How does listening to music decrease stress? I'm interested in how listening to different types of music (such as jazz, classical, etc.) can help some people calm down.

More specifically, how does the brain form a link between music heard and processed to the stress system? Is it some cortical association area or a direct circuit?
This may be happening due to beat entrainment. Different music genres have different beat and rhythm patterns. The ones that are calming will generally have a lower beat and rhythm frequencies. The lower beat and rhythm frequencies are similar to the frequency of heartbeat and breathing when a person is feeling calm and/or relaxed. Through the process of entrainment, the person's breathing and heartbeat may synchronize with the music, thus calming the person. The mechanism could be working by counter-acting the effects of shallow breathing.