Many talented brass players have problems in high note playing which seem inexplicable. Often there is no obvious reason. These days the general standard of teaching and playing sophistication at a professional level is at an all-time high, but there are, of course, many amateurs who have not had access to the best teaching. These brass players who have no aspirations to earn their living at anything so potentially precarious, but who derive much satisfaction and pleasure from 'taming the tubes' can perhaps benefit from a few words of advice from a teacher who has seen most aspects of playing over many years.
Let us assume that the embouchure is sensibly formed, that the mouth-corners are pointed downwards with no stretching of the upper lip, and that the skin of the chin, under the mouthpiece, is slightly stretched.
There are two areas that must be checked. First of all, try playing without the instrument, just using the mouthpiece. There are various aids to this,(B.E.R.P or Buzzaid) which help focus the sound, although they are not absolutely essential. Listen carefully to the sound. Usually, the hissing of the air predominates. Repeated work will reduce this hissing, improving the quality of the sound. Practice long notes louder, softer, higher and lower, for at least 15 minutes with short (10-second) rests. This exercise helps every aspect of playing, but is particularly useful to help focus high notes. Eventually the upper register becomes much clearer.
This has proved to be the most effective warm-up, and has helped me on so many occasions when there was not enough time to do a more carefully paced preparation...
The second area of work is to reduce mouthpiece pressure. Take a pattern of 5 semitones, beginning on, say, concert D or treble clef E and play a long (8 second) note, crescendo – diminuendo, with the loudest point on the 5th count on each note. Notice that as the sound becomes louder, the pressure slightly increases. This is quite normal. NOW - try to reduce the pressure.at the loudest point. This will almost destroy the note altogether at first. Press JUST hard enough to keep the note going. It may be difficult at first, but persevere! After a few tries it will begin to take effect and there will eventually be a slight feeling of tiredness in the mouth-corners.
Proceed upwards by semitones, note by note. The pressure will increase as the notes go higher. Back off! Rest a little. Repeat the exercise as many times as you can. Next day add a further semitone (or more!). As the notes get higher, the feeling of muscle-stress in the mouth-corners will increase. Miraculously, the upward range will increase by perhaps 2 or 3 semitones each day. This exercise, combined with the mouthpiece practice is almost certain to improve the high register, by minimizing the mouthpiece pressure that in most cases was the cause of the problem.