David Julyan, composer for several other Nolan films like Following and Prestige put together a synthesized soundtrack to underscore the disorienting direction of Memento.
Influenced by other synth heavy scores like Blade Runner, Julyan's sounds provide a gentle ambience to assist in creating Leonard's world without overtaking the film. Like the use of black and white vs. color scenes, the music also helps the audience distinguish where they are on the confusing timeline of Leonard's mind.
In James Mottram's The Making of Memento, Julyan describes the sound of colored, regressing scenes as "broody and classical" while the black and white progressing scenes are "oppressive and rumbly."
We can see what he means just by taking a look at the movie's opening scene. As we watch Leonard kill Teddy in reverse we hear this very mellow and melancholy classical track, and as soon as the scene cuts to black and white with Leonard in the hotel, the music shifts to an eerie, steady beat with some sharp, electronic notes that hold the scene in suspense (Ebert would call them "subliminal blips of Leonard's defragmented mind").
A more extreme example of this might be the track "All is Full of Love," which has this sense of staccato flicker that doesn't allow us to predict what we'll hear next.
The narrative structure of the film puts us firmly in Leonard's head and the score is meant to do the same. The music isn't as disorienting as the timeline, but the synthetic tracks have a sort of directionless drifting, never giving the audience firm ground like the heavy beats of an action flick. Some of the classical music, like "Remember Me," which plays as Leonard burns the mementos of his wife, invoke a sense of heartache.
But, like Leonard, we're left wondering, unsure of exactly what is missing that causes the melody's sadness.