We will assume that the phenomenon of beating is perceived as a kind of dissonance, where the rate of beating is proportional to the amount of dissonance. It is not our purpose here to justify this assumption any more than to say that it is fairly commonly held, and has always been used as a means to evaluate tunings. Discussions of beating as a form of dissonance can be found in [8], [12], and many other works on tuning and/or psycho-acoustics. Our purpose is to proceed with this assumption and see what theoretical and practical consequences it leads us to.
Since M3 and P5 are used as strong consonances in diatonic music, we will assume that when they are rendered harmonically, it is desirable to tune them so that they beat as slowly as possible, ideally not at all.