A student wrote in looking for suggestions of materials to increase tonguing speed (single and double) and also to improve transposition.
The exercises I most often go to for improvement in single tonguing are in The Brass Gym for horn, published by Focus on Music. Goal tempo for single tonguing of sixteenth notes is 126 to the quarter. It may take some time to get there, but if you can do that you can play 99% of anything you will need to play on the horn single tongued.
For that other 1% you need materials for multiple tonguing. They are not presented as such, but the same Brass Gym materials can be played double tongued. Honestly, despite it being an essential skill, there are not a lot of horn-based materials for double tonguing. I put some in my technique book, which is now out of print, but some helpful instructions and short exercises are included in my mellophone book. Of course, you can use an Arban book in a pinch, but I’m not a fan. If you can track down a copy I actually most prefer the exercises for double and triple tonguing found in the Milan Yancich book, A Practical Guide to French Horn Playing.
Back to tonguing speed in general, older publications frequently have text that is way off from physiological reality of how tonguing works. Teachers tend to repeat these same words, thinking them helpful, but they are not. Don’t over think the topic but remember that “less is more” and try to keep the tonguing motion small and very forward out at the teeth. Also, be aware, you can only work on tonguing speed for short periods of time. When the tongue starts feeling sluggish give it a rest and come back to the skill again later.
To the topic of transposition, it is not a skill to ignore. The standard way to teach this is to use the Kopprasch studies. I’m not convinced this is a great tactic to learn the skill; I would prefer that the etudes be shorter and look more like typical natural horn music. In that regard, I have used materials from my natural horn book with students to work on transposition and had some short exercises in my technique book. It seems less systematic than it should be but in the end in lessons I rely on working on excerpts and solos in a variety of keys (no transposed parts!) and the intrinsic motivation of students to get better.
Which is really the key to both skills, tonguing speed and transposition: motivation. You know you need to work on it, so work on it! Good luck!