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Porcupine family: Difference between revisions

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Update keys; POTE -> CTE; review comma lists and GPV sequences (2/2)
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[[Mapping]]: [{{val| 1 2 3 }}, {{val| 0 -3 -5 }}]
[[Mapping]]: [{{val| 1 2 3 }}, {{val| 0 -3 -5 }}]


: Mapping generators: ~2, ~10/9
: mapping generators: ~2, ~10/9


[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~10/9 = 164.1659
[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~10/9 = 164.1659
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Sval mapping: [{{val| 1 5 8 8 2 }}, {{val| 0 -6 -10 -8 3 }}]
Sval mapping: [{{val| 1 5 8 8 2 }}, {{val| 0 -6 -10 -8 3 }}]


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


Optimal tuning (CTE): ~2 = 1\1, ~88/65 = 518.2094
Optimal tuning (CTE): ~2 = 1\1, ~88/65 = 518.2094
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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|15EDO]]. They can try the even sharper fifth of hystrix in [[68edo|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
[[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
[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~10/9 = 165.1845


[[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]]: ~10/9 = {{monzo| 3/5 0 -1/5 }}
: Eigenmonzos (unchanged intervals): 2, 5/4
: [[Eigenmonzo basis]]: 2.5


{{Val list|legend=1| 7, 8d, 15d }}
{{Val list|legend=1| 7, 8d, 15d }}
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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
Optimal tuning (CTE): ~2 = 1\1, ~11/10 = 164.7684


Optimal GPV sequence: {{val list| 7, 8d, 15d }}
Optimal GPV sequence: {{val list| 7, 8d, 15d }}
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== Porky ==
== Porky ==
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 225/224, 250/243
[[Comma list]]: 225/224, 250/243
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{{Multival|legend=1| 3 5 16 1 17 23 }}
{{Multival|legend=1| 3 5 16 1 17 23 }}


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


[[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]]: 2.7/5


{{Val list|legend=1| 7d, 15d, 22, 29, 51, 73c }}
{{Val list|legend=1| 7d, 15d, 22, 29, 51, 73c }}
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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
Optimal tuning (CTE): ~2 = 1\1, ~11/10 = 164.3207


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
: Eigenmonzo basis: 2.7/5


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


Badness: 0.027268
Badness: 0.027268
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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
Optimal tuning (CTE): ~2 = 1\1, ~11/10 = 164.4782


Optimal GPV sequence: {{val list| 7d, 22, 29, 51f, 80cdeff }}
Optimal GPV sequence: {{val list| 7d, 22, 29, 51f, 80cdeff }}
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== Coendou ==
== Coendou ==
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 250/243, 525/512
[[Comma list]]: 250/243, 525/512
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{{Multival|legend=1| 3 5 -13 1 -29 -44 }}
{{Multival|legend=1| 3 5 -13 1 -29 -44 }}


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


[[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]]: 2.3


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


[[Badness]]: 0.118344
[[Badness]]: 0.118344
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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
Optimal tuning (CTE): ~2 = 1\1, ~11/10 = 165.9246


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
: Eigenmonzo basis: 2.3


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


Badness: 0.049669
Badness: 0.049669
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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
Optimal tuning (CTE): ~2 = 1\1, ~11/10 = 166.0459


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
: Eigenmonzo basis: 2.3


Optimal GPV sequence: {{val list| 7, 29, 65cef, 94cdef }}
Optimal GPV sequence: {{val list| 7, 22d, 29, 65cef }}


Badness: 0.030233
Badness: 0.030233


== 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 }} (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.


Subgroup: 2.3.5.7
[[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]]: [{{val| 2 1 1 2 }}, {{val| 0 3 5 5 }}]
: mapping generators: ~7/5, ~9/7


{{Multival|legend=1| 6 10 10 2 -1 -5 }}
{{Multival|legend=1| 6 10 10 2 -1 -5 }}


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


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


[[Badness]]: 0.043983
[[Badness]]: 0.043983
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Mapping: [{{val| 2 1 1 2 4 }}, {{val| 0 3 5 5 4 }}]
Mapping: [{{val| 2 1 1 2 4 }}, {{val| 0 3 5 5 4 }}]


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


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


Badness: 0.023095
Badness: 0.023095
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Mapping: [{{val| 2 1 1 2 4 3 }}, {{val| 0 3 5 5 4 6 }}]
Mapping: [{{val| 2 1 1 2 4 3 }}, {{val| 0 3 5 5 4 6 }}]


