Hi,

” don’t feel I am squeezing – but the small amount of muscle activation required to hold the shape as air passes through (passively) gets harder to hold the higher i go.”

My teacher made me remark once that even for low register at a big volume, the corner strength is really the thing that can be failing. I couldn’t make a really big F# at the same volume because my corner couldn’t hold it.
So all of this to say that yes, Greg emphasizes on shape and air, which is really helpful because too much emphasize is done on strength sometimes.
But I remember one video of Doc Severinsen sayin at the end that yes, there’s undoubtedly a corner strength involved so that you can hold a note, whatever the pitch or volume.

Yes, at some point you will hold a C in the staff and the lack of air will stop you. But at some point, I guess in the upper register, as there is less air, it’s your muscles that will hold you I guess.
The more you train, the better you get, but you have to train smart. Overtraining leads to failure. I haven’t been playin my trumpet for a while, but I have been reading books about training for mountaineering and applying those principles as well in my weekly training.
I will risk an analogy, but it is really easy to get into overtraining and get quick results at some point. But by overdoing your training workouts, maybe after 6 month, a year, or 18 month, your body will crash, eg you’ll get injured or fall into a neuro-physical fatigue that it will be hard to get out of.
All of this to say that the exercices in windworks explain well that analogy with the singing C series. Sometimes, we can blow a note, let’s say a A above the staff. And by doing Singing C-series exercices just proves someone that he actually can do barely a D above C in the staff at a low volume. It is somehow the exact same thing as in sport training : we build something to quick and we plateau or crash. I have to admit I crashed !
It is a bit frustrating because we want to play some music and we are not ready for it.
So yes, we have to train smart for trumpet (or any instrument in the end). The better you train, and the more efficient you become. ANd the less tiring it is gonna be for your embouchure. But still, we have to build those embouchure muscles gently and slowly. And yes, corner will burn sometime. Our biggest enemy is our willing to improve too quick and don’t respect the time our muscles need to build up : a lot of rest is required.
I hope I was no too much out of the topic and that it does make sense.