The Identity of a Song

Two days ago I heard a story on NPR about the rock group Nickelback. A music student in Alberta (I've been told they have a pretty good music program there) superimposed two songs by the group in an effort to show that they are really the same song. You can listen to his efforts here. What really struck me was the claim that these songs were exactly the same. The melodies are distinctly different, though the harmonies are the same and the changes in timbre line up. This student has really created a quodlibet, two different melodies that fit together like a jigsaw puzzle. It is interesting that this student focuses solely on the harmonic progression for the identity of the song. It reminds me of a story that Kyle Gann shared, on how his students judged his piece by the unchanging (vertical time) aspects rather than the dynamic qualities (horizontal time). Nickelback has created two songs (three, according to the claims of the listener) that share some vertical time aspects and some horizontal time aspects, but do not share all of them. Yet they are apparently identical. Who knew?