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


Optimal GPV sequence: {{val list| 8d, 14cf, 22 }}
Optimal GPV sequence: {{val list| 8d, 14cf, 22 }}
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Mapping: [{{val| 2 1 1 2 4 6 }}, {{val| 0 3 5 5 4 2 }}]
Mapping: [{{val| 2 1 1 2 4 6 }}, {{val| 0 3 5 5 4 2 }}]


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


Optimal GPV sequence: {{val list| 14c, 22f }}
Optimal GPV sequence: {{val list| 14c, 22f }}
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Mapping: [{{val| 2 1 1 2 12 }}, {{val| 0 3 5 5 -7 }}]
Mapping: [{{val| 2 1 1 2 12 }}, {{val| 0 3 5 5 -7 }}]


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


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


Badness: 0.068406
Badness: 0.068406


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


== Nautilus ==
== Nautilus ==
Subgroup: 2.3.5.7
[[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]]: [{{val| 1 2 3 3 }}, {{val| 0 -6 -10 -3 }}]
: mapping generators: ~2, ~21/20


{{Multival|legend=1| 6 10 3 2 -12 -21 }}
{{Multival|legend=1| 6 10 3 2 -12 -21 }}


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


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


[[Badness]]: 0.057420
[[Badness]]: 0.057420
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Mapping: [{{val| 1 2 3 3 4 }}, {{val| 0 -6 -10 -3 -8 }}]
Mapping: [{{val| 1 2 3 3 4 }}, {{val| 0 -6 -10 -3 -8 }}]


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


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


Badness: 0.026023
Badness: 0.026023
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Mapping: [{{val| 1 2 3 3 4 5 }}, {{val| 0 -6 -10 -3 -8 -19 }}]
Mapping: [{{val| 1 2 3 3 4 5 }}, {{val| 0 -6 -10 -3 -8 -19 }}]


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


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


Badness: 0.022285
Badness: 0.022285
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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 = 81.759
Optimal tuning (CTE): ~2 = 1\1, ~21/20 = 82.0342


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


Badness: 0.029816
Badness: 0.029816


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


== Ammonite ==
== Ammonite ==
Subgroup: 2.3.5.7
[[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]]: [{{val| 1 5 8 10 }}, {{val| 0 -9 -15 -19 }}]
: mapping generators: ~2, ~9/7


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


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


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


[[Badness]]: 0.107686
[[Badness]]: 0.107686
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Mapping: [{{val| 1 5 8 10 8 }}, {{val| 0 -9 -15 -19 -12 }}]
Mapping: [{{val| 1 5 8 10 8 }}, {{val| 0 -9 -15 -19 -12 }}]


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


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


Badness: 0.045694
Badness: 0.045694
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Mapping: [{{val| 1 5 8 10 8 9 }}, {{val| 0 -9 -15 -19 -12 -14 }}]
Mapping: [{{val| 1 5 8 10 8 9 }}, {{val| 0 -9 -15 -19 -12 -14 }}]


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


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


Badness: 0.027168
Badness: 0.027168


== Ceratitid ==
== Ceratitid ==
Subgroup: 2.3.5.7
[[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]]: [{{val| 1 2 3 3 }}, {{val| 0 -9 -15 -4 }}]
: mapping generators: ~2, ~36/35


{{Multival|legend=1| 9 15 4 3 -19 -33 }}
{{Multival|legend=1| 9 15 4 3 -19 -33 }}


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


{{Val list|legend=1| 1c, 21c, 22 }}
{{Val list|legend=1| 1c, 21c, 22 }}
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Mapping: [{{val| 1 2 3 3 4 }}, {{val| 0 -9 -15 -4 -12 }}]
Mapping: [{{val| 1 2 3 3 4 }}, {{val| 0 -9 -15 -4 -12 }}]


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


Optimal GPV sequence: {{val list| 1ce, 21ce, 22 }}
Optimal GPV sequence: {{val list| 1ce, 21ce, 22 }}
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Mapping: [{{val| 1 2 3 3 4 4 }}, {{val| 0 -9 -15 -4 -12 -7 }}]
Mapping: [{{val| 1 2 3 3 4 4 }}, {{val| 0 -9 -15 -4 -12 -7 }}]


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


Optimal GPV sequence: {{val list| 1ce, 21cef, 22 }}
Optimal GPV sequence: {{val list| 1ce, 21cef, 22 }}
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