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Fixed typo (CWE tuning of 11-limit 3&5, mother)
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The '''father family''' of temperaments tempers out [[16/15]], the just diatonic semitone. This equates [[4/3]] with [[5/4]], so these are "fourth-thirds", or father, temperaments.
{{Technical data page}}
In a sense, what father is all about is using [[semisixth]]s or [[subfourth]]s and pretending that's 5-limit, and like any temperament which seems to involve pretending, father is at the edge of what can sensibly be called a temperament at all. In other words, it is an [[exotemperament]].
The '''father family''' is a family of [[rank-2 temperament]]s which [[temper out]] the classic diatonic semitone, [[16/15]]. This equates [[4/3]] with [[5/4]] and [[8/5]] with [[3/2]], so the generator is a "fourth-third" (or "fifth-sixth"), hence the name ''father''. In a sense, what father is all about is using [[semisixth]]s or [[subfourth]]s and pretending that these are 5-limit, and like any temperament which seems to involve a lot of "pretending", father is close to the edge of what can be sensibly called a temperament at all. In other words, it is an [[exotemperament]].


== Father ==
== Father ==
{{Main| Father }}
[[Subgroup]]: 2.3.5
[[Subgroup]]: 2.3.5


Line 11: Line 13:
: mapping generators: ~2, ~3
: mapping generators: ~2, ~3


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 743.986
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1180.875{{c}}, ~3/2 = 732.129{{c}}
: [[error map]]: {{val| -19.125 +11.048 +24.181 }}
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 742.290{{c}}
: error map: {{val| 0.000 +40.335 +71.396 }}


[[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 basis|Eigenmonzo (unchanged-interval) basis]]: 2.5/3
: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) 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 }}


[[Badness]]: 0.014884
[[Badness]] (Sintel): 0.349


=== Overview to extensions ===
=== Overview to extensions ===
Line 25: Line 31:


Temperaments discussed elsewhere include:  
Temperaments discussed elsewhere include:  
* ''[[Baba]]'' → [[Slendro clan #Baba|Slendro clan]]
* ''[[Baba]]'' → [[Semaphoresmic clan #Baba|Semaphoresmic clan]]
* ''[[Walid]]'' → [[Jubilismic clan #Walid|Jubilismic clan]]
* ''[[Walid]]'' → [[Jubilismic clan #Walid|Jubilismic clan]]


== Septimal father ==
== Septimal father ==
{{See also| Trienstonic clan #Father }}
{{Main| Father }}
{{See also| Trienstonic clan }}
 
Septimal father tempers out [[28/27]], making it a strong extension of [[trienstonian]].


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
Line 37: Line 46:
{{Mapping|legend=1| 1 0 4 -2 | 0 1 -1 3 }}
{{Mapping|legend=1| 1 0 4 -2 | 0 1 -1 3 }}


{{Multival|legend=1| 1 -1 3 -4 2 10 }}
[[Optimal tuning]]s:
 
* [[WE]]: ~2 = 1180.634{{c}}, ~3/2 = 730.027{{c}}
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 742.002
: [[error map]]: {{val| -19.366 +8.706 +25.561 +1.890 }}
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 738.443{{c}}
: error map: {{val| 0.000 +36.488 +75.244 +46.502 }}


[[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 basis|Eigenmonzo (unchanged-interval) basis]]: 2.7/5
: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) 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
: [[Eigenmonzo basis|Eigenmonzo (unchanged-interval) basis]]: 2.9/7
: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) 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 }}


[[Badness]]: 0.021312
[[Badness]] (Sintel): 0.539


=== 11-limit ===
=== 11-limit ===
Line 58: Line 69:
Mapping: {{mapping| 1 0 4 -2 -3 | 0 1 -1 3 4 }}
Mapping: {{mapping| 1 0 4 -2 -3 | 0 1 -1 3 4 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 747.156
Optimal tunings:
* WE: ~2 = 1180.894{{c}}, ~3/2 = 735.260{{c}}
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 743.387{{c}}


{{Optimal ET sequence|legend=1| 2de, 3de, 5, 8d }}
{{Optimal ET sequence|legend=0| 2de, 3de, 5, 8d }}


Badness: 0.020589
Badness (Sintel): 0.681


== Mother ==
== Mother ==
Line 71: Line 84:
{{Mapping|legend=1| 1 0 4 6 | 0 1 -1 -2 }}
{{Mapping|legend=1| 1 0 4 6 | 0 1 -1 -2 }}


{{Multival|legend=1| 1 -1 -2 -4 -6 -2 }}
[[Optimal tuning]]s:
 
