3 2 4 3 }}, {{val| 0 -3 -5 6 -4 5 }}]
Mapping: [{{val| 1 2 3 2 4 3 }}, {{val| 0 -3 -5 6 -4 5 }}]


POTE generator: ~10/9 = 163.688
Optimal tuning (CTE): ~2 = 1\1, ~11/10 = 163.6778


Minimax tuning:  
Minimax tuning:  
* 13- and 15-odd-limit: ~10/9 = {{monzo| 1/6 -1/6 0 1/12 }}
* 13- and 15-odd-limit: ~11/10 = {{monzo| 1/6 -1/6 0 1/12 }}
: Eigenmonzos (unchanged intervals): 2, 9/7
: Eigenmonzo basis: 2.9/7


Optimal GPV sequence: {{val list| 7, 15f, 22 }}
Optimal GPV sequence: {{val list| 7, 15f, 22 }}
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