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'''Meanquad''' is a [[4/1|double octave]]-repeating temperament that tempers [[81/80]] in the 4.5.6 subgroup. Similarly to [[meantone]], it has a flat [[3/2]] as generator and equates [[5/4]] and [[81/64]]. It possesses [[MOS scales]] of the forms [[3L 4s<4/1>]], [[7L 3s<4/1>]], and [[7L 10s<4/1>]], which could be viewed as analogues to the meantone pentatoic, diatonic, and chromatic scales respectively.
'''Meanquad''' is a [[4/1|double octave]]-repeating [[rank-2 temperament]] that tempers [[81/80]] in the 4.5.6 subgroup. Similarly to [[meantone]], it has a flat [[3/2]] as generator and equates [[5/4]] and [[81/64]]. It possesses [[MOS scales]] of the forms [[3L 4s (4/1-equivalent)|3L 4s<4/1>]], [[7L 3s (4/1-equivalent)|7L 3s<4/1>]], and [[7L 10s (4/1-equivalent)|7L 10s<4/1>]], which could be viewed as equivalents to the pentatonic, diatonic, and meantone chromatic scales respectively. For more techincal data, see [[7L 3s (4/1-equivalent)#Meanquad]].
 
== Interval chain (POTE tuning) ==
== Interval chain (POTE tuning) ==
{|class="wikitable"
{|class="wikitable"
|-
|-
!Generators up
! Generators up
!Cents
! Cents
|-
|-
|0
| 0
|0.0
| 0.0
|-
|-
|1
| 1
|696.8
| 696.8
|-
|-
|2
| 2
|1393.6
| 1393.6
|-
|-
|3
| 3
|2090.4
| 2090.4
|-
|-
|4
| 4
|387.2
| 387.2
|-
|-
|5
| 5
|1084.0
| 1084.0
|-
|-
|6
| 6
|1780.8
| 1780.8
|-
|-
|7
| 7
|77.6
| 77.6
|-
|-
|8
| 8
|774.4
| 774.4
|-
|-
|9
| 9
|1471.2
| 1471.2
|-
|-
|10
| 10
|2168.0
| 2168.0
|-
|-
|11
| 11
|464.8
| 464.8
|-
|-
|12
| 12
|1161.6
| 1161.6
|}
|}
== Tunings ==
== Tunings ==
10ed4 ([[5edo]] duplicate) is a non-modal equalized tuning similar to [[7edo]] for meantone. [[17ed4]] is the smallest tuning that can be said to support this temperament at all. Like [[12edo]], it can be viewed as the boundary between meanquad and the double-octave version of [[archy]]. Larger options include 24ed4 (12edo duplicate), [[31ed4]] and [[55ed4]].
[[17ed4]] is the smallest tuning that [[support]]s this temperament and features the decatonic scale. Like [[12edo]], it can be viewed as the boundary between meanquad and the double-octave version of [[archy]]. Larger options include 24ed4 (12edo duplicate), [[31ed4]] and [[55ed4]].
 
== Scales ==
== Scales ==
* [[Meanquad10]]
* [[Meanquad10]]
== Temperament data ==
 
[[Subgroup]]: 4.5.6
[[Category:Meanquad| ]] <!-- main article -->
[[Comma list]]: 81/80
[[Category:Rank-2 temperaments]]
[[Mapping]]: [{{val|1 0 1}},{{val|1 4 1}}]
[[Category:Non-octave temperaments]]
Retrieved from "https://en.xen.wiki/w/Meanquad"