Marvel family: Difference between revisions

m Cleanup +4
m Cleanup +5
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Badness: 1.009 × 10<sup>-3</sup>
Badness: 1.009 × 10<sup>-3</sup>


=Apollo=
= Apollo =
[[Comma]]s: 100/99, 225/224
[[Comma list]]: 100/99, 225/224


Related linear temperament: [[Magic]]
Subgroup: 2.3.5.7.11


Eigenmonzo subgroup: 2.7/5.11/9
Associated temperament: [[Magic family #magic|magic]]


Map: [&lt;1 0 0 -5 2|, &lt;0 1 0 2 -2|, &lt;0 0 1 2 2|]
Mapping: [{{val| 1 0 0 -5 2 }}, {{val| 0 1 0 2 -2 }}, {{val| 0 0 1 2 2 }}]


{{EDOs|legend=1| 12, 19, 22, 41, 104, 157ce, 198ce, 220ce, 261ce }}
Minimax tuning: 11-odd-limit eigenmonzo subgroup: 2.7/5.11/9
 
{{Val list|legend=1| 12, 19, 22, 41, 104, 157ce, 198ce, 220ce, 261ce }}


Projection pairs: 7 225/32 11 100/9
Projection pairs: 7 225/32 11 100/9


==13-limit==
== 13-limit ==
[[Comma]]s: 100/99, 225/224, 245/243
[[Comma list]]: 100/99, 225/224, 245/243
 
Subgroup: 2.3.5.7.11.13


Eigenmonzo subgroup: 2.11/9.13/9
Mapping: [{{val| 1 0 0 -5 2 7 }}, {{val| 0 1 0 2 -2 -5 }}, {{val| 0 0 1 2 2 2 }}]


Map: [&lt;1 0 0 -5 2 7|, &lt;0 1 0 2 -2 -5|, &lt;0 0 1 2 2 2|]
Minimax tuning: 13-odd-limit eigenmonzo subgroup: 2.11/9.13/9


{{EDOs|legend=1| 22, 29, 41, 63, 104, 179cef, 242cde, 283def, 346bcdef }}
{{Val list|legend=1| 22, 29, 41, 63, 104, 179cef, 242cde, 283def, 346bcdef }}


Projection pairs: 7 225/32 11 100/9 13 3200/243
Projection pairs: 7 225/32 11 100/9 13 3200/243


= Artemis =
= Artemis =
Commas: 121/120, 225/224
Comma list: 121/120, 225/224
 
Subgroup: 2.3.5.7.11


Map: [<1 0 1 -3 2|, <0 1 1 4 1|, <0 0 2 4 1|]
Mapping: [{{val| 1 0 1 -3 2 }}, {{val| 0 1 1 4 1 }}, {{val| 0 0 2 4 1 }}]


{{EDOs|legend=1| 9, 20, 22, 31, 53 }}
{{Val list|legend=1| 9, 20, 22, 31, 53 }}


== 13-limit ==
== 13-limit ==
Commas: 105/104, 121/120, 196/195
Comma list: 105/104, 121/120, 196/195


Map: [<1 0 1 -3 2 -5|, <0 1 1 4 1 6|, <0 0 2 4 1 6|]
Subgroup: 2.3.5.7.11.13


{{EDOs|legend=1| 9, 20, 29, 31 }}
Mapping: [{{val| 1 0 1 -3 2 -5 }}, {{val| 0 1 1 4 1 6 }}, {{val| 0 0 2 4 1 6 }}]
 
{{Val list|legend=1| 9, 20, 29, 31 }}


== Diana ==
== Diana ==
Commas: 121/120, 225/224, 275/273
Comma list: 121/120, 225/224, 275/273
 
Subgroup: 2.3.5.7.11.13
 
Mapping: [{{val| 1 0 1 -3 2 7 }}, {{val| 0 1 1 4 1 -2 }}, {{val| 0 0 2 4 1 1 }}]


Map: [<1 0 1 -3 2 7|, <0 1 1 4 1 -2|, <0 0 2 4 1 1|]
{{Val list|legend=1| 22, 29, 31, 53 }}


