The principle of all flutes is that the player blows a jet of air against an edge, positioned at the top of a tube, and resonances of the long air-column in the tube disturb the air-jet, causing more or less of it to flow above or below the edge. The resonances are the notes that we hear, and the frequency of the resonance, which is inversely proportional to the tube length, determines the pitch of the notes. Some of the energy of the air-jet provided by the player’s blowing, is transferred to the resonating air column, which not only sustains the resonance but also provides energy for the radiated sound waves that leave the instrument. A simple example is blowing across the top of an empty bottle. The pitch, primarily determined by the length of the tube, is modifiied (always increased) by the presence of any open holes along its length.
In practice, a range of notes can usually be played with any particular fingering, because the effective tube-length, as modified by the fingering, determines the fundamental note for that fingering. Blowing harder can excite overtones of this fundamental, and for the all-fingers-down position, these will be successive octaves of the fundamental. Things get more complex when there are open holes but generally the pitches produced by over-blowing are still related to the fundamental by simple numerical ratios.
With the transverse flute, the strength, shape and direction of the air is controlled by the player’s lips (their “embouchure”), allowing a wide range of control over tone and dynamics. In effect the player’s lips form the windway.
With the recorder however, the windway is created by the block or fipple in the end of the instrument, which directs the air stream onto the lip. It is this fixed windway which determines the flow of air, making it relatively easy to produce notes, but allowing little variation in their characteristics.
The furniture maker Tim Killen has some illustrations on the construction of the recorder mouthpiece.