Step 1: Cut a length of drinking straw
Commonly available drinking straws come in appximately 4-6mm sizes. There is apparently such a thing as a "stirring straw" for alcoholic drinks. which is about 3mm. I've found some straws of this size sold as stalks for balloons.
Step 2: Dunk in boiling water and squeeze tip
Step 3: Sandpaper tip
Experiment with different angles.
If the straw is stiff, it might need a shallow angle from horizontal and lots of passes. If it's lightweight it might just need a few at close to 30 degrees from horizontal.
The straw will now produce a noise if blown like a double reed.
Step 4: Wrap straw in brown packing tape, leaving a small area near the tip exposed
I think this works because the stiff packing tape only lets the straw vibrate near the tip. The less of the tip is exposed, the higher the pitch.
Step 5: Refinement
Sand the tip some more to work on the tone. Trim the tip back a tiny amount to raise the pitch, if it isn't quite high enough.
Step 6: Play
The reed needs to make an airtight seal with the instrument, or it may squeak. This might require a little extra tape to pad out the diameter, and some cork grease.
For the upper register to be in tune with the lower register, the length of reed extending out of the instrument needs to be correct.