Marvel family: Difference between revisions

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@@ Line 476: / Line 476: @@
 Badness: 0.916 × 10<sup>-3</sup>
-=Hestia=
+= Hestia =
-Commas: 225/224, 125000/124509
+Comma list: 225/224, 125000/124509
-Map: [&lt;1 0 0 -5 9|, &lt;0 2 0 4 -7|, &lt;0 0 1 2 0|]
+Subgroup: 2.3.5.7.11
-{{EDOs|legend=1| 19, 29, 43, 53, 72, 197e, 269ce, 341ce, 610bce }}
+Mapping: [{{val| 1 0 0 -5 9 }}, {{val| 0 2 0 4 -7 }}, {{val| 0 0 1 2 0 }}]
-Badness: 0.00154
+{{Val list|legend=1| 19, 29, 43, 53, 72, 197e, 269ce, 341ce, 610bce }}
-==13-limit==
+Badness: 1.54 × 10<sup>-3</sup>
-Commas: 169/168, 225/224, 1001/1000
-Map: [&lt;1 0 0 -5 9 -1|, &lt;0 2 0 4 -7 3|, &lt;0 0 1 2 0 1|]
+== 13-limit ==
+Comma list: 169/168, 225/224, 1001/1000
-{{EDOs|legend=1| 19, 29, 43, 53, 72, 125f, 197ef, 269cef }}
+Subgroup: 2.3.5.7.11.13
-Badness: 0.001062
+Mapping: [{{val| 1 0 0 -5 9 -1 }}, {{val| 0 2 0 4 -7 3 }}, {{val| 0 0 1 2 0 1 }}]
-=Malcolm=
+{{Val list|legend=1| 19, 29, 43, 53, 72, 125f, 197ef, 269cef }}
-Commas: 225/224, 2200/2187
-Map: [&lt;1 0 0 -5 -3|, &lt;0 1 0 2 7|, &lt;0 0 1 2 -2|]
+Badness: 1.062 × 10<sup>-3</sup>
-{{EDOs|legend=1| 41, 53, 94, 229c, 248ce, 289ce, 342ce, 383ce }}
+= Malcolm =
+Comma list: 225/224, 2200/2187
-Badness: 0.001250
+Subgroup: 2.3.5.7.11
-==13-limit==
+Mapping: [{{val| 1 0 0 -5 -3 }}, {{val| 0 1 0 2 7 }}, {{val| 0 0 1 2 -2 }}]
-commas: 225/224, 275/273, 325/324
-Map: [&lt;1 0 0 -5 -3 2|, &lt;0 1 0 2 7 4|, &lt;0 0 1 2 -2 -2|]
+{{Val list|legend=1| 41, 53, 94, 229c, 248ce, 289ce, 342ce, 383ce }}
-{{EDOs|legend=1| 41, 53, 94, 429cdef, 523cdef }}
+Badness: 1.250 × 10<sup>-3</sup>
-Badness: 0.001075
+== 13-limit ==
+Comma list: 225/224, 275/273, 325/324
-=Prodigy=
+Subgroup: 2.3.5.7.11.13
-Prodigy shrinks 1024/1029, 243/242, 384/385 and 2400/2401 down to the same tiny interval. Hence in practice it probably makes the most sense to temper this out as well, leading to [[miracle temperament]]. This, however, does not render it pointless to consider prodigy; for one thing, scales in prodigy such as hobbit scales translate into interesting scales for miracle.
+Mapping: [{{val| 1 0 0 -5 -3 2 }}, {{val| 0 1 0 2 7 4 }}, {{val| 0 0 1 2 -2 -2 }}]
+{{Val list|legend=1| 41, 53, 94, 429cdef, 523cdef }}
-[[Comma]]s: 225/224, 441/440
+Badness: 1.075 × 10<sup>-3</sup>
-Related linear temperament: [[Gamelismic clan#Miracle|miracle]]
+= Prodigy =
+Prodigy shrinks 1024/1029, 243/242, 384/385 and 2400/2401 down to the same tiny interval. Hence in practice it probably makes the most sense to temper this out as well, leading to [[miracle temperament]]. This, however, does not render it pointless to consider prodigy; for one thing, scales in prodigy such as hobbit scales translate into interesting scales for miracle.
