The following is a copy of the post which Shooshie (the founder of this famous exercise, I believe) posts from time to time. This exercise, in my opinion, is one of the finest ways to improve your tone you can try. It's not meant to be easy but if you can do it, you'll notice the results pretty quickly. Experienced players and newcomers should at least try this for a few days because it's not a common thing to come across by word of teachers and so on. It's worth the time. It's also the crux of several other methods, notably circular breathing and vibrato, which are covered elsewhere.
Ok, there have been a couple of requests here, and a couple in email, so here goes again. This is pretty simple. It is not something that should ever become a source of anxiety. If you have an inflexible airstream right now, it may seem frustrating at first, but you will "discover" the methods through practice. While at first you may want to spend a little time on it fifteen or twenty minutes seems excessive to me, maybe ten would be more like it - from then on you probably don't need more than a couple of minutes of it as a warm-up exercise to get your bearings.
The objective of this exercise is to put you in touch with the muscles which control your airstream and teach you the coordinated movements of them which enable absolute pitch and timbre control at any volume level (within reason), which I will call "velocity" from here on out, borrowing the MIDI term for attack rate. Velocity, then refers to the speed of the airstream, not the tempo of the music as in Czerny's exercises for piano.
Along with the muscular coordination and control, we will need to learn a way to remember specific positions of those muscles so as to enable their quick recall when attempting to practice a difficult passage for consistent perfection. I use a phonetic system for this, since we each have learned phonetic systems since birth to enable us to perform the miraculous muscular acrobatics of speech. The tongue is a free-form muscle, and very few of us really have any idea what it's shape is at a given moment. I've seen people do fiber-optic cable photos and videos of the tongue so as to determine these shapes, but such studies have little practical applications for three reasons:
1) the people doing the study do not necessarily know which positions are "right" for airstreams.
2) the subjects being studied (saxophonists) may find it difficult to produce the proper positions with the apparatus in their mouths
3) even if the above two points are corrected for, a picture doesn't give us any connection with a physical means to produce the positions in the photographs.
So in response to that last point, I searched for a means of locating and coordinating the airstream positions necessary to play the saxophone, and a means of describing and recalling them. The solution was extraordinarily simple. We have both right here in our mouths - the mouthpiece and our ability to speak.
Here is the exercise, and following the exercise a description of the phonetic tools to help you recall certain positions, and then a discussion of how to apply the exercise to your other exercises and to playing (also, how NOT to).
For first-timers: Holding only the mouthpiece (with reed and ligature mounted and fully ready for playing), play a sound, keeping your hands away from the back of the mouthpiece. This will all be controlled by voicing the airstream. Find a pitch that is comfortable and begin by attacking that pitch a few times with different velocities. Now that you have a feel for playing on the mouthpiece alone, try lowering the pitch. You may at first just imitate a slide whistle until you get some control over it. Immediately upon success of this little glissando down and back up you will be aware of at least two things: something is at work with your tongue and throat positions, and you have to support the sound with a lot of diaphragm pressure. No namby-pamby little toots; you will need long, broad lines of airstream sitting on top of a solid set of stomach muscles. (Later you will need to learn to do it with minimum effort, but we're just getting started.)
Now that you're an expert slide-whistle-duck-calling mouthpiece tooter, it's time to control it and learn coordination. Play a comfortable pitch. The pitches will depend on the size of the mouthpiece: soprano: anywhere from a concert "A" to "C" alto: concert "A" tenor: concert "F"-"G" (some small chambered mp's may do well with "A") bari: I honestly don't remember. It's been 10 years since I sold my bari.
Using the above determined pitch as your starting point, set your tuner to that pitch (playing an audible sound, not measuring your pitch) and begin playing a scale downward. Match each interval as closely as you can, listening for "beats" between your sound and your tuner's sound. (A synthesizer will do if you don't have a sound-producing tuner). Attempt to play an entire octave. As you get down to about a sixth below, your jaw position will change, and you will go to something like a subtone embouchure. These lower notes represent extreme flexibility and changes, but I think they serve a purpose. Don't feel lost if you can't get them, though; the real meat of this exercise can be had even if you only can play an interval of a fifth or sixth.
Now that you have accomplished the scale, or at least the beginnings of it, let's move on to the real stuff - the part that gives you control over some coordination: dynamic control. Begin your scale again. At a tempo of approximately quarter note = 126, make each note 8 beats long (or longer if you like). Begin each pitch rather forcefully, being considerate of your neighbors, though, and again match the pitch to your fixed pitch reference tone. Now decrescendo to PPP over four beats and then crescendo back up to your starting velocity over the next four beats. Keep the pitch constant. Then repeat it for each note of your scale, always keeping focused on the pitch. Consistent pitch is the key to this exercise.
Ok, that's it. Now you've done it. Do this exercise as a warm-up on a daily basis, before you do your harmonic (overtone) exercises.
