Ok, I wanted to start a nice constructive thread! I feel that I sorta owe that. So let's pose a question: how do we hit high notes? Do we do it by making the lip muscles tight - via tension (force)? Or, is there another mechanisim that works here?
Lets use a model, albeit a rather oversimplified one, to begin the discussion. Let's assume the lips work like a guitar string. The more tension in the string, the higher the note, correct? We all know how string players are "supposed" to "tune" their instruments!
Let's assume for the moment that the lips work the same way.
There is an equation for this. f2/f1 = (T2/T1)^.5. f = frequency and T = tension. Ok. Now, let's recall what an octave is. Each time we double the frequency, we hear a new octave.
Now, let's see what this means for the trumpeter. Let's consider a pedal C. A double high C is 4 octaves higher. So if f1 is pedal C and f2 is double high C, ratio of frequencies is 2^4 which is equal to 16. So the frequency of a double C is 16 times that of a pedal C.
Now, lets assume we use 1 pound of tension to produce the pedal C. This is a convienient number, and may not be too far off to keep the lips together as we blow through the horn. Well, then T1 = 1. So what does T2 have to be? Subbing in, we get, (T2/1)^.5 = 16 or T2 = 16^2 = 256 pounds!
Now, I can hit double C's but I'll guarantee that I can't bend over and suck up on a 256 pound barbell with just my lips!
So what else can be going on? Well there is another equation that descibes string behavior. I'm going to simplfy it a bit, so I'll assume the length of the string doesn't change length. The new equation that applies is, f2/f1 = (m1/m2)^.5, where f = frequency and m = mass of the vibrating ting (lips being loosely modeled by strings).
Using the same analysis we use above yeilds m2 = 1/256 of m1. THIS is can do! All I need to do is make the vibrating mass of my lips LESS, independent of tension. Now, If some tension gets in there, it can help the frequency go up a bit, too.
Now ho do I do that? This is where it gets individual. Also, I'm going to add some more posts as ideas bubble to the surface.
Personally, I strive the "vibrating aperature" smaller as I ascend in pitch. This reduces the vibrating mass. I personally do this by bringing my lower lip up slightly towards the upper lip. As i do so, the lower rim of the mouthpiece tends to follow, in part (there is some slippage), my lower lip. This means, that as I ascend in pitch, my bell goes DOWN. Hence, my pivot.
There's more, but I'll post this ow and lets see what, if any discussion, ensues.
Peace, all!
Nick