There has been a lot of misunderstanding of the role the mouthpiece plays in brass playing. It was and is generally thought that the best approach is what used to be called the “no pressure system.” Players were told to suspend the horn on a string and play it with hands held behind the back. This sounded like an excellent way to get the lips vibrating freely without the mouthpiece being used as a crutch. Today that has evolved into the concept of buzzing without the mouthpiece or any part thereof.
What was not understood however, was a principal of basic physics; to every action there is an equal and opposite reaction. That opposite reaction must be accounted for somewhere in the body. If it’s in the embouchure area we are in good shape. If it’s somewhere else in the body it’s a big problem, because that will put a big damper on resonance. Try buzzing without the mouthpiece and try to stay relaxed with the diaphragm and torso muscles. It’s almost impossible because something has to take up the slack of the opposite reaction to the air flow forward. Now imagine playing fortissimo, high and staying relaxed without the mouthpiece, impossible!
A good way to think about the role of the mouthpiece is; hold your arm out in midair and concentrate as hard as possible on keeping the fingers absolutely still. Now imagine someone trying to move you by pulling. That is what blowing air through a tube equates to. The action of blowing air forward causes the mouthpiece to depart from the face, disrupting the vibration of the lips. Now lean against a wall with your hand and arm to keep the hand and fingers still; that’s what the mouthpiece does. We don’t push against the wall, just lean against it with the weight of the body. The wall stabilizes the hand and fingers and the mouthpiece stabilizes the embouchure so that the lips can vibrate in a continuous manner. This allows the rest of the body to stay relaxed and lets the sound resonate in the most efficient way possible.
An important basic concept to remember is; do as much work from the chin up as possible. For you trombone players this includes the slide arm as well! The current worldwide style of moving the slide fast and muscularly plays havoc with the embouchure. Besides, speed comes from relaxation, not tension. I like to see someone with firm corners in the embouchure and a completely relaxed hand and arm on the slide. This lets the rest of the body become a “concert hall’ with lots of warm reverberation. As we ask more of the embouchure in the form of more volume and/or more extremes of register the embouchure needs more support or stability. This comes from increased mouthpiece pressure to keep the embouchure still. The more extreme the dynamic or register becomes, the more stability the embouchure requires. This is like leaning against the wall as before, but someone trying to pull you away from it. More seal is needed to the wall (and mouthpiece) to keep the hand (and embouchure) still. When I use more mouthpiece pressure to keep the embouchure still so a note will stay steady, I always feel like I am leaning on the mouthpiece or going to it, rather than bringing the mouthpiece to the embouchure. This is a subtle but important mental difference. It helps to avoid too much pressure or seal for the amount of air flow forward. As I’ve said before: producing a sound on a brass instrument is a combination of 3 things; sufficient firmness in the corners of the embouchure, sufficient air flow forward and sufficient seal backward. (Remember the opposite reaction law?)
Those 3 components must be in equal and correct balance to achieve the optimum result. When they are, the rest of the body can be at rest and this will produce the most amount of resonance for the least amount of work, something we all should aim for.
Buzzing the mouthpiece is an excellent way to increase lip flexibility and increase vibration. I believe the time spent buzzing on the mouthpiece is more important than what is played. The best way to maximize ease of sound production is to buzz at a soft dynamic and try to produce maximum resonance for a minimum amount of energy. A player should try to feel like the rim of the mouthpiece is becoming a part of the lips. I remember years ago my friend Joe Alessi saying he was on the way to a concert and had a drive of several hours. He buzzed the mouthpiece all the way to the destination. When he arrived he said “I was a different player.” Great advice.