the ending of eternal sonata is a bit tricky to understand. this is what I got out of it after reading a few comments and playing the game 3 times through. This is also from how I thought the game ended so it might not be the same as what you thought!
The point of the game was so the story kept repeating itself over and over again. (Hence the name, Eternal Sonata, so for those of you who didnt know, sonata's repeat themselves... eternaly... eternal sonata) Allegretto's rock and the creepy fortune teller was proof of the dream to keep repeating.
At first, way before the game starts, Frederic is not in the dream. Every time he sleeps, he watches the dream, but never grows attached between any of the characters. (or else he would have saved polka before and there would be no game) When he falls unconcious and he knows it's his last dream, they all meet each other (for who knows how many times again) and quest.
When they climb Double Reed Tower of Sand and get to the top, Polka realizes that they are standing at the end of the earth (which just so happens to be a destroyed and burned version of Tenuto's flower field mentioned in the ps3 ver.) and it is her time to die. They defeat Frederic after he forces them into a fight to test to see if he really is a weak human being. Frederic watches the dream from above after finally accepting death.
Polka, on the other hand, knows that Frederic finally accepted death and knows its her time. She tells them that her mother planned all of this and she knew that she would have to kill herself to save the world. Polka accepts this, not knowing that the dream repeats itself. She backs away slowly to the edge of the cliff and readies herself to jump after whispering to Allegretto that she loves him.
Allegretto finally understands and tries to stop Polka from jumping. He tries everything he can to stop her, but Polka jumps and he screams. After Frederic is actually a part of the dream this time, he accepts his death to save Polka's life. (so pretty much he sacrifices himself for her) But it's too late to save Polka; she has already died and has been reborn into her younger self. (thats the scene where you see Solfege catching her as she falls into the flower field)
But since Frederic has accepted death (which im pretty sure you know by now) Polka can be saved. When she is walking with Solfege in the flower field, she hears his voice telling her to come. Solfege understands and says she is hearing the person who shares the same astra as her, or the person who she believes in. After putting a purple flower in her hair, the Agogo's send her off, back to her old life.
While Frederic is back alive in the dream world, Allegretto is so busy thinking that Beat has to point out to him that Polka is floating in the air, held up by the glowing Agogo's that saved her so many times. Polka realizes that it's the world where she jumped that needed saving and peace restored. When the Agogo's lower her to the ground, her astra recreates the world with peace. While everyone stares at her in awe, Allegretto and Polka run to each other and they both share their love by a tight embrace.
Things that I didn't cover-
Allegretto's purple rock- When the story began, Allegretto gave this rock to Polka as a present to express his love to her. As the dream kept repeating, Polka got to keep the rock and would throw the rock over the edge as Allegretto gave her a new one. Polka claims it was given to her "by the person whom she loved most."
The "creepy" fortune teller-
In the PS3 version of the game, the beginning starts off with Frederic, Solfege, and the fortune teller talking. The fortune teller talks about how a new journey has begun again and she was waiting for Polka to come. After you beat "To Coda Ruins," the group meets the fortune teller at her house and tells Polka that she knows her, but obviously Polka doesn't remember anything about her past lives. She tells Polka to pick a fortune and tie it to Cello Tree. When Polka does so, she tells her that every fortune on the tree is unlucky and Frederic should follow because he shares the same fate as Polka.
It was really long and stuff... and probably a really bad explanation... I hoped you enjoyed it though!
~ Tenuto07