I've lost count of the number of times that clients say to me "The music goes really well!" when I present them with an animation which has been choreographed to music.
What they perhaps don't realise is that actually it's the graphics that are going well with the music (not the other way around), and that is because I've painstakingly spotted all the 'cues' within the music (beats, bars and musical nuances) and made sure the motion coincides with those musical events. Not quite the happy coincidence it's often perceived to be!
This is why it's key to choose (and settle on) a piece of music before starting work on a project - it really does influence everything else in the process, and changing it further down the line will add a lot of time and therefore cost to the project.