If it's distant, through observation. Across cultures. Different styles. Global.
Unless they're us or they've been here this whole time, they probably travelling here. I'd assume some awesome technology. They could remotely monitor the brains of audience members or just anyone who hears music. A control group who doesn't really listen to any music would be good for comparison. If needed the aliens could abduct an entire audience and put implants in them. Hopefully they can figure out which end is which.
A longitudinal study would be good. They could travel at near light speed for a few minutes, come back, and something like a few years would have gone by here. Although if they mastered space travel, I'd assume they have some good ideas on controlling time. Their call.
I'd study the brain. The profession could be through the media or probing a few people in the field. That sounds easy enough. There's sound in nature, but I'm not sure animals or creatures are creating music the same way humans are. So study the effect of music on the human brain.