msu_ggtrumpet,
A piece of information that I found very helpful was something that David Krauss (Metropolitan Opera) said which relates directly to your question. He said, “It’s common to work too hard and make the aperture accept more air than it needs to respond based on excessive movement.” This is especially true in the lower register, which will then hurt you as you try to ascend.
About 6-7 years ago I found the James Thompson Buzzing Basics book. He mentioned that some players use more air than lip and other players use more lip than air (I was clearly in the first group). The key to having everything work well was to discover the appropriate balance between lip and air.
When I play today, it feels so much different than when I was struggling to get the mechanics working properly. I would describe the way that I produce sound today simply as EASY.
Coming from the more air than lip camp, I found that keeping the corners slightly firmer (NOT tight) to be very beneficial (I like the cooling soup analogy). I also incorporated breath attacks (starting the note without the tongue) into my daily practice (this helps to reinforce the slightly firmer corners and improves response so I don’t have to “blow harder”). Letting the air out instead of “pushing” the air out was also an important component for me to add into my playing so that I could get the sound I heard from my instructors and from my favorite performers.
When I am in the resonant center of the sound with the proper set up (firm corners, letting the air out), I literally don’t have to do anything more than “think” the interval and it happens effortlessly (“moving from note center to note center”). Knowing that it can be easy was really the key for me. Then reading to find out how I needed to modify my thinking and time with the appropriate exercises made the difference for me.
You might enjoy some further posts about
David Krauss and
James Thompson’s Buzzing Book with respect to air and sound.
Hope this helps!