Different aspects of benefits
Following benefits are most likely not to occur simultaneously, and they depend on what type of music you listen to or play.
Long term mental cognitive and simulating benefits. Applies to both children and elderly. Interestingly, it only affects our brain, but largely affects the chemical interface between the brain and our body. Music seems to have right amount of stimuli to keep the interaction at healthy levels.
Short term simulative effects, both neural and hormonal. Similar to a coffee cup, with less side effects. Works best with either known piece of music or something simple and inspiring.
Short term balancing effect, on breath, hearth rate by affecting somatic nervous system. This is achieved best by rhythmically predictable music.
Medium term calming effects, especially by contemplative music and vocal music. Strangely calming effects may be a result of non-predictable music leading to sensory overload where music is perceived as white noise.
Functional: Using brain to consume sugar, especially during improvisation or when trying to follow unknown pattern.