Exotic vocal

Little Jimmy Scott
Exotic? Yes. Female? Not really, but you be the judge....

https://www.youtube.com/watch?v=dDei1D72XAQ

https://www.youtube.com/watch?v=JtqGpgdD_6k

https://www.washingtonpost.com/entertainment/music/jimmy-scott-hard-luck-singer-with-a-haunting-voice-dies-at-88/2014/06/13/270725b6-48c3-11e3-a196-3544a03c2351_story.html

Throat singing? Tuvan throat singing??
Try Paul Pena in Genghis Blues. Pena, by the way, wrote the Steve Miller hit, Jet Airliner.
Not female, of course.

https://www.youtube.com/watch?v=itrN11AwNMo

Surprised no one has yet mentioned Bjork.  

Hey many still to mention...
Not only Bjork, but I believe Sinead O'Connor uses throat singing as well.

Hmmm.  Czarivey - didn't mention Bjork 'cause I associated her with throat singing but that's an interesting connection.  


https://en.wikipedia.org/wiki/Inuit_throat_singing

Jacintha
https://www.youtube.com/watch?v=yS69mWUgotw 

I have al of her SACD's.
Her semi-acapella version of Moon River is one of the finest. 
I really enjoy the deep intakes of air between passages.