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Porcupine family: Difference between revisions

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Restore POTE tuning by request (and correct the tunings for undecimation)
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* [[49/48]], the slendro diesis, for [[#Nautilus|nautilus]].
* [[49/48]], the slendro diesis, for [[#Nautilus|nautilus]].


Temperaments discussed elsewhere include [[Dicot family #Jamesbond|jamesbond]].
Temperaments discussed elsewhere include [[7th-octave temperaments #Jamesbond|jamesbond]].


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


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


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


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


{{Optimal ET sequence|legend=1| 7, 15, 22, 73ce, 95ce }}
{{Optimal ET sequence|legend=1| 7, 15, 22, 73ce, 95ce }}
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: sval mapping generators: ~2, ~65/44
: sval mapping generators: ~2, ~65/44


Optimal tuning (CTE): ~2 = 1\1, ~88/65 = 518.2094
Optimal tunings:
* CTE: ~2 = 1\1, ~88/65 = 518.0865
* POTE: ~2 = 1\1, ~88/65 = 518.2094


{{Optimal ET sequence|legend=1| 7, 23bc, 30, 37, 44 }}
{{Optimal ET sequence|legend=1| 7, 23bc, 30, 37, 44 }}
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{{Multival|legend=1| 3 5 -6 1 -18 -28 }}
{{Multival|legend=1| 3 5 -6 1 -18 -28 }}


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


[[Minimax tuning]]:  
[[Minimax tuning]]:  
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Mapping: {{mapping| 1 2 3 2 4 | 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:
* CTE: ~2 = 1\1, ~11/10 = 163.1055
* POTE: ~2 = 1\1, ~11/10 = 162.747


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 (unchanged-interval basis): 2.9/7
: eigenmonzo basis (unchanged-interval basis): 2.9/7


Tuning ranges:  
Tuning ranges:  
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Mapping: {{mapping| 1 2 3 2 4 4 | 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:
* CTE: ~2 = 1\1, ~11/10 = 163.4425
* POTE: ~2 = 1\1, ~11/10 = 162.708


Minimax tuning:  
Minimax tuning:  
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Mapping: {{mapping| 1 2 3 2 4 6 | 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:
* CTE: ~2 = 1\1, ~11/10 = 162.6361
* POTE: ~2 = 1\1, ~11/10 = 162.277


Minimax tuning:  
Minimax tuning:  
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Mapping: {{mapping| 1 2 3 2 4 1 | 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:
* CTE: ~2 = 1\1, ~11/10 = 163.3781
* POTE: ~2 = 1\1, ~11/10 = 162.482


Minimax tuning:  
Minimax tuning:  
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Mapping: {{mapping| 1 2 3 2 4 3 | 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:
* CTE: ~2 = 1\1, ~11/10 = 163.6778
* POTE: ~2 = 1\1, ~11/10 = 163.688


Minimax tuning:  
Minimax tuning:  
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{{Multival|legend=1| 3 5 16 1 17 23 }}
{{Multival|legend=1| 3 5 16 1 17 23 }}


[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~10/9 = 164.3913
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1\1, ~10/9 = 164.3913
* [[POTE]]: ~2 = 1\1, ~10/9 = 164.412


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


Optimal tuning (CTE): ~2 = 1\1, ~11/10 = 164.3207
Optimal tunings:
* CTE: ~2 = 1\1, ~11/10 = 164.3207
* POTE: ~2 = 1\1, ~11/10 = 164.552


Minimax tuning:  
Minimax tuning:  
Line 307: Line 329:
Mapping: {{mapping| 1 2 3 5 4 3 | 0 -3 -5 -16 -4 5 }}
Mapping: {{mapping| 1 2 3 5 4 3 | 0 -3 -5 -16 -4 5 }}


Optimal tuning (CTE): ~2 = 1\1, ~11/10 = 164.4782
Optimal tunings:
* CTE: ~2 = 1\1, ~11/10 = 164.4782
* POTE: ~2 = 1\1, ~11/10 = 164.953


