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 |
CompactStar (talk | contribs) No edit summary |
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== Tunings == | == Tunings == | ||
[[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 == | == Scales == | ||
* [[Meanquad10]] | * [[Meanquad10]] | ||
Revision as of 07:23, 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
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