German-American composer Franz Waxman was the John Williams of his day, one of the premier film composers of the 1940s and '50s who contributed gorgeous music to a number of classic films. (Source) He studied music in Dresden, Germany, and was just getting started as a film composer when the Nazis took over Germany in 1933. As a Jewish man who'd had the stuffing kicked out of him by a gang of goose-stepping Nazis on the street, Waxman, with his wife, decided that America might be a little more welcoming.
They moved to Paris, then to Hollywood. He soon got the attention of director James Whale, who was working on a sequel to his smash hit Frankenstein. Waxman scored the music for Bride of Frankenstein, which became a classic, and he was off to the races. His real big break came in 1940, when Alfred Hitchcock used him for his movie Rebecca. The film was a huge hit and won two Oscars, although Waxman had to settle for a nomination that year. But, no matter. He was the toast of Hollywood, all of the big directors wanted to be his bestie, and Hitchcock came back to him multiple times to score his movies. And, he managed to score two Oscars himself before Hitch hired him again to compose the music for Rear Window.
You'd think the music of a guy with that resume would fill a film. But, in fact, Rear Window uses his score only sparsely, notably in the opening credits and toward the end. (Waxman also composed the song "Lisa," supposedly written by Jeff's musician neighbor in the movie.) The rest of the film doesn't use a musical soundtrack at all. Hitchcock wanted to stress the diegetic elements of the movie's soundtrack—the sounds that occur within the "real" world of the movie, such as the traffic down the street, the pouring rain, and the distant conversations and radios of Jeff's neighbors.
That makes Waxman's modest score something of a scene-setting endeavor instead of a constant mood accompaniment. Most of the time, the score tells us what to feel in a given scene. But Hitchcock didn't want that cluttering up his movie. So he let Waxman prep us during the opening credits (with a very hepcat '50s beat, no less) and then told him to take a break until the end. It's a bold choice, and it makes for a very unusual movie, especially for a big-time studio production like this one. Hitch never did things the way people expected, and Waxman was more than happy to give him a hand.
Waxman continued composing throughout the '50s and into the '60s, when he tried his hand at television scores as well. Sadly, he died rather young, in 1967, at the age of 60. He left behind a staggering number of musical scores, but wouldn't it have been great to see what he would have done with Star Wars?