Unlike almost every other rhythm game I and most people know of, A Dance of Fire and Ice is actually about your sense of rhythm rather than anything else.
It's fairly easy to think of rhythm games whose premise is "hitting a certain sequence of keys to the beat of the song". It's harder to think of games where your only objective is to keep up with the beat.

It's fairly intuitive, really. Just hit any button on your keyboard (or mouse) when the ball is about to land on a platform and you're good. But it escalates very quickly with offbeats, triplets, swing, and many other rhythmic concepts. All of which are borrowed from actual... You know, music.

Have I even TALKED about the visuals? This game is gorgeous!
The levels may start out fairly simple, but there's lots of eye candy buried in there, especially towards the second half of the game. Jungle City has tiles that grow to fill out the gaps between the gaps between the other tiles. there are these UFOs in Classic Pursuit that suck up the tiles you've passed through. Heracles has this big rat boss that you attack by going through tiles and launching them at him.

But the main selling point of this game is still the elegance. Telegraphing the patterns through geometrical shapes and the angles they make with each other is one of the best ideas I've ever come across. Because shapes are understandable. All of us can grasp shapes. We can all see them. That turns the rhythms and patterns which are vague and abstract ideas to most of us into easily digestible, mathematical forms in a way you don't even notice.

Also the music is great too, obviously.