Lip slurs.
Lip slurs.
Lip slurs.
At the very least, try ones that stay in one position. For example, a simple Bb to D repeated in 1st position, say, in 8th notes for a measure or two should work. Then repeat, all the way down the slide, making sure to take a break in between. Or, you can do four 8ths and four sixteenths followd by a quarter note. Harder than I expected to type out on the internet but if you write it down before interpreting it, you should be able to get it.
Also, one of my favorites is that same one, but extended a bit (at the top, to your elusive high G!). It goes Bb-D-F-G-F-D-Bb, in 8th notes, again all the way down the slide.
To recap:
Slur pattern one= Tonic (root note/first note of scale) - Major 3rd - Tonic - Major 3rd - Tonic, etc.
Slur pattern two= Tonic - Major 3rd - Perfect 5th - Major 6th, and then back down again.
Once you have the pitches, buzzing these on your mouthpiece without the trombone attached is a good idea as well. I'm actually going on a trip with my school this weekend to VA, have a concert monday and Wednesday, and packed my mouthpiece especially for this purpose. I have a few solos I'd rather not screw up.
Important: Don't tongue. This will do very little to help your embrochure. Especially, no tongue, since you're playing a Rochut etude-make it as legato as possible- they'll be impressed.
Make sure to keep the air stream steady, increasing the speed instead of trying to strain your lips to get the high notes out.
Good luck on the college audition. I've got one in the fall, for jazz, that I ought to start preparing for.
I ought to practice what I preach

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Jared