Threedie
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Threedie, the interval 13^3/3^7, is a 3.13 analog of the 2.5 diesis, 2^7/5^3. Tempering by it, instead of chopping the octave into three sharp 5/4s, chops the tritave (3) into three slightly flat 13/9s, since (13/9)^3/3 = 2197/2187. 596 provides the optimal patent val for the corresponding rank five temperament.