Meanquad: Difference between revisions
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CompactStar (talk | contribs) After experimenting with this tuning in 17ed4, I think the decatonic scale is actually quite tonally ambiguous much like the chromatic scale, so I am calling it a chromatic-analog rather than a diatonic-analog |
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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 | '''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 diatonic, meantone chromatic, and meantone enharmonic scales respectively. | ||
== Interval chain (POTE tuning) == | == Interval chain (POTE tuning) == | ||
{|class="wikitable" | {|class="wikitable" | ||
Revision as of 07:21, 21 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 equivalents to the diatonic, meantone chromatic, and meantone enharmonic 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