Quasisuper: Difference between revisions

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

}}

'''Quasisuper''' is an alternative extension of [[2.~~3.7 subgroup~~|~~2.3.~~7]] [[~~archy~~]] to prime [[5/1|5]]~~. This extension maps prime 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]].

'''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]].

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

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

~~{{todo|expand|review|cleanup|improve synopsis|improve readability}}~~

~~{{Clear}}~~

== Interval chain ==

In the following table, odd harmonics and subharmonics ~~1–15~~ are in '''bold'''.

In the following table, odd harmonics and subharmonics 1–11 are in '''bold'''.

{| class="wikitable"

{| class="wikitable center-1 right-2"

~~|+ style="font~~-~~size: 105%~~" ~~| Intervals of quasisupra (11-limit)~~

! #

! ~~Generators~~

! Cents*

! ~~Intervals~~

! Approximate ratios

|-

| 0

Line 50:

| 5

| 1141.6

| 27/14~~, 21/11~~

| 21/11, 27/14

|-

| 6

Line 58:

| 7

| 158.2

| 12/11~~, 11/10~~

| 11/10, 12/11

|-

| 8

Line 78:

| 12

| 99.8

| ~~'''~~16/15~~'''~~

| 16/15

|-

| 13

Line 103:

== Tunings ==

[[Category:Rank-2 temperaments]]

[[Category:Archytas clan]]

[[Category:Nuwell temperaments]]

@@ Line 14: / Line 14: @@
 | Odd limit 2 = (11-limit) 15 | Mistuning 2 = 14.9 | Complexity 2 = 17
 }}
-'''Quasisuper''' is an alternative extension of [[2.3.7 subgroup|2.3.7]] [[archy]] to prime [[5/1|5]]. This extension maps prime 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]].
+'''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]].
+For technical data see [[Archytas clan #Quasisuper]].
-For technical data see [[Archytas clan#Quasisuper]].
-{{todo|expand|review|cleanup|improve synopsis|improve readability}}
-{{Clear}}
 == Interval chain ==
-In the following table, odd harmonics and subharmonics 1–15 are in '''bold'''.
+In the following table, odd harmonics and subharmonics 1–11 are in '''bold'''.
-{| class="wikitable"
+{| class="wikitable center-1 right-2"
-|+ style="font-size: 105%" | Intervals of quasisupra (11-limit)
+! #
-! Generators
 ! Cents*
-! Intervals
+! Approximate ratios
 |-
 | 0
@@ Line 50: / Line 50: @@
 | 5
 | 1141.6
-| 27/14, 21/11
+| 21/11, 27/14
 |-
 | 6
@@ Line 58: / Line 58: @@
 | 7
 | 158.2
-| 12/11, 11/10
+| 11/10, 12/11
 |-
 | 8
@@ Line 78: / Line 78: @@
 | 12
 | 99.8
-| '''16/15'''
+| 16/15
 |-
 | 13
@@ Line 103: / Line 103: @@
 == Tunings ==
-{{todo|complete section|inline=1}}
+{{Todo|inline=1|complete section}}
 [[Category:Rank-2 temperaments]]
 [[Category:Archytas clan]]
 [[Category:Nuwell temperaments]]