Meanquad: Difference between revisions
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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>]], [[7L 3s<4/1>]], and [[7L 10s<4/1>]], which could be viewed as analogues to the meantone pentatoic, diatonic, and chromatic scales respectively. | ||
== Interval chain (POTE tuning) == | == Interval chain (POTE tuning) == | ||
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== Temperament data == | == Temperament data == | ||
[[Subgroup]]: 4.5.6 | [[Subgroup]]: 4.5.6 | ||
[[Comma list]]: 81/80 | |||
[[Comma list]]: [[81/80]] | |||
[[Mapping]]: [{{val|1 0 1}},{{val|1 4 1}}] | [[Mapping]]: [{{val|1 0 1}},{{val|1 4 1}}] | ||
[[POTE generator]]: ~3/2 = 696.837 | |||
[[Category:Temperaments]] | |||
[[Category:Rank-2 temperaments]] | |||
Revision as of 03:57, 20 March 2023
Meanquad is a 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>]], [[7L 3s<4/1>]], and [[7L 10s<4/1>]], which could be viewed as analogues to the meantone pentatoic, diatonic, and chromatic scales respectively.
Interval chain (POTE tuning)
| Generators up | Cents |
|---|---|
| 0 | 0.0 |
| 1 | 696.8 |
| 2 | 1393.6 |
| 3 | 2090.4 |
| 4 | 387.2 |
| 5 | 1084.0 |
| 6 | 1780.8 |
| 7 | 77.6 |
| 8 | 774.4 |
| 9 | 1471.2 |
| 10 | 2168.0 |
| 11 | 464.8 |
| 12 | 1161.6 |
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.
Scales
Temperament data
Subgroup: 4.5.6
Mapping: [⟨1 0 1],⟨1 4 1]]
POTE generator: ~3/2 = 696.837