The unspecified future...
A peaceful time. Technology has advanced, the world is connected, and with mankind's continued evolution has come the discovery of strange new mental abilities known as Septima. Those who display such powers are called Adepts. A mighty energy
zaibatsu known as the Sumeragi Group has risen to power, overseeing and providing for almost every aspect of comfort and protection in life. In particular, it has acted to protect and shelter Adepts and help them to utilize their powers for the benefit of all.
One such psychic is known to the world as Lumen. A wildly popular virtual pop idol under the auspices of the Sumeragi Corporation, her songs capture hearts around the world, not to mention her sweet, almost fey appearance. There are few her songs cannot charm, and it's said that even the dead will dance at hearing her sweet voice...
Of course, there wouldn't be much of a story if there weren't more to this. The Sumeragi Group is more interested in the psychic powers of individuals such as Lumen, attaining its goals by controlling these young psychics... whether they desire it or not. And Lumen is, in a sense, a fabrication, far more so than an ordinary idol; she is in fact the "muse" or avatar of a 13-year old psychic girl named Joule, far more plain and shy than her muse.
Joule's full power is at present unknown, but her sweet disposition and haunting songs make her a valuable asset. When the lightning psychic Gunvolt, a member of the rebel group Feature (QUILL in the localization) seeking to destroy the Sumeragi Group's power, hesitates to carry out his orders to kill her, she becomes his ally in the fight to come, aiding and even reviving him with her songs.
Fanchar from Azure Striker Gunvolt. More to come after I've had a chance to actually play through. Also, here's Joule.