Ancient City Music Dropoff

Right now, the Ancient City is a very good structure. The horror is there, the vibes, everything. There is only one problem with it right now though. If I find the structure while some of the games soundtrack is already playing, it ruins the whole mood. The structure goes from spooky to non-threatening. A possible solution for this would be to cut off the music once you enter the city. I see it has been done before with the Pale Garden, and I think it would work perfectly in the Ancient City.