One thing that I talk a lot about with my horn students is tongue placement and vowels. Vowels (and the tongue positions that result) are crucial to the horn’s extended range.
This is certainly not a new concept. I know I first read about it from Eli Epstein’s book Horn Playing from the Inside Out, but this idea has been around for a long time. It’s also very effective at matching airspeed to register, so it’s a tool I use with my students quite a lot.
Additionally, the placement of the tongue in articulation is different in different registers of the horn. Having students pay attention to where the best articulation happens for different registers is important for clear articulations. This is especially true as a students range increases above 2 octaves.
I can’t remember how I stumbled upon this phonetic infographic, but it’s mesmerizing to say the different sounds while focusing on how they happen. Noticing the different placement of the jaw, tongue, etc. can have a huge impact on your playing.
If that charts is not enough to waste away 15 minutes of your time, there’s an interactive version here. Be warned – this site does produce sound after you click on it, and it is both fascinating and annoying.