Why do I get a strange spiritual feeling while playing or listening to music?

Music is one of the languages which communicate directly with the soul, through the medium of the emotions. This is why, when a prophet (Elisha) was not relaxed and needed to hear the counsel of God, he asked to hear music being played (2 Kings 3:15).

That reaction is simply a compendium of your particular cerebral-psychological-emotional make-up. Another person may get the same reaction when they stand on top of a mountain and take in the view or look at a beautiful painting.