Different music packs in DoTA 2 have icons that all seem to have the same note sheet as a background. Some examples:
What is the composition's name? Who is the author? What is the history of its creation and usage?
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Perhaps it's from the game's music itself? I'm not sure enough of it is visible to really say with any certainty, but regarding copyrights it would be simplest to use the game's own music.
Watching a video of the orchestra recording the music, they definitely have actual sheet music printed out. So there was probably music files stored away which would have been easily accessible when creating these graphics.
According to this page, the composer of the orchestral music is Jason Haynes.