The music of Once Upon a Time in America was composed by Sergio Leone's long-time collaborator, Ennio Morricone. Due to the film's unusually long production, Morricone had finished composing most of the soundtrack before many scenes had even been filmed. Some of Morricone's pieces were actually played on set as filming took place (a technique that Leone had used for Once Upon a Time in the West). "Deborah's Theme" was in fact originally written for another film in the 1970s but rejected; Morricone presented the piece to Leone, who was initially reluctant, considering it too similar to Morricone's main title for Once Upon a Time in the West.

Ramifications represents a further development of my method of composition with complex musical net-formations. it is, as it were, a terminus in the development from dense and static to broken-up and mobile. The title refers to the polyphonic technique of the part-writing. in one skein, individual parts that are twisted together move in divergent directions so that the strand of the voice gradually become disentangled. The total form is made up of the alternation of ramification and unification of the parts and of the rents or bunching together of the net-formation that ensues from this. And as well as that, there are in this piece new aspects of a micro-tonal harmony. Even earlier I was occasionally working with deviations from the equal temperament (Requiem, Volumina, Harmonies, Second String Quartet). But what is new here is the consistent application of an idea of hyperchromatic harmony. This is made possible by one half of the string instruments being tuned a quarter-tone higher than the others. From the automatically ensuing differences in intonation when the instruments are played, arises a fluctuation in pitch such that one can hardly ever hear exact quarter-tone intervals. In only a few dense places approximative quarter-tone clusters result. apart from that we find a totally new kind of uncertain harmony, as though the harmonies had rotted: thex have a strong taste and decay has permeated the music.
- Gyorgy Ligeti.