House MD - Identify some music?

In the season 2 episode of House, Who’s Your Daddy, we’re given to understand that there was a genius piano player named Jesse Baker, who was the grandfather of our poor patient.

Now I’ll frankly admit that I couldn’t tell the difference between a genius player and someone who is merely good enough to play at a nice restaurant, but I did like the clip of music that they played. The Wikipedia doesn’t turn up a Jesse Baker, so perhaps you all could identify who that really is playing? (And yes I realise it’s possible that it’s just some house musician.)