“On the seventh day of Christmas, my true love gave to me, seven swans a-swimming ...”
Allowing for corruptions evolving the text as described earlier, the "seven swans a-swimming" completes the first seven days being represented by birds, in honor of the seven sacraments. The song is just more than half over, and we can already see that someone obviously put a great deal of thought into it.
What do birds and sacraments have in common? We may never know, but we already know this much ...
Today is the Feast of Saint Sylvester, who was Pope from January 31, 314, until his death on this day in 335. He was the first bishop of Rome to refer to himself as "Pope," or more specifically, "Father (Papa)." His reign would have occurred during that of Emperor Constantine, as well as the First Council of Nicea in 325, which composed the Nicene Creed proclaimed at Mass on Sunday. (Sylvester did not attend this council, but sent a delegation.) He is also one of the ten longest-reigning popes in history.
In present-day Germany, this day of New Year's Eve is known as "Silvester." Other countries know the day better by the saints name as well (such as "la Saint-Sylvestre" in France).