So I work in a call center and am frequently on the other side of this exchange. In a lot of cases, you can request to be on hold with no music! They play music on those lines as a way of letting the caller know that the representative can't hear you right now. If you ask 'Instead of placing me on hold, can you just mute yourself while you work because the music bothers me?' 90% of the time they'll do just that, since having people on hold is bad for their metrics.
This won't work in situations where the representative needs to call someone and speak to them on a separate line as the system is always going to play music on an inactive line, but in those instances you can request they merge the call so you're on the same line with them!
Either way, most places are going to have a phone system that can get around the annoying music, and if you ask politely, most reps are going to be fine with trying to spare you the music. Hope this helps :)