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Breedsmic temperaments: Difference between revisions

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[[POTE generator]]: ~49/40 = 351.113
[[POTE generator]]: ~49/40 = 351.113


{{Val list|legend=1| 41, 188, 229, 270, 1121, 1391, 1661, 1931, 2201, 6333bc }}
{{Val list|legend=1| 41, 188, 229, 270, 1121, 1391, 1661, 1931, 2201, 6333bbcc }}


[[Badness]]: 0.041878
[[Badness]]: 0.041878
Line 623: Line 623:
= Maviloid =
= Maviloid =
{{see also| Ragismic microtemperaments #Parakleismic }}
{{see also| Ragismic microtemperaments #Parakleismic }}
Subgroup: 2.3.5.7


[[Comma list]]: 2401/2400, 1224440064/1220703125
[[Comma list]]: 2401/2400, 1224440064/1220703125
Line 637: Line 639:


= Subneutral =
= Subneutral =
Subgroup: 2.3.5.7
[[Comma list]]: 2401/2400, 274877906944/274658203125
[[Comma list]]: 2401/2400, 274877906944/274658203125


Line 649: Line 653:
[[Badness]]: 0.045792
[[Badness]]: 0.045792


=Osiris=
= Osiris =
Commas: 2401/2400, 31381059609/31360000000
Subgroup: 2.3.5.7
 
[[Comma list]]: 2401/2400, 31381059609/31360000000
 
[[Mapping]]: [{{val|1 13 33 21}}, {{val|0 -32 -86 -51}}]
 
{{Multival|legend=1|32 86 51 62 -9 -123}}
 
[[POTE generator]]: ~2800/2187 = 428.066


POTE generator: ~2800/2187 = 428.066
{{Val list|legend=1| 157, 171, 1012, 1183, 1354, 1525, 1696, 6955dd }}


Map: [<1 13 33 21|, <0 -32 -86 -51|]
[[Badness]]: 0.028307


Wedgie: <<32 86 51 62 -9 -123||
= Gorgik =
Subgroup: 2.3.5.7


EDOs: 157, 171, 1012, 1183, 1354, 1525, 1696, 6955d
[[Comma list]]: 2401/2400, 28672/28125


Badness: 0.028307
[[Mapping]]: [{{val|1 5 1 3}}, {{val|0 -18 7 -1}}]


=Gorgik=
{{Multival|legend=1|18 -7 1 -53 -49 22}}
Commas: 2401/2400, 28672/28125


POTE generator: ~8/7 = 227.512
[[POTE generator]]: ~8/7 = 227.512


Map: [<1 5 1 3|, <0 -18 7 -1|]
{{Val list|legend=1| 21, 37, 58, 153bc, 211bccd, 269bccd }}


Wedgie: <<18 -7 1 -53 -49 22||
[[Badness]]: 0.158384


EDOs: 21, 37, 58, 153bc, 211bcd, 269bcd
== 11-limit ==
Subgroup: 2.3.5.7.11


Badness: 0.1584
Comma list: 176/175, 2401/2400, 2560/2541


==11-limit==
Mapping: [{{val|1 5 1 3 1}}, {{val|0 -18 7 -1 13}}]
Commas: 176/175, 2401/2400, 2560/2541


POTE generator: ~8/7 = 227.500
POTE generator: ~8/7 = 227.500


Map: [<1 5 1 3 1|, <0 -18 7 -1 13|]
Vals: {{Val list| 21, 37, 58, 153bce, 211bccdee, 269bccdee }}
 
Badness: 0.059260


EDOs: 21, 37, 58, 153bce, 211bcde, 269bcde
== 13-limit ==
Subgroup: 2.3.5.7.11.13


Badness: 0.059
Comma list: 176/175, 196/195, 364/363, 512/507


==13-limit==
Mapping: [{{val|1 5 1 3 1 2}}, {{val|0 -18 7 -1 13 9}}]
Commas: 176/175, 196/195, 364/363, 512/507


POTE generator: ~8/7 = 227.493
POTE generator: ~8/7 = 227.493


Map: [<1 5 1 3 1 2|, <0 -18 7 -1 13 9|]
Vals: {{Val list| 21, 37, 58, 153bcef, 211bccdeeff }}
 
Badness: 0.032205
 
= Fibo =
Subgroup: 2.3.5.7


EDOs: 21, 37, 58, 153bcef, 211bcdef
[[Comma list]]: 2401/2400, 341796875/339738624


Badness: 0.0322
[[Mapping]]: [{{val|1 19 8 10}}, {{val|0 -46 -15 -19}}]


=Fibo=
{{Multival|legend=1|46 15 19 -83 -99 2}}
Commas: 2401/2400, 341796875/339738624


POTE generator: ~125/96 = 454.310
[[POTE generator]]: ~125/96 = 454.310


Map: [<1 19 8 10|, <0 -46 -15 -19|]
{{Val list|legend=1| 37, 103, 140, 243, 383, 1009cd, 1392ccd }}


Wedgie: <<46 15 19 -83 -99 2||
Badness: 0.100511


EDOs: 37, 103, 140, 243, 383, 1009cd, 1392cd
== 11-limit ==
Subgroup: 2.3.5.7.11


Badness: 0.1005
Comma list: 385/384, 1375/1372, 43923/43750


==11-limit==
Mapping: [{{val|1 19 8 10 8}}, {{val|0 -46 -15 -19 -12}}]
Commas: 385/384, 1375/1372, 43923/43750


POTE generator: ~100/77 = 454.318
POTE generator: ~100/77 = 454.318


Map: [<1 19 8 10 8|, <0 -46 -15 -19 -12|]
Vals: {{Val list| 37, 103, 140, 243e }}
 
Badness: 0.056514


EDOs: 37, 103, 140, 243e
== 13-limit ==
Subgroup: 2.3.5.7.11.13


Badness: 0.0565
Comma list: 385/384, 625/624, 847/845, 1375/1372


==13-limit==
Mapping: [{{val|1 19 8 10 8 9}}, {{val|0 -46 -15 -19 -12 -14}}]
Commas: 385/384, 625/624, 847/845, 1375/1372


POTE generator: ~13/10 = 454.316
POTE generator: ~13/10 = 454.316


Map: [<1 19 8 10 8 9|, <0 -46 -15 -19 -12 -14|]
Vals: {{Val list| 37, 103, 140, 243e }}
 
EDOs: 37, 103, 140, 243e


Badness: 0.0274
Badness: 0.027429


=Mintone=
= Mintone =
In addition to 2401/2400, mintone tempers out 177147/175000 = |-3 11 -5 -1> in the 7-limit; 243/242, 441/440, and 43923/43750 in the 11-limit. It has a generator tuned around 49/44. It may be described as the 58&103 temperament, and as one might expect, 25\161 makes for an excellent tuning choice.
In addition to 2401/2400, mintone tempers out 177147/175000 = |-3 11 -5 -1> in the 7-limit; 243/242, 441/440, and 43923/43750 in the 11-limit. It has a generator tuned around 49/44. It may be described as the 58&103 temperament, and as one might expect, 25\161 makes for an excellent tuning choice.


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