2EDO, if the attempt is made to use it as an actual scale, would divide the octave into two equal parts, each of size 600 cents, which is to say sqrt(2). It represents the [3-limit]] consistently, and it can be used to give a skeletonized version of the 3-limit music such as was used in Medieval Europe, by mapping the fifth and therefore the fourth to 600 cents. That entails mapping 81/64 to the unison, and if we do the same for 5/4 we end up with the val (mapping) <2 3 4|. This could be used to crush all of the 5 out of 5-limit music, and to then attempt to turn what remains into neo-Medieval harmony.
If we want to consider it to be a temperament, it tempers out 9/8.
Factoids about 2EDO
Dichotomy by Kaiveran Lugheidh