“The 12 Days of Christmas” by Straight No Chaser:
Video by Randy of Straight No Chaser
Of course “The Twelve Days of Christmas” was not written by a Jewish songwriter, so far as we know–it’s one of those songs whose creator is generally rendered as “Trad.” (Possibly originally a French Trad.) But I hesitate to call it the “main” melody here, since there are so many other Trad.–and non-Trad.–bits in it. So … erm … It has the dreidel song in it, that’s a Chanukah song, and Chanukah songs all qualify. Yeah, that could be it!
Ah, well, let’s be honest: It’s just here because it makes me laugh. Happy whichever day it is!