I came here to say the same thing. Moonlight has a complex harmonic structure which is completely hidden by the repetitive arpeggio and tiny interval changes.

I came here to say the same thing. Moonlight has a complex harmonic structure which is completely hidden by the repetitive arpeggio and tiny interval changes. Seeing it on the circle of fifths would make it much clearer. While listening, it occurred to me that Beethoven probably did not use a piano tuned to equal temperament. I wonder what temperament he would have used.