The airstream coming out of the windway interacts with the air column in the instrument's bore and oscillates around the edge or labium, as shown in the pictures below.
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The interaction between the windway and the recorder's air column
The airstream oscillating around the edge of the labium. Photos : Univesity of Eindhoven (Netherlands)
The air column can be shortened by opening holes, giving higher notes, since the vibrating length is shortened.
If the holes were large enough, opening a hole would be equivalent to cutting the air column completely at that point,
but the holes are too small for this, which is why we can use fork fingerings (also called cross fingerings) to play semitones in particular
Of course, we can also lengthen the air column again by closing the open holes.
To play higher notes we can force the air column to divide into two parts. On the recorder this is done by making the thumb hole
leak. We now have two nodes and each vibrating segment is shorter. This enables us to use the same holes again for other notes.
middle a (2nd register)
(Click on the picture for more details)
By making two leaks (the thumb hole and one on the other side of the instrument), we can force the air column to divide into
three parts, giving notes higher still, using the same holes once more.
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high e (3rd register)
(Click on the picture for more details)
By making three leaks (the thumb hole and two holes on the top of the instrument) we can force the air column to divide into four parts, giving even higher notes.
high g (4th register)
(Click on the picture for more details)
In this way we can play over a range of two octaves and a half (about 30 notes) using only 8 holes. However, the design of the instrument must be correct to enable this.