In the story of the anime, one day a black meteorite fell on the world, and the world completely changed. The meteorite produced grotesque monsters called D2, which started running rampant. D2 very quickly banned all music, which was the one thing able to overcome them. But there were some people who resisted the D2. They are young women who hold the power of music, the "Musicart." These young women hold "scores" that are able to defeat the monsters. And there are also people who lead these women, the Conductor.
The anime takes place in America in the year 2047, which has fallen to ruin thanks to the D2. Takt, a Conductor, is partnered with a Musicart named Unmei. Takt yeans for music to be returned to the world, and Unmei wishes to destroy the D2. Their aim is to travel to New York.
(Source: ANN)