The longer story:
If you were to blow a note on just the mouthpiece, it should sound a certain pitch. For a classical sound and on mouthpieces that lend themselves more easily to that sound these pitches are more or less:
C for Soprano
A for Alto
G for Tenor
D for Bari
For a jazz sound, you would typically shoot for a focus pitch lower than what is listed above, but this can vary greatly depending on the sound you are after. For example, to emulate Parker you will need a different focus pitch than you will for Desmond. Regardless of the sound you are after, you should practice sounding the focus pitch by playing it loud and as stable as possible, using a keyboard for reference and pitch accuracy. That is step one. Warning: you will annoy anyone nearby and possibly even yourself.
Step two is the ability to bend this pitch in a controlled manner as low as possible down to an octave below the focus pitch. To do this you must learn to control the muscles in the back of the mouth and down into the throat. These are the same muscles you use to control the pitch of your voice. Although, you won't use them in quite the same way on the saxophone. Controlling these muscles will allow you to control the airstream into the saxophone, thus having a great effect on pitch and tone. As you do this pitch bending exercise, it is important to minimize jaw motion. This step should be practiced everyday at various intervals throughout a practice session. Don't get discouraged if you can't do this right away. It can take months or more to even gain proficiency.
The ability to pitch bend will have a huge impact on your ability to play in the altissimo register, as well as harmonics and multiphonics.
There are indeed other ways to practice this same skill. You can pitch bend on the instrument. For example, play high Eb, D, Eb, C#, Eb, C. Now try to do it without moving your fingers; you will keep fingering high Eb and just bend the pitch with your throat. Don't worry. I couldn't do it at first either. In fact, I wouldn't have thought it was possible if I had not just heard Dr. Rousseau do it right in front of me. But, with practice I was able to do it too, and -- this is the good news -- as soon as I learned to do this, my ability to play harmonics and altissimo improved immensely. I do find this much more difficult on tenor and bari. In fact, the higher the note, the easier it is. I spent at least a year pitch bending all of my altissimo notes every time I played the instrument, even while warming up for band rehearsals, and I think it is the single most important factor that allowed me some control of that register.
Harmonics are another great way to gain control of the tongue and throat muscles, and many great exercises are available in various method books. In fact, everything on this page is available in greater detail from other sources.
One of my favorite new resources is Eugene Rousseau's Saxophone Artistry in Performance and Pedagogy, available from www.jeanne-inc.com.
For more detail, however, look to Rousseau's Saxophone High Tones and Donald Sinta's Voicing: An Approach to the Saxophone's Third Register. They provide different and complementary strategies for mastery of the altissimo register and ultimately the saxophone as a whole. Each of these books is very important and can greatly aid saxophonists of all levels... well, maybe not beginners. Sigurd Rascher has a book on this subject as well, but I have found that Rousseau's and Sinta's books make it obsolete.
I do feel that simple pitch bending exercises on the mouthpiece alone are of great benefit to beginners and will lay a solid foundation for further study in the Rousseau and Sinta books in later years.
Best wishes on your journey with the saxophone, and now, go learn how to pitch bend.
