I stopped to write about strange, often abrasive voices once, and there are some peculiar voices I did not mention, and one I was unfamiliar with myself, that was mentioned to me outside the comments there.
First was one I'd heard about repeatedly anyway, and then a friend told me was a perfect example of peculiar voicing after that article. I picked up a few of her albums on and around Record Store Day, and discovered that, indeed, her voice is odd, though, as is often the case with me, didn't faze me beyond recognition of its oddity: Kate Bush.
She had a huge hit with "Wuthering Heights" (which was apparently an achievement in many senses, as the first self-penned female #1 in the UK), which should make it clear enough what's odd about her voice:
It's operatic in the dramatic sense, and otherwise filled with that kind of melodrama that fits and describes her music appropriately.