You can also get wild and choose to work on a particular extension in this exercise. So, Dominant 7 #11 for example. You would emphasize that sound/color all the way through, to really get comfortable with it. Have fun!
This is the first thing I do on flute every morning, a la Marcel Moyse from his book “De La Sonorite”. It’s great for warming up your embouchure, developing an even sound in all ranges, tightening up your intonation, and honing in on the tone you strive for. Great for all horns but I demo on flute!
My second favorite longtone exercise in addition to HA TA TAs! If you haven't already seen the HA TA TA video that I reference, here it is: https://thealexaapproach.vhx.tv/videos/longtones-ha-ta-ta-demonstration