I've talked about this at length with others and I'll give you one of my favorite answers from a pianist I talked with concerning the 9th. It's very long but comprehensive, brace yourselves:
"Like a great, expansive painting in which every brush stroke is just so and all of them combine to make a picture that transports the viewer from the here and now to a space of aesthetic joy, every note in Beethoven's 9th Symphony is perfect and all of them combine to make one of the most magnificent musical compositions ever conceived by the mind of a human being. The panorama experienced in just over an hour in this work is vast.
Imagine attending a performance never having heard it before. There on stage is a large symphony orchestra, four vocal soloists, and a massive chorus. Imagine your expectations seeing this assembly of sheer musical potential. Imagine your surprise when the conductor raises a baton to bring forth the simplest, quietest, open fifth (A-E) in tremolo strings in the middle of the orchestra's tonal register. The open fifth is utterly static. Harmonically, it doesn't "want" to go anywhere. It is a state of being in very simple form. One might think, "In the beginning…" The harmony still goes nowhere, but the rhythm starts to emerge with downward E-A strokes, which in turn become more complexly expressed, while the entirety of what you're hearing grows unrelentingly loader and therefore closer. And as it approaches, the harmony finally shifts from the A-E open fifth to the D-A open fifth, for the first time establishing the tonic foundation (D) and bursting out with such force that you think, now, "Let there be light!" Or at least, let there be energy!
The movement is highly energetic and turbulent, pushing you forcibly along to its end. In the second movement you would normally expect a slow relaxing contrast to the highly energized first movement, but what you get instead is a loud, romping scherzo. Only then do you get your slow movement, by the end of which, you have been engulfed in glorious music -- but what of those four soloists and that entire choir still standing there looking at you. You have not heard a peep from any of them and you have enjoyed about three-quarters of an hour of groundbreaking music… significantly longer than most other symphonies of the era.
The fourth movement opens with urgently to launch a finale that, after getting you full attention, combines some reminiscences from prior movements with a hint of the main theme to come. It is a lengthy introduction with some fits and starts, more looking back at past material alternating with ever clearer predictions of the main theme to come, and then, the first human voice heard in the symphony, the clarion call from the baritone solo, "Oh Fruende," .. "Oh, joy!!" and soon the entire chorus is involved with the soloists and the orchestra singing Schiller's Ode to Joy. What had already been big, quickly becomes vast.
Why is it beautiful?
Humans are naturally tuned in to beauty. It is not unusual to watch a sunset and be moved. To know that millions of others like us are moved even by this very sunset or by other sunsets all around the world everyday. The color and grandeur arrest us. But even in the great variety of sunsets we see, the structure of a sunset remains constant and that grounds us as humans able to understand what we are seeing and able to understand that it is immense and outside of us, but we can still take it into ourselves and be moved by it.
When we consider music, there is a new dimension to the experience. Unlike a sunset, music is made by humans and we relate to it on many levels. Sweet melodies make us want to sing. Strong rhythmic patterns with regular and repeating motifs make us want to dance. Even without the suggestion of a dance, strong rhythms at least tempt us to tap or stomp our feet. In tribal dances when the members of the tribe join in, it is a coming together of individuals but the expression of a group awareness, a celebration of many individuals joined in a common expression of their togetherness. It is generally experienced as a happy thing to do. A "beautiful" experience.
In classical music we experience some of the same elements.. melodies that make us want to sing, rhythms that make us want to move, even dance, sad passages that seem to be able to express our own sadness. And all of this assembled in structures and progressions that make sense inherently, and that help us know comfortably our place in the unraveling musical narrative. And we appreciate the balance and continuity in these musical structures. And at then end, if it was beautiful, we have the sense of having been lifted out of the everyday world and taken by other human beings (the composer, the performers) to another pleasurable state of being. That's beautiful.
But What of Beethoven's 9th in particular?
Here again is the achievement of a other humans that speak powerfully to us as humans. Here is the musical equivalent of a cathedral. It's structure is large, but balanced. It can be seen from many perspectives from far away to close from the outside, to panoramic (gazing up at the dome) to detailed and allegorical up close on the inside. A cathedral can be experienced as the story of creation to the triumph of man.
This musical parallel that we are considering does all those things. It can comfortably express to the listener the void at the beginning of creation, creation itself, struggles and contemplations as humans develop, and triumph at the finale. And it is on this same vast scale as a cathedral. We individuals are so small in its presence, and yet we swell with pride that a single human being made it and a relatively small group of human beings can bring it to life in performance.
And in the end, having traversed this most massive and detailed canvas, can you imagine a single note (a single brush stroke) that could be changed to make the whole better? No? Then you have experienced perfection. How could that not be beautiful?"
And then he dropped the mic...