When I was in high school, my math teacher would play Mozart during tests, claiming it would help us. It would drive me crazy, and I doubt that my grades improved as a result of the distraction.
For what it's worth, I have a BMus in Piano Performance. I love music... but never as "background noise"!
The closest thing I'll do to address my particular problem is find audio of stuff like thunderstorms or waterfalls and more ambient stuff. Personally, I find that much easier to tune out.
It's not 100%, but they'll get rid of like 80% of the background noise without playing anything. To get that last 20% yeah you need something playing to help mask it(even at an extremely low volume).
Sometimes I wear mine with nothing playing while at work just to get rid of random office chatter.