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Sometimes you will find a cravat (or be given one). This is a wider length of fabric and double sided so that when it is tied, there is no right or wrong side. Usually there are pleats to manage the fabric that goes around the neck. These ties are cut on grain, so don't have the stretch problems there are with standard neckties. They are used with an open-necked shirt and are tied in a loose half or whole knot and the ends tucked into the shirt opening.
When you sew a lining into a garment, a skinny piping in the seam adds a nice finish. First prepare a skinny piping using a long 1 1/4” wide bias strip (pieced as necessary) and a narrow cord (#1) or sport-weight yarn. A piping trim tool is handy for trimming the seam allowance to 1/4”. Then sew the piping to the garment on the seam line before sewing the lining over. If you sew over the stitching used to add the piping, you will not have stitches showing on the finished edge.