SPOILER
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To upgrade the horn, take it to the shopkeeper on the raised platform on west side of Waulkeen's Promenade. When you speak to him, one of the dialogue options will be to ask if he makes any magical weapons. He will tell you no, but he can make musical horns. You also need gems and money - a diamond to upgrade to silver, and a beljuril gem to upgrade from silver to iron.
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Time is an illusion. Lunchtime doubly so.