Quasisuper: Difference between revisions

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'''Quasisuper''' is an alternative [[extension]] of the [[archy]] [[chain of fifths]] to [[superpyth]]. Like superpyth, it is a [[regular temperament|temperament]] generated by a perfect fifth, where stacking two of them reaches the interval of [[8/7]][[~]][[9/8]], [[tempering out]] [[64/63]]. The difference is that this extension maps [[prime interval|prime]] [[5/1|5]] to -13 [[generator]]s, as a double-diminished fifth (C–G𝄫). This extension works in the range [[17edo|17c-edo]] to [[22edo|22-edo]]. In contrast, full 7-limit [[superpyth]] does not work in this range, as tunings with a flatter fifth than 22edo swap the sizes of [[7/5]] and [[10/7]]. This extension may be preferred over superpyth due to having a softer [[5L 2s|diatonic]] scale, with a small step of around 60 [[cent]]s compared to about 50 cents in regular 7-limit superpyth.

The best extension to the [[11-limit]], '''quasisupra''', ~~uses the [[supra]] mapping of~~ prime [[11/1|11]] to -6 generators, as a diminished fifth (C–G♭)~~. This tempers~~ out [[99/98]] ~~as in supra,~~ as well as [[121/120]] and [[540/539]].

The best extension to the [[11-limit]], '''quasisupra''', maps prime [[11/1|11]] to -6 generators as a diminished fifth (C–G♭), tempering out [[99/98]] as well as [[121/120]] and [[540/539]]. Removing prime 5 from quasisupra results in a 2.3.7.11-subgroup restriction, called '''supra''', which is notable for its simplicity. Finally, taking every other step of supra gives a 2.9.7.11-subgroup restriction, called [[machine]].

For technical data see [[Archytas clan #Quasisuper]].

For technical data see [[Archytas clan #Quasisuper]] and [[Archytas clan #Supra|#Supra]].

== Interval chain ==

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 '''Quasisuper''' is an alternative [[extension]] of the [[archy]] [[chain of fifths]] to [[superpyth]]. Like superpyth, it is a [[regular temperament|temperament]] generated by a perfect fifth, where stacking two of them reaches the interval of [[8/7]][[~]][[9/8]], [[tempering out]] [[64/63]]. The difference is that this extension maps [[prime interval|prime]] [[5/1|5]] to -13 [[generator]]s, as a double-diminished fifth (C–G𝄫). This extension works in the range [[17edo|17c-edo]] to [[22edo|22-edo]]. In contrast, full 7-limit [[superpyth]] does not work in this range, as tunings with a flatter fifth than 22edo swap the sizes of [[7/5]] and [[10/7]]. This extension may be preferred over superpyth due to having a softer [[5L 2s|diatonic]] scale, with a small step of around 60 [[cent]]s compared to about 50 cents in regular 7-limit superpyth.
-The best extension to the [[11-limit]], '''quasisupra''', uses the [[supra]] mapping of prime [[11/1|11]] to -6 generators, as a diminished fifth (C–G♭). This tempers out [[99/98]] as in supra, as well as [[121/120]] and [[540/539]].
+The best extension to the [[11-limit]], '''quasisupra''', maps prime [[11/1|11]] to -6 generators as a diminished fifth (C–G♭), tempering out [[99/98]] as well as [[121/120]] and [[540/539]]. Removing prime 5 from quasisupra results in a 2.3.7.11-subgroup restriction, called '''supra''', which is notable for its simplicity. Finally, taking every other step of supra gives a 2.9.7.11-subgroup restriction, called [[machine]].
-For technical data see [[Archytas clan #Quasisuper]].
+For technical data see [[Archytas clan #Quasisuper]] and [[Archytas clan #Supra|#Supra]].
 == Interval chain ==