I've wanted a Kazoo, so I designed and printed one. :)
This is what it sounds like (with a piece of an envelope window as membrane).
It prints without supports. Depending on the bridging capabilities of your printer, you might need to clean up the top part of the body's thread with a knife. But the threads are pretty coarse, which makes them quite forgiving and easy to clean.
You just need to cut a membrane from the window of an envelope (use the washer as a template – wax paper also works, but imho doesn't sound as nice), put it in the opening of the Kazoo, place the washer on top (smoother side down) and screw the nut in. That's it. :)
PS: A Kazoo is played by humming into it. ;)
Hint by Dryphter: "Hint for others - use the outside of the washer to draw a circle on the cellophane or wax paper, but then cut it out a bit smaller than that."
Edit 25.09.2018: I've printed a Kazoo in PETG and realized that the increased friction makes it nearly impossible to screw both pieces together, so I've added a second version of the lock nut with 0.2mm more clearence.
Edit 11.10.2018: I've added a third version of the lock nut with 0.4mm more clearence.
No Name PLA