SHAME by Salman Rushdie, the Muslim infidel.
BEAUTIFUL LOSERS by Leonard Cohen, the singer-songwriter.
I suppose they're not truly obscure. They're both available in your local Enormous Retailer of Books. I would throw in THE BOOK OF DANIEL by E.L. Doctorow.
A really obscure one that's good, and also by a musician, is a book called I, FLATHEAD by Ry Cooder.
Another one I like that isn't a novel, and I don't know how sung it is - SADE: AN EROTIC BEYOND, by Octavio Paz. Soft surrealism take that.