The reason I bring the plot up is that it forms the basis of one of my favorite pieces of music, Nikolai Rimsky-Korsakov's Scheherazade (1888). It is a commonly-performed piece, and I recommend trying to find a local performance of it (the LPO and Loyola Symphony both performed it last year), but short of that here is a YouTube video of a very good performance (Gergiev is probably the most prominent living conductor, and the Vienna Philharmonic is pretty generally considered the most reputable orchestra):
If you listen to and/or watch the video, you'll probably realize that it says little to nothing about Islamic literature. I just included it here because it's a convenient time to put it and I'm a Rimsky-Korsakov fanboy.
Scheherazade is a good example of programmatic music, which means that it represents a story or mood. The initial trombone part, for example, represents the Shah, while the concertmaster's (first violin) solo is Scheherazade's theme. Both parts invoke the feeling and texture that Rimsky-Korsakov wanted to associate with those characters. If you actually watch the entire piece, you'll see that it starts with the Shah's theme, and then Scheherazade is introduced, and it begins a series of episodes depicting stories from the Nights, thus reflecting the plot of the original story. The dream-like ending conveys a sense of extraordinary tiredness, and the end of the piece is supposed to be Scheherazade falling asleep after hundreds of anxious nights of telling stories. Meanwhile, the piece is also an example of orientalism, the fashion in the West for imitating Eastern culture (which remains in modern times most saliently in the form of Persian rugs and imitation Chinese designs on porcelain).
The tonality (relations between the notes; scales or chords) of the piece, and moreover the ornamentation and rhythm, convey a vaguely Middle Eastern feel. I find that especially clear in the oboe solos, which sort of make me think of a snake charmer.
The reason I really love the piece, though, is the combination of inventive orchestration (Rimsky-Korsakov is remembered mostly as a master orchestrator) and clear, memorable melodies. For example, if you listen to the section beginning around 14:17, you get a very clear sense of energy, both from the tense, syncopated melodies in the first violins and from the frantic, high-pitched effects of the pizzicato (plucked, as opposed to bowed, strings) second violins, piccolo, and flutes. I don't know of any other composer that can achieve that kind of effect simply with orchestral colors. I've listened to the finale over and over again, and I am still amazed by the symmetrical closure that he brings to each thematic group (each set of elements based on a single melody).
Anyway, I think that Scheherazade is an interesting and worthwhile, if loose, rendering of One Thousand and One Nights.