Ok, now that you have learned to play scales (and a few of you have probably even been playing tunes) on your mouthpiece alone, what can you do with it besides surprise your friends with a mouthpiece serenade? Plenty. If you have mastered the velocity/pitch control, then you have accomplished a lot. You already found out that as the velocity of the airstream diminishes, the pitch goes up, and vice-versa. You learned that you could control it, though, without necessarily even having to know what you were doing. It's just a natural and intuitive act of compensation. You also learned that tightness and reliance upon jaw pressure alone (biting) is the enemy of airstream control, and yet it is very much a part of the overall act. Learning to coordinate these actions is what makes you a virtuoso.
Now at this point, I could launch into a lengthy dissertation of exactly what is happening in your mouth, and give you exact descriptions of tongue positions, and thus-and-so, and do this and don't do that, and if it's not precisely my way then it's not right, and blah, blah, blah. But I won't, and for good reason, too. I don't really know. Well... I kinda know after all these years, but it's really not important, and I sure wouldn't want anyone out there going around saying "Shooshie says it has to be this way," and starting a whole new "school of thought." Schools of thought are good ways to lock you up and inhibit your ability to learn. As soon as someone points a school of thought at you, get ready to run or be shackled. Not that what they tell you may necessarily be wrong, but simply because they're liable to say it's the only way. "School" in this sense translates into something like a "cult."
So, instead of telling you what's what, I'd rather tell you how to use this to find what works for you. That is, I'd rather give you some tools than to tell you what to build with them. So here goes:
What is it that enables you to change pitch on the mouthpiece alone? Is it "lipping down"? No. I can bite the reed nearly shut and still do the scale. Your lips are involved, and must be supported with muscle, but it would be wrong to say that we are lipping down. Are we opening our throats or closing them? Maybe. It's not so important to know this, since whatever it is happens automatically in order to successfully do the exercise. But one thing is for sure. The tongue and other things do move as you get softer or louder or change notes or correct the pitch, just as they do on the horn, and they do so in a coordinated "dance" just as they do on the horn. This range of motion, whatever it is, and the positions of things in your mouth and throat are all important in finding what will work for a given musical circumstance.
For instance, you are playing in the lower middle register and have a quick leap into the altissimo and back. You can play the altissimo note fine by itself. You can play the middle register fine by itself. But putting the two together you always squeak, squawk, and get all tense. How can you nail it as if nothing happened? Simple. Remember the positions of each one. Reduce the changes between those positions to the very barest minimum necessary to accomplish it. It is much less of a change than you might imagine if you are playing correctly to begin with. Now comes our trick.
Determine the phonetic positions of your mouth for those two different ranges on the instrument at the volume you want them to happen. Now put them together. It's as simple as saying a phrase like "any ann." Notice what happens when you say "any ann." Your tongue locks quickly into two different positions and back. It is not difficult at all, but it produces completely different sounds. That is how simple it should be on sax. But you may be like a baby when it comes to speaking on the sax. It takes a little time to learn, therefore you should practice things slowly until you get the hang of it. Soon you will be talking full speed. Back to the mouthpiece exercise. As you play the scale, determine the phonetic positions for each pitch and volume. Notice that you will be addressing three parts of the tongue - at least that's how I've divided it up: Back, Middle, and Tip.
The back of your tongue stays the same pretty much all the time. You've heard some people say that you keep your throat open, while others say that you close it down. Some will talk about warm air or cold air, fast air or slow air. There is a great deal of confusion about this, and nobody seems to agree. There's good reason for that. Nobody really knows what's going on back there. But you do know, even if you can't put it into words, because you've done the mouthpiece exercise. Rather than speculate on all these dichotomies, let's focus on practicality. In order to successfully render the mouthpiece exercise, the back of the tongue is in a position to create the sound of "K" at moment's notice. It doesn't actually create that K, but it's close. It's kind of in between a "K" and a hard "G" (as in "gate"). You could articulate a sound with this position. This is very handy, since when we begin double tonguing, our tongues will already know how to do it. The position is a bit stretched for either of those consonant sounds, but we are going to use "K" or "G" to describe the position, since they are pretty close. Remember, we're using the letters to describe something we actually are doing. We're not trying to make what we are doing match the letters as we would normally speak them. The mouthpiece exercise is the authority to whom we turn in order to tell us the proper positionings. We just apply the phonetic symbols as tools to help us remember those positions.
Now... let's skip the middle of the tongue and come back to it later. Let's look at the tip of the tongue. It seems to function as a focal point for the airstream before it enters the mouthpiece. When it is focused, it adopts a kind of pointy shape somewhere between English "R" and "L". It is able, at moment's notice, to pop up to the reed and make a "T" or "D" shape which can be very handy for single tonguing. (Gee... it's just amazing how all this is working out, isn't it?) :-) Again, remember that you take what works (from the mouthpiece exercise) and use the phonetic symbols to describe them, not vice versa.
