As you might know, analogue synthesisers used to do this in reverse, start off with a fundamental note, a sine wave, and mix in higher frequency harmonics in varying proportions until it sounded like a rather naff version of an instrument. Then you'd apply an envelope to replicate the attack and sustain characteristics of an instrument, slow attack for a bowed violin, fast for a xylophone.
Going the other way there's an device called a vocoder which started out as a form of lossy analogue data compression , these get some use when people want an 'angelic' or 'robotic' vocal effect.
If you're interested in hearing some, there's synths and vocoder on the soundtrack to the film 'clockwork orange' and probably plenty of other places too. You can *probably* download a vocoder effect for your pc.