The woman here may refers to the elder sister in “The Twa Sisters”, a Scottish ballad, who murdered her sister by pushing her into a river out of jealousy. In many varieties of the story, the elder sister was described as having dark hair, while the younger sister was fair. After the younger sister had died, her body was made into a musical instrument with her hair being the strings that played the song of her murder. In the context of lines 377-378, music isn’t played with the younger sister’s hair, the elder sister is fiddling with her own hair. Perhaps we’re seeing her in some level of Inferno, contemplating on her murderous act, just as one would look back at what the war have done to Europe.
However, the woman could also be the younger sister. In this case, Europe is playing the song of its fate.