Millinery Petersham
Millinery petersham is a very specific creature: it is woven from fibres which are actually required to shrink so will always be cotton/rayon/viscose/acetate or a mixture. This way it can be encouraged with steam to shape around curves. The woven edge, on very close inspection, is scalloped which allows for stretching and shrinking: something which grosgrain ribbon, with a rigid knitted edge and a polyester fibre, can simply never do.