Maurice Jarre and Peter Weir
Music? What music?
One thing about the score that you might have noticed right away: you don't really notice much music. But that doesn't mean it doesn't play an important role in the film.
Sure, the (super emotional) story and the (super emotional) acting do most of the work in the film. And yes, the atmospheric setting helps, too. But music can establish atmosphere in a special way, and Peter Weir and composer Maurice Jarre use it to up the ante—emotionally—all the time.
For example, as the boys venture into the night for their first DPS meeting, Jarre underscores the scene with eerie, shimmery music. It matches the mist of the forest and sets a downright spooky tone.
Later, he allows for a touch of rock'n'roll to a backdrop of fencing and traditional Welton activities. This provides a contrast, rather than a distraction. While other young people are out dancing and relaxing, the Welton boys are engaged in more traditional activities. No rock'n'roll for them. And that's a shame, because by 1959, the style was just getting good.
But it isn't all light-hearted and whimsical. When Neil dies, the underscore is tragic and light; the boys' grief takes front stage. And when Mr. Keating leaves the classroom for the final time, the tone is one of victory. We hear bagpipes and are brought right back to the opening scene, before the drama even begins.
And once you notice that, we're betting you can't listen with dry eyes.
Jarre knew what he was doing. The composer has scored a number of big-hit films, like Lawrence of Arabia, Mad Max Beyond Thunderdome, and Ghost (among a ton of others). He's a pro at letting the music help tell the story, rather than distract from it.
If this film had too many distracting songs, we might not notice the subtle emotional changes that characters like Mr. Keating, Todd, or Neil experience. And that's part of the film's magic: we're too busy wiping our eyes to notice what's happening behind the scenes.