Beauty is Truth
It’s probably Keats’ most famous pair of lines:
I believe he’s right on the money. I think that when we experience beauty, it’s because we have seen a little deeper into the nature of things.
This seems especially true of mathematical beauty. I had a college friend who found math exquisitely beautiful. He bought a blackboard for his room, and stayed up until all hours, glorying in the work. Elegance, simplicity (but not too much!), and beauty are important guidelines to the rightness of a solution or direction of research. A sense of beauty guides the scientist as well as the artist. I’m really familiar with this from my engineering career.
So there is the nugget of my own epiphany:
The beauty of music is the beauty of mathematics, perceived in real time.
We see this in its visual manifestations all the time. The curve of the cables of the Golden Gate Bridge, the pattern of seeds in the sunflower, the rings of Saturn — all clear manifestations of the way the universe works, that can be described by math, and that we find beautiful.
Music presents a pure, distilled form of this: beauty created by small, whole numbers and their relationships to each other.