Here is a collection of synthetic cord materials used in the construction of turks head bracelets. Obviously this is but a small sample of available materials but this shows the size difference between the very lightweight 1 millimeter cords shown on the left and the common 3 mm nylon braid.
All of these are nylon or some blend of synthetic fibers. The 1/8" (3 mm) cord is available in most hardware stores in the US. I use this material to make some of the wider designs. The 2 mm material is a very fine braided cover and I'm just beginning to see how some of the more complex weave designs look in this more delicate cord.
The 1 mm cords were found in a salvage shop and I only have a small amount of each color. I use this for making the square sennit braid grommets. It's pretty dense and stiff when working it up into tight pattern.