The goal of BE is to use these and other exercises, plus specific tonguing and breathing techniques to give the brass player the technical skill to use a continuous flexing of the lips to navigate the full range of the instrument minimizing and ultimately eliminating awkward embouchure changes.
In the quote below, David G. aptly described this goal as "unifying the embouchure" in his memory of a past insight that embodies a key principle of the BE development system:
For some unknown reason . . . I remembered that years ago someone wrote to the horn list about having a break in embouchure somewhere in the midst of our tessitura - a point where he/she had to change embouchures. I wrote in to recommend practicing playing a simple scale from the bottom to see where the break occurred, then playing a scale from the top down to see where the break occurred, and assuming that there was overlap - there had to be - that it was worthwhile to extend those breakpoints as much as possible until it might happen that there would no longer be any break point. There was a bit of other advice, but the one that stood out in my mind was the one that pooh-poohed the notion of unifying the embouchure. Well, that's a chortle. I guess the idea was a very primitive first pass at BE.
Thanks for sharing, David.