-[[Minimax tuning]]:
+[[Comma list]]: 225/224, 441/440
-[|1 0 0 0 0&gt;, |13/12 1/2 -1/4 0 1/12&gt;,
+Subgroup: 2.3.5.7.11
-|13/6 -1 1/2 0 1/6&gt;,
-|3/2 -1 1/2 0 1/2&gt;, |0 0 0 0 1&gt;]
-[[Eigenmonzo subgroup]]: 2.9/5.11
+[[Associated temperament]]: [[Gamelismic clan #Miracle|miracle]]
-Lattice basis: secor length 0.9111, 3/2 length 0.9477
+Mapping: [{{val| 1 0 0 -5 -13 }}, {{val| 0 1 0 2 6 }}, {{val| 0 0 1 2 3 }}]
-Angle(secor, 3/2) = 65.933
+Mapping generators: ~2, ~3, ~5
-Map to lattice: [&lt;0 0 -1 -2 -3|, &lt;0 1 -1 0 3|]
+Map to lattice: [{{val| 0 0 -1 -2 -3 }}, {{val| 0 1 -1 0 3 }}]
-Map: [&lt;1 0 0 -5 -13|, &lt;0 1 0 2 6|, &lt;0 0 1 2 3|]
+Lattice basis:
+: secor length = 0.9111, 3/2 length = 0.9477
+: Angle (secor, 3/2) = 65.933
-[[Generator]]s: 2, 3, 5
+[[Minimax tuning]]:
+* 11-odd-limit
+: [{{monzo| 1 0 0 0 0 }}, {{monzo| 13/12 1/2 -1/4 0 1/12 }}, {{monzo| 13/6 -1 1/2 0 1/6 }}, {{monzo| 3/2 -1 1/2 0 1/2 }}, {{monzo| 0 0 0 0 1 }}]
+: [[Eigenmonzo subgroup]]: 2.9/5.11
-{{EDOs|legend=1| 10, 12, 29, 31, 41, 72, 247c, 319bcde, 391bcde, 463bcde }}
+{{Val list|legend=1| 10, 12, 29, 31, 41, 72, 247c, 319bcde, 391bcde, 463bcde }}
-Badness: 0.000344
+Badness: 0.344 × 10<sup>-3</sup>
 [[Projection pair]]s: 7 225/32 11 91125/8192
@@ Line 545: / Line 552: @@
 Scales: [[prodigy11]], [[prodigy12]], [[prodigy29]]
-=== Hobbit bases ===
+; Hobbit bases
 {2, 3, 5} subgroup
+* 31: 81/80, 34171875/33554432
+* 41: 34171875/33554432, 32805/32768
+== 13-limit ==
+Comma list: 105/104, 196/195, 352/351
-: 81/80, 34171875/33554432
+Subgroup: 2.3.5.7.11.13
-: 34171875/33554432, 32805/32768
+Mapping: [{{val| 1 0 0 -5 -13 -8 }}, {{val| 0 1 0 2 6 3 }}, {{val| 0 0 1 2 3 3 }}]
-==13-limit==
+{{Val list|legend=1| 10, 29, 31, 41, 60e, 72f, 91e, 101cd, 132def, 233cdef, 274cdef, 305cdef }}
-Commas: 105/104, 196/195, 352/351
-Map: [&lt;1 0 0 -5 -13 -8|, &lt;0 1 0 2 6 3|, &lt;0 0 1 2 3 3|]
+Badness: 0.736 × 10<sup>-3</sup>
-{{EDOs|legend=1| 10, 29, 31, 41, 60e, 72f, 91e, 101cd, 132def, 233cdef, 274cdef, 305cdef }}
+== Prodigious ==
+Comma list: 225/224, 441/440, 364/363
-Badness: 0.000736
+Subgroup: 2.3.5.7.11.13
-==Prodigious==
+Mapping: [{{val| 1 0 0 -5 -13 -23 }}, {{val| 0 1 0 2 6 11 }}, {{val| 0 0 1 2 3 4 }}]
-Commas: 225/224, 441/440, 364/363
-Map: [&lt;1 0 0 -5 -13 -23|, &lt;0 1 0 2 6 11|, &lt;0 0 1 2 3 4|]
+{{Val list|legend=1| 29, 41, 72, 113, 185cf, 341cf, 413bcf, 526bcdf }}
-{{EDOs|legend=1| 29, 41, 72, 113, 185cf, 341cf, 413bcf, 526bcdf }}
+Badness: 0.900 × 10<sup>-3</sup>
-Badness: 0.000900
+== Prodigal ==
+Comma list: 225/224, 441/440, 351/350
-==Prodigal==
+Subgroup: 2.3.5.7.11.13
-Commas: 225/224, 441/440, 351/350
-Map: [&lt;1 0 0 -5 -13 -4|, &lt;0 1 0 2 6 -1|, &lt;0 0 1 2 3 4|]
+Mapping: [{{val| 1 0 0 -5 -13 -4 }}, {{val| 0 1 0 2 6 -1 }}, {{val| 0 0 1 2 3 4 }}]
-{{EDOs|legend=1| 31, 72, 103, 175f }}
+{{Val list|legend=1| 31, 72, 103, 175f }}
-Badness: 0.000889
+Badness: 0.889 × 10<sup>-3</sup>
 [[Category:Theory]]
@@ Line 583: / Line 594: @@
 [[Category:Marvel]]
 [[Category:Rank 3]]
-{{todo|cleanup}}