No secret for trombone and other brass players that practicing flexibility is one of the keys to good technique and chops! Playing the same exercise on both mouthpiece and instrument is great both for building up strength and gaining more control over the instrument.
Slightly re-inventing the wheel, I have made a bunch of trombone exercises that focus on playing both on the trombone and the mouthpiece. They are supposed to be played first on trombone and then on mouthpiece, but as a variation you could start with the mouthpiece. There will be some fiddling around with the mouthpiece on and off, but please bare with me on this one.
You should focus on keeping the same embouchure both on the trombone and on the mouthpiece. When you play on the mouthpiece, you need more strength and control in order to hit the (right) notes. Try to do it the same way on the trombone – making sure that your lips (and ears) know what pitch to hit will really help you improve your instrument control.
You will find this exercise and many others in the book Flexibility for Trombone – 38 pages in print friendly pdf format.
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