Everyone has their own approach to the mouthpiece. Mine is no different to those who espouse proper mouthpiece buzzing habits as well as indoctrinating those habits into everyday performance practice.
Below are two exercises that must be employed every day. It is important to expand your range while playing on the mouthpiece. Doing so eliminates variables and insists on YOU creating the correct sound quality rather than relying on the horn.
Make sure you are holding the mouthpiece correctly. Use your index finger and thumb to hold the mouthpiece on the shank as pictured below.
Gripping the mouthpiece any other way will invite un-needed pressure into the exercise.
Before diving into the exercises, first, make sure to know what to practice. If you are new to mouthpiece buzzing, skip the first exercise entirely. In fact, I advise you to go back one page and click on the 3 note warmup. Play that exercise on the mouthpiece until you achieve the sound quality you desire. Secondly, make a point to listen for “white noise.” This is a sound quality that occurs while inefficiently buzzing. It is a waste of air and effort. You can find this sound by simply blowing through the mouthpiece without buzzing. Listen for that sound while buzzing.
If “white noise” is occurring, unused air is flying past your aperture. Back off on the amount of air you are pushing through the mouthpiece and concentrate on how your aperture is manipulating the airstream. It may seem counterintuitive, but relax your embouchure and make the air stream do the work.