Lately I've been interested in understanding more about the cube. I learned the Heise method a while back and was quite happy with it. I like the idea of using commutators to solve certain situations on the spot. However, from my understanding you can't use a commutator to swap two edges and two corners at once (like a T perm would). I don't know any of those permutations because I never bothered memorizing algorithms (I'm not really interested in speed cubing). My goal is to understand how to come up with such permutations on the spot without memorizing them. Is there any method along a vein similar to commutators that could accomplish this?