To me this sounds similar to the problem of how to execute a timing-based attack over a network with variable latency. The key is to make lots of requests very

To me this sounds similar to the problem of how to execute a timing-based attack over a network with variable latency. The key is to make lots of requests very quickly. You can then statistically narrow down very small variations even though they're built on top of a larger trend signal like the network latency or a piece of music. As another commenter suggested, there may also be signal processing techniques to "mod out" the interference from the music (perhaps measured with a probe on the audio output?) and measure only what's left.