The “other-worldly” sound of overtone singing is hard to master, say those who know a thing or two about singing. The technique is “native” to Mongolia, called sygyt, meaning throat singing in Mongolian.
Anna-Maria Hefele, a classical soprano who also plays a dozen or so musical instruments, has been practicing the art of overtone singing for over 10 years.
The skills she displays on the video far outweigh what the thousands of viewers, including musicians, thought possible for a human being. At the 25-second mark she starts off with the basics, but then the real show begins: she starts shifting the fundamental note, while independently controlling the frequency of the overtone.
In case this sounds confusing: every note has a fundamental frequency. For instance, an E in the third octave sits somewhere at the 40-42Hz mark. But every note also has higher, subtle frequencies at which it resonates – those are called harmonics. They are multiples of the fundamental frequencies (an E in the fourth octave would be somewhere around 80Hz, then 160Hz and so on). (Polyphonic German soprano does the impossible – sings 2 notes at once!)
Miroslav Grosser can teach you basics of overtone singing.
YouTube has many videos featuring “the original” Mongolian throat singing as well as several of its “derivatives” — Tuvan and Siberian in particular.