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.
I'm afraid my boy would shred that thing to pieces.. he had been noisy but not destructive when left alone but today, I had to leave for 1.5 hours and came back to utter chaos. He had tried to break out of his crate (managed to move it a couple feet) and wrecked his crate cover somehow. Yeesh. Never seen him go this nuts.
Not sure what the source of his SA would be but it's been tough to see.. I'm staying at my moms for a bit now and even when one person is home, he can have fits of panic seeing the other person go (apparently its much worse when I leave, still gets upset seeing mom go, especially when he can see her in the backyard).
Really would like to get him more comfortable