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This tempers out the fifive comma, 9765625/9565938 = {{monzo|-1 -14 10}}.
{{Technical data page}}
The '''fifive family''' of [[regular temperament|temperaments]] [[tempering out|tempers out]] the [[fifive comma]] ({{monzo|legend=1| -1 -14 10 }}, [[ratio]]: 9765625/9565938).


== Fifive  ==
The name ''fifive'' was given by [[Petr Pařízek]] in 2011 for it splits the [[3/2|perfect fifth]] in five.<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_101780.html Yahoo! Tuning Group | ''Suggested names for the unclasified temperaments'']</ref>
Comma: 9765625/9565938


POTE generator: ~27/25 = 140.624
Considered below are crepuscular, fifives, and fourfives.  


Map: [&lt;2 2 3|, &lt;0 5 7|]
== Fifive ==
[[Subgroup]]: 2.3.5


EDOs: {{EDOs|8, 26, 34, 94, 128}}
[[Comma list]]: 9765625/9565938


Badness: 0.2058
{{Mapping|legend=1| 2 2 3 | 0 5 7 }}


== Crepuscular  ==
: mapping generators: ~78125/50421, ~27/25
{{see also|Jubilismic clan #Crepuscular}}


Commas: 50/49, 4375/4374
[[Optimal tuning]]s:
* [[CTE]]: ~78125/50421 = 1\2, ~27/25 = 140.6349
* [[POTE]]: ~78125/50421 = 1\2, ~27/25 = 140.624


POTE generator: ~27/25 = 140.349
{{Optimal ET sequence|legend=1| 8, 18bc, 26, 34, 94, 128 }}


Map: [&lt;2 2 3 4|, &lt;0 5 7 7|]
[[Badness]]:
* Smith: 0.205812
* Dirichlet: 4.828


Wedgie: &lt;&lt;10 14 14 -1 -6 -7||
=== 2.3.5.13 subgroup ===
Subgroup: 2.3.5.13


EDOs: {{EDOs|8d, 26, 34d, 60d}}
Comma list: 325/324, 20000/19773


Badness: 0.0867
Mapping: {{mapping| 2 2 3 6 | 0 5 7 6 }}


=== 11-limit  ===
: mapping generators: ~351/250, ~13/12
Commas: 50/49, 99/98, 864/847


POTE generator: ~12/11 = 140.587
Optimal tunings:
* CTE: ~351/250 = 1\2, ~13/12 = 140.5685
* CWE: ~351/250 = 1\2, ~13/12 = 140.6232


Map: [&lt;2 2 3 4 6|, &lt;0 5 7 7 4|]
Optimal ET sequence: {{Optimal ET sequence| 8, 18bcf, 26, 34, 94, 128 }}


EDOs: {{EDOs|8d, 26, 34d, 60d}}
Badness:  
* Smith: 0.0240
* Dirichlet: 0.800


Badness: 0.0408
=== 2.3.5.13.17 subgroup ===
Subgroup: 2.3.5.13.17


=== 13-limit  ===
Comma list: 170/169, 289/288, 325/324
Commas: 50/49, 78/77, 99/98, 144/143


POTE generator: ~12/11 = 140.554
Mapping: {{mapping| 2 2 3 6 7 | 0 5 7 6 5 }}


Map: [&lt;2 2 3 4 6 6|, &lt;0 5 7 7 4 6|]
: mapping generators: ~17/12, ~13/12


EDOs: {{EDOs|8d, 26, 34d, 60d}}
Optimal tunings:
* CTE: ~17/12 = 1\2, ~13/12 = 140.5958
* CWE: ~17/12 = 1\2, ~13/12 = 140.6057


Badness: 0.0244
Optimal ET sequence: {{Optimal ET sequence| 8, 18bcfg, 26, 34, 94, 128 }}


== Fifives  ==
Badness:
Commas: 875/864, 83349/81920
* Smith: 0.0110
* Dirichlet: 0.488


POTE generator: ~27/25 = 139.909
== Crepuscular ==
{{See also| Jubilismic clan #Crepuscular }}


Map: [&lt;2 2 3 7|, &lt;0 5 7 -6|]
[[Subgroup]]: 2.3.5.7


EDOs: {{EDOs|8, 26, 34, 60, 94d}}
[[Comma list]]: 50/49, 4375/4374


Badness: 0.1306
{{Mapping|legend=1| 2 2 3 4 | 0 5 7 7 }}


== Fourfives  ==
[[Optimal tuning]] ([[POTE]]): ~7/5 = 1\2, ~27/25 = 140.349
Commas: 245/243, 235298/234375


POTE generator: ~27/25 = 140.754
{{Optimal ET sequence|legend=1| 8d, 26, 34d, 60d }}


Map: [&lt;4 4 6 7|, &lt;0 5 7 9|]
[[Badness]]: 0.086669


EDOs: {{EDOs|8d, 60, 68, 128}}
=== 11-limit ===
Subgroup: 2.3.5.7.11


Badness: 0.1141
Comma list: 50/49, 99/98, 864/847


=== 11-limit  ===
Mapping: {{mapping| 2 2 3 4 6 | 0 5 7 7 4 }}
Commas: 245/243, 385/384, 235298/234375


