Marvel family: Difference between revisions
Deprecate "unimarv" cuz no one uses that name. + some intros and dissolve associated temps into those text blocks |
→Apollo: expand and document two other extensions |
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{{See also| Ptolemismic clan #Apollo }} | {{See also| Ptolemismic clan #Apollo }} | ||
Apollo tempers out not only [[100/99]] but [[896/891]]. | [[File:Lattice Apollo.png|thumb|Lattice for apollo.]] | ||
Apollo tempers out not only [[100/99]] but [[896/891]]. Note that marvel tempers together [[25/24]] and [[28/27]], and apollo further equates it with [[33/32]] via the vanishing of 100/99. This makes it a weak extension of [[parapyth]], and [[associated temperament|associates]] it with [[magic]]. The lattice structure is very compact, comparable to that of [[ares]], from which apollo only differs in the mapping of [[prime interval|prime]] [[7/1|7]]. | |||
The canonical [[13-limit]] extension is implied by parapyth, tempering out [[352/351]] and [[364/363]], but there are a number of other extenions to consider, these being called phoebus and musagetes, after epithets of Apollo. Phoebus tempers out [[105/104]] and finds ~[[13/8]] as a stack of three [[secor]]s. Musagetes tempers out [[144/143]] and finds conflates 16/13 and [[11/9]], which in this case is simply a stack of two ~[[10/9]]'s. These extensions are [[support]]ed by 13-limit [[magic]], unlike the canonical one. | |||
[[Subgroup]]: 2.3.5.7.11 | [[Subgroup]]: 2.3.5.7.11 | ||
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Projection pairs: <code>7 225/32 11 100/9 13 3200/243</code> | Projection pairs: <code>7 225/32 11 100/9 13 3200/243</code> | ||
=== Phoebus === | |||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 100/99, 105/104, 196/195 | |||
Mapping: {{mapping| 1 0 0 -5 2 1 | 0 1 0 2 -2 3 | 0 0 1 2 2 3 }} | |||
Optimal tunings: | |||
* WE: ~2 = 1200.3724{{c}}, ~3/2 = 702.5274{{c}}, ~5/4 = 379.6345{{c}} | |||
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.3357{{c}}, ~5/4 = 379.6830{{c}} | |||
{{Optimal ET sequence|legend=0| 12f, 19, 22f, 29, 41 }} | |||
Badness (Sintel): 0.886 | |||
=== Musagetes === | |||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 100/99, 144/143, 225/224 | |||
Mapping: {{mapping| 1 0 0 -5 2 2 | 0 1 0 2 -2 4 | 0 0 1 2 2 -2 }} | |||
Optimal tunings: | |||
* WE: ~2 = 1199.2695{{c}}, ~3/2 = 702.5589{{c}}, ~5/4 = 382.7715{{c}} | |||
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.7998{{c}}, ~5/4 = 382.7740{{c}} | |||
{{Optimal ET sequence|legend=0| 19, 22f, 34d, 41, 75e, 94e, 116ef }} | |||
Badness (Sintel): 1.14 | |||
== Potassium == | == Potassium == | ||