A silk scarf is a good way to complete a tie-less look once the weather begins to turn cool. Not cashmere or wool mind you, but silk. Not quite warm enough for winter nor a fabric to sweat into in the heat of summer, silk is best in shoulder season (this advice also applies to silk suits, odd jackets and sweaters in addition to scarves, in my opinion). The best choices are non-directional patterns like polka dots or paisleys in colors that don't match.
I'd been looking to add another silk scarf to my wardrobe this year and found one yesterday at Drake's London which, by the way, has an expanded line of autumn and winter offerings going up on its web site even as I write. I'll wear the Oyster model, pictured above, with a covert coat and the orange polka dot on navy scarf that it supercedes will assume new duties as a necktie replacement with tweed jackets and sweaters.
Fall is silk scarf season.