High range development is a topic that comes up with every horn student, and every horn teacher has his or her ideas as to the most effective ways to improve the high range. These comments are from Douglas Hill, Professor of horn at the University of Wisconsin-Madison.
Performing well in the high range of the horn, though it seems difficult to many, is based on only a few important concepts. Success depends first and foremost on an efficient mid-range mouthpiece placement and pressure, a refined and solid mid-range air control, and appropriately open and relaxed throat position, oral cavity and aperture size in the mid-range, and the setting of the cheek and chin muscles just firm enough to avoid air pockets and remain flush with the teeth and gums again in the mid range. The way one produces the third octave (middle C up to third space C) is the foundation for success in the high range. It is all a 2:1 ratio between the octaves. If the third space C is tense and overblown, there will be no way to double that set of parameters and create the high C successfully.
Douglas Hill, Collected Thoughts on Teaching and Learning, Creativity, and Horn Performance, p. 31