For me, learning that piece on the piano took a while. I'm not a pianist. I'm an oboist. It's simple enough, really, though, and I learned the notes and hand positions pretty quickly. Then came the interpretation, which is far more difficult.
While it's true that music theory lies under the effect of the piece, most people who hear it aren't aware of the theory. Satie, of course, was, but his training and long practice allowed him to express something unique by using it. And so it is with all great composers. They create a new thing from their knowledge of theory and how to manipulate it.
I was introduced to Satie by playing a woodwind quintet he composed with the quintet I was part of for several years. That's what led me to the piano and that Gymnopedie #1. I understood the harmonies he used, because I know music theory, too. I more or less understand why he used them as he did. Still, I have never played that piece on the piano for any audience. Just for myself. I've played it many different ways, interpretation-wise, looking for the answer that the music asks. I'm not sure I ever got the answer just right. I would like to have heard the composer play it, but I suspect that he also played it differently at different times. It lends itself to that.
The notes on the piano are fixed in frequency. The scales and chords that can be produced are known and their interactions can be varied enormously. Satie, no doubt, sat down one day at his piano and explored the keyboard to come up with that composition. It came from his brain, not any deity. He created it, using the instrument at hand, also created by humans.
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