I had a green parrot some years ago!
and he even could speak)
but he couldn't do such music for sure-))
you're right, there are maaaany tiny details which are in the shadow while first listening, and they are catched by ears only when it's playing again and again. It's like a multiply level pie, the taste of which is opened when we are eating more and more pieces and slowly chewing them-)
tasty music like a tasty pie)