I think music is able to stop one from his though life of from thinking about his problem and connects him to his spirit which is the source of Life. Thus one feel at home when they are connected to their own spirit. But this can be done consciously by renewing the mind to allow the spirit to dominate it. and Jesus says, the words that i speak unto you, they are spirit and truth.
Music is energy and Music consists of waves (various pitches and sounds) which are excitating space.
Music is also consisting of rhythms and therefore is corresponding to the pulses of our body (heart and breathing etc.). This - I believe - is the key to their power.