Originally, Alex North was commissioned to provide 2001: A Space Odyssey with an original score, but after Kubrick used classical compositions to edit the film, he liked them so much that he decided to keep them. Sorry, Alex. If it's any consolation, your soundtrack will eventually be released on CD for fans to enjoy.
Kubrick's decision resulted in a score that's very different from a traditional soundtrack. In a traditional score, the music gives the audience cues about how to feel about what's happening onscreen. Just consider the bubbly pop music used in romantic comedies or the fast-paced tempo of a chase sequence, and you've got the idea.
But in 2001, "Kubrick sections the soundtrack so that extra-diegetic music never accompanies dialogue scenes, leaving the audience bereft of normative emotional cues." (Source). In other words, Kubrick's choices of music heighten the mystery and wonder of the images on screen but still require the audience to contemplate what's presented. They can't rely on the soundtrack to tell them how to feel—like how a horror movie screams at you with shrill strings to tell you that you should be frightened.
In Space No One Can Hear You Sing
Let's look at some of the compositions Kubrick choose:
"The Blue Danube Waltz," by Johann Strauss, is played during Floyd's space travel scenes. The waltz's upbeat winds and strings invite the audience to explore the wonders of spaceflight. The ships and satellites move in a graceful way, turning and turning around a focal point like a couple waltzing. The ship and station are turning in sequence while they spin (orbit) around the Earth. The combination of imagery and music transforms space travel into a technological dance of mathematically precise proportions. The major key says, "This is beautiful, safe, and natural."
György Litgeti's "Requiem" (the Kyrie) is used when the monolith is discovered by both the early hominids and Dr. Floyd. This piece is used to give a sense of mystery and gravity to the monolith. Although there's a choir, they don't sing in words but rather intone, as though words can't properly explain their feelings. This strengthens the sense of the awe in the unknown. The music also adds a mournful quality to the scene. This wailing, mourning choir foreshadows impending death—first of the early hominids, who are replaced by humans, and then of the human species, who will be replaced by the Star Child.
The opening section of "Also Sprach Zarathustra op. 30," by Richard Strauss, plays during the opening credits, the invention of the bone club, and the reveal of the Star Child. The section of Strauss's work is called "Sunrise," and the film made it hugely famous. It's everywhere—commercials for Toyota Camry and Coca Cola have used it; Jimmy Fallon and Justin Timberlake even a capella-ed it for an iPhone 6 ad.
The piece has an epic quality to it. The grand boom of the percussion and the triumphant blare of the horns signal the coming of an important transitional event, stunning and scary at the same time. It fits these scenes perfectly. The discovery of tools will change the evolutionary game for the hominids; meanwhile, the Star Child ushers in the next step of human evolution, from human to something beyond human. If God ever appears on earth again, we suggest he play "Zarathustra" before he arrives; everyone will know what's happening and change into a clean pair of jeans.
A quick bit of history: Strauss named his musical composition after philosopher Friedrich Nietzsche's book Thus Spoke Zarathustra, which introduced Nietzsche's idea of the ubermensch ("over-man" or "super-man"). An ubermensch is beyond the control of others and lives by his own values. He dominates others and can change the course of history. He will sacrifice himself to enhance humanity. (Source) You can see how this concept might fit the idea of humanity's eventual evolution into the Star Child.
The Sounds of Silence
Equally important are the scenes that lack music altogether but instead rely on diegetic sounds to set the mood.
One example is the scene where Bowman takes a spacewalk to retrieve the AE-35 antenna unit. Instead of a musical cue, we get the simple, rhythmic breathing of the astronaut. To focus on something as simple as breathing reminds us just how dangerous a spacewalk really is, providing an anxious mood without any music telling us how to feel.
Another great example is the scene where HAL murders the three hibernating scientists. Instead of bad-guy stalking music—or worse, some Hans Zimmer "Bwahh!" bleating in the background—we are serenaded with technological warning beeps on the life support monitoring equipment. It's unnerving, and the mechanical wailings characterize the violence of HAL's actions even though it's only presented by way of vital signs on a computer screen.
No silence is more loaded with meaning than the scene where HAL refuses to open the pod bay doors. Dave keeps repeating, "Hal, do you read me?" and gets no response. Kubrick shows us extended shots of the pod and the ship suspended in the darkness of space. The utter silence conveys a sense of foreboding; Bowman is absolutely alone out there.