Lord of the Rings is full of songs sang by a lot of people. Tolkien never mentions anything about musical isntruments. Did they use any? Eru and the Valar didn't need instruments. But what about Elves, Men and other creatures in Middle Earth?
I do wonder if they left their "viols as big as themselves" in Bag End when they left on their quest?"Now for some music!" said Thorin. "Bring out the instruments!"
Kili and Fili rushed for their bags and brought back little fiddles; Dori, Nori, and Ori brought out flutes from somewhere inside their coats; Bombur produced a drum from the hall; Bifur and Bofur went out too, and came back with clarinets that they had left among the walking-sticks Dwalin and Balin said: "Excuse me, I left mine in the porch!" "Just bring mine in with you," said Thorin. They came back with viols as big as themselves, and with Thorin's harp wrapped in a green cloth. It was a beautiful gold-en harp, and when Thorin struck it the music began all at once, so sudden and sweet that Bilbo forgot everything else, and was swept away into dark lands under strange moons, far over The Water and very far from his hobbit-hole under The Hill.