Does the Ar tonelico 3 story has any relationship with the first two Ar tonelico stories?

I haven't played so I can't give you a 100% accurate answer, BUT as far as I've read the only involvement is a nod-back: one of the characters in 3 was also in 2 at a younger age. I've never played the original but I have played 2, which did the same thing with another character, and I was able to understand everything just fine.