Every year at Passover, my family, at the end of the seder, sings the three traditional songs that accompany it. Or we attempt to at any rate. We do a decent job with "Chad Gadya," for which we all basically agree on the tune. And we manage to stumble through "Adir Hu" alright too, as we generally agree on the lack of tune. But "Echad Mi Yodea" gives us particular trouble, and we end up going back and forth between a couple of "tunes" and eventually force our way through the thirteen ever-lengthening verses. It's a sort of Jewish "The Twelve Days Of Christmas," but worse because it goes to thirteen.
This year I decided to do some research and settle this matter once and for all. I found some work done by acclaimed Jewish musicologist Cantor Yokannan Ze'ev in the eighties in conjunction with Marshall College. The study, directed by Rabbi Sholom ben Arnold, and conducted in Egypt by Doctor Henry Jones Jr. was focused on archeological artifacts related to the Exodus, and the Cantor ended up deriving a historically-informed melody for "Echad Mi Yodea."
There are some interesting things about this melody. The repeated open intervals (fourths and fifths) indicate that this tune might have been devised for trumpet (or, more likely, the shofar or hazozerah), but then the use of an augmented fourth interval (not that it would have been called an augmented fourth in bliblical times) means it would have required two shofars to play, one in the dominant key of the other. (In this transcription, D and A, though ultimately the key is arbitrary and you can sing it wherever you like.) The melody is not exactly modal, but if we were to apply modern musical theory to it, we might call it lydian. Note also the brief melismatic lines characteristic of cantorial singing, and the interative bar which is written so simply as to accomodate the variety of syllables depending on which verse you're on.
So try this tune at your next seder and enjoy!
If you're interested in learning more about Cantor Yokannan's work, there was a documentary made that's pretty informative.