Quasisuper: Difference between revisions

Line 8:

| Generators tuning = 708.3

| Optimization method = CWE

| MOS scales = [[5L 2s]], [[5L 7s]], [[5L 12s]], [[17L 5s]]

| MOS scales = [[5L 2s]], [[5L 7s]], [[5L 12s]], [[17L 5s]]

| Pergen = (P8, P5)

| Color name = Sasaguti

Line 14:

| Odd limit 2 = 11-limit 15 | Mistuning 2 = 14.9 | Complexity 2 = 17

}}

'''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''', 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]].

'''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''', 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]] and [[Archytas clan #Supra|#Supra]].

@@ Line 8: / Line 8: @@
 | Generators tuning = 708.3
 | Optimization method = CWE
-| MOS scales = [[5L 2s]], [[5L 7s]], [[5L 12s]], [[17L 5s]]
+| MOS scales = [[5L&nbsp;2s]], [[5L&nbsp;7s]], [[5L&nbsp;12s]], [[17L&nbsp;5s]]
 | Pergen = (P8, P5)
 | Color name = Sasaguti
@@ Line 14: / Line 14: @@
 | Odd limit 2 = 11-limit 15 | Mistuning 2 = 14.9 | Complexity 2 = 17
 }}
-'''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''', 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]].
+'''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''', 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]] and [[Archytas clan #Supra|#Supra]].