The cornett was a late medieval instrument that came into its own in the Renaissance, when it was often played in consorts with sackbuts, a type of trombone.
It was a wooden instrument, made from a piece of wood split in half lengthwise. The interior of each half was removed and the two halves were joined together forming a tube. Holes were bored at the front and back. The two pieces of wood were glued together and wrapped in a piece of leather to keep everything in place. The fingering system is very like that of the recorder, in that it has six holes at the front and one at the back for the left thumb, but the cornett looks very different. It’s slightly curved and has a mouthpiece made out of horn, bone or ivory, similar to that used with brass instruments.
The sound is produced by making the lips vibrate against the mouthpiece and the pitch of the notes is changed by covering or uncovering the holes.
Unfortunately I haven’t been able to find a piece played by a medieval cornett, but this Renaissance piece will give you a good idea of the sound. I have no idea why the player is playing it from the side of his mouth. In other videos and pictures I’ve seen, the instrument is played from the middle of the mouth, as you would expect.
A History of Western Music by J. Peter Burkholder, Donald Jay Grout and Claude V. Palisca