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The 166 equal temperament (in short 166-EDO) divides the octave into 166 equal steps of size 7.229 cents each. Its principle interest lies in the usefulness of its approximations; it tempers out 1600000/1594323, 225/224, 385/384, 540/539, 4000/3993, 325/324 and 729/728. It is an excellent tuning for the rank three temperament marvel, in both the 11-limit and in the 13-limit extension hecate, and the rank two temperament wizard, which also tempers out 4000/3993, giving the optimal patent val for all of these. In the 13-limit it tempers out 325/324, leading to hecate, and 1573/1568, leading to marvell, and tempering out both gives gizzard, the 72&94 temperament, for which 166 is an excellent tuning through the 19 limit.

Its prime factorization is 166 = 2 * 83.

166edo (as 83edo) contains a very good approximation of the harmonic 7th. It's 0.15121 cent flat of the just interval 7:4.

Scales