While on the topic of wrapping (see Mahanpots’ version of thumbrest), I thought I’d share my wrapping of a badly cracked wooden whistle. I used monofilament fishing line to keep the cracks closed. In the right light, you can hardly see it’s there sometimes. The wood is Lignum Vitae, which a whistle maker told me is difficult to glue because it’s so oily.
Michael
Very neat work.
If you wish to close the cracks completely, I suggest Rawhide.
Rings of warm/wet Rawhide will shrink when dry and close the cracks as well as seal them. This is an “Old Mountain Man” trick used to repair a busted wooden rifle stock, but would be effective in this situation. Dry Rawhide can accept different colored dyes as a “bonus”.
What does it look like where the ends of the fishing line are? In other words, how did you secure it so it looks so smooth and doesn’t unwrap?
That’s what I wanted to see too.
Michael provided this link, which explains the wrapping method. But I still don’t understand how you get the end secured either. 
If you turn the whistle around to the other side, you can see where I’ve tucked the line under several wraps of the line. I’ll show a picture tomorrow.
Michael
Very old Scottish bagpipe chanters often have fine wire wrapped around them, in some cases between each finger hole. (Nowadays we would just toss a cracked chanter, back then they made do.)
Yes. Japanese Bamboo Flutes use twisted Cherry Bark wrappings. The cross sectional diagram here shows the entire flute wrapped in cherry bark twine.
Even before seeing the demonstration of wrapping a fishing pole (thanks for that, by the way) that is how I guessed it to be done. I had wrapped the threads on my flute that way. But thread is much different than monofilament line. It looks so perfect in those pictures.