Diminished (temperament)
From Xenharmonic Reference
Diminished, 12 & 16, is a 5-limit temperament tempering out 648/625, the difference between four 6/5 minor thirds and the octave. Diminished has period 1\4 and generator 3/2 (or 25/24); it is associated with tetrawood (4L 4s), called the diminished scale in conventional music theory.
Many tuning optimization algorithms rate diminished as optimal near 12edo, but if you want a better 5/4, you have to flatten the fifth (as in 28edo or 40edo).
