I would urge you to read Andrew's short post first and then come back to this one.
Deuteronomy 31: 15,19
Then the Lord appeared at the tent in a pillar of cloud, and the cloud stood over the entrance to the tent.
Now write down this song and teach it to the Israelites and have them sing it, so that it may be a witness for me against them.
2 Kings 3:15
But now bring me a minstrel. And it came to pass, when the minstrel played, that the hand of the Lord came upon him.
1 Samuel 16:14-23
Now the Spirit of the Lord had departed from Saul, and an evil[a] spirit from the Lord tormented him. Saul’s attendants said to him, “See, an evil spirit from God is tormenting you. Let our lord command his servants here to search for someone who can play the lyre. He will play when the evil spirit from God comes on you, and you will feel better.”
So Saul said to his attendants, “Find someone who plays well and bring him to me.”
One of the servants answered, “I have seen a son of Jesse of Bethlehem who knows how to play the lyre. He is a brave man and a warrior. He speaks well and is a fine-looking man. And the Lord is with him.” Then Saul sent messengers to Jesse and said, “Send me your son David, who is with the sheep. ” So Jesse took a donkey loaded with bread, a skin of wine and a young goat and sent them with his son David to Saul.
David came to Saul and entered his service. Saul liked him very much, and David became one of his armor-bearers. Then Saul sent word to Jesse, saying, “Allow David to remain in my service, for I am pleased with him.”
Whenever the spirit from God came on Saul, David would take up his lyre and play. Then relief would come to Saul; he would feel better, and the evil spirit would leave him.
One theory I have about the significance of music is that music is not merely some "right" brain experience, that there is a "left" brain element. The composer Paul Hindemith wrote that in order to perceive any emotional impact for music we must be capable of forming a musical impression within the memory through which we can develop emotional associations. Realizing that not many people thrill to Hindemith's symphonic suite Mathis der Maler I nevertheless suggest that Hindemith's proposal that emotional engagement with music is predicated on the understanding of the mind before the heart can be stirred has merit.
I would build a step or two beyond Hindemith's ideas and away from them. I happen to think that where some people want to go with these sort of ideas would be to try to prove from "nature" that this or that method of pitch organization is the "right" one. Believe me, I've seen it done and it tends to be done for the relatively recent innovation of major and minor diatonic keys by people in Idaho who don't know as much musical history as they may think they do.
Now, having said that, what I think can be said is that associative memory is a vital component of music and that this can be what makes it so powerful. God instructs Israel to learn a song so as to have it be a witness against them both to remind them of the Lord and to remind them of their wayward hearts. The prophet Elisha sent for a musician and as the musician played the hand of the Lord came upon the prophet. Saul found the Spirit of the Lord left him and was replaced by an evil spirit from the Lord, an evil spirit whose torments were ameliorated by David's music.
I leave it to you, dear reader, to look into ways in which music is considered to have therapeutic and restorative effects. The power of music to lodge in the memory is such that even people whose memories have been ravaged by Alzheimer's or dementia can up to a point remember their favorite songs. Though I admit I don't get this part, lovers often have songs they share through which hearing the song reminds them of each other. Perhaps I may get that legendarily potent catalyst of associative memory some time in the future, perhaps not.
The Psalms are an entire collection of texts that were set to music, music which was obviously intended to impress within the hearts of God's people a memory of God's ways and nature.
This may risk being too sweeping an observation in light of the reality that there have been protest songs but generally speaking music tends to be about the things that are most ritualized into our societies. Music may be thought of as a giant collection of the songs we sing about the things and people we hold dear, the things and people we love, and the values and people and experiences we want or cherish. We tend to imagine this will apply to the most high-minded ideals and values which was why Hindemith writing an opera with an aria devoted to praising hot running water and indoor plumbing was a subversive gesture. We still prefer to have our songs be about endless love and not flushable toilets. We still want our songs to be about freedom and romantic love and ideals rather than about dishwashing detergent or baby wipes or toys.
But we still remember those jingles, don't we? More than meets the eye, right?