{{Optimal ET sequence|legend=1| 7d, 22, 29, 51f, 80cdeff }}
{{Optimal ET sequence|legend=1| 7d, 22, 29, 51f, 80cdeff }}
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{{Multival|legend=1| 3 5 -13 1 -29 -44 }}
{{Multival|legend=1| 3 5 -13 1 -29 -44 }}


[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~10/9 = 166.0938
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1\1, ~10/9 = 166.0938
* [[POTE]]: ~2 = 1\1, ~10/9 = 166.041


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


Optimal tuning (CTE): ~2 = 1\1, ~11/10 = 165.9246
Optimal tunings:
* CTE: ~2 = 1\1, ~11/10 = 165.9246
* POTE: ~2 = 1\1, ~11/10 = 165.981


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


Optimal tuning (CTE): ~2 = 1\1, ~11/10 = 166.0459
Optimal tunings:
* CTE: ~2 = 1\1, ~11/10 = 166.0459
* POTE: ~2 = 1\1, ~11/10 = 165.974


Minimax tuning:  
Minimax tuning:  
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{{Multival|legend=1| 3 5 1 1 -7 -12 }}
{{Multival|legend=1| 3 5 1 1 -7 -12 }}


[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~10/9 = 165.1845
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1\1, ~10/9 = 165.1845
* [[POTE]]: ~2 = 1\1, ~10/9 = 158.868


[[Minimax tuning]]:  
[[Minimax tuning]]:  
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Mapping: {{mapping| 1 2 3 3 4 | 0 -3 -5 -1 -4 }}
Mapping: {{mapping| 1 2 3 3 4 | 0 -3 -5 -1 -4 }}


Optimal tuning (CTE): ~2 = 1\1, ~11/10 = 164.7684
Optimal tunings:
* CTE: ~2 = 1\1, ~11/10 = 164.7684
* POTE: ~2 = 1\1, ~11/10 = 158.750


{{Optimal ET sequence|legend=1| 7, 8d, 15d }}
{{Optimal ET sequence|legend=1| 7, 8d, 15d }}
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{{Multival|legend=1| 3 5 2 1 -5 -9 }}
{{Multival|legend=1| 3 5 2 1 -5 -9 }}


[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~10/9 = 161.3408
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1\1, ~10/9 = 161.3408
* [[POTE]]: ~2 = 1\1, ~10/9 = 169.112


{{Optimal ET sequence|legend=1| 7d }}
{{Optimal ET sequence|legend=1| 7d }}
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{{Multival|legend=1| 6 10 10 2 -1 -5 }}
{{Multival|legend=1| 6 10 10 2 -1 -5 }}


[[Optimal tuning]] ([[CTE]]): ~7/5 = 1\2, ~9/7 = 435.2580
[[Optimal tuning]]s:
* [[CTE]]: ~7/5 = 1\2, ~9/7 = 435.2580
* [[POTE]]: ~7/5 = 1\2, ~9/7 = 435.648


{{Optimal ET sequence|legend=1| 8d, 14c, 22 }}
{{Optimal ET sequence|legend=1| 8d, 14c, 22 }}
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Mapping: {{mapping| 2 1 1 2 4 | 0 3 5 5 4 }}
Mapping: {{mapping| 2 1 1 2 4 | 0 3 5 5 4 }}


Optimal tuning (CTE): ~7/5 = 1\2, ~9/7 = 435.5281
Optimal tunings:
* CTE: ~7/5 = 1\2, ~9/7 = 435.5281
* POTE: ~7/5 = 1\2, ~9/7 = 435.386


{{Optimal ET sequence|legend=1| 8d, 14c, 22, 58ce }}
{{Optimal ET sequence|legend=1| 8d, 14c, 22, 58ce }}
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Mapping: {{mapping| 2 1 1 2 4 3 | 0 3 5 5 4 6 }}
Mapping: {{mapping| 2 1 1 2 4 3 | 0 3 5 5 4 6 }}


