I have another blog about pedals. Check the archives. This one is just a short post about the fingerings I use because I have changed them over the years.
OK, we all know the fingers down to low F#. From the F just below that (a non resonant note in any way) I tend to use the fingerings of the octave just above to keep track of where I am, but they are utterly meaningless from a note production point of view since the wind column is NOT resonating in any way. There is no standing wave. You can use any fingering you want to down to the C# below low F#.
The business gets a little weird when we get to the so called pedal C. On a TRUMPET (and to a lesser extent on a cornet) as soon as you attempt to go from that C# below middle C, by going to open horn (the next fingering in the pattern), the note will try to drop down a half step flat - pedal B, not pedal C. This is correct and follows the actual resonance pattern of a trumpet.
Claude Gordon said that the pedal C is very flat and that we just have to learn how to play it in tune. One can certainly rationalize things this way, if they want to. I choose to stick with an acoustical model as it makes more sense to me scientifically.
Yes, I can play the pedal C in tune, but the timbre is different. This is because there is no "pedal C." You are lipping that B way up onto the topside of the natural pitch - an extreme pitch bend. It would be just as effective to just use 123 and lip it down to the "pedal C." In fact, you can use any fingering you want to for the "pedal C" because there is no natural resonance on a pedal C.
So, I use open or 123 on pedal C. Then, as I progress downwards, I use open for pedal B (an actual resonant note) and progress downward to 123, which is actually a pedal F (not F#) .
Below that I use the regular fingerings just s place markers, again, because the horn is not resonating anymore. The note production is all a matter of embouchure control.
A nutshell review of the acoustics brings it all into focus. The trumpet produces the series it does by taking a fundamentally closed ended cylindrical pipe (a closed end regiment because there is ALWAYS a pressure antinode at one end - the mouthpiece, and a pressure node at the other - near the bell) and correcting the odds only series by the addition of taper to the tubing - in particular the bell, and mouthpiece/lead-pipe combo. The series works out nicely but the bell portion doesn't sufficiently correct the tuning of the low end, hence the apparent extreme flatness of the actual fundamental modes. This is why it is a chore and more of an athletic stunt to do a lot of performance in the pedals. Most composers skip those.
Of course, everyone who plays flugelhorn knows that the open pedal C is virtually in tune. This is due to the far more extreme taper to the tubing, in particular the bell. So, on flugel, I just use the regular fingerings for the tritone from pedal C down to pedal F#.
Check out the John Backus book, "The Acoustical Foundations of Music" for a more thorough discussion.
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