POTE generator: ~27/25 = 140.771
Optimal tuning (POTE): ~7/5 = 1\2, ~12/11 = 140.587


Map: [&lt;4 4 6 7 19|, &lt;0 5 7 9 -11|]
{{Optimal ET sequence|legend=1| 8d, 26, 34d, 60d }}


EDOs: {{EDOs|8de, 60, 68, 128, 196}}
Badness: 0.040758


Badness: 0.1202
=== 13-limit ===
Subgroup: 2.3.5.7.11.13


=== 13-limit  ===
Comma list: 50/49, 78/77, 99/98, 144/143
Commas: 196/195, 245/243, 385/384, 20000/19773


POTE generator: ~13/12 = 140.760
Mapping: {{mapping| 2 2 3 4 6 6 | 0 5 7 7 4 6 }}


Map: [&lt;4 4 6 7 19 12|, &lt;0 5 7 9 -11 6|]
Optimal tuning (POTE): ~7/5 = 1\2, ~12/11 = 140.554


EDOs: {{EDOs|8de, 60, 68, 128, 196f}}
{{Optimal ET sequence|legend=1| 8d, 26, 34d, 60d }}


Badness: 0.0674
Badness: 0.024368


[[Category:Theory]]
=== 17-limit ===
[[Category:Temperament family]]
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 50/49, 78/77, 85/84, 99/98, 144/143
 
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 ET sequence|legend=1| 8d, 26, 34d, 60d }}
 
Badness: 0.018567
 
== Fifives ==
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 875/864, 83349/81920
 
{{Mapping|legend=1| 2 2 3 7 | 0 5 7 -6 }}
 
[[Optimal tuning]] ([[POTE]]): ~567/400 = 1\2, ~27/25 = 139.909
 
{{Optimal ET sequence|legend=1| 8, 26, 34, 60 }}
 
[[Badness]]: 0.130589
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 100/99, 385/384, 3969/3872
 
Mapping: {{mapping| 2 2 3 7 6 | 0 5 7 -6 4 }}
 
Optimal tuning (POTE): ~63/44 = 1\2, ~12/11 = 139.884
 
{{Optimal ET sequence|legend=1| 8, 26, 34, 60 }}
 
Badness: 0.080306
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 100/99, 105/104, 144/143, 1352/1331
 
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 ET sequence|legend=1| 8, 26, 34, 60 }}
 
Badness: 0.044253
 
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 100/99, 105/104, 144/143, 170/169, 221/220
 
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 ET sequence|legend=1| 8, 26, 34, 60 }}
 
Badness: 0.029429
 
== Fourfives ==
{{See also| Sensamagic clan }}
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 245/243, 235298/234375
 
{{Mapping|legend=1| 4 4 6 7 | 0 5 7 9 }}
 
: mapping generators: ~25/21, ~27/25
 
[[Optimal tuning]] ([[POTE]]): ~25/21 = 1\4, ~27/25 = 140.754
 
{{Optimal ET sequence|legend=1| 8d, 60, 68, 128 }}
 
[[Badness]]: 0.114143
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 245/243, 385/384, 235298/234375
 
Mapping: {{mapping| 4 4 6 7 19 | 0 5 7 9 -11 }}
 
Optimal tuning (POTE): ~25/21 = 1\4, ~27/25 = 140.771
 
{{Optimal ET sequence|legend=1| 8de, 60, 68, 128, 196 }}
 
Badness: 0.120165
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 196/195, 245/243, 385/384, 20000/19773
 
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 ET sequence|legend=1| 8de, 60, 68, 128, 196f }}
 
Badness: 0.067365
 
=== Quadrafives ===
Subgroup: 2.3.5.7.11
 
Comma list: 121/120, 245/243, 1375/1372
 
Mapping: {{mapping| 4 4 6 7 11 | 0 5 7 9 6 }}
 
Optimal tuning (POTE): ~25/21 = 1\4, ~27/25 = 140.630
 
{{Optimal ET sequence|legend=1| 8d, 60e, 68, 128e }}
 
Badness: 0.057268
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 121/120, 196/195, 245/243, 275/273
 
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 ET sequence|legend=1| 8d, 60e, 68, 128e }}
 
Badness: 0.036128
 
==== 17-limit ====
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 121/120, 154/153, 170/169, 196/195, 245/243
 
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 ET sequence|legend=1| 8d, 60e, 68, 128e }}
 
Badness: 0.024796
 
== Notes ==
 
[[Category:Temperament families]]
[[Category:Pages with mostly numerical content]]
[[Category:Fifive family| ]] <!-- main article -->
[[Category:Fifive| ]] <!-- key article -->
[[Category:Rank 2]]
[[Category:Rank 2]]
[[Category:Fifive]]
Retrieved from "https://en.xen.wiki/w/Fifive_family"