Neil,
I am nearly ignorant on Tuvan overtones, but what I do know is that there are ways of sounding notes with the human voice that allows you to get two notes going at the same time. I believe the techniques were often devised by monks for chanting (obviously they had a lot of spare time on their hands) Tuvan overtones is just one of these methods. This next part may be a lie. I believe some of these monks are able to get three notes going at the same time.
If you like Gregorian chanting, these overtones may appeal to you.
Roger in Baltimore