Jake Gittes and Jake Berman during the golf game

So, I was rewatching this recently and noticed something that I never noticed before: during the golf game that Berman and Gittes are having, Berman seems to be humming a song that seems to be the theme song from Chinatown whenever Gittes is making a golf shot during the game.

Did anybody else catch this? Is it actually the theme from Chinatown that he is singing? Or does it just sound similar?