Mouthpiece-buzzing, the neglected weapon.
"Now, Phil, I need you to put your trumpet down for a while and let's play that Mahler on your mouthpiece." The instructor was the great performer/teacher Arnold Jacobs. My response was respectful and agreeable outwardly, but inwardly I was greatly annoyed. I was too impatient to stop music-making and just buzz. This was about to be a time-wasting exercise in humiliation!
Before I was permitted to attempt any Mahler, he had me buzz Christmas Carols. And it wasn't even in season! Actually, I knew I would sound bad, and that any listeners would be unimpressed with my pitchless chirpings. But I cooperated with the master nonetheless.
After a good 15 to 20 minutes of painstaking detail for PITCH, RHYTHM and TONE, we were both much impressed with the results. He was absolutely determined to make me hear and experience the difference, which is one of many reasons for his fame as an instructor.
Lesson learned: If it's sloppy on the horn, it will be even worse on the mouthpiece. Therefore, perfect the buzz, and the playing with the trumpet will be many times improved. Even the best instrument cannot make up for shabby input.
Skills developed: patience, improved listening, and the ability to focus on precision. The refinement that can be acquired by diligent mouthpiece work is amazing and well worth the time invested.
Note: It can be argued that there is a slight difference in mouthpiece tone production and actual trumpet playing. Regardless, we have seen that including good mouthpiece detail always improves the final product. And that's the buzz.