Meanquad

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 pentatonic, diatonic, and meantone chromatic scales respectively. For more techincal data, see 7L 3s (4/1-equivalent)#Meanquad.

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 supports 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

• Meanquad10