I do make up entire words and talk to my chinchilla like she can only understand over-enunciated high pitched talk. But I don't sing to her.
The relief vet she saw a couple weeks ago did, though. It was awkward. He picked her up and started rocking her and singing in some foreign language. Then he started telling me how much he liked Lady Gaga and spouting asian sounding proverbs about mother earth and what not. He was a little odd, but he actually seemed to be one of the better vets I've seen.