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Father family: Difference between revisions

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"optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence
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== Father ==
== Father ==
Subgroup: 2.3.5
[[Subgroup]]: 2.3.5


[[Comma list]]: 16/15
[[Comma list]]: 16/15


[[Mapping]]: [{{val| 1 0 4 }}, {{val| 0 1 -1 }}]
{{Mapping|legend=1| 1 0 4 | 0 1 -1 }}


Mapping generators: ~2, ~3
: mapping generators: ~2, ~3


[[POTE generator]]: ~3/2 = 743.986
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 743.986


[[Minimax tuning]]:  
[[Minimax tuning]]:  
* [[5-odd-limit]]: ~3/2 = {{monzo| 1 1/2 -1/2 }}
* [[5-odd-limit]]: ~3/2 = {{monzo| 1 1/2 -1/2 }}
: [[Eigenmonzo]]s (unchanged-intervals): 2, 6/5
: [[Eigenmonzo basis|Eigenmonzo (unchanged-interval) basis]]: 2.5/3


{{Optimal ET sequence|legend=1| 1, 2, 3, 5, 8, 13c, 21bcc }}
{{Optimal ET sequence|legend=1| 1, 2, 3, 5, 8, 13c, 21bcc }}
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== Septimal father ==
== Septimal father ==
{{see also| Trienstonic clan #Father }}
{{See also| Trienstonic clan #Father }}


Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 16/15, 28/27
[[Comma list]]: 16/15, 28/27


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


{{Multival|legend=1| 1 -1 3 -4 2 10 }}
{{Multival|legend=1| 1 -1 3 -4 2 10 }}


[[POTE generator]]: ~3/2 = 742.002
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 742.002


[[Minimax tuning]]:  
[[Minimax tuning]]:  
* [[7-odd-limit]]: ~3/2 = {{monzo| 1/2 0 -1/4 1/4 }}
* [[7-odd-limit]]: ~3/2 = {{monzo| 1/2 0 -1/4 1/4 }}
: [[Eigenmonzo]]s (unchanged-intervals): 2, 7/5
: [[Eigenmonzo basis|Eigenmonzo (unchanged-interval) basis]]: 2.7/5
* [[9-odd-limit]]: ~3/2 = {{monzo| 1 -2 0 1 }} = 14/9
* [[9-odd-limit]]: ~3/2 = {{monzo| 1 -2 0 1 }} = 14/9
: Eigenmonzos (unchanged-intervals): 2, 9/7
: [[Eigenmonzo basis|Eigenmonzo (unchanged-interval) basis]]: 2.9/7


{{Optimal ET sequence|legend=1| 2d, 3d, 5, 8d, 13cd, 21bccdd }}
{{Optimal ET sequence|legend=1| 2d, 3d, 5, 8d, 13cd, 21bccdd }}
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Comma list: 16/15, 22/21, 28/27
Comma list: 16/15, 22/21, 28/27


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


POTE generator: ~3/2 = 747.156
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 747.156


{{Optimal ET sequence|legend=1| 2de, 3de, 5, 8d }}
{{Optimal ET sequence|legend=1| 2de, 3de, 5, 8d }}
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== Mother ==
== Mother ==
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 16/15, 21/20
[[Comma list]]: 16/15, 21/20


[[Mapping]]: [{{val| 1 0 4 6 }}, {{val| 0 1 -1 -2 }}]
{{Mapping|legend=1| 1 0 4 6 | 0 1 -1 -2 }}


{{Multival|legend=1| 1 -1 -2 -4 -6 -2 }}
{{Multival|legend=1| 1 -1 -2 -4 -6 -2 }}


[[POTE generator]]: ~3/2 = 721.569
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 721.569


{{Optimal ET sequence|legend=1| 2, 3, 5 }}
{{Optimal ET sequence|legend=1| 2, 3, 5 }}
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Comma list: 11/10, 16/15, 21/20
Comma list: 11/10, 16/15, 21/20


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


POTE generator: ~3/2 = 717.364
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 717.364


{{Optimal ET sequence|legend=1| 2, 3, 5 }}
{{Optimal ET sequence|legend=1| 2, 3, 5 }}
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== Pater ==
== Pater ==
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 16/15, 126/125
[[Comma list]]: 16/15, 126/125


[[Mapping]]: [{{val| 1 0 4 11 }}, {{val| 0 1 -1 -5 }}]
{{Mapping|legend=1| 1 0 4 11 | 0 1 -1 -5 }}


{{Multival|legend=1| 1 -1 -5 -4 -11 -9 }}
{{Multival|legend=1| 1 -1 -5 -4 -11 -9 }}


[[POTE generator]]: ~3/2 = 753.113
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 753.113


{{Optimal ET sequence|legend=1| 3, 5d, 8d }}
{{Optimal ET sequence|legend=1| 3, 5d, 8d }}
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Comma list: 16/15, 22/21, 100/99
Comma list: 16/15, 22/21, 100/99


