Bernard Hermann's soundtrack, which he wrote shortly before his death, turns Travis's ordinary life into what is sometimes a heroic epic, sometimes a horror film, and other times no more than just another New York story. Two major themes dominate the score of Taxi Driver. The first features an eight-bar melodic sighing of a solo saxophone. The theme evokes the lonely melancholy of an individual alienated from his environment. The smooth, jazzy tones of the saxophone also complement New York's urban terrain, which we see as Travis passes through the various neighborhoods of the city in his taxi. The theme varies somewhat, particularly in tempo, but it follows Travis in his taxi as he drives his often sordid passengers around the city.
Travis's psychotic tendencies shine through in a second theme, characterized by an unresolved, dissonant chord played by trumpets over rhythmic snare drums. At various points in the movie, a harp joins the trumpets and snare. At the beginning of the movie, the trumpets punctuate moments that augur Travis's instability, such as when he hits Iris with his car. While Travis descends gradually into psychosis, this theme becomes dominant in the score. The unresolved chords of the blaring trumpets echo Travis's feelings of discord with the city, and the snare drums propel him to action. The unresolved quality of this theme is characteristic of several Hitchcock movie scores, particularly that of Vertigo, which Hermann also composed.
These two themes clash with one another in the climactic shootout at the end of the movie, which is originally dominated by the discord of the trumpets playing over an arpeggio in the harp, evoking an atmosphere of surreality around the nightmarish scene. As the camera pans from above across the carnage of the shootout, the trumpets continue to blare, bearing witness to the horror of Travis's actions. They pierce the silence like an alarm, which segues nicely to the imagined sirens of the police cars outside. When the camera pulls away from the upstairs room with the corpses and descends the staircase, the saxophone theme blends with the trumpets, slowed down and played rhythmically out of joint, to emphasize Travis's transformation from a lonely taxi driver into a murderer. This theme serves as a lyric contemplation of Travis's deranged story.
Also you should note that "Diary of a Country Priest"(1951) by Robert Bresson had a considerable influence on the film.
The character Travis Bickle drives a taxi around and complains about all the pimps,pushers,perverts,skunkpussies,prostitutes and lowlifes that trash the streets of the city. He imagines that it needs cleaned up by him being the hero. Then he meets a young prostitute thats like 12 year old (played by Jodi Foster in movie) He don't have sex with her but just talks to her. He feels the street hustler he met earlier is holding a threat over her forcing the minor into prostitution. So he buys two guns an goes into rundown apartment building shoot... Read more→
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Very very very good analysis... Excellent!