This article
http://www.sciam.com/article.cfm?id=the-human-instrument&ec=su_sing
in Scientific American is the first thing I’ve ever found that adequately addresses something I’ve wondered about for as long as I can remember: Given the nature of the hardware, why in the world is the human singing voice capable of so much power, range, and richness? Highly recommended reading.
That’s an intense article.
From what I read, sounds like they’re saying–
the human voice is not just like a saxophone (with a vibrating reed, and a tube for the sound waves to resonate in)-- it’s that the body of the saxophone is “rubbery” and the shape can be morphed at will. This produces a different kind of resonance than they previously thought it was. This information is new! 
I’ll have to get my mathematician husband to talk me through that. I understand “resonance” but this is “inertive reactance” 
The article didn’t mention the sinuses!
I’ve been in a church choir for the past 6 yrs and our director does as much teaching as she can. One thing she keeps reinforcing is that you can feel your voice resonating in different places for different pitches, and if you can learn to “send” your voice there, you’ll have a clearer and more beautiful tone. When we have trouble with the higher notes, she always says "pop it out the top of your head! ". 
I didn’t have a clue what that meant until one day I actually felt the sound in my upper sinuses. When I figured out how to “send it there” I got a couple more notes in my range. 