Marvel family: Difference between revisions
Sorting (putting prodigy next to undecimal marvel cuz it deserves that spot) |
Deprecate "unimarv" cuz no one uses that name. + some intros and dissolve associated temps into those text blocks |
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{{Main| Marvel }} | {{Main| Marvel }} | ||
The head of the marvel family is marvel, which tempers out [[225/224]]. Marvel has a [[normal | The head of the marvel family is marvel, which tempers out [[225/224]]. Marvel has a [[normal forms|normal generator list]] 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]], with which it shares the [[optimal patent val]]. Another temperament which does little damage to tuning accuracy is [[compton]], for which [[240edo]] may be used. See [[ | Little is gained in tuning accuracy by not tempering out 4375/4374 as well as 225/224, leading to [[catakleismic]], with which it shares the [[optimal patent val]]. Another temperament which does little damage to tuning accuracy is [[compton]], for which [[240edo]] may be used. See [[Marvel temperaments]] for some other rank-2 temperaments. | ||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
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=== Overview to extensions === | === Overview to extensions === | ||
The second comma of the [[ | The second comma of the [[normal forms #Normal forms for commas|normal comma list]] defines which 11-limit family member we are looking at. 4125/4096 gives unidecimal marvel; 91125/90112 gives prodigy; 5632/5625 gives minerva. These and many others considered below use the same generators as marvel. | ||
Temperaments discussed elsewhere include | Temperaments discussed elsewhere include | ||
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* ''[[Mirage]]'' (+243/242, +385/384) → [[Rastmic rank-3 clan #Spectacle|Rastmic rank-3 clan]] | * ''[[Mirage]]'' (+243/242, +385/384) → [[Rastmic rank-3 clan #Spectacle|Rastmic rank-3 clan]] | ||
== Undecimal marvel | == Undecimal marvel == | ||
{{Main| Marvel }} | {{Main| Marvel }} | ||
Undecimal marvel tempers out [[385/384]] as well as [[540/539]], and is loosely [[associated temperament|associated]] with [[wizard]]. [[197edo]] remains useful as a tuning, with the 197e val, but [[166edo]], which among other things has a virtually pure 7, works as well. | |||
[[Subgroup]]: 2.3.5.7.11 | [[Subgroup]]: 2.3.5.7.11 | ||
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[[Complexity spectrum]]: 5/4, 4/3, 7/6, 8/7, 7/5, 6/5, 9/7, 12/11, 9/8, 11/8, 11/9, 10/9, 11/10, 14/11 | [[Complexity spectrum]]: 5/4, 4/3, 7/6, 8/7, 7/5, 6/5, 9/7, 12/11, 9/8, 11/8, 11/9, 10/9, 11/10, 14/11 | ||
Scales: [[marvel22_11]], [[unimarv19]], [[unimarv22]] | Scales: [[marvel22_11]], [[unimarv19]], [[unimarv22]] | ||
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=== Hecate === | === Hecate === | ||
Hecate tempers out [[325/324]], the marveltwin comma, such that [[16/13]] is found by a stack of two ~[[10/9]]'s, similar to how [[8/7]] is found by a stack of two [[15/14]]~[[16/15]]'s. Hecate has a natural extension to include [[prime interval|prime]] [[19/1|19]], where it further tempers out [[400/399]] and [[513/512]], taking advantage of the factorization 225/224 = (400/399)⋅(513/512). For both of these cases [[166edo]] remains an excellent tuning. | |||
==== 13-limit ==== | ==== 13-limit ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
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== Prodigy == | == Prodigy == | ||
Prodigy shrinks | Prodigy tempers out [[441/440]] and shrinks [[243/242]], [[385/384|384/385]], [[1029/1024|1024/1029]] and [[2401/2400|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]]. 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. | ||
[[Subgroup]]: 2.3.5.7.11 | [[Subgroup]]: 2.3.5.7.11 | ||
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Scales: [[prodigy11]], [[prodigy12]], [[prodigy29]] | Scales: [[prodigy11]], [[prodigy12]], [[prodigy29]] | ||
{{Databox|Hobbit bases| | {{Databox|Hobbit bases| | ||
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== Minerva == | == Minerva == | ||
Minerva tempers out [[99/98]] as well as [[176/175]]. It may be described as 12 & 22 & 31, and is loosely [[associated temperament|associated]] with [[würschmidt]]. | |||
[[Subgroup]]: 2.3.5.7.11 | [[Subgroup]]: 2.3.5.7.11 | ||
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Scales: [[minerva12]], [[minerva22x]] | Scales: [[minerva12]], [[minerva22x]] | ||
=== Athene === | === Athene === | ||
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== Apollo == | == Apollo == | ||
{{See also| Ptolemismic clan #Apollo }} | {{See also| Ptolemismic clan #Apollo }} | ||
Apollo tempers out not only [[100/99]] but [[896/891]]. It is notably [[associated temperament|associated]] with [[magic]]. | |||
[[Subgroup]]: 2.3.5.7.11 | [[Subgroup]]: 2.3.5.7.11 | ||
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[[Projection pair]]s: <code>7 225/32 11 100/9</code> | [[Projection pair]]s: <code>7 225/32 11 100/9</code> | ||
Scales: [[apollo wholetone]], [[indigo17]] | Scales: [[apollo wholetone]], [[indigo17]] | ||