For any brass player, a strong high range can be a great confidence booster. Conversely, a weak high range can be terribly frustrating. Many players, especially younger players, tend to obsess over high range. The best advice is to BE PATIENT! It takes time and diligence to correctly build a strong high range.
SHORT CUTS
It can be tempting to try a shortcut to achieve quick results. Two shortcuts
are commonly used:
(1) increased mouthpiece pressure
(2) a "smiling" embouchure.
Both of these shortcuts may yield results at first but lead to dead ends.
For more information, see the sections on embouchure formation and mouthpiece pressure.
AIR
One of the keys to a strong high range is a fast "jet" of air flowing past the embouchure. Take a deep breath and blow focused air. Pretend that you are trying to blow out a candle in the distance. Often I find that students' concern about missing a note causes them to hold back their air and attempt to "pinch" the note out. You can't "back into" a high note. Take a deep breath and go for it.
Another common mistake is to confuse the increased back pressure of a high note with static internal pressure set up within the body. Keep the air flowing.
Get two straws: one regular straw and one of those tiny straws
used to stir coffee. Try placing the regular straw in your mouth and blowing
through it. Now do the same with the coffee straw. You will encounter greater
resistance with the coffee straw. This increased resistance is similar to
that encountered as you ascend into the high range.
This exercise may be useful in two ways: (1) It can used to catch and prevent
sympathetic muscle tension in the face and throat during high notes, and (2)
it can be used in alternation with high notes played on the instrument to
reinforce the concept of fast flowing air (vs. static air pressure). This
second point may require more explanation. Try going back and forth between
playing a high note and blowing through the coffee straw. As you play the
high note, imagine that you are blowing through the straw. The air encounters
resistance but continues to flow.
PATTERNS FOR HIGH RANGE DEVELOPMENT
To develop high range, choose patterns that ascend gradually. For example, you might try a series of lip slurs on the overtone series. Start in 6th or 7th position and then repeat the ascending slurs in successively higher positions. You may also try playing legato scale patterns that smoothly ascend into the high register (if you are comfortable with the slide positions!). It can be helpful to play these patterns glissando without the tongue interrupting the air stream.
If you are stuck on a particular note, try sliding into it from a longer position. For example, if you can't get a high G (sharp second position), you might try playing an E-flat in sharp 6th and then sliding into the G.
Long glissandos on the mouthpiece can also be helpful. These patterns are sometimes referred to as "sirens" or "arches." Start in the mid-range and smoothly slide up and then down again. Keep the glissando continuous and don't pinch off the air.
One unusual exercise is to "rip" up through the overtone series with abandon. Start on a mid-range note and quickly slur up as high as possible. Start this exercise out in 6th or 7th position. Don't be timid. Imitate an elephant!
If you can do them, high lip trills are great for building embouchure strength. These patterns quickly fatigue the embouchure and, if used sparingly, can help build strength. If you can't manage a fast lip trill, at least do 2-note slurs at the speed of quarter notes. Another excellent technique to develop high range strength is to spend a fair amount of time playing just below your limit. If your highest note is a B-flat, build strength by playing a lot patterns up to G, A-flat and A.
You may also try buzzing or playing simple melodies by ear. Choose melodies that naturally ascend so that momentum of the music helps to carry you into the high register.
As you build high register, ascend as high as you can. Don't stop just when the notes becomes less clean. Ideally, your high range exercises should take you higher than any of your music.
FATIGUE AND TENSION
Remember that, when you are building your high range, you are essentially doing "weight lifting" exercises for your embouchure. Therefore some of the principles that apply to weight lifting apply to high range development. After giving the embouchure a hard workout, give it a chance to rest. Once the muscles have become fatigued, they need time to recover and strengthen. If you push them constantly, you only break them down into a state of chronic fatigue. You might try a schedule of intense high range work every few days. Follow heavy workout days with less taxing days.
Tension can easily creep into your playing as you work to build high range. Alternate high patterns with relaxing low playing. Perhaps you can use some mezzo-piano glisses down from a low B-flat.
I believe that the low range supports the high range. Whereas high notes tend to promote a pinched air stream, relaxed playing in the low register helps to promote the flow of relaxed air. Low playing also serves to loosen the muscles of the embouchure so they can vibrate more readily when playing high. Just as a weight lifter stretches and relaxes before trying to break a record, good low notes can help your high notes.
BE PATIENT BUT PERSISTENT! DON'T OVERDO IT!