Meanquad: Difference between revisions
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'''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]]. | '''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 == | ||
[[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]]. | [[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]] | ||
[[Category: | [[Category:Meanquad| ]] <!-- main article --> | ||
[[Category:Rank-2 temperaments]] | [[Category:Rank-2 temperaments]] | ||
[[Category:Subgroup temperaments]] | |||
[[Category:Nonoctave]] | [[Category:Nonoctave]] | ||