{{EDOs|legend=1| 22, 29, 31, 53 }}
= Potassium =
Comma list: 45/44, 56/55


=Potassium=
Subgroup: 2.3.5.7.11
Commas: 45/44, 56/55


Eigenmonzo subgroup: 2.9/7.11
Mapping: [{{val| 1 0 0 -5 -2 }}, {{val| 0 1 0 2 2 }}, {{val| 0 0 1 2 1 }}]


Map: [&lt;1 0 0 -5 -2|, &lt;0 1 0 2 2|, &lt;0 0 1 2 1|]
Minimax tuning: 11-odd-limit eigenmonzo subgroup: 2.9/7.11


{{EDOs|legend=1| 9, 10, 12, 19, 31e, 50e }}
{{Val list|legend=1| 9, 10, 12, 19, 31e, 50e }}


Badness: 0.000464
Badness: 0.464 × 10<sup>-3</sup>


Projection pairs: 7 225/32 11 45/4
Projection pairs: 7 225/32 11 45/4


==13-limit==
== 13-limit ==
Commas: 45/44, 56/55, 78/77
Comma list: 45/44, 56/55, 78/77


13-limit eigenmonzo subgroup: 2.9/7.13/9
Subgroup: 2.3.5.7.11.13


15-limit eigenmonzo subgroup: 2.9/7.13/9
Mapping: [{{val| 1 0 0 -5 -2 -8 }}, {{val| 0 1 0 2 2 3 }}, {{val| 0 0 1 2 1 3 }}]


Map: [&lt;1 0 0 -5 -2 -8|, &lt;0 1 0 2 2 3|, &lt;0 0 1 2 1 3|]
Minimax tuning:  
* 13-odd-limit eigenmonzo subgroup: 2.9/7.13/9
* 15-odd-limit eigenmonzo subgroup: 2.9/7.13/9


{{EDOs|legend=1| 9, 10, 19, 31e, 50e }}
{{Val list|legend=1| 9, 10, 19, 31e, 50e }}


Badness: 0.000733
Badness: 0.733 × 10<sup>-3</sup>


Projection pairs: 7 225/32 11 45/4 13 3375/256
Projection pairs: 7 225/32 11 45/4 13 3375/256


=Fantastic=
= Fantastic =
Commas: 225/224, 4375/4356
Comma list: 225/224, 4375/4356
 
Subgroup: 2.3.5.7.11
 
Mapping: [{{val| 2 0 0 -10 -7 }}, {{val| 0 1 0 2 0 }}, {{val| 0 0 1 2 3 }}]


Map: [&lt;2 0 0 -10 -7|, &lt;0 1 0 2 0|, &lt;0 0 1 2 3|]
{{Val list|legend=1| 12, 22, 50, 72, 166, 238c, 310c }}


{{EDOs|legend=1| 12, 22, 50, 72, 166, 238c, 310c }}
Badness: 0.743 × 10<sup>-3</sup>


Badness: 0.000743
= Catakleismoid =
Comma list: 225/224, 4375/4374


=Catakleismoid=
Subgroup: 2.3.5.7.11
Commas: 225/224, 4375/4374


Map: [&lt;1 0 1 -3 0|, &lt;0 6 5 22 0|, &lt;0 0 0 0 1|]
Mapping: [{{val| 1 0 1 -3 0 }}, {{val| 0 6 5 22 0 }}, {{val| 0 0 0 0 1 }}]


{{EDOs|legend=1| 19, 53, 72, 197e, 269ce }}
{{Val list|legend=1| 19, 53, 72, 197e, 269ce }}


Badness: 0.001275
Badness: 1.275 × 10<sup>-3</sup>
 
== 13-limit ==
Comma list: 169/168, 225/224, 325/324


==13-limit==
Subgroup: 2.3.5.7.11.13
Commas: 169/168, 225/224, 325/324


Map: [&lt;1 0 1 -3 0 0|, &lt;0 6 5 22 0 14|, &lt;0 0 0 0 1 0|]
Mapping: [{{val| 1 0 1 -3 0 0 }}, {{val| 0 6 5 22 0 14 }}, {{val| 0 0 0 0 1 0 }}]


{{EDOs|legend=1| 19, 53, 72, 125f, 197ef, 269cef }}
{{Val list|legend=1| 19, 53, 72, 125f, 197ef, 269cef }}


Badness: 0.000916
Badness: 0.916 × 10<sup>-3</sup>


=Hestia=
=Hestia=