Bud, I'm a journeyman lineman and posses an electrical engineering degree. Let me explain a couple things; the SINGLE phase transformer outside of your house is just that, a single phase of either a Wye system or delta. While it may have two actually phases to it, merely to obtain voltage, it is a true single phase in a vector. Now, if I could visually show you how a vector works, this would be a simple lesson, but I hate referring to source material of other's websites so ill verbally explain the best I can. Most common these days is a single phase padmount transformer. It is single phase high side and therefore contains a single vector line. To obtain your 120/240 aka 110/220 your secondary vector line too, only contains a single vector line, but if you take that line and draw a dot in the middle of it, and one at each end, from center dot to either end is 120volts and end dot to end dot is your 240, all while still being the same single.phase vector line. These individual legs are not phases, they are legs of the same single phase.