I'm pretty sure the song, or at least that portion of it is in minor.
From what I remember, the song was fairly mellow; possibly a piano solo or orchestral piece. What I have in my head is either a piano or bells, like a music box, but it sounds just as familiar as strings.
I don't know whether that bit is at the beginning of the mix, but I believe it is at the beginning of the source song.
When I think of the song, multiple games come to mind, all of which are RPG's. Suprisingly, none of which have "final" in its name.
I could be totally wrong, but I think it's from either one of the three bazillion chrono remixes, a mana game, a star ocean game, or a phantasy star game.
I found it.
It's Ice Crystal from Star Ocean 3.