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Ragismic family: Difference between revisions

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Temperaments not discussed here include [[Breed family #Ennealimmic|ennealimmic]].
Temperaments not discussed here include [[Breed family #Ennealimmic|ennealimmic]].


== Ragismic ==
== Ragismic ==
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


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Scales: [[Ragismic19]]
Scales: [[Ragismic19]]


== Thor ==
== Beyla ==
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


[[Comma list]]: 3025/3024, 4375/4374
[[Comma list]]: 385/384, 4375/4374
 
[[Mapping]]: [{{val| 1 0 0 1 6 }}, {{val| 0 1 0 7 -6 }}, {{val| 0 0 1 -4 3 }}]


[[Mapping]]: [{{val|2 0 0 2 5}}, {{val|0 1 0 7 5}}, {{val|0 0 1 -4 -3}}]
Mapping generators: ~2, ~3, ~5


Mapping generators: ~99/70, ~3, ~5
{{Val list|legend=1| 7, 19, 26, 45, 46, 53, 72, 118, 190, 315e, 361e, 433de, 623cdee }}
 
[[Badness]]: 0.721 × 10<sup>-3</sup>


[[Minimax tuning]]:
=== 13-limit ===
* [[11-odd-limit]] eigenmonzos: 2, 11/10, 8/7
Subgroup: 2.3.5.7.11.13


{{Val list|legend=1| 26, 34d, 46, 72, 118, 152, 224, 270, 342, 494, 612, 836, 1106, 1448, 2554, 4002e, 5720e, 7168cee }}
Comma list: 169/168, 325/324, 385/384


[[Badness]]: 0.0888 × 10<sup>-3</sup>
Mapping: [{{val| 1 0 0 1 6 2 }}, {{val| 0 1 0 7 -6 4 }}, {{val| 0 0 1 -4 3 -2 }}]


Projection pairs: 2 = ~9801/4900, ~7 = ~21434787/3062500, ~11 = ~2310905821257/210087500000 to 3.5.14/11
Mapping generators: ~2, ~3, ~5


=== Donar ===
Vals: {{Val list| 7, 19, 26, 46, 53, 72, 118f, 125f, 171ef, 190ff, 197ef, 243eff }}
Subgroup: 2.3.5.7.11.13


Comma list: 3025/3024, 4225/4224, 4375/4374
Badness: 0.840 × 10<sup>-3</sup>


Mapping: [{{val|2 0 1 -2 2 7}}, {{val|0 1 0 7 5 3}}, {{val|0 0 2 -8 -6 -5}}]
== Thor ==
Subgroup: 2.3.5.7.11


Mapping generators: ~99/70, ~3, ~220/117
[[Comma list]]: 3025/3024, 4375/4374


Map to lattice: [{{val|0 2 2 6 4 1}}, {{val|0 -1 -2 1 1 2}}]
[[Mapping]]: [{{val| 2 0 0 2 5 }}, {{val| 0 1 0 7 5 }}, {{val| 0 0 1 -4 -3 }}]


Lattice basis:  
Mapping generators: ~99/70, ~3, ~5
: 44/39 length = 0.3480, 6/5 length = 0.7828
: Angle (44/39, 6/5) = 85.3977°


Minimax tuning:
[[Minimax tuning]]:
* 13-odd-limit eigenmonzos: 2, 11/10, 8/7
* [[11-odd-limit]] eigenmonzos: 2, 11/10, 8/7
* 15-odd-limit eigenmonzos: 2, 8/7, 15/11


Vals: {{Val list| 34d, 46, 80, 144, 178, 190, 224, 494, 684, 764, 954, 1178, 1448, 6970ceeff, 8418ceeff }}
{{Val list|legend=1| 26, 34d, 46, 72, 118, 152, 224, 270, 342, 494, 612, 836, 1106, 1448, 2554, 4002e, 5720e, 7168cee }}


Badness: 0.322 × 10<sup>-3</sup>
[[Badness]]: 0.0888 × 10<sup>-3</sup>


Scales: [[Donar46]]
Projection pairs: 2 = ~9801/4900, ~7 = ~21434787/3062500, ~11 = ~2310905821257/210087500000 to 3.5.14/11


=== Thunor ===
=== Thunor ===
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Badness: 0.549 × 10<sup>-3</sup>
Badness: 0.549 × 10<sup>-3</sup>


== Vidar ==
=== Donar ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11.13
 
Comma list: 3025/3024, 4225/4224, 4375/4374
 
Mapping: [{{val| 2 0 1 -2 2 7 }}, {{val| 0 1 0 7 5 3 }}, {{val| 0 0 2 -8 -6 -5 }}]
 
