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Composer Yuki Kajiura is responsible for many memorable anime themes and background music. Also, she sometimes collaborates with a singer or a group of singers to form her "solo" project, FictionJunction.
Ditto for Xenosaga, one of her few Video Game soundtracks (to be specific, the cut scene themes for Episode II and the entirety of Episode III. Her work is all kinds of awesome in both).
Most of Noir's soundtrack is composed by Yuki Kajiura and is absolutely fucking brilliant.
"Canta Per Me". You've got a somewhat melancholy romance song, sung by a Japanese woman in Italian, mostly used to score either awesome shootouts or the buildup to awesome shootouts, and somehow it just works.
"In the Land of Twilight, Under The Moon" is a wonderfully composed song that fleshes out a very descriptive atmosphere primal, chaotic, and hedonistic urges and celebrations through its lyrics and chaotic use of saxophone and guitar riffs. There is nothing you can't like about this song.
The live version sung by FictionJunction manages to blow the original out of the water.
"Aura" is an absolutely haunting theme that perfectly portrays Morganna's plotting regarding the birth of Aura, showing both the dark and light sides of "The World".
The entire soundtrack of Le Portrait de Petite Cossette amounts to this, but the "Main Theme" is probably the best example, if only for its use at the end of the series when Eiri uses his own blood to paint a portrait of Cossette in order to defeat the spirit of the grudge contained in the portrait that Cossette's murderer painted of her, which was why he killed her.
Kalafina sampled this song and gave us the gorgeous "Manten", the ending song to Episodes 18 & 19. It's worth noting that the song is very fitting for the episodes it was used in, especially since the lyrics are possibly hinting at Kiritsugu'sdark and troubled past.
FictionJunction graces us with their epic live rendition of "let the stars fall down".
"Point Zero", the epic song that is used when Kiritsugu, Kariya, Tokiomi, and Waver are summoning their servants.