So this is purely anecdotal, but it seems to me that bird songs work kind of like drum circles. A bird can sing a pattern, and see if anyone else can replay the pattern. If you can, then the initiating bird will slightly modify the pattern, and see if you are able to pick up on the nuance. With drum circles, people typically play off of patterns set by others. And both the leader and follower can tell that they are in sync with each other. I suspect that this dynamic is at the core of a lot of bird song interactions. And to try to translate that into a human language would not work well.