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Fifive family: Difference between revisions

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{{Mapping|legend=1| 2 2 3 | 0 5 7 }}
{{Mapping|legend=1| 2 2 3 | 0 5 7 }}
: mapping generators: ~78125/50421, ~27/25
: mapping generators: ~78125/50421, ~27/25


[[Optimal tuning]]s:
[[Optimal tuning]]s:
* [[CTE]]: ~78125/50421 = 1\2, ~27/25 = 140.6349
* [[CTE]]: ~78125/50421 = 600.0000{{c}}, ~27/25 = 140.6349{{c}}
* [[POTE]]: ~78125/50421 = 1\2, ~27/25 = 140.624
* [[POTE]]: ~78125/50421 = 600.0000{{c}}, ~27/25 = 140.624{{c}}


{{Optimal ET sequence|legend=1| 8, 18bc, 26, 34, 94, 128 }}
{{Optimal ET sequence|legend=1| 8, 18bc, 26, 34, 94, 128 }}


[[Badness]]:
[[Badness]] (Sintel): 4.83
* Smith: 0.205812
* Dirichlet: 4.828


=== 2.3.5.13 subgroup ===
=== 2.3.5.13 subgroup ===
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Mapping: {{mapping| 2 2 3 6 | 0 5 7 6 }}
Mapping: {{mapping| 2 2 3 6 | 0 5 7 6 }}
: mapping generators: ~351/250, ~13/12
: mapping generators: ~351/250, ~13/12


Optimal tunings:
Optimal tunings:
* CTE: ~351/250 = 1\2, ~13/12 = 140.5685
* CTE: ~351/250 = 600.0000{{c}}, ~13/12 = 140.5685{{c}}
* CWE: ~351/250 = 1\2, ~13/12 = 140.6232
* CWE: ~351/250 = 600.0000{{c}}, ~13/12 = 140.6232{{c}}


Optimal ET sequence: {{Optimal ET sequence| 8, 18bcf, 26, 34, 94, 128 }}
{{Optimal ET sequence|legend=0| 8, 18bcf, 26, 34, 94, 128 }}


Badness:
Badness (Sintel): 0.800
* Smith: 0.0240
* Dirichlet: 0.800


=== 2.3.5.13.17 subgroup ===
=== 2.3.5.13.17 subgroup ===
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Mapping: {{mapping| 2 2 3 6 7 | 0 5 7 6 5 }}
Mapping: {{mapping| 2 2 3 6 7 | 0 5 7 6 5 }}
: mapping generators: ~17/12, ~13/12
: mapping generators: ~17/12, ~13/12


Optimal tunings:
Optimal tunings:
* CTE: ~17/12 = 1\2, ~13/12 = 140.5958
* CTE: ~17/12 = 600.0000{{c}}, ~13/12 = 140.5958{{c}}
* CWE: ~17/12 = 1\2, ~13/12 = 140.6057
* CWE: ~17/12 = 600.0000{{c}}, ~13/12 = 140.6057{{c}}


Optimal ET sequence: {{Optimal ET sequence| 8, 18bcfg, 26, 34, 94, 128 }}
{{Optimal ET sequence|legend=0| 8, 18bcfg, 26, 34, 94, 128 }}


Badness:
Badness (Sintel): 0.488
* Smith: 0.0110
* Dirichlet: 0.488


== Crepuscular ==
== Crepuscular ==
{{See also| Jubilismic clan #Crepuscular }}
[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7


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{{Mapping|legend=1| 2 2 3 4 | 0 5 7 7 }}
{{Mapping|legend=1| 2 2 3 4 | 0 5 7 7 }}


[[Optimal tuning]] ([[POTE]]): ~7/5 = 1\2, ~27/25 = 140.349
[[Optimal tuning]] ([[POTE]]): ~7/5 = 600.000{{c}}, ~27/25 = 140.349{{c}}


{{Optimal ET sequence|legend=1| 8d, 26, 34d, 60d }}
{{Optimal ET sequence|legend=1| 8d, 26, 34d, 60d }}


[[Badness]]: 0.086669
[[Badness]] (Smith): 0.086669


=== 11-limit ===
=== 11-limit ===
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Mapping: {{mapping| 2 2 3 4 6 | 0 5 7 7 4 }}
Mapping: {{mapping| 2 2 3 4 6 | 0 5 7 7 4 }}


Optimal tuning (POTE): ~7/5 = 1\2, ~12/11 = 140.587
Optimal tuning (POTE): ~7/5 = 600.000{{c}}, ~12/11 = 140.587{{c}}


