My rescue Basenji used to have bad separation anxiety (due to being abandoned twice) but I found that getting her a snuggle puppy has helped her greatly. I used to always play music but I never found that it was much help with my Basenji.
I currently leave my basenji in her crate when she is alone (never for longer than 3 hours I am currently in the process of completely dog proofing my room for her to roam free in) she used to scream the whole time she was alone but once I placed the snuggle puppy in her crate she began to feel much more comfortable being alone and now does not even cry when I leave. I am also sure to provide her with something to entertain her while I am gone.
My vet also recommended a pheromone room spray/collar that mimics mother dog smells to help with anxiety. I personally have not used it so I can not speak to its effectivenes.