There are many good candidate ideas that could explain why the recorder isn't seen as an ideal instrument to play (good quality) jazz. One of my favorite is the one about dynamics: the recorder has none, so you can not play much more than baroque music, and certainly not jazz at all.
Well, of course this idea is wrong, at least in principle.
The fact is that you can play dynamics with a recorder but it is not as easy as it can be with other instruments.
Let us clarify one first basic fact. We can subsequently discuss how to play dynamics.
Everybody knows that the more air goes into a recorder the higher the note emitted and vice versa. The most important and underestimated consequence of this fact is a strong connection between intonation and the quality of sound.
More simply put: if you "disturb" the soundwave by blowing incorrectly (i.e. too much or too less, with uncontrolled vibratos, etc.), you not only lose intonation, but you also lose harmonics, which are partial components of sound and are responsible for its timbre.
On the other hand, playing an out of tune note affects your sound: it will be worse than usual.
So, the equation is: out of tune implies bad sound, and vice versa. If we reverse the concept positively: play in tune and your sound quality will improve (and vice versa).
Of course there are other important factors to be considered with regards to sound and intonation, but the idea is that it is impossible to face one problem without facing the other.
Having said that, I benefited greatly from a group lesson Heiko ter Schegget held last October 2006 in Leiden, the Netherlands. ter Schegget is renowned for having a wonderful sound and for being one of the few musicians that can play great dynamics on the recorder, while maintaining intonation (!).
What follows is a partial summary of that lesson (any misreporting of concepts is my responsibility ;)
The first idea is simple and illuminating. Establish your basic intonation with other instruments by playing a piano note, then you can play forte by simply blowing more and adding fingers onto the instrument.
It should be clear enough that if you establish your intonation with another instrument by playing forte, it will be very difficult to be in tune during piano passages, but it can conversely be relatively easier to lower high (forte) notes by partially adding fingers from the right hand.
On the other hand, if you need to raise low (piano) notes, you can adjust intonation by leaking from the left hand.
Let's make an experiment by playing a piano C, first octave on an alto recorder. Let's play it in tune, with the aid of an electronic turner. Then try to blow more (to make a forte) but also add (partially at first) a finger or more with the right hand to lower the intonation of the note, and check it with the tuner. This way you should have a forte or fortissimo C that is still in tune.
Now slowly go back to the original piano C and gradually decrease breath, until you reach a pianissimo. In the meantime, in order to maintain intonation, raise the right fingers, then move the left medium finger slightly from its hole and allow some air leakage. This way, the note goes up while you blow less, maintaining a correct intonation. Now go back to the original note by blowing more and closing the air leak. The idea is that you move the left finger which affects the note least: in the case of C it's the medium finger.
It's not easy, I admit, to control dynamics with this method. ter Schegget says that if you want the recorder to be considered a "real" instrument, it has to play dynamics. The technique sketched above might not be the only possible one, but it certainly is one of the easier ones.
The second part of the lesson featured sound production. This is what I learned. First of all, pay attention to how you inhale. The throat must remain open and the two movements of inhalation and exhalation, although supported by the diaphragm, must be viewed as one single big movement. There shouldn't be any difference between the two, especially with regards to the throat. You could blow into the recorder as if you were aiming at something in front of you, but the sound can be better if you think of inhaling, even when you are blowing out the air. Of course this is a contradiction, but it helps maintain the body and throat relaxed and opened while blowing out, instead of contracting it.
The advice to think that the recorder sound has to go not in front of us, but behind us also follows this logic. This helps psychologically to maintain relaxation and openness of the body, as previously mentioned. However it also has a physical base: one of the most advised places where to put a microphone to capture a recorder is, in fact, at the back of the player.
In that same lesson ter Schegget said many other interesting things about sound, but I think this is enough for our purposes.
Let's summarize it:
Always be relaxed, especially during breathing movements. Keep your body and throat open and aim the sound behind you.
Play normally in tune and piano. Play louder and in tune by correcting the intonation with the right hand. Play softer and in tune by allowing the air to leak from the left hand.
Two simple ideas that, I must admit, could take years to master. But the most basic advice of all is always the same: have a good teacher, in the flesh! Don't ever think you can learn everything on your own.