My understanding / recollection is what you’re referring to is “mouth compression”.
Greg talks about this in the Ruby or Emerald (or upper levels) levels, if I recall correctly.
Lately, I’ve been playing a shallow “lead” mouthpiece and have been encountering this both through purposeful experimentation AND accidentally–given the ability of the new mouthpiece to compress air more than a deeper cup mouthpiece.
With a little additional squeezing from the sides of the mouth (cheek muscles?), I’ve been accidentally and intentionally getting some notes above High C with relative ease.
I’m still learning how to use this effectively myself, but I have seen some glimpses into how effective this can be.
I believe some attribute the ability to do “circular breathing”, which is using mouth compression to expel air into the mouthpiece/instrument while simultaneously breathing in through the nose, to mastery of the extreme upper register.
This new shallow mouthpiece has been interesting–I’m definitely getting the sensation that less air is moving through the instrument the higher I play, it’s just faster. The higher notes don’t seem/fell harder to hit from a strength standpoint, which is helping avoid the temptation of clenching my throat and tensing the lips to get “up” there…it seems to help by thinking of singing as I play, sometimes using a “h” (which, admittedly does probably start to involve Active air, but this is above High C…). I saw somewhere that a player described high notes as not being “higher” or harder, just “closer”–I like that as it does seem to me that the vibration begins happening more and more inside the aperture the higher I go. I feel that I’m kind of “anchoring” things with the aperture corners and bottom lip/jaw and leaving the top lip as relaxed as possible.
The biggest thing though, for me, is taking a big breath and releasing the “weight” of that air through a smaller aperture (compared to the next note down, etc.) and supporting the air “faster” not blowing more air through the aperture. The higher notes seem to me to be much more resonant and seem louder despite using less air, which is compounded by the shallow mouthpiece I’m using–it can be quite loud, actually, without trying to play loudly.