It's not a thrush, a cardinal, a mockingbird, a blue jay, a robin, or a mourning dove, and I don't even know what to try after that.
Edit: Having gone through a lot of "Whatbird"'s sound archives, I've ruled out a lot of stuff, but come no closer to my goal. It sounded most like a long-eared owl, if slightly higher pitched, but it seems unlikely that owls would call and answer each other during the morning. If you crossed a long-eared owl with a mourning dove (an experiment unlikely to occur in nature) that'd be right about it.
Oh, well, another Mystery Bird for the file...