* [[WE]]: ~2 = 1186.985{{c}}, ~3/2 = 713.743{{c}}
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 721.569
: [[error map]]: {{val| -13.015 -1.228 +60.898 -48.372 }}
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 722.866{{c}}
: error map: {{val| 0.000 +20.911 +90.820 -14.559 }}


{{Optimal ET sequence|legend=1| 2, 3, 5 }}
{{Optimal ET sequence|legend=1| 2, 3, 5 }}


[[Badness]]: 0.024152
[[Badness]] (Sintel): 0.611


=== 11-limit ===
=== 11-limit ===
Line 86: Line 101:
Mapping: {{mapping| 1 0 4 6 5 | 0 1 -1 -2 -1 }}
Mapping: {{mapping| 1 0 4 6 5 | 0 1 -1 -2 -1 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 717.364
Optimal tunings:
* WE: ~2 = 1192.016{{c}}, ~3/2 = 712.592{{c}}
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 718.370{{c}}


{{Optimal ET sequence|legend=1| 2, 3, 5 }}
{{Optimal ET sequence|legend=0| 2, 3, 5 }}


Badness: 0.021957
Badness (Sintel): 0.726


== Pater ==
== Pater ==
Line 99: Line 116:
{{Mapping|legend=1| 1 0 4 11 | 0 1 -1 -5 }}
{{Mapping|legend=1| 1 0 4 11 | 0 1 -1 -5 }}


{{Multival|legend=1| 1 -1 -5 -4 -11 -9 }}
[[Optimal tuning]]s:
 
* [[WE]]: ~2 = 1179.316{{c}}, ~3/2 = 740.132{{c}}
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 753.113
: [[error map]]: {{val| -20.684 +17.493 +11.503 +6.412 }}
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 755.156{{c}}
: error map: {{val| 0.000 +53.201 +58.530 +55.392 }}


{{Optimal ET sequence|legend=1| 3, 5d, 8d }}
{{Optimal ET sequence|legend=1| 3, 5d, 8d, 27bbccdd }}


[[Badness]]: 0.053001
[[Badness]] (Sintel): 1.34


=== 11-limit ===
=== 11-limit ===
Line 114: Line 133:
Mapping: {{mapping| 1 0 4 11 10 | 0 1 -1 -5 -4 }}
Mapping: {{mapping| 1 0 4 11 10 | 0 1 -1 -5 -4 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 751.396
Optimal tunings:
 
* WE: ~2 = 1180.290{{c}}, ~3/2 = 739.054{{c}}
{{Optimal ET sequence|legend=1| 3, 5de, 8d }}
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 753.774{{c}}
 
Badness: 0.035487
 
== Ternary ==
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 10/9, 16/15
 
{{Mapping|legend=1| 3 5 7 0 | 0 0 0 1 }}
 
: mapping generators: ~5/4, ~7
 
{{Multival|legend=1| 0 0 3 0 5 7 }}
 
[[Optimal tuning]] ([[POTE]]): ~5/4 = 1\3, ~7/4 = 1034.013
 
{{Optimal ET sequence|legend=1| 3d, 6, 9bd, 15bbd }}
 
[[Badness]]: 0.028673
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 10/9, 16/15, 22/21
 
Mapping: {{mapping| 3 5 7 0 2 | 0 0 0 1 1 }}
 
Optimal tuning (POTE): ~5/4 = 1\3, ~7/4 = 1033.153
 
{{Optimal ET sequence|legend=1| 3de, 6, 15bbdee }}
 
Badness: 0.025592
 
== Quint ==
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 16/15, 27/25
 
{{Mapping|legend=1| 5 8 12 0 | 0 0 0 1 }}
 
: mapping generators: ~9/8, ~7
 
{{Multival|legend=1| 0 0 5 0 8 12 }}
 
[[Optimal tuning]] ([[POTE]]): ~9/8 = 1\5, ~7/4 = 1017.903


{{Optimal ET sequence|legend=1| 5, 15ccd }}
{{Optimal ET sequence|legend=0| 3, 5de, 8d }}


[[Badness]]: 0.048312
Badness (Sintel): 1.17


[[Category:Temperament families]]
[[Category:Temperament families]]
[[Category:Father family| ]] <!-- main article -->
[[Category:Father family| ]] <!-- main article -->
[[Category:Father| ]] <!-- key article -->
[[Category:Rank 2]]
[[Category:Rank 2]]
Retrieved from "https://en.xen.wiki/w/Father_family"