{{Optimal ET sequence|legend=1| 8d, 26, 34d, 60d }}
{{Optimal ET sequence|legend=0| 8d, 26, 34d, 60d }}


Badness: 0.040758
Badness (Smith): 0.040758


=== 13-limit ===
=== 13-limit ===
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Mapping: {{mapping| 2 2 3 4 6 6 | 0 5 7 7 4 6 }}
Mapping: {{mapping| 2 2 3 4 6 6 | 0 5 7 7 4 6 }}


Optimal tuning (POTE): ~7/5 = 1\2, ~12/11 = 140.554
Optimal tuning (POTE): ~7/5 = 600.000{{c}}, ~12/11 = 140.554{{c}}


{{Optimal ET sequence|legend=1| 8d, 26, 34d, 60d }}
{{Optimal ET sequence|legend=0| 8d, 26, 34d, 60d }}


Badness: 0.024368
Badness (Smith): 0.024368


=== 17-limit ===
=== 17-limit ===
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Mapping: {{mapping| 2 2 3 4 6 6 7 | 0 5 7 7 4 6 5 }}
Mapping: {{mapping| 2 2 3 4 6 6 7 | 0 5 7 7 4 6 5 }}


Optimal tuning (POTE): ~7/5 = 1\2, ~12/11 = 140.405
Optimal tuning (POTE): ~7/5 = 600.000{{c}}, ~12/11 = 140.405{{c}}


{{Optimal ET sequence|legend=1| 8d, 26, 34d, 60d }}
{{Optimal ET sequence|legend=0| 8d, 26, 34d, 60d }}


Badness: 0.018567
Badness (Smith): 0.018567


== Fifives ==
== Fifives ==
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{{Mapping|legend=1| 2 2 3 7 | 0 5 7 -6 }}
{{Mapping|legend=1| 2 2 3 7 | 0 5 7 -6 }}


[[Optimal tuning]] ([[POTE]]): ~567/400 = 1\2, ~27/25 = 139.909
[[Optimal tuning]] ([[POTE]]): ~567/400 = 600.000{{c}}, ~27/25 = 139.909{{c}}


{{Optimal ET sequence|legend=1| 8, 26, 34, 60 }}
{{Optimal ET sequence|legend=1| 8, 26, 34, 60 }}


[[Badness]]: 0.130589
[[Badness]] (Smith): 0.130589


=== 11-limit ===
=== 11-limit ===
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Mapping: {{mapping| 2 2 3 7 6 | 0 5 7 -6 4 }}
Mapping: {{mapping| 2 2 3 7 6 | 0 5 7 -6 4 }}


Optimal tuning (POTE): ~63/44 = 1\2, ~12/11 = 139.884
Optimal tuning (POTE): ~63/44 = 600.000{{c}}, ~12/11 = 139.884{{c}}


{{Optimal ET sequence|legend=1| 8, 26, 34, 60 }}
{{Optimal ET sequence|legend=0| 8, 26, 34, 60 }}


Badness: 0.080306
Badness (Smith): 0.080306


=== 13-limit ===
=== 13-limit ===
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Mapping: {{mapping| 2 2 3 7 6 6 | 0 5 7 -6 4 6 }}
Mapping: {{mapping| 2 2 3 7 6 6 | 0 5 7 -6 4 6 }}


Optimal tuning (POTE): ~55/39 = 1\2, ~12/11 = 139.867
Optimal tuning (POTE): ~55/39 = 600.000{{c}}, ~12/11 = 139.867{{c}}


{{Optimal ET sequence|legend=1| 8, 26, 34, 60 }}
{{Optimal ET sequence|legend=0| 8, 26, 34, 60 }}


Badness: 0.044253
Badness (Smith): 0.044253


=== 17-limit ===
=== 17-limit ===
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Mapping: {{mapping| 2 2 3 7 6 6 7 | 0 5 7 -6 4 6 5 }}
Mapping: {{mapping| 2 2 3 7 6 6 7 | 0 5 7 -6 4 6 5 }}


Optimal tuning (POTE): ~17/12 = 1\2, ~12/11 = 139.868
Optimal tuning (POTE): ~17/12 = 600.000{{c}}, ~12/11 = 139.868{{c}}


{{Optimal ET sequence|legend=1| 8, 26, 34, 60 }}
{{Optimal ET sequence|legend=0| 8, 26, 34, 60 }}


