Forgive me. It's been quite a while since I wrote anything insanely technical. When I found out people actually read this, I became intensely self-conscious. It is more fun to just write whatever I want.
I used the term "falsettist" instead of "countertenor" on several occasions and thought perhaps I should try to see if anyone fully explains falsetto. Ugh. Unfortunately everything I find is nonsense, including Wikipedia.
Falsetto is not breathiness. It's not a register. It's a technique. It means that only the edges of the folds are vibrating and not the whole thing, specifically not the cartilages. It is generally accompanied by a relatively high larynx since the force of pulling the larynx down might pull you out of falsetto. Anyone can do it, I suppose on any note, but it is more easily identifiable when a man does it on relatively high notes.
David Daniels is doing it in this film.
But so is this guy. Skip ahead to 1:50. Warning. Not for the faint of heart.
I'd have to have a guinea pig to try this on, but can a man messa di voce from a falsetto into a normal tone? You'd have to pick the right note, I suppose.
Maybe there are other books. I haven't spent huge amounts of time looking for them. But for me the only real book on vocal technique is William Vennard Singing the Mechanism and the Technic. I have the 1967 version. If you want a complete explanation, see Vennard, but don't expect it to be easy to understand.
A countertenor is singing falsetto, and it is certainly not breathy. It has been a feature of certain pop singers. I'll try to find a good example. There's a song on YouTube called "Falsetto," which I will not post, where the guy sings most of the time in his normal voice and slips into falsetto to imitate a woman. The normal singing is breathier than the falsetto, resulting in an excellent comparison between the two methods.
Here we go. I buy this as falsetto.
I am baffled by the videos on YouTube purporting to explain this and not succeeding.