Mapping: [{{val| 1 0 4 11 10 }}, {{val| 0 1 -1 -5 -4 }}]
Mapping: {{mapping| 1 0 4 11 10 | 0 1 -1 -5 -4 }}


POTE generator: ~3/2 = 751.396
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 751.396


{{Optimal ET sequence|legend=1| 3, 5de, 8d }}
{{Optimal ET sequence|legend=1| 3, 5de, 8d }}
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== Baba ==
== Baba ==
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 16/15, 49/45
[[Comma list]]: 16/15, 49/45


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


Mapping generators: ~2, ~7/4
: mapping generators: ~2, ~7/4


[[POTE generator]]: ~7/4 = 973.296
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~7/4 = 973.296


{{Multival|legend=1| 2 -2 1 -8 -4 8 }}
{{Multival|legend=1| 2 -2 1 -8 -4 8 }}
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Comma list: 16/15, 22/21, 49/45
Comma list: 16/15, 22/21, 49/45


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


POTE generator: ~7/4 = 978.164
Optimal tuning (POTE): ~2 = 1\1, ~7/4 = 978.164


{{Optimal ET sequence|legend=1| 5, 11b, 16bc, 27bbcc }}
{{Optimal ET sequence|legend=1| 5, 11b, 16bc, 27bbcc }}
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== Walid ==
== Walid ==
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 16/15, 50/49
[[Comma list]]: 16/15, 50/49


[[Mapping]]: [{{val| 2 0 8 9 }}, {{val| 0 1 -1 -1 }}]
{{Mapping|legend=1| 2 0 8 9 | 0 1 -1 -1 }}


Mapping generators: ~7/5, ~3
: mapping generators: ~7/5, ~3


{{Multival|legend=1| 2 -2 -2 -8 -9 1 }}
{{Multival|legend=1| 2 -2 -2 -8 -9 1 }}


[[POTE generator]]: ~3/2 = 749.415
[[Optimal tuning]] ([[POTE]]): ~7/5 = 1\2, ~3/2 = 749.415


{{Optimal ET sequence|legend=1| 2, 6, 8d }}
{{Optimal ET sequence|legend=1| 2, 6, 8d }}
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Comma list: 16/15, 22/21, 50/49
Comma list: 16/15, 22/21, 50/49


Mapping: [{{val| 2 0 8 9 7 }}, {{val| 0 1 -1 -1 0 }}]
Mapping: {{mapping| 2 0 8 9 7 | 0 1 -1 -1 0 }}


POTE generator: ~3/2 = 749.756
Optimal tuning (POTE): ~7/5 = 1\2, ~3/2 = 749.756


{{Optimal ET sequence|legend=1| 2, 6, 8d }}
{{Optimal ET sequence|legend=1| 2, 6, 8d }}
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== Ternary ==
== Ternary ==
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 10/9, 16/15
[[Comma list]]: 10/9, 16/15


[[Mapping]]: [{{val| 3 5 7 0 }}, {{val| 0 0 0 1 }}]
{{Mapping|legend=1| 3 5 7 0 | 0 0 0 1 }}


Mapping generators: ~5/4, ~7
: mapping generators: ~5/4, ~7


{{Multival|legend=1| 0 0 3 0 5 7 }}
{{Multival|legend=1| 0 0 3 0 5 7 }}


[[POTE generator]]: ~7/4 = 1034.013
[[Optimal tuning]] ([[POTE]]): ~5/4 = 1\3, ~7/4 = 1034.013


{{Optimal ET sequence|legend=1| 3d, 6, 9bd, 15bbd }}
{{Optimal ET sequence|legend=1| 3d, 6, 9bd, 15bbd }}
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Comma list: 10/9, 16/15, 22/21
Comma list: 10/9, 16/15, 22/21


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


POTE generator: ~7/4 = 1033.153
Optimal tuning (POTE): ~5/4 = 1\3, ~7/4 = 1033.153


{{Optimal ET sequence|legend=1| 3de, 6, 15bbdee }}
{{Optimal ET sequence|legend=1| 3de, 6, 15bbdee }}
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== Quint ==
== Quint ==
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 16/15, 27/25
[[Comma list]]: 16/15, 27/25


[[Mapping]]: [{{val| 5 8 12 0 }}, {{val| 0 0 0 1 }}]
{{Mapping|legend=1| 5 8 12 0 | 0 0 0 1 }}


Mapping generators: ~9/8, ~7
: mapping generators: ~9/8, ~7


{{Multival|legend=1| 0 0 5 0 8 12 }}
{{Multival|legend=1| 0 0 5 0 8 12 }}


[[POTE generator]]: ~7/4 = 1017.903
[[Optimal tuning]] ([[POTE]]): ~9/8 = 1\5, ~7/4 = 1017.903


{{Optimal ET sequence|legend=1| 5, 15ccd }}
{{Optimal ET sequence|legend=1| 5, 15ccd }}
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