On the sprawling Universal Studios lot, inside the bungalow where John Williams wrote the music for "Saving Private Ryan," "Schindler's List" and a handful of "Star Wars" films, the composer's office is carpeted, quiet, and without a computer or screens of any kind. He works at a small drafting desk, writing notation in pencil on lined paper, within a chair swivel of a Steinway grand.

It's the piano on which Steven Spielberg hears all the main themes of his movies for the first time—and almost always the last—before Mr. Williams...