Now the Spirit of the Lord had left Saul, and the Lord sent a tormenting spirit that filled him with depression and fear. Some of Saul's servants suggested a remedy. "It is clear that a spirit from God is tormenting you," they said. "Let us find a good musician to play the harp for you whenever the tormenting spirit is bothering you. The harp music will quiet you, and you will soon be well again." "All right," Saul said. "Find me someone who plays well and bring him here." ....Whenever the tormenting spirit from God troubles Saul, David would play the harp. Then Saul would feel better, and the tormenting spirit would go away. (1 Samuel 16:14-17, 23)

This passage clearly shows what an influence music can have over our emotions. I have always felt a little sympathetic for Saul, because I know the torment that anxiety and depression bring. I also have experienced the relief that music brings to this "spirit from God."  My Bible has a note that the tormenting spirit was a result of Saul's disobedience, and is not stating that God was tormenting Saul. It's a little tricky here---one would think by this translation that God was tormenting Saul, but God doesn't do that. He was allowing Saul to experience the consequences of his actions. However, David showed Saul much kindness by playing for him.
I've also come up with a theory that music is good for my chemical imbalance. I admittedly listen to a lot of music during my time off, but I think it keeps my spirits up. I'd kind of like to hook my brain up to electrodes and see what parts of my brain lights up when I'm listening to my favorite music, and what parts light up when I listen to music I can't stand. The results would be fascinating.
However, there is a time when music can become tormenting in and of itself. In Psalm 137, the psalmist writes (sings??):

Beside the rivers of Babylon, we sat and wept as we thought of Jerusalem. We put away our lyres, hanging them on the branches of the willow trees. For there our captors demanded a song of us. Our tormentors requested a joyful hymn: "Sing us one of those songs of Jerusalem!" But how can we sing the songs of the Lord while in a foreign land? (1-4)

This was obviously written after Jerusalem fell to Babylonia, and the Edomites came in and looted. Israel's tormentors demanded a cheerful song to add insult to injury. Their city was destroyed, families and lives were destroyed, but this was not enough for their enemies. No, they had to taunt them as well. I could see where music would be intolerable in this situation. However, this was not the end of the story. Babylonia eventually fell, and has never been rebuilt to this day. God has the final say, and on the day Christ comes to redeem his church, the music would be absolutely amazing and unlike anything heard before. Praise God!