Exercises solely on the mouthpiece of the saxophone are a great way to improve your embouchure and with it, your tone. The great saxophonist and one of my former tutors, Dave Liebman writes in his Developing a Personal Saxophone Sound book, ‘the closer one gets to the source of the sound, the greater effect that has on the overall sound’. Therefore how you breathe and interact with the mouthpiece, (your embouchure) has a greater effect on your sound that the actual saxophone – try telling vintage saxophone shops that one!
Here are the drone pitches that I refer to in the video