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Porcupine family: Difference between revisions

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= Porcupine =
= Porcupine =
Subgroup: 2.3.5


[[Comma list]]: 250/243
[[Comma list]]: 250/243
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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.
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


[[Comma list]]: 64/63, 250/243
[[Comma list]]: 64/63, 250/243
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== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
Comma list: 55/54, 64/63, 100/99
Comma list: 55/54, 64/63, 100/99


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=== 13-limit ===
=== 13-limit ===
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: [{{val| 1 2 3 2 4 4 }}, {{val| 0 -3 -5 6 -4 -2 }}]


POTE generator: ~10/9 = 162.708
POTE generator: ~11/10 = 162.708


Minimax tuning:  
Minimax tuning:  
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=== Porcupinefish ===
=== Porcupinefish ===
{{see also| The Biosphere }}
{{see also| The Biosphere }}
Subgroup: 2.3.5.7.11.13


Comma list: 55/54, 64/63, 91/90, 100/99
Comma list: 55/54, 64/63, 91/90, 100/99
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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
POTE generator: ~11/10 = 162.277


Minimax tuning:  
Minimax tuning:  
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=== Pourcup ===
=== Pourcup ===
Subgroup: 2.3.5.7.11.13
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: [{{val| 1 2 3 2 4 1 }}, {{val| 0 -3 -5 6 -4 20 }}]


POTE generator: ~10/9 = 162.482
POTE generator: ~11/10 = 162.482


Minimax tuning:  
Minimax tuning:  
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=== Porkpie ===
=== Porkpie ===
Subgroup: 2.3.5.7.11.13
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: [{{val| 1 2 3 2 4 3 }}, {{val| 0 -3 -5 6 -4 5 }}]


POTE generator: ~10/9 = 163.688
POTE generator: ~11/10 = 163.688


Minimax tuning:  
Minimax tuning:  
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= Hystrix =
= Hystrix =
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]]. They can try the even sharper fifth of hystrix in [[68edo]] and see how that suits.
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]]. They can try the even sharper fifth of hystrix in [[68edo]] and see how that suits.
Subgroup: 2.3.5.7


[[Comma list]]: 36/35, 160/147
[[Comma list]]: 36/35, 160/147
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{{Multival|legend=1| 3 5 1 1 -7 -12 }}
{{Multival|legend=1| 3 5 1 1 -7 -12 }}


[[POTE generator]]: ~8/7 = 158.868
[[POTE generator]]: ~10/9 = 158.868


[[Minimax tuning]]:  
[[Minimax tuning]]:  
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== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
Comma list: 22/21, 36/35, 80/77
Comma list: 22/21, 36/35, 80/77


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


POTE generator: ~8/7 = 158.750
POTE generator: ~11/10 = 158.750


Vals: {{val list| 7, 8d, 15d }}
Vals: {{val list| 7, 8d, 15d }}
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= Porky =
= Porky =
Subgroup: 2.3.5.7
[[Comma list]]: 225/224, 250/243
[[Comma list]]: 225/224, 250/243


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== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
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: [{{val| 1 2 3 5 4 }}, {{val| 0 -3 -5 -16 -4 }}]


POTE generator: ~10/9 = 164.552
POTE generator: ~11/10 = 164.552


Minimax tuning:  
Minimax tuning:  
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== 13-limit ==
== 13-limit ==
Subgroup: 2.3.5.7.11.13
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: [{{val| 1 2 3 5 4 3 }}, {{val| 0 -3 -5 -16 -4 5 }}]


POTE generator: ~10/9 = 164.953
POTE generator: ~11/10 = 164.953


Vals: {{val list| 7d, 22, 29, 51f, 80cdeff }}
Vals: {{val list| 7d, 22, 29, 51f, 80cdeff }}
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= Coendou =
= Coendou =
Subgroup: 2.3.5.7
[[Comma list]]: 250/243, 525/512
[[Comma list]]: 250/243, 525/512


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== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
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: [{{val| 1 2 3 1 4 }}, {{val| 0 -3 -5 13 -4 }}]


POTE generator: ~10/9 = 165.981
POTE generator: ~11/10 = 165.981


Minimax tuning:  
Minimax tuning:  
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== 13-limit ==
== 13-limit ==
Subgroup: 2.3.5.7.11.13
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: [{{val| 1 2 3 1 4 3 }}, {{val| 0 -3 -5 13 -4 5 }}]


POTE generator: ~10/9 = 165.974
POTE generator: ~11/10 = 165.974


Minimax tuning:  
Minimax tuning:  
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= 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.
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.
Subgroup: 2.3.5.7


[[Comma list]]: 50/49, 245/243
[[Comma list]]: 50/49, 245/243
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== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
Comma list: 50/49, 55/54, 99/98
Comma list: 50/49, 55/54, 99/98


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=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Comma list: 50/49, 55/54, 65/63, 99/98
Comma list: 50/49, 55/54, 65/63, 99/98


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=== Urchin ===
=== Urchin ===
Subgroup: 2.3.5.7.11.13
Comma list: 40/39, 50/49, 55/54, 66/65
Comma list: 40/39, 50/49, 55/54, 66/65


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== Hedgepig ==
== Hedgepig ==
Subgroup: 2.3.5.7.11
Comma list: 50/49, 245/243, 385/384
Comma list: 50/49, 245/243, 385/384


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= Nautilus =
= Nautilus =
Subgroup: 2.3.5.7
[[Comma list]]: 49/48, 250/243
[[Comma list]]: 49/48, 250/243


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== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
Comma list: 49/48, 55/54, 245/242
Comma list: 49/48, 55/54, 245/242


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=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Comma list: 49/48, 55/54, 91/90, 100/99
Comma list: 49/48, 55/54, 91/90, 100/99


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=== Belauensis ===
=== Belauensis ===
Subgroup: 2.3.5.7.11.13
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: [{{val| 1 2 3 3 4 4 }}, {{val| 0 -6 -10 -3 -8 -4 }}]


POTE generator: ~21/20 = ~14/13 = 81.759
POTE generator: ~21/20 = 81.759


Vals: {{val list| 14c, 15, 29f, 44df }}
Vals: {{val list| 14c, 15, 29f, 44df }}
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= Ammonite =
= Ammonite =
Comma list: 250/243, 686/675
Subgroup: 2.3.5.7
 
[[Comma list]]: 250/243, 686/675


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


{{Multival|legend=1| 9 15 19 3 5 2 }}
{{Multival|legend=1| 9 15 19 3 5 2 }}


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


{{Val list|legend=1| 29, 37, 66 }}
{{Val list|legend=1| 29, 37, 66 }}


Badness: 0.1077
[[Badness]]: 0.1077


== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
Comma list: 55/54, 100/99, 686/675
Comma list: 55/54, 100/99, 686/675


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== 13-limit ==
== 13-limit ==
Subgroup: 2.3.5.7.11.13
Comma list: 55/54, 91/90, 100/99, 169/168
Comma list: 55/54, 91/90, 100/99, 169/168


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


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== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
Comma list: 55/54, 100/99, 5324/5145
Comma list: 55/54, 100/99, 5324/5145


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== 13-limit ==
== 13-limit ==
Subgroup: 2.3.5.7.11.13
Comma list: 55/54, 65/63, 100/99, 352/343
Comma list: 55/54, 65/63, 100/99, 352/343


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