Optimal tuning (CTE): ~7/5 = 1\2, ~9/7 = 436.3087
Optimal tunings:
* CTE: ~7/5 = 1\2, ~9/7 = 436.3087
* POTE: ~7/5 = 1\2, ~9/7 = 435.861


{{Optimal ET sequence|legend=1| 8d, 14cf, 22 }}
{{Optimal ET sequence|legend=1| 8d, 14cf, 22 }}
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Mapping: {{mapping| 2 1 1 2 4 6 | 0 3 5 5 4 2 }}
Mapping: {{mapping| 2 1 1 2 4 6 | 0 3 5 5 4 2 }}


Optimal tuning (CTE): ~7/5 = 1\2, ~9/7 = 435.1856
Optimal tunings:
* CTE: ~7/5 = 1\2, ~9/7 = 435.1856
* POTE: ~7/5 = 1\2, ~9/7 = 437.078


{{Optimal ET sequence|legend=1| 14c, 22f }}
{{Optimal ET sequence|legend=1| 14c, 22f }}
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Mapping: {{mapping| 2 1 1 2 12 | 0 3 5 5 -7 }}
Mapping: {{mapping| 2 1 1 2 12 | 0 3 5 5 -7 }}


Optimal tuning (CTE): ~7/5 = 1\2, ~9/7 = 435.3289
Optimal tunings:
* CTE: ~7/5 = 1\2, ~9/7 = 435.3289
* POTE: ~7/5 = 1\2, ~9/7 = 435.425


{{Optimal ET sequence|legend=1| 22 }}
{{Optimal ET sequence|legend=1| 22 }}
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{{Multival|legend=1| 6 10 3 2 -12 -21 }}
{{Multival|legend=1| 6 10 3 2 -12 -21 }}


[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~21/20 = 81.9143
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1\1, ~21/20 = 81.9143
* [[POTE]]: ~2 = 1\1, ~21/20 = 82.505


{{Optimal ET sequence|legend=1| 14c, 15, 29, 44d }}
{{Optimal ET sequence|legend=1| 14c, 15, 29, 44d }}
Line 520: Line 568:
Mapping: {{mapping| 1 2 3 3 4 | 0 -6 -10 -3 -8 }}
Mapping: {{mapping| 1 2 3 3 4 | 0 -6 -10 -3 -8 }}


Optimal tuning (CTE): ~2 = 1\1, ~21/20 = 81.8017
Optimal tunings:
* CTE: ~2 = 1\1, ~21/20 = 81.8017
* POTE: ~2 = 1\1, ~21/20 = 82.504


{{Optimal ET sequence|legend=1| 14c, 15, 29, 44d }}
{{Optimal ET sequence|legend=1| 14c, 15, 29, 44d }}
Line 533: Line 583:
Mapping: {{mapping| 1 2 3 3 4 5 | 0 -6 -10 -3 -8 -19 }}
Mapping: {{mapping| 1 2 3 3 4 5 | 0 -6 -10 -3 -8 -19 }}


Optimal tuning (CTE): ~2 = 1\1, ~21/20 = 81.9123
Optimal tunings:
* CTE: ~2 = 1\1, ~21/20 = 81.9123
* POTE: ~2 = 1\1, ~21/20 = 82.530


{{Optimal ET sequence|legend=1| 14cf, 15, 29, 44d }}
{{Optimal ET sequence|legend=1| 14cf, 15, 29, 44d }}
Line 546: Line 598:
Mapping: {{mapping| 1 2 3 3 4 4 | 0 -6 -10 -3 -8 -4 }}
Mapping: {{mapping| 1 2 3 3 4 4 | 0 -6 -10 -3 -8 -4 }}


