Yea, David Sanborn has the same kind of effect. I myself strive everyday to try to get to an altissimo G. On my tenor (which is brand new, no pad leaks or whatever, not that I think it matters) I squeaked it out once or twice but then it cut out. So that must mean something. The thing I've found that has helped me in all aspects of my playing is a new embouchure. I'm not sure if you do it, you might, and I'm pretty sure the knights will agree with me on this. Instead of curling your bottom lip over your teeth and resting the mouthpiece on that, try forming your lips like you're saying "ooo" and put the mouthpiece on that. Your bottom lip now cushions the reed but allows it to vibrate a little bit more. I've found this to help out even in the middle altissimo range (D, E, F). Overall I think your sound will change for the better. We can keep swapping stories. Even if they are failures, we all can learn from one another. Good luck and cross yer fingers.

It's kind of a combination of airflow, jaw pressure, and your throat. A similar effect would be when you play, say, an 'e' on the staff and "lip down" to where the lower octave begins to come out. It's not growling, it's just allowing some of the partials to come out...it's one of those things that takes a while to master, but when you do you can do it pretty easily. Something that really helps is to master playing overtones (the old 'top tones' trick of fingering low Bb and playing bugle calls without moving your fingers). Working on overtones will also help make your sound become much richer and fuller.