Two scarves cut to identical dimensions can behave in entirely different ways, one holding a knot cleanly and the other sliding apart. The difference sits in the material and the construction rather than in the size.
Weight per area governs how far the fabric falls
Textiles are specified by weight for a given area, and that figure describes how much material is present in every part of the scarf.
A heavier fabric carries more mass hanging below any fold, so it pulls itself downward and forms long, sustained folds rather than short ones.
A very light fabric has too little mass to pull itself straight, which is why fine silk floats and crumples while a heavy wool falls in defined columns.
Weave structure decides how easily fabric bends
A plain weave interlaces every thread alternately, producing the most contact between yarns and therefore the most resistance to bending.
A twill or satin construction floats yarns over several others before interlacing, so there are fewer crossing points and the fabric folds far more readily.
This is why a satin-woven scarf slides and drapes closely while a plain-woven one of the same fibre and weight holds its shape and resists being tied tightly.
Fibre character sits underneath both
Silk is strong and smooth, so it slips against itself and produces fluid folds that will not stay knotted without friction from somewhere.
Wool fibres are crimped and slightly scaled, which creates grip between yarns and gives a knot the friction it needs to hold all day.
Cashmere combines fineness with that surface character, which is why it drapes softly and still stays where it is put, and why it costs what it does.
Edge finishing changes the whole hand
A hand-rolled edge on a silk square adds a small ridge of rolled fabric around the perimeter, which weights the border and helps the scarf fall open.
A machine-stitched hem is flatter and stiffer, and it can make the edge fight the fold rather than following it.
Raw or fringed edges add no stiffness at all, so the fabric behaves exactly as its weave dictates and frays gradually with wear.
Bias cutting is the deliberate override
Fabric cut on the diagonal of the weave stretches and moulds in ways it cannot along the straight grain, because the yarns can shift relative to each other.
A bias-cut scarf therefore curves around the neck rather than crossing it in straight lines, and it holds a shape it was not woven to hold.
The cost is fabric, since diagonal pattern pieces waste far more of a roll than straight ones, which is why bias construction appears mainly at higher prices.