Mapping generators: ~99/70, ~3, ~220/117
 
Map to lattice: [{{val| 0 2 2 6 4 1 }}, {{val| 0 -1 -2 1 1 2 }}]
 
Lattice basis:
: 44/39 length = 0.3480, 6/5 length = 0.7828
: Angle (44/39, 6/5) = 85.3977°


[[Comma list]]: 4375/4374, 100663296/100656875
Minimax tuning:
* 13-odd-limit eigenmonzos: 2, 11/10, 8/7
* 15-odd-limit eigenmonzos: 2, 8/7, 15/11


[[Mapping]]: [{{val| 1 0 0 1 5 }}, {{val| 0 1 -1 11 1 }}, {{val| 0 0 5 -20 -4 }}]
Vals: {{Val list| 34d, 46, 80, 144, 178, 190, 224, 494, 684, 764, 954, 1178, 1448, 6970ceeff, 8418ceeff }}


Mapping generators: ~2, ~3, ~55/32
Badness: 0.322 × 10<sup>-3</sup>


{{Val list|legend=1| 46, 224, 270, 494, 764, 1395, 1889 }}
Scales: [[Donar46]]


=== 13-limit ===
== Heimdall ==
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11


Comma list: 4225/4224, 4375/4374, 6656/6655
[[Comma list]]: 4375/4374, 117649/117612


Mapping: [{{val| 1 0 0 1 5 6 }}, {{val| 0 1 -1 11 1 2 }}, {{val| 0 0 5 -20 -4 -7 }}]
[[Mapping]]: [{{val| 1 0 0 1 2 }}, {{val| 0 2 0 14 37 }}, {{val| 0 0 1 -4 -12 }}]


Mapping generators: ~2, ~3, ~55/32
Mapping generators: ~2, ~343/198, ~5


Vals: {{Val list| 46, 224, 270, 494, 764, 1395, 1889 }}
{{Val list|legend=1| 270, 342, 612, 954, 1547, 1817 }}


== Bragi ==
== Bragi ==
Line 139: Line 154:
{{Val list|legend=1| 46, 224, 270, 494, 764, 1053, 1547 }}
{{Val list|legend=1| 46, 224, 270, 494, 764, 1053, 1547 }}


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 150: Line 165:
Vals: {{Val list| 19, 46, 224, 270, 494, 764 }}
Vals: {{Val list| 19, 46, 224, 270, 494, 764 }}


== Beyla ==
== Vidar ==
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


[[Comma list]]: 385/384, 4375/4374
[[Comma list]]: 4375/4374, 100663296/100656875


[[Mapping]]: [{{val| 1 0 0 1 6 }}, {{val| 0 1 0 7 -6 }}, {{val| 0 0 1 -4 3 }}]
[[Mapping]]: [{{val| 1 0 0 1 5 }}, {{val| 0 1 -1 11 1 }}, {{val| 0 0 5 -20 -4 }}]


Mapping generators: ~2, ~3, ~5
Mapping generators: ~2, ~3, ~55/32


{{Val list|legend=1| 7, 19, 26, 45, 46, 53, 72, 118, 190, 315e, 361e, 433de, 623cdee }}
{{Val list|legend=1| 46, 224, 270, 494, 764, 1395, 1889 }}
 
[[Badness]]: 0.721 × 10<sup>-3</sup>


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Comma list: 169/168, 325/324, 385/384
Comma list: 4225/4224, 4375/4374, 6656/6655


Mapping: [{{val| 1 0 0 1 6 2 }}, {{val| 0 1 0 7 -6 4 }}, {{val| 0 0 1 -4 3 -2 }}]
Mapping: [{{val| 1 0 0 1 5 6 }}, {{val| 0 1 -1 11 1 2 }}, {{val| 0 0 5 -20 -4 -7 }}]


Mapping generators: ~2, ~3, ~5
Mapping generators: ~2, ~3, ~55/32


Vals: {{Val list| 7, 19, 26, 46, 53, 72, 118f, 125f, 171ef, 190ff, 197ef, 243eff }}
Vals: {{Val list| 46, 224, 270, 494, 764, 1395, 1889 }}
 
Badness: 0.840 × 10<sup>-3</sup>
 
== Heimdall ==
Subgroup: 2.3.5.7.11
 
[[Comma list]]: 4375/4374, 117649/117612
 
[[Mapping]]: [{{val| 1 0 0 1 2 }}, {{val| 0 2 0 14 37 }}, {{val| 0 0 1 -4 -12 }}]
 
Mapping generators: ~2, ~343/198, ~5
 
{{Val list|legend=1| 270, 342, 612, 954, 1547, 1817 }}


[[Category:Regular temperament theory]]
[[Category:Regular temperament theory]]
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