Which reminds me of another pair of songs with the same tune. When I was in high school, I was so misguided as to buy an album by the group The Starland Vocal Band. Their only hit was a song that deserves oblivion, Afternoon Delight. However, on the album was a lovely rendition in 4-part harmony of a song called "American Tune," which, it turns out was written by Paul Simon.
I loved the tune, and shortly afterwards at a Good Friday service recognized it as "O Sacred Head Now Wounded."
Original composer J.S. Bach. It's part of his St. Matthew's Passion.