Auk

Auk is a nonoctave regular temperament in the 3/2.7.13 subgroup that tempers out the comma 87808/85293. It thus equates 3 7/1 (fifth-reduced to 112/81) with 13/1 (fifth-reduced to 832/729). The generator when reduced is in the neighborhood of 550 cents, representing 112/81. It possesses non-trivial MOS of the families 1L 3s<3/2> ("neptunian"), 4L 1s<3/2>, 5L 4s<3/2>, and 9L 5s<3/2>. 9edf is a particularly good equal temperament that supports it.

Interval chain

#	Cents	Approximate ratios
0	0.00	1/1
1	546.95	112/81
2	392.94	26/21, 25088/19683
3	236.93	832/729
4	81.92	1352/1323
5	628.87
6	473.86