OK. For the middle of the tongue, we have our vowel sounds. The whole range of them. You can feel them for yourself as you do the mouthpiece exercise. Play a pitch and freeze into that position. Remove the mouthpiece and vocalize whatever comes out without moving from that position. There's your phonetic position for that pitch. You can even write it down! At least you can write an approximation that has meaning for you. That helps greatly when you're trying to remember how to make that two-octave altissimo leap on a sixteenth note.
One other important position to note is the sides of the tongue. When correctly in place, the "rails" of the tongue slide forward and backward between a pair or two of the upper molars. It's not a big slide, but just enough. This helps create an actual chamber for the air to travel through. In doing all these different things with the tongue, we have created a space to act as a resonating chamber to help reinforce the desired overtones and pitches which emerge from that other resonating chamber... known as a saxophone. Put the two chambers back to back and you get harmonic reinforcement. Your resonating chamber can also act as a detriment to the sound by not reinforcing the harmonics of the tone you are trying to produce. On the mouthpiece alone, this will cause squeaks, grunts, or just a locked-in high pitch which you cannot control. The shaping of this chamber is very subtle, but ultra-important. Without it, you could not do overtones, altissimo, or pitch correction. You would have trouble tonguing some registers of the horn. You'd have trouble with large-interval leaps at speed. Sound familiar? Then you've probably been needing to do this for a while!
Let's review our phonetic positions. If you put together our back, middle, and front positions, you get something like [K(G)] + [a,o,u,e,i] + [R(L)]. You won't mind if I simplify a particular position to something like [KAR]. Or how about [KIR]? We know that the K is not a real K, and that the R is really more of an L. We're just using these symbols as shorthand for what we want to remember.
Now you have a tool to help you recall specific airstreams, and you have a reference exercise - the mouthpiece - to coordinate those airstreams into dynamic, practical usage.
Next, you will want to apply the same airstream positions to your harmonic (overtone) exercises. Simply do the same thing. Play each harmonic on your horn and change velocities. Crescendo and decrescendo (or vice versa), noting the changes. Work on getting the timbres to match the sound you desire. Note the phonetic positions. Now play the regular fingerings. Apply the same phonetic positions. You may have to compensate, but very little.
You're ready to use these exercises, now. Applying them to your actual playing, you should notice improvement and greater control in your pitch and pitch correction after an attack, vibrato (shape, speed, depth, flexibility and consistency) dynamic control (and its relation to pitch), tonguing, double tonguing, timbral consistency, altissimo, and general playing in all registers. Anywhere that you find problems you will be prepared to isolate those problems and work them out with your new-found tools. In each case, you will:
1) figure out exactly where the problem lies
2) play individually the notes giving you the problems
3) determine the ideal position for each note
4) note the phonetic positions and their changes between notes
5) practice for the minimum change between them
6) make the change as fluid as speaking
7) apply it to the music and increase the tempo until perfected
Now, we're talking a lot about changes. Haven't we all been drilled with the idea that nothing changes? That we're supposed to play everything in one position? What about Daniel Deffayet (and others) who delight in public demonstrations in which they have a student blow the horn while the clinician stands behind them fingering the horns? It's amazing to see that the student really CAN play the music if someone else is doing the fingerings. That's because the student cannot predict a change and respond to it in their (bad) habitual ways.
What gets demonstrated is that students typically change the wrong things, and change them too much. I can also do Deffayet's trick, but if someone does it for me, I can foil them by not changing anything. Just try playing a low Bb and freezing in that position and playing and altissimo G, or a high F. It won't come out most of the time. The secret is the three parts of the tongue. The back and the tip do not change. This is where we get the idea that nothing changes. But that idea is not entirely right: the middle changes. The demonstration trick is possible because if the back and tip do not change, nearly any note is possible with the middle of the tongue in a neutral position. In fact, some of the correct changing will happen naturally. But control over the precise pitch and velocity present a whole set of problems not demonstrated by this public exhibition. This new set of problems is pretty much completely addressed by the mouthpiece exercise when applied to harmonic exercises and altissimo studies, and then applied to music in general.
So what it all boils down to, once you've established all the right positions, is that a little portion of your tongue - the same part that makes all your vowel sounds - is of utmost importance in aiding your flexibility on the instrument. It determines your pitch, timbre, and harmonic reinforcement of the sound. And it's as natural as speaking or whistling. In fact, you might think of this whole thing as "whistling while you work."
The same stuff applies to flute, clarinet, and all other woodwinds, as well. In each case, the feel is dramatically different, but the principles are the same. The changes on flute are ultra-tiny, but even of more importance since you cannot lean on octave keys to do part of your work for you. On clarinet the air column overblows at a twelfth, so the feel is again very different, but it's there. Oboe is like flute - very subtle. I can't report on bassoon, since I never played one outside of a woodwinds class. But the same principles apply to brass instruments as well. In fact, you couldn't play brass instruments without these principles.
In closing, let me reinforce the fact that these tools enable you to find what works for you. Maybe your sound ideal and mouthpiece and the shape of your mouth, not to mention your colloquial speaking accent (Brooklyn comes to mind), all require that you do something way different from what I do. But still we use the same tools to find them and apply them."