The smarter birds are easier to study. As are the great apes and dolphins. Research has been finding it isn't brain size so much as density and architecture of particular parts that leads to what we call 'intelligence', and I would assume what we could call a 'conversation'. Not that we shouldn't study whale songs, but that the scope is much larger than you indicated. We can communicate with gorillas with English words (but not English grammar last I heard?), but I'm not sure if we even know what noises and gestures gorillas make that are communication or are just them clearing their throats. But I've gone past studies working out the vocabularies of birds and meerkats.