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Breedsmic temperaments: Difference between revisions

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= Newt =
= Newt =
This temperament has a generator of neutral third (0.2 cents flat of [[49/40]]) and tempers out the [[garischisma]].
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


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= 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 = {{monzo|-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.
 
Subgroup: 2.3.5.7
 
[[Comma list]]: 2401/2400, 177147/175000
 
[[Mapping]]: [{{val|1 5 9 7}}, {{val|0 -22 -43 -27}}]
 
{{Multival|legend=1|22 43 27 17 -19 -58}}


Commas: 2401/2400, 177147/175000
[[POTE generator]]: ~10/9 = 186.343


POTE generator: ~10/9 = 186.343
{{Val list|legend=1| 45, 58, 103, 161, 586b, 747bc, 908bbc }}


Map: [<1 5 9 7|, <0 -22 -43 -27|]
[[Badness]]: 0.125672


EDOs: 45, 58, 103, 161, 586b, 747bc, 908bc
== 11-limit ==
Subgroup: 2.3.5.7.11


Badness: 0.12567
Comma list: 243/242, 441/440, 43923/43750


==11-limit==
Mapping: [{{val|1 5 9 7 12}}, {{val|0 -22 -43 -27 -55}}]
Commas: 243/242, 441/440, 43923/43750


POTE generator: ~10/9 = 186.345
POTE generator: ~10/9 = 186.345


Map: [<1 5 9 7 12|, <0 -22 -43 -27 -55|]
Vals: {{Val list| 58, 103, 161, 425b, 586b, 747bc }}
 
Badness: 0.039962


EDOs: 58, 103, 161, 425b, 586b, 747bc
== 13-limit ==
Subgroup: 2.3.5.7.11.13


Badness: 0.0400
Comma list: 243/242, 351/350, 441/440, 847/845


==13-limit==
Mapping: [{{val|1 5 9 7 12 11}}, {{val|0 -22 -43 -27 -55 -47}}]
Commas: 243/242, 351/350, 441/440, 847/845


POTE generator: ~10/9 = 186.347
POTE generator: ~10/9 = 186.347


Map: [<1 5 9 7 12 11|, <0 -22 -43 -27 -55 -47|]
Vals: {{Val list| 58, 103, 161, 425b, 586bf }}


EDOs: 58, 103, 161
Badness: 0.021849


Badness: 0.0218
== 17-limit ==
Subgroup: 2.3.5.7.11.13


==17-limit==
Comma list: 243/242, 351/350, 441/440, 561/560, 847/845
Commas: 243/242, 351/350, 441/440, 561/560, 847/845
 
Mapping: [{{val|1 5 9 7 12 11 3}}, {{val|0 -22 -43 -27 -55 -47 7}}]


POTE generator: ~10/9 = 186.348
POTE generator: ~10/9 = 186.348


Map: [<1 5 9 7 12 11 3|, <0 -22 -43 -27 -55 -47 7|]
Vals: {{Val list| 58, 103, 161, 425b, 586bf }}


EDOs: 58, 103, 161, 264
Badness: 0.020295


=Catafourth=
= Catafourth =
{{see also| Sensipent family }}
{{see also| Sensipent family }}


Commas: 2401/2400, 78732/78125
Subgroup: 2.3.5.7
 
[[Comma list]]: 2401/2400, 78732/78125


POTE generator: ~250/189 = 489.235
[[Mapping]]: [{{val|1 13 17 13}}, {{val|0 -28 -36 -25}}]


Map: [<1 13 17 13|, <0 -28 -36 -25|]
{{Multival|legend=1|28 36 25 -8 -39 -43}}


Wedgie: <<28 36 25 -8 -39 -43||
[[POTE generator]]: ~250/189 = 489.235


EDOs: 27, 76, 103, 130
{{Val list|legend=1| 27, 76, 103, 130 }}


Badness: 0.0796
Badness: 0.079579


==11-limit==
== 11-limit ==
Commas: 243/242, 441/440, 78408/78125
Subgroup: 2.3.5.7.11
 
Comma list: 243/242, 441/440, 78408/78125
 
Mapping: [{{val|1 13 17 13 32}}, {{val|0 -28 -36 -25 -70}}]


POTE generator: ~250/189 = 489.252
POTE generator: ~250/189 = 489.252


Map: [<1 13 17 13 32|, <0 -28 -36 -25 -70|]
Vals: {{Val list| 103, 130, 233, 363, 493e, 856be }}


EDOs: 103, 130, 233, 363, 493e, 856be
Badness: 0.036785


Badness: 0.0368
== 13-limit ==
Subgroup: 2.3.5.7.11.13


==13-limit==
Comma list: 243/242, 351/350, 441/440, 10985/10976
Commas: 243/242, 351/350, 441/440, 10985/10976
 
Mapping:  [{{val|1 13 17 13 32 9}}, {{val|0 -28 -36 -25 -70 -13}}]


POTE generator: ~65/49 = 489.256
POTE generator: ~65/49 = 489.256


Map: [<1 13 17 13 32 9|, <0 -28 -36 -25 -70 -13|]
Vals: {{Val list| 103, 130, 233, 363 }}
 
EDOs: 103, 130, 233, 363


Badness: 0.0217
Badness: 0.021694


= Cotritone =
= Cotritone =
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[[Category:Theory]]
[[Category:Theory]]
[[Category:Temperament]]
[[Category:Temperament]]
[[Category:Temperament collection]]
[[Category:Breed]]
[[Category:Breed]]
[[Category:Rank 2]]
[[Category:Rank 2]]
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