Breaking news! I just tiled that video and Noteworthy Composer, and I've made a MIDI file fo the melody. That song is being played in the key of E. Maybe there's a capo at work, so that the finger positions are for C, but that melody is in E.

So if you pick up your ax, play a C, and it just doesn't sound right, that's why.

It's a beautiful and interesting melody. Thanks for bringing it up, borborygmus.