There are many ways of producing overtones in music. Anyone who vibrates air in a tube for a living produces overtones as their way of making music. THis includes brass players, didgeridoo, alpenhorn and so on. Buglers get their notes strictly from overtones, as they have no keys on their instruments. And of course, vocally, it is possible to produce overtomes as well, giving the eerie sounds of Tuuvan throat singing.
i love overtones because they remind me that there is so much more to the music than what is immediately audible. It is a good teaching that the ethereal lives in the mundane.
Today I stumbled on the site of the Swiss duet Stimmhorn and I found some amazing overtones. Have a listen for yourself.