They say that if you add up all the gifts in The Twelve Days of Christmas, you get 364.
The Twelve (witches would say Thirteen) Days of Yule are a microcosm, a year in little.
So Yule is actually the Yules: Twelve (witches would say Thirteen) of them, and every one a Yule.
The same pattern of the Twelve Between turns up elsewhere. The old Zoroastrian New Year, Nawrúz, at the vernal equinox, is a festival of thirteen days.
Mircea Eliade suggests that the intercalary dozen serves to reconcile a solar year of 365 days with a lunar year (= 12 lunations) of 352.
There's actually an old (15th century) Scots song kin to the one you may know called The Thirteen Days of Yule. It begins: