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Fold-over hem
Every piece has loose ends. The fabric is woven, the threads cut, but all those warp threads have to be fastened off somehow.
The purpose often dictates how a piece is finished. Most of what I weave needs a durable finish. I don’t want my handwovens to fray away in the wash. Towels, placemats, napkins, anything that will be washed frequently calls for a folded hem.
Twisted Fringe
I can also twist the fringe. Picture handwoven scarves, shawls,and even blankets, and most often they are finished with fringe. Twisting the fringe controls it. Some yarns have so much life, they just want to tango (or is that “tangle”?) as soon as they are cut from the loom. One of my weaving friends adds beads to give her fringes a little glitz.
And then there is hemstitching. Hemstitching is a decorative finish done on the loom. It binds the warps so when you cut the piece off the loom, it is essentially finished with the exception of washing the piece. The ends can be left to form a fringe or worked with twists, loops, or knots.
When I choose to hemstitch a piece, I leave enough warp at the beginning and end for a fringe. Using weft from the shuttle, I stitch up and over, up and over, across the warp. The first part of the stitch catches the warp.
The second part is worked around the tail of the first stitch to tie the bundle.
Each stitch binds two, three, four or more warps in a bundle.
I use a very simple hemstitch, but there are some wonderfully creative techniques to dress up the hem. Virginia M. West details many hemstitching variations as well as fringes, knots, and added bands in her book Finishing Touches for the Handweaver (1988: Loveland, CO Interweave Press). I know it’s an older book, but so worth it if you can find a copy.
What is your favorite way to tie up loose ends?
jeanweaves 
I use all the methods you’re writing about but I really love hem stitching, simply because, as you say, the piece is done when you take it off the loom! My least favorite is fringe twisting–I like the look but the process is so tedious to me.
It’s a good thing to do while watching TV or listening to a podcast. I also have a little tool with alligator clips and a small crank that lets me do two at a time. Handy!
I’m also not a twister. Don’t mind a four strand braid, a folded hem and love Damascus edging on a rug. Still need to try the rug finishing technique where you weave the warp threads into each other.
I tried Damascus edging once and I liked the look, but my execution needed practice. I will have to try it again sometime soon.