Pivot
The topic from the Doug Hill master classes at ASU last weekend that has generated the most discussion in lessons this week is that of pivoting on the horn.
While not utilized by all hornists, many players find a slight downward pivot to be helpful in obtaining the highest notes on the horn. The pivot is seen most easily when buzzing on the mouthpiece alone, where the best, light buzz of the high notes may often be produced at a slightly lower angle than normal. In the low range the opposite pivot is often of use, where the angle of the horn in relation to the embouchure will be raised. In either case this principle is much easier to employ if one plays off the leg.
I have noted this before in the blog, that there are essentially two ways to approach the horn embouchure. One method is what I call a “square” approach, as described by Farkas. This is how I worked things out as an on the leg player; no pivot is involved and going low you are mainly thinking in terms of a straight jaw drop, firm but very open. The other way is, well, the other way, where the jaw is not normally out as square as that described by Farkas. The drawings on pages 8-9 of The Art of Brass Playing illustrate extreme versions of the two approaches pretty well, and a number of other horn texts describe elements of the “other” approach, including Randy Gardner, Douglas Hill, and Gunther Schuller.
Reality is most horn players are somewhere between the two extremes. In my teaching I have students who make use of elements of both approaches.
On a personal level I switched to playing off the leg in the middle of my time playing in Nashville, which made a pivot more of a possibility. I am noting that a slight pivot on both ends of my range produces interesting results. It could be a part of the puzzle you need in putting together your range.
Be a 
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