dennis hill wrote:
>one reason for the confusion is that you can find 3 very good teachers,
>with 3 divergent opinions (trumpet voodoo?) plus some pros that don't
>believe in them at all.
I think it is possible to become a very good player without ever playing a pedal note. However I think that there are some exercises employing pedal notes that can provide big benefits to many players.
Pedal notes are not magic. It's not the fact that you play them, or don't, that makes all the difference. The key IMO is whether you have an efficient "embouchure approach" to playing trumpet. It is extremely difficult for even the best teachers to describe an embouchure approach so that a given student understands and can implement it. So any exercise or technique that helps to train the student's embouchure to do things correctly is of great value.
To me, pedals are like "isolation" exercises to a weightlifter. If you want to be sure you are exercising your bicep, you can design an exercise where only that muscle is used (oversimplification I know), overcoming the tendency to "cheat". In a way, pedals can be used as an isolation exercise. If you want to play a false-pedal-E (for example), you MUST adjust the pitch with the lips and oral cavity. If you want to play a scale from pedal C to standard low C, you must form each of the notes in the first half-octave with the lips and oral cavity. You cannot get lazy and use the same formation for adjacent notes, as many beginner-to-intermediate players do in the normal range--resulting in uncentered sound and frequent "clams" due to a slight mismatch between what the embouchure is trying to play and what the horn is trying to play.
As for example exercises, try playing two-octave arpeggios, up and down (starting on pedal C and going up, play C-E-G-C-E-G-C, then back down: C-G-E-C-G-E-C, all half notes... then up a half-step, then up another half-step, etc) beginning on pedal C (or lower if possible), using the same fingerings as for the non-pedal notes an octave higher. Do not permit yourself to reset the mouthpiece between notes. Don't just play the arpeggio, PERFORM it. Work at it until you can go all the way up on a single breath, then all the way down on a single breath. Then all the way up and back down on a single breath.
Also try the Clarke Technical studies (#1, #2, #3 etc) in the pedal range. A good place to start might be Clarke technical study #2, in the key of D, starting on the false-pedal-D. Try it playing the F# with just 2nd valve and the G open. Very slowly at first, working for precise intonation. And work at it until it sounds like music.
The purpose is not necessarily to be able to use these notes in performance. Rather, it is to train the embouchure to adust for each note, and to be able to ascend throughout your range, and descend again, using the same embouchure setup. (This is really hard to describe...) For example, consider Arban's Characteristic Study #1. It begins around low C. You do an arpeggio to G above the staff (a couple of times), then noodle your way back down from the G to low C. The goal is, when you return to the low C, your embouchure is the same as it was when you started on the first C--relaxed, right in the center of the note. And the same for every note in-between. If you correctly adjust the lips and oral cavity (tongue, soft palate) to get each note centered, there will be no clams and no unclear notes. Each note will speak.
I think the pedal exercises I described can contribute a lot to developing this technique.
I hope this helps!