Marvel family: Difference between revisions

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= Marvel =

The head of the marvel family is marvel, which tempers out [[225/224]]. Marvel has a [[Normal lists|normal list basis]] of [2, 3, 5]; hence a [[~~Harmonic Limit|~~5-limit]] scale can be converted to marvel simply by tempering it. One way to do that, and an excellent marvel tuning, is given by [[197edo]].

The head of the marvel family is marvel, which tempers out [[225/224]]. Marvel has a [[Normal lists|normal list basis]] of [2, 3, 5]; hence a [[5-limit]] scale can be converted to marvel simply by tempering it. One way to do that, and an excellent marvel tuning, is given by [[197edo]].

Little is gained in tuning accuracy by not tempering out 4375/4374 as well as 225/224, leading to [[catakleismic temperament]]. Another temperament which does little damage to tuning accuracy is [[compton temperament]], for which [[240edo]] may be used.

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 = Marvel =
-The head of the marvel family is marvel, which tempers out [[225/224]]. Marvel has a [[Normal lists|normal list basis]] of [2, 3, 5]; hence a [[Harmonic Limit|5-limit]] scale can be converted to marvel simply by tempering it. One way to do that, and an excellent marvel tuning, is given by [[197edo]].
+The head of the marvel family is marvel, which tempers out [[225/224]]. Marvel has a [[Normal lists|normal list basis]] of [2, 3, 5]; hence a [[5-limit]] scale can be converted to marvel simply by tempering it. One way to do that, and an excellent marvel tuning, is given by [[197edo]].
 Little is gained in tuning accuracy by not tempering out 4375/4374 as well as 225/224, leading to [[catakleismic temperament]]. Another temperament which does little damage to tuning accuracy is [[compton temperament]], for which [[240edo]] may be used.
-See also [[Marvel temperaments]].
+See also [[marvel temperaments]].
 == Vital statistics ==
-[[Comma]] c = 225/224
+[[Comma list]]: c = 225/224
-Related linear temperament: [[catakleismic temperament]]
+[[Associated temperament]]: [[catakleismic]]
--limit minimax: 3 and 5 1/4c flat, 7 just
+Lattice basis:
+: secor length = 1.256, 3/2 length = 1.369
+: Angle (secor, 3/2) = 106.958 degrees
-[|1 0 0 0&gt;, |5/4 1/2 -1/2 1/4&gt;, |5/4 -1/2 1/2 1/4&gt;, |0 0 0 1&gt;]
+Map to lattice: [{{val| 0 0 -1 -2 }}, {{val| 0 1 -1 0 }}]
-[[Eigenmonzo subgroup]]: 2.5/3.7
+Mapping: [{{val| 1 0 0 -5 }}, {{val| 0 1 0 2 }}, {{val| 0 0 1 2 }}]
--limit minimax: 3 1/6c flat, 5 1/3c flat, 7 just
+Mapping generators: ~2, ~3, ~5
-[|1 0 0 0&gt;, |5/6 2/3 -1/3 1/6&gt;, |5/3 -2/3 1/3 1/3&gt;, |0 0 0 1&gt;]
+Minimax tuning:
+* 7-odd-limit: 3 and 5 1/4c flat, 7 just
+: [{{monzo| 1 0 0 0 }}, {{monzo| 5/4 1/2 -1/2 1/4 }}, {{monzo| 5/4 -1/2 1/2 1/4 }}, {{monzo| 0 0 0 1 }}]
+: [[Eigenmonzo subgroup]]: 2.5/3.7
+* 9-odd-limit minimax: 3 1/6c flat, 5 1/3c flat, 7 just
+: [{{monzo| 1 0 0 0 }}, {{monzo| 5/6 2/3 -1/3 1/6 }}, {{monzo| 5/3 -2/3 1/3 1/3 }}, {{monzo| 0 0 0 1 }}]
+: [[Eigenmonzo subgroup]]: 2.9/5.7
-[[Eigenmonzo subgroup]]: 2.9/5.7
+{{Val list|legend=1| 10, 12, 19, 22, 31, 41, 72, 197, 269c }}
-Lattice basis: secor length 1.256, 3/2 length 1.369
-Angle(secor, 3/2) = 106.958 degrees
-Map to lattice: [&lt;0 0 -1 -2|, &lt;0 1 -1 0|]
-Map: [&lt;1 0 0 -5|, &lt;0 1 0 2|, &lt;0 0 1 2|]
-Generators: 2, 3, 5
-{{EDOs|legend=1| 10, 12, 19, 22, 31, 41, 72, 197, 269c }}
 Badness: 0.0000365
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 [[Projection pair]]s: 7 225/32
-[[Spectrum]]: 4/3, 5/4, 7/5, 7/6, 8/7, 6/5, 9/8, 9/7, 10/9
+[[Complexity spectrum]]: 4/3, 5/4, 7/5, 7/6, 8/7, 6/5, 9/8, 9/7, 10/9
 Scales: [[marvel9]], [[marvel10]], [[marvel11]], [[marvel12]], [[marvel19]], [[marvel22]], [[pump12_1]], [[pump12_2]], [[pump13]], [[pump14]], [[pump15]], [[pump16]], [[pump17]], [[pump18]]