h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

Think about how the flute is made in relation to other woodwind instruments and to brass instruments; With most instruments, all the air you can make goes directly into the mouthpiece. Flutes are different. Part of your air stream is separated off the top by the back of your embochure plate and wasted,the other portion of your air hits the back "wall" and begins spinning down the pipe to make the pretty sounds, part of THAT air is lost in friction. Its no wonder this instrument takes more air than nearly any other.

It is the vibration of the airstream in your flute that makes the sound. Obviously, not all notes you play need the same vibration or wave pattern. Some notes require long, slow waves, some are short and fast.

The more efficiently you use your air, the better, and more consistant your sound will be.

That is where your embochure, (your mouth muscles), comes into play.

Now I'm thinking about engineering. How can you make the same amount of water/gas move more quickly? With pressure:
You can push the air using the muscles in your abdoman, (squeeze your diaphragm) and, narrow the channel at a particular point. Although you can't change the diameter of your flute at a particular point, you can change the size of the opening through which your air will pass...your mouth. As the air is forced through the smaller area, it speeds up. When it speeds up, it will vibrate faster in your flute.

When going for those high notes, narrow the opening and hold it firmly. Think about passing the same amount of air you use in the mid range through a smaller hole - you need to put some pressure behind it and continue to control the size of the hole. This can take a lot of muscle control. You really want that portion of your air that goes down the pipe to vibrate precisely.
Now,don't forget to aim your airstream - the smaller the stream the better your aim has to be. Roll your embochure plate away from your mouth and back in until you hear a clear tone and steady pitch.

Practice manipulating the air on a single note. Take its lowest form and see if you can get an overtone by manipulating your embochure. Then see if you can move up to the next octave (no finger changing). You need to learn to play all three at the same dynamic level.

Any idiot can learn to count eventually. It takes a little more finesse to get that Rampal/Galway kinda sound.
Thats my philosophy.