If you're curious about overtone singing, listen to this -- it's insane: https://www.youtube.com/watch?v=vC9Qh709gas

The principle is actually the same -- she is modifying her singing apparatus to emphasize different upper partials that are already in her voice. Barbershoppers do this as well, though less explicitly (we do vowel matching, which helps emphasize upper partials to produce greater ring).

Here's a video from a perennial favorite quartet (the Gas House Gang): https://www.youtube.com/watch?v=pvYT_yWiLqU The top/tenor note is often the same note as the primary overtone produced by the other 3 parts (adding further emphasis to the overtone), but this effect is what gives barbershop the quality of sounding like more than 4 voices, and produces the "ring" in the sound.