This video of a cymbal vibrating in slo-mo has been making the rounds for the past few days. It reminded me of an article I read once which discussed synthesizing the sound that cymbals make. After some searching, I found that article. It’s by Gordon Reid, whose “Synth Secrets” column in Sound on Sound is required reading for anyone who would seek to make their own special kind of noise.
Gordon’s article goes into the basics of how a cymbal vibrates, but doesn’t actually tackle any equations. As he says, that would go beyond the scope of his article. So I found some equations for you too (PDF). Even if you don’t know anything about differential equations, you might want to check that PDF out, because it has some neat photos of the vibration modes of various things you hit with a stick.