I was driven off this list by a deluge of Winton-bashing, Monette-bashing, etc nearly a year ago, but I could not resist sneaking back on. It looks just fine now. (I can't say I read everything though!)
Pedal notes: I have been doing the Claude Gordon exercises for a year or so now, and I think they are great. I do a session first thing every day. My tone is cleaner, I have better endurance and range. I have moved up to a Bach 1 mpc that gives me the kind of sound that I am after. And I have more top lip in the mpc than before.
The breakthrough comes when you can go from double pedal C to above top C without moving the embouchure. Particularly in the midrange there is a really sweet effortless feel to the sound.
I have a pet theory that I am bound to get some flack over: If you practice lip buzzing then you will not have good pedal notes. (Head down!) To me buzzing and pedals seem to be doing opposite things. Buzzing tightens up the lips whereas pedals frees them up. When I am talking good pedals I mean a big resonant in-tune sound from pedal C down to Fsharp, and lower. Playing a good (true) pedal (ie C or lower) is all about blowing air freely through the instrument and getting it to resonate to the point where your hands tingle. You can't do that buzzing.
While I am on this, I have some comments about Claude's video. There were some negatives. I found it disappointing that a man of his stature had to spend so much time running down other teachers. Then there were some things like "proving" that your lips move on the mouthpiece because you can not walk downstairs with straight legs! And his whole tirade about "diaphragm" breathing seemed a bit off the mark. His system of holding the chest out ensures that you can only breath with the abdominal muscles, which is what everyone means by using the diaphragm anyway. OK.
I have got that out of the way. The positive is that after sitting through the tape I went and picked up my trumpet and played like I had never done before! The big thing that really comes through watching and listening to him is blowing air through the instrument! It really works I tell you!
OK that's enough typing. These opinions are not worth your expensive ammunition. Cheap shots are welcome tho.
Cheers - Vere Smyth