Long tones are an essential part of learning to play the saxophone. They help with breath control and support, embouchure development as well as developing an overall good tone.
This exercise is very simple but extremely effective for improving your sound. Even though this is a simple exercise, it is one that involves constant awareness. As I'm playing this exercise, you will hear variations in my sound due to slight adjustments I'm making in my airstream and embouchure. I'm also keeping a close eye on my tuner and trying to stay in perfect tune. Staying in tune without adjusting your embouchure is difficult, especially if you have an instrument like the saxophone that is know to have some intonation issues.
Before getting started, relax and take a deep breath from your diaphram. Let the breath out slowly and try to release all the tension from your body especially in your shoulders. For the purpose of time, I'm simply going to play one octave asending, so you have an idea of how to perform this exercise. Be sure that when you're playing that you listen to yourself closely. I recommend you record yourself so you can critique your own playing. You're now ready to play.
As a variation to this exercise, you can start soft and play progressively louder, then softer again for each note or when you move from one note to the next. Be sure to keep the tone as steady as possible.