In its simplest terms, playing the trumpet is transferring air from your lungs through the horn and out. The purest, fullest sound is achieved when the air meets the least resistance. Posture, breathing, muscle tension and mouth position are major factors that change the tone and sound. Michael Droste in "The Ultimate Warm Up" says playing high notes requires a combination of tongue and lip position, and releasing small amounts of air super fast.

Air Compression

Playing the double C on a trumpet in a full, clear tone is the ultimate achievement, and it takes practice, says Clint "Pops" McLaughlin of the Trumpet College. Exercises that strengthen the lips, teach control of breathing and even make the hands stronger to enable a tighter grip on the horn all help the player produce a pure high tone. Breathing is the basic ingredient in trumpet sound. Without air, there is no sound. Breath control is not natural and must be learned and practiced. Droste says a trumpet player should think of his lungs as a high-pressure air tank that releases short, fast bursts to produce high tones. Trumpet players benefit from practicing yoga breathing, McLaughlin says. By filling first the diaphragm below the lungs, then the lungs up to the collarbone and releasing the air slowly, in stages or in one great expulsion, you can learn breath control.

Practicing

McLaughlin lists three things that prevent a player from reaching high notes: inadequate air speed; lips that separate; and compressing the lips too much with excessive pressure on the mouthpiece. He has students practice arpeggios using minimal lip pressure on the mouthpiece, producing the notes with air pressure alone. McLaughlin has his students "blow" their notes five feet in front of the trumpet, then 10 feet, then 20. He lights a match to show them they can blow it out using their breath. This increases their air control for the high notes.

Exercises

Exercises for the lips improve the embouchure, the mix of facial muscles that control how the air compressed in the lungs gets to the trumpet. High notes are produced when the tongue arches. Start with a relaxed "ahhhh" and raise the middle of your tongue. As it lifts, it compresses and speeds up the air, changing the pitch to a high "eeee." Put a pencil between your lips and push them together. Hold the pencil straight out for 3 to 4 minutes a day. The muscles that burn are the ones used to play high notes. Practice playing so softly that you can barely hear the notes. You use the same lip opening to play soft and high notes. McLaughlin recommends erect posture to keep the airways open, extending the lower jaw slightly to open the esophagus and using just a half or quarter breath to produce pure high notes.

Source:

Trumpet Studio: The Ultimate Warm UP.

Pops Trumpet College: Tongue Arch & Hiss.

Trumpet Studio: High Note Range Playing.

More Information:

Pops Trumpet College: Air on the Move.