I would suggest first going through your open windows to see if you should have some program there that is playing the music. It could for example be coming from a browser tab. If you're using Safari, those tabs are usually marked clearly with a small speaker icon.
If you're not able to locate the process using this method, you can go through each running program one by one, temporarily pausing each one to see if the music stops. Do that by first opening up Activity Monitor to identify running programs.
At first I would use the View menu to select Windowed Processes - the list is usually much shorter, and it is likely to be one of those programs. When you have gone through this list without luck, I would advance to Active Processes, then My Processes - and eventually trying All processes.
Now that you have a list of potential culprits, open up Terminal.app and go through the list one by one, writing the following command to pause a program:
kill -STOP <PID>
where should be replaced with the number listed in the "PID" column in Activity Monitor. For example with actual numbers, it could look like this:
kill -STOP 72104
If the music does not stop playing, you can resume the program again with this command:
kill -CONT <PID>