Optimal tuning (CTE): ~2 = 1\1, ~21/20 = 82.0342
Optimal tunings:
* CTE: ~2 = 1\1, ~21/20 = 82.0342
* POTE: ~2 = 1\1, ~21/20 = 81.759


{{Optimal ET sequence|legend=1| 14c, 15, 29f, 44dff }}
{{Optimal ET sequence|legend=1| 14c, 15, 29f, 44dff }}
Line 566: Line 620:
{{Multival|legend=1| 9 15 19 3 5 2 }}
{{Multival|legend=1| 9 15 19 3 5 2 }}


[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~9/7 = 454.5500
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1\1, ~9/7 = 454.5500
* [[POTE]]: ~2 = 1\1, ~9/7 = 454.448


{{Optimal ET sequence|legend=1| 8d, 21cd, 29, 37, 66 }}
{{Optimal ET sequence|legend=1| 8d, 21cd, 29, 37, 66 }}
Line 579: Line 635:
Mapping: {{mapping| 1 5 8 10 8 | 0 -9 -15 -19 -12 }}
Mapping: {{mapping| 1 5 8 10 8 | 0 -9 -15 -19 -12 }}


Optimal tuning (CTE): ~2 = 1\1, ~9/7 = 454.5050
Optimal tunings:
* CTE: ~2 = 1\1, ~9/7 = 454.5050
* POTE: ~2 = 1\1, ~9/7 = 454.512


{{Optimal ET sequence|legend=1| 8d, 21cde, 29, 37, 66 }}
{{Optimal ET sequence|legend=1| 8d, 21cde, 29, 37, 66 }}
Line 592: Line 650:
Mapping: {{mapping| 1 5 8 10 8 9 | 0 -9 -15 -19 -12 -14 }}
Mapping: {{mapping| 1 5 8 10 8 9 | 0 -9 -15 -19 -12 -14 }}


Optimal tuning (CTE): ~2 = 1\1, ~13/10 = 454.4798
Optimal tunings:
* CTE: ~2 = 1\1, ~13/10 = 454.4798
* POTE: ~2 = 1\1, ~13/10 = 454.529


{{Optimal ET sequence|legend=1| 8d, 21cdef, 29, 37, 66 }}
{{Optimal ET sequence|legend=1| 8d, 21cdef, 29, 37, 66 }}
Line 609: Line 669:
{{Multival|legend=1| 9 15 4 3 -19 -33 }}
{{Multival|legend=1| 9 15 4 3 -19 -33 }}


[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~36/35 = 54.8040
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1\1, ~36/35 = 54.8040
* [[POTE]]: ~2 = 1\1, ~36/35 = 54.384


{{Optimal ET sequence|legend=1| 1c, 21c, 22 }}
{{Optimal ET sequence|legend=1| 1c, 21c, 22 }}
Line 622: Line 684:
Mapping: {{mapping| 1 2 3 3 4 | 0 -9 -15 -4 -12 }}
Mapping: {{mapping| 1 2 3 3 4 | 0 -9 -15 -4 -12 }}


Optimal tuning (CTE): ~2 = 1\1, ~36/35 = 54.7019
Optimal tunings:
* CTE: ~2 = 1\1, ~36/35 = 54.7019
* POTE: ~2 = 1\1, ~36/35 = 54.376


{{Optimal ET sequence|legend=1| 1ce, 21ce, 22 }}
{{Optimal ET sequence|legend=1| 1ce, 21ce, 22 }}
Line 635: Line 699:
Mapping: {{mapping| 1 2 3 3 4 4 | 0 -9 -15 -4 -12 -7 }}
Mapping: {{mapping| 1 2 3 3 4 4 | 0 -9 -15 -4 -12 -7 }}


Optimal tuning (CTE): ~2 = 1\1, ~36/35 = 54.5751
Optimal tunings:
* CTE: ~2 = 1\1, ~36/35 = 54.5751
* POTE: ~2 = 1\1, ~36/35 = 54.665


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