Just P5 and M3 Impossible in Diatonic Tunings

A fundamental problem common to all diatonic tunings is that they cannot have all P5 and all M3 just. Definitely only a regular tuning could accomplish this if it were possible, because it is the only type of tuning in which an interval is tuned the same no matter where it occurs. But since Pythagorean (just P5) and QCM (just M3) tunings are different, we know that having just P5 and M3 in the same tuning is impossible. In regular tunings, this problem leads to compromise tunings like 12TET that lie in between the extremes of Pythagorean and QCM on the line $\ensuremath{\underline{\Theta}} = \ensuremath{\underline{C_S}} + 4\ensuremath{\underline{\Phi}}$.12TET, for example, is close to Pythagorean on that line, so it has P5 that are close to just and M3 that are far from just.