"It's tempting to assume that "Inter Diabolus et Virgo" had a tune in 1450 because there are many trad variants from later centuries fitted with various tunes. A poem confined to a 15th C. manuscript would be unlikely to develop a tune later.
However, as is true of so many things, we really don't know."

Indeed we don't. But I wonder whether the absence of a refrain (cf. all the other texts in Child) might argue against it having been sung in that form? And of course we don't know the source from which 'Inter Diabolus et Virgo' was copied into that book in 1450.

Just by the way, I was interested to find some of the riddles from Child 1 turning up in an otherwise unrelated spoken piece by Harry Green, Essex pub singer, as recently as the 1960s (to be found on Veteran's 'The Fox and the Hare' CD.

Steve, thanks for the kind comment.