Isomorphisms, Popular Hymns, Equivalence Classes, and Gilligan's Island

I have known for some time that an isomorphism of timing exists between certain popular hymns (e.g., Amazing Grace, and the verse of Oh, How I Love Jesus), campfile songs (e.g., Fill Up My Cup), and the theme song from Gilligan's Island. As a result, the music and lyrics are interchangeable, so you can sing the words from one to the tune of another.

It has now come to my attention that the popular Christmas carol, Joy to the World, is also a member of this same equivalence class. So if you've ever wanted to sing Joy to the World to the tune of Gilligan's Island, now you can.