I was at the MET the other day when I came across this very early 16th C pendant:
I'm thinking it's probably 1490's based on the style of the hood and the dress. What I found interesting is the way the back of the hood is stylized. It doesn't look like a tube, to my eye, as other have speculated, but a separate veil. The black velvet band across the top of the head is folded back- popular in the early ages of the French Hood.
I've been working on a theory that the Mysterious White Band we see a bit later is actually the straps to the coif worn beneath the hoods. The theory is based on something I saw in Italian portraits like this one:
This painting is only a few years before the French hood pops up in fashion in...France! Given the interaction between France and the Italian City States (like near constant war) at that point, it's completely possible that a few French soilders brought back some lovely Italian veils for their wives to wear.
Although not shown, we know they did wear coifs or veils beneath the French Hoods. As the French Hoods got smaller, the veils may have stayed the same size and continued to go over the front of the arms (like the French hoods originally did and the veil in the Italian portrait). With the Mysterious White Band, what we are probably seeing is just the veil tails or coif lapels being pinned to the front of the dress during a known fashion transition period. We always see crazy holdovers during transition periods.