All registers are not the same. They respond differently to breath support and require different treatment to speak well.
It isn’t as much breath support as the CHANGE in breath support that helps us to play. Low notes respond better with no support and high notes need a lot. It is a sliding scale between these extremes.
I have nothing against the wedge except that it takes a long time to learn. So I teach the support that the wedge was based on.
Relax the stomach muscles. Tensing the stomach muscles does NOT create a smaller body cavity or pressurize the lungs to any great extent.
Bringing the abs in toward the spine and contracting the muscles around the girdle does create a smaller body cavity. That moves your guts and since the pelvic bones won’t let them go down; they have to go up. That makes the part of your chest cavity available for your lungs smaller. And that places the air in the lungs under pressure.
Pull the stomach in farther for each higher open note starting at the top of the staff. Pull it in fast and before the note starts. (The air has to start moving before you tongue.)
Jake (Don Jacoby) used to try to get people to use visualization to understand breath support. He used to tell use how far in feet we should send the note.
Based on this I started years ago to use throwing a baseball as an example of how much body/support we want for each note. I’ll give you an example.
If you were to drop a ball onto the floor you would just let it roll off of your hand. Jake used to say to let the low notes roll out of the bell and land on the floor.(That is like a Low G. I sigh to relax my breath for these notes. Just the weight of the shoulders moving down during the sigh is all the support they get.)
If you were trying to throw a ball to someone 4 or 5 feet away then you would use a slight wrist action to gently toss the ball. (That is a low C. Gentle and no muscular support.)
If I threw to someone 15 feet away then I would use my whole arm but again gently. (That is like a middle C again not really pushing with support.)
If I throw a ball 40 Feet then I use my arm and get some hip into it. (That is like a High C. I have now engaged support muscles but not to their max. I use the muscles under my navel to pull everything in and up slightly. The motion has to be fast but it isn’t far. When I relax the muscles above my navel and pull in with the muscles below my navel, I become skinny. (Sort of) The motion moves my internal organs and they really only have one way to move. They push against the diaphragm and in turn it pushes against the lungs and the air is compressed. If you do it slowly then you get very little help. If you do it very fast then you forcefully push high notes through the horn. )
If I throw a ball 80 Feet I need to put my whole body into it. I wind up, I step, I engage the hip… (That is like a DHC. I am using lots of breath support. I use the muscles under my navel to pull everything in and up a lot. The motion has to be fast and far. At this point I need some support from my back and sides. Everything below the ribs is contracting in but the front does the most work and moves in twice as far as it did for High C. Somewhere above High C we start adding support from the back and sides too. Squeeze the air from the bottom up.)
If I needed to throw the ball 200 feet. I need something else to help. (That is like a THC. I use the support and I add an actual crunching motion to increase the air compression. The crunch at the end is not often needed but useful sometimes. That is a feeling of the weight of the upper torso also squeezing against the air. It has to happen last so that it doesn’t shut things off. Some people use this really high and some for big leaps. I have learned to make my crunch always 1 full octave. No matter what I play when I crunch it goes up 1 octave. )
This is what Bud Brisbois used as well as many great teachers like Don ‘Jake’ Jacoby.