A Clockwork Orange is an excellent choice for a discussion on the usage of music in films. Given that the premise of the film revolves around the affect of music on an individual, it is rather appropriate.
As everyone has probably mentioned, extra diegetic music plays in the background whenever Alex believes he’s in control. For instance, when he successfully enrolls in the Ludovico programme, “Pomp and Circumstance” plays. Other classical music plays consistently in the background, as during the scene when Alex beats down and intimidates his crew.
The interesting part of the main theme (written by Walter Carlos, pioneer of the Moog Synthesizer) is that it incorporates the “Dies Irae” theme of the Catholic church, which is not only a chant for the dead, but also indicative of dread.
Beethoven is a common theme of the film, most obvious in the “Ode To Joy”, which is instrumental in Alex’s rehabilitation. The 9th, first associated to Alex with absolute joy and ultraviolence, is “subverted” in his mind, gradually shifting his association with violence to that of a sickening distaste. Beethoven’s Fifth also makes a small cameo, in the nameless writer’s doorbell tone, also indicative of anger, revenge, and dread.
I am slightly disappointed that Kubrick left out the 21st chapter of the book, which entirely changes the perspective of the novel, transforming it from a cyclical, nihilistic story, to one of maturation.