While Pedals do not, by themselves, increase your range they are a great key in developing properly and therefore having a strong range. As Jesse McQuire said at a clinic I helped host, "If you want to play those notes way up there you have to play the notes way down there first, with a big fat sound." Claude Gordons books were excellent in this regard as he had you expand your range DOWN and UP using the pedal register. The key is in adjusting your embochure thereby learning to always find the center of the pitch where the note will be in tune and sound the best. Claude's books were masterful in doing this, as he forces you on the Part 1 to connect the pedals as you go DOWN and on Part 2 to connect the pedals as you go UP. The key again is in CONNECTING the pedal register to the other registers. The instrument does not make the pitch center. You do by adjusting your embochure. Pedals make you form things properly as these notes do not fall on the instrument naturally. You have to make the sound. When you learn to do this properly and CONNECT,it benefits you in ALL registers. Pedals are not so much about developing lip muscles as they are about developing many aspects of playing, number one of which is AIR.
As Mr. Gordon states about pedals in his book,Systematic Approach
to Daily Practice, starting on page 8:
When done properly they will
1. Correct your embochure-therefore, help high register.
2.Give you great command of your instrument.
3.Give you more power and fluency.
4. Aid your attack and sureness.
5. Develop better vibration.
6. Develop intervals and fluency.
7. Bigger sound in all registers.
8. Develop endurance.
Playing pedals the way Mr. Gordon taught them is time well spent. Just listen to Arturo. He does it beautifully.