The brain interprets everything through an extremely complex web of filters and processes. Some of that is linked to the amygdala, a part of the brain that is responsible for most of the emotional responses (e.g. fear). The amygdala responds fairly consistently (and thus predictably) to certain stimuli, which is why the same music will have very similar responses in most humans. To whatever extent that the response may be different, it’s due to the way in which memories and past experiences (which differ from person to person) are part of the processing.
This applies not just to music. It applies the same way to paintings, sculptures, stories and movies. Most people have a very similar basal reaction to the same scene or the same work of art, but whenever two people’s reactions are different, it’s because the work might trigger different memories or relate to different past experiences in each of them.