Beginning Thursday, “Black Mountain Songs,” a series of choral works organized by Richard Reed Parry of Arcade Fire and Bryce Dessner of the National will play for four evenings at the Brooklyn Academy of Music. Inspired by Black Mountain College, the rural arts school with known for its loose curriculum and attended by art world greats like John Cage, Merce Cunningham, Cy Twombly, and Robert Rauschenberg, the band members created the works for the Brooklyn Youth Chorus, who range in age from 12 to 17, to perform.