I'm not gonna rehash the debate that's going on now about this FANTASTIC method book written by one of the best brass teachers ever to live. However, I do want to add one or two things. John touched on one of them briefly.
In the first part of every
lesson in SA, Claude has you hold the note for as long as you can hold
it and longer.
When you do this, you must keep your chest up while your stomach collapses in as the air empties out of your lungs. This method of practice is the ONLY method I've ever seen that actually develops the muscles of your stomach and surrounding your rib cage that are used to play trumpet. Basically, Claude is developing your lungs and muscles of the rib cage and stomach. To speak in terms of lip fatigue is to completely miss the point of these exercises, since there ISN'T any lip fatigue when you do them. You're resting as long as you play, and you're descending lower and lower, with a starting point of low C. Lip fatigue is a non-issue.
The other thing that this method of practice in the first part of the lesson does is it teaches your playing apparatus, by repetition, to keep your embouchure relaxed while you're blowing hard. The tendency, at least for me, was to over-tighten my embouchure when I would blow hard.
There is an important error in the book, however. It's actually an error of omission, but it's what I consider to be a big error. After you've rested 15 minutes after the pedal exercises, you ascend. When you ascend, you DO NOT hold out the note for as long as you can (as in the first part of the lesson). You merely establish the note and then stop, again resting as long as you played. Claude doesn't say to hold out the last note when ascending, but I think he should have made a note saying NOT to on the 2nd part.