my translation note! it got eaten in the typesetting, apparently.
the poem that miss du performs here is actually called 怨歌行 'song of grievances.' author is unknown, but it's often attributed to ban jinyi. i love poetry a lot, so here's my bastardized attempt to translate the full thing:
fine, newly cut silk from qi, as white as frost or snow;
embroidered for joyful reunions: a fan as round as the bright moon.
my lord keeps the fan about him, waved to make a gentle breeze;
often i fear the coming autumn: cool winds replacing the summer heat.
the fan, abandoned to a box; my love, broken mid-romance.
it's a poem where the speaker compares herself to a fan, used for the summer heat but discarded when autumn comes. in other words, she's calling out men for subjecting women to their fickle whims. you go, girl.