Badness: 0.029429
Badness (Smith): 0.029429


== Fourfives ==
== Fourfives ==
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{{Mapping|legend=1| 4 4 6 7 | 0 5 7 9 }}
{{Mapping|legend=1| 4 4 6 7 | 0 5 7 9 }}
: mapping generators: ~25/21, ~27/25
: mapping generators: ~25/21, ~27/25


[[Optimal tuning]] ([[POTE]]): ~25/21 = 1\4, ~27/25 = 140.754
[[Optimal tuning]] ([[POTE]]): ~25/21 = 300.000{{c}}, ~27/25 = 140.754{{c}}


{{Optimal ET sequence|legend=1| 8d, 60, 68, 128 }}
{{Optimal ET sequence|legend=1| 8d, 60, 68, 128 }}


[[Badness]]: 0.114143
[[Badness]] (Smith): 0.114143


=== 11-limit ===
=== 11-limit ===
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Mapping: {{mapping| 4 4 6 7 19 | 0 5 7 9 -11 }}
Mapping: {{mapping| 4 4 6 7 19 | 0 5 7 9 -11 }}


Optimal tuning (POTE): ~25/21 = 1\4, ~27/25 = 140.771
Optimal tuning (POTE): ~25/21 = 300.000{{c}}, ~27/25 = 140.771{{c}}


{{Optimal ET sequence|legend=1| 8de, 60, 68, 128, 196 }}
{{Optimal ET sequence|legend=0| 8de, 60, 68, 128, 196 }}


Badness: 0.120165
Badness (Smith): 0.120165


==== 13-limit ====
==== 13-limit ====
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Mapping: {{mapping| 4 4 6 7 19 12 | 0 5 7 9 -11 6 }}
Mapping: {{mapping| 4 4 6 7 19 12 | 0 5 7 9 -11 6 }}


Optimal tuning (POTE): ~25/21 = 1\4, ~13/12 = 140.760
Optimal tuning (POTE): ~25/21 = 300.000{{c}}, ~13/12 = 140.760{{c}}


{{Optimal ET sequence|legend=1| 8de, 60, 68, 128, 196f }}
{{Optimal ET sequence|legend=0| 8de, 60, 68, 128, 196f }}


Badness: 0.067365
Badness (Smith): 0.067365


=== Quadrafives ===
=== Quadrafives ===
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Mapping: {{mapping| 4 4 6 7 11 | 0 5 7 9 6 }}
Mapping: {{mapping| 4 4 6 7 11 | 0 5 7 9 6 }}


Optimal tuning (POTE): ~25/21 = 1\4, ~27/25 = 140.630
Optimal tuning (POTE): ~25/21 = 300.000{{c}}, ~27/25 = 140.630{{c}}


{{Optimal ET sequence|legend=1| 8d, 60e, 68, 128e }}
{{Optimal ET sequence|legend=0| 8d, 60e, 68, 128e }}


Badness: 0.057268
Badness (Smith): 0.057268


==== 13-limit ====
==== 13-limit ====
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Mapping: {{mapping| 4 4 6 7 11 12 | 0 5 7 9 6 6 }}
Mapping: {{mapping| 4 4 6 7 11 12 | 0 5 7 9 6 6 }}


Optimal tuning (POTE): ~25/21 = 1\4, ~13/12 = 140.728
Optimal tuning (POTE): ~25/21 = 300.000{{c}}, ~13/12 = 140.728{{c}}


{{Optimal ET sequence|legend=1| 8d, 60e, 68, 128e }}
{{Optimal ET sequence|legend=0| 8d, 60e, 68, 128e }}


Badness: 0.036128
Badness (Smith): 0.036128


==== 17-limit ====
==== 17-limit ====
Line 245: Line 233:
Mapping: {{mapping| 4 4 6 7 11 12 14 | 0 5 7 9 6 6 5 }}
Mapping: {{mapping| 4 4 6 7 11 12 14 | 0 5 7 9 6 6 5 }}


Optimal tuning (POTE): ~25/21 = 1\4, ~13/12 = 140.718
Optimal tuning (POTE): ~25/21 = 300.000{{c}}, ~13/12 = 140.718{{c}}


{{Optimal ET sequence|legend=1| 8d, 60e, 68, 128e }}
{{Optimal ET sequence|legend=0| 8d, 60e, 68, 128e }}


Badness: 0.024796
Badness (Smith): 0.024796


== References ==
== References ==
Retrieved from "https://en.xen.wiki/w/Fifive_family"