Archytas clan: Difference between revisions
-5-limit superpyth (moved to superpyth-22 equivalence continuum); update linking |
-5-limit sixix (covered in syntonic-chromatic continuum) |
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== Superpyth == | == Superpyth == | ||
{{Main| Superpyth }} | {{Main| Superpyth }} | ||
: ''For the 5-limit version, see [[Superpyth–22 equivalence continuum]].'' | : ''For the 5-limit version, see [[Superpyth–22 equivalence continuum #Superpyth (5-limit)]].'' | ||
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. | 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. | ||
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== Sixix == | == Sixix == | ||
: ''For the 5-limit version, see [[Syntonic–chromatic equivalence continuum #Sixix (5-limit)]].'' | |||
{{See also| Dual-fifth temperaments #Dual-3 Sixix }} | {{See also| Dual-fifth temperaments #Dual-3 Sixix }} | ||
Sixix is related to the [[kleismic family]] in a way similar to the one between [[meantone]] and [[mavila]]. In both cases the generator is nominally a 6/5 and the complexity to generate major and minor chords is the same, but in sixix it is tuned extremely sharply, to the point where the 3rd and 5th harmonics are reached by going down instead of up, inverting the logic of chord construction. | Sixix is related to the [[kleismic family]] in a way similar to the one between [[meantone]] and [[mavila]]. In both cases the generator is nominally a 6/5 and the complexity to generate major and minor chords is the same, but in sixix it is tuned extremely sharply, to the point where the 3rd and 5th harmonics are reached by going down instead of up, inverting the logic of chord construction. | ||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||