This simple little mouthpiece exercise is actually quite effective. I recently had one of those days where both breathing and embouchure felt a bit locked in. I used these patterns to kickstart both, and was impressed with the result after just few minutes.
Before you take the ride, please read the following instructions:
1. Play all patterns on your mouthpiece with a smooth glissando.
2. Do not push the air to reach the upper notes, make sure there are no dynamics involved, a steady mf or mp all the way is best.
3. Change pitch with your embouchure. Jaw, lips and tongue should be used to change the shape of the air flow, thus changing the pitch.
4. Do not use your body as a compressor in order to play a higher note. Free flow all the way through.
5. Try to make the intervals feel as small as possible, even the octaves.
6. If you find it difficult to play the right notes by ear (some of the pitches are quite tricky), play them on a piano first.
This works great as a brass warmup exercise. You can of course play this any brass instrument, just transpose the exercise to make it fit.