This is one of my go-to buzzing exercises. I first wrote it to work on buzzing upwards with a minimum of effort. Using a slingshot affect to propel the pitch from the tonic of the scale diatonically upwards to the 2nd, 3rd, 4th and 5th scale degrees. Then turning around and doing the same downwards. It is excellent for working on clarity of pitch, nuanced airflow and efficiency in manueuvering upwards and downwards.
I don't recommend going beyond the interval of a fifth, until the player becomes very accomplished and efficient playing it as it is written. To go further invites tension to creep back into the embouchure and airflow - so resist the temptation to go further until you are very relaxed playing this exercise as it stands.
Notice that it starts on the 2nd scale degree, swinging downwards through the tonic on it's pendulum/slingshot trajectory and setting the player up for the interval jump. Don't lunge at the interval, let the rhythmic motion and airflow do the work for you.
Buzz this while playing the exercise on the piano. This promotes pitch accuracy plus rhythmic timing. This is strongly recommended as the benefits are incredible and easy to monitor. Without the piano, a lot of inaccuracies can creep in... I don't usually tongue this exercise as it is designed to fine tune airflow. Tonguing this is an advanced and more difficult version of this pattern. So make sure that you can do this great without tongue before adding it in!
I do suggest playing this on the horn as well - transposing the pattern through the keys up and down. Doing so addresses the awkwardness of many keys and gives you a chance to work through the possible slide patterns enhancing your ability to play these common intervals.
It works equally well for high range and low range. Plus, it highlights the function of the corners of the embouchure and their structural role. Corners need to be strong and stable while the interior of the embouchure (the aperture) must remain flexible and relaxed. You will notice that this exercise will really tire those corners if you are doing it accurately and spend some time transposing it gradually into the high range and/or the low range.