This test packs a punch—not just in dollars, but in perception. Nora Ali pens a warm confession of skepticism: she played her trusty childhood violin since age 12, but now she's been handed a legendary $14 million Stradivarius.

The birth of the violin.

Antonio Stradivari is generally considered the greatest violin maker of all time. His violins are played by some of the top musicians in the world and sell for as much as $16 million. For centuries people have puzzled over what makes his violins so great...