On Wikipedia, I read the following tidbit:
"The only song (not counting Adventuring and Friends for Dinner) played in the TV series that never shares its original melody is The Amazing Threehorn Girl. People who have seen the episode believe that the theme for the song is original. They also believe that the song melodically different than other songs played on this show."
However, before I'd even finished hearing it for the first time, I immediately recognized the melody from somewhere else. I don't know where, but I'm absolutely positive I've heard that tune from somewhere. Does any one else recall it, maybe from one of the movies?