Plenty of literary novels have inspired musicals—Winesburg, Ohio, Moby-Dick, and The Color Purple, to name a few—and a few band names too. But I’m hard-pressed to think of a novel that’s inspired a musical composition. So until a commenter corrects me, I’ll think of Sam Shalabi as a pioneer; he’s written a 60-minute free-improv suite based on Thomas Pynchon‘s 2006 novel, Against the Day. Performed with a Montreal collective called Land of Kush, the piece has five sections named after the novel’s five sections, and Shalabi tells the McGill Daily he was particularly inspired by one of the book’s main themes:
The novel “is structured around light,” he explains, “and [light] becomes a character in a really interesting way.” One narrative thread traces the groundbreaking scientific advances made in the West in the years leading up to World War I – the discovery of the photon, and the connection between electromagnetism and visible light – that led to a widespread obsession with illumination. Nikola Tesla, one of the pioneers of the second Industrial Revolution, makes a cameo; Tesla “was doing many interesting things with light,” says Shalabi, “but was seen as a freak.” The story, he further explains, “is about those moments where no one knows what’s going on, but it’s all really exciting.”
I haven’t read the book, so I can’t speak to how well the piece evokes it. But on the evidence of the sample available on Constellation Records’ Web page for the album, the album stands on its own quite well—it’s busy but tuneful, full of the kind of martial drumming and chanting that would excite any modern day freak-folk and psych-rock fan. A sample from part four, the title track, is available as a free download.
markathitakis.com 
By “musical composition” do you include pop songs. “Wuthering Heights” by Kate Bush is one.
I should’ve been clearer. I didn’t want to say “classical composition,” because that’s not what the Pynchon piece is, but I was thinking of “non-pop” songwriting. (Almost immediately after I posted this, I remembered Richard Buckner’s “The Hill,” an interesting album whose lyrics are mostly (entirely?) drawn from Edgar Lee Masters’ “Spoon River Anthology.”
Quite a lot of music, popular and otherwise, has been inspired by Pynchon, going back almost 40 years to the earliest examples: “Esther’s Nose Job” on Soft Machine’s 3rd album and “The Eyes Of A New York Woman” on the Insect Trust’s Hoboken Saturday Night. (Not to be confused with a similarly titled song that was a hit for B.J. Thomas about the same time.)
In the 1980s, Camper Van Beethoven credited “T. Slothrop” on one of their albums. (The band was based in Santa Cruz and spent a lot of their spare time searching for Pynchon around town – this was when he lived a few miles south of there.)
In 2005, the band Thrice released the album Vheissu which went to #15 on the Billboard charts. Yes, part of it was based on V.
A few years before that, James Taylor and Mark Knopfler recorded “Sailing To Philadelphia,” based on Mason & Dixon. I heard it being played on the sound system at a McDonald’s around that time.
And of course there are the liner notes Pynchon wrote for “Nobody’s Cool” by Lotion and a Spike Jones compilation in the 1990s.
Opera:
Benjamin Britten / Turn of the Screw (James)
JCOates has had her works treated as opera and songs (classical and pop):
http://jco.usfca.edu/music.html
Forgot about Philip Glass who has written many works based on literature: Doris Lessing and J.M. Coetzee novels, Kafka and Poe stories, poetry by Allen Ginsberg and Rumi.
So, do we no longer consider Don Quixote a novel, with all the myriad music pieces it has inspired? Or Faust?
Since you’re excluding musicals, I assume you’re also excluding operas. Fair enough. I assume you’re also excluding other long non-novel literary forms that have inspired musical composition (Sheherazade, Manfred, Walden, et al.).
I think you’ll find there’s much in classical music, especially from the Romantic era, that was inspired by literature and, yes, a few novels.