One of these days I'm going to write what i know about various aspects of embouchure usage. Meaning what works within a given chops system vs. what doesn't. That second category being the ideas which while possibly helpful in a given case are less relevant to the general masses.
What I've seen from ALL the high note and other brass systems so far has been inadequate. How do i know this? Well because no one has talked about the basic REAL PHYSICAL principles of what goes on within a chop setting when it's placed upon the mouthpiece of a brass instrument. Had they done this we'd see a description of those elements defined in a way we can clearly understand.
Example: We all know that a stringed instrument (like the guitar) has a neck, bridge, nut, frets and tuning pegs. As well as the sound chamber and various other necessary parts that help the musician create music. There is of course is a vast difference between blowing air through vibrant lips and plucking the strings of a guitar. Not the least of which is that we can SEE those essential parts on the guitar. Except for the hand muscles and related motor neurons in the body of the guitarist all portions of the instrument are clearly visible from the outside.
Not so with the trumpet. In a brass instrument those physical parts which affect tone and (especially) range are enclosed inside the mouthpiece and mouth cavity. Most chop systems define what they call "proper" embouchure based only upon what the instructor or student can visually observe from the outside. "Two thirds upper, one third lower" or vice versa for example... And like the tip of the iceberg this approach is way deficient.
You may have noticed that a mouthpiece rim with a sharp bite makes for more "pop" in the attack. Know why this happens?
Same reason as a fretted bass pops better than a smooth necked fret-less bass. You didn't know that did you?
OK so the inner rim "bite" of your mouthpiece is somewhat analogous to the frets or nut of a guitar. Similar except that one can switch the frets on a guitar to change notes. On a trumpet you can't switch while playing. Would have to remove the mouthpiece and change the piece to larger, smaller, sharper, softer etc.
How to profit from this physical matter???
Just as the guitarist avoids any unintentional contact of his fingers along the vibrating length of his plucked string we can COMPLETELY RELAX that portion of our chops which rests inside the mouthpiece. Regardless of the register low to high.
Truthfully in order to blow in the extreme register of the trumpet we simply must leave our chops relaxed inside the mouthpiece. The ability to blow extreme register is in fact dependent upon how supple we can allow our chops to remain inside the mouthpiece. While we may and must reduce the aperture size in order to ascend but this is not controlled by the flesh remaining inside the inner rim "bite" of the mouthpiece.
Instead the aperture size is dependent upon the flexing of those facial muscles on or outside the mouthpiece rim. This facial control may or may not include some tongue movement but does not effect the chops from the traditional tongue arch idea. That and a mild jaw closure which pushes the teeth together (within acceptable limits) will change pitch. This jaw closure is only slight but always necessary.
When doing some portion of each or most these ideas one needs only to increase the air pressure to shift range. Yeah well you would need to practice for a while in order to coordinate these controls too. The amount of jaw closure and facial movements would vary from one player to another but each would be required.
What i just wrote above will always help you. At least if you desired to be a good lead player. You might not reach a Triple C with these ideas because a lot of chop settings can not allow this to happen*.
Sure we could go into the minutiae of other embouchure matters. Such as forward jaw vs. receded jaw, upstream, dry lips puckering vs, rolling. And in some cases these more detailed thoughts would help. the problem with them is these concepts fall into the category of what i would call "Deep Embouchure Physical Theory". Few people would understand them and even less would be able to apply them successfully at all.
Refute these ideas at your own risk. Accept them and you will find yourself and all your students gaining the simple grasp of the embouchure control quite quickly and easily. It's as simple as accepting that water seeks it's own level.
From that concept comes Maynard Ferguson's wise adage:
"Whatever (brass) system you choose to follow try and pick the one with the fewest rules"
See 0.37 minutes here: Maynard Ferguson Clinic: 03. The Warmup - YouTube
*Quote: You might not reach a Triple C with these ideas because a lot of chop settings can not allow this to happen.
"Deep Embouchure Theory" can explain why this is so, but is irrelevant to music. Who needs a Triple C anyway?