Medieval shawls?

I have a baby wolf with a practical weaving width of about 22". I have a closet full of relatively bulky knitting yarns -- sock weight up to worsted. I'd like to turn these into shawls, but would also like them to be period-plausible. Are there times/places in medieval Europe where comparatively coarse textiles were used as anything but blankets? I know, for instance, that a relatively coarse (say 10 epi) shawl would be fine for Viking-age Norse. But what if I want to make a shawl using the same yarn for someone with, say, a 14th c. Burgundian persona? Is there a way for that to look appropriate? Or will it look as out of place as a granny afghan at the Inaugural Ball?(I'm posting this in a couple of places. My apologies if you're seeing it multiple times.)