Archytas clan: Difference between revisions
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{{Main| Superpyth }} | {{Main| Superpyth }} | ||
In the 5-limit, superpyth tempers out 20480/19683 | In the 5-limit, superpyth tempers out 20480/19683. This temperament has a fifth generator of ~3/2 = ~710¢ and ~5/4 is found at +9 generator steps, as an augmented second (C-D#). It also has a weak extension, [[Jubilismic clan #Bipyth|bipyth]] (10cd & 22), tempering out the same 5-limit comma as the superpyth, but with a half-octave period and the jubilisma (50/49) rather than the Archytas comma tempered out. | ||
[[Subgroup]]: 2.3.5 | [[Subgroup]]: 2.3.5 | ||
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=== 11-limit === | === 11-limit === | ||
The canonical extension to the 13-limit finds the ~11/8 at +16 generator steps, as a double augmented second (C-Dx) and finds the ~13/8 at +13 generator steps, as a double augmented fourth (C-Fx). | |||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
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=== Suprapyth === | === Suprapyth === | ||
Suprapyth finds the ~11/8 at the diminished fifth (C-Gb), and finds the ~13/8 at the diminished seventh (C-Bbb). | |||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
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== Quasisuper == | == Quasisuper == | ||
Quasisuper can be described as 17c & 22, with the ~5/4 mapped to -13 generator steps, as a double diminished fifth (C-Gbb). | |||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
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== Ultrapyth == | == Ultrapyth == | ||
Ultrapyth can be viewed as an extension of the excellent 2.3.7.13/5 [[The Biosphere #Oceanfront|oceanfront]] temperament, | Ultrapyth can be viewed as an extension of the excellent 2.3.7.13/5 [[The Biosphere #Oceanfront|oceanfront]] temperament, mapping the ~5/4 to +14 fifths as a double augmented unison (C-Cx). | ||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
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== Schism == | == Schism == | ||
{{ | {{See also| Schismatic family #Schism }} | ||
Schism tempers out the [[schisma]], mapping the ~5/4 to -8 fifths as a diminished fourth (C-Fb) as does any schismic temperament. | |||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
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; Music | ; Music | ||
* [http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Herman/beatles-improv.mp3 Beatles Improv] by Herman Miller | * [http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Herman/beatles-improv.mp3 ''Beatles Improv''] by [[Herman Miller]] | ||
=== 11-limit === | === 11-limit === | ||