When in 1979 The New Yorker's Andrew Porter suggested that Elliott Carter was by consensus the world's greatest living composer, there was pushback. Some find his music's intricately glittering surfaces impenetrable and self-indulgent, its complexity mere aggression. (That Carter never seemed to demur at his canonization was another sticking point; as Virgil Thomson quipped, "When Aaron [Copland] reached the top, at least he sent the elevator back down.") But other listeners have felt that the music of Carter's prolific last years—like that of so many composers—had mellowed; no less intricate, it seemed to want to beguile rather than baffle. For example, in his 2008 Flute Concerto, the knotty orchestral chaos remains subordinate to a flute line of Debussyan lyricism; the celestial aria for the soloist in the middle of his 2001 Cello Concerto is even lovelier. This weekend, the Seattle Symphony will earn a special place in Carter's life story when they premiere his last completed orchestral work, Instances, finished last April before his November death at age 103. (By coincidence, on Wednesday, the Juilliard String Quartet, long associated with Carter, will play his 1995 String Quartet no. 5 in Meany Hall.) Benaroya Hall, Third Avenue and Union Street, 215-4747, seattlesymphony.org. $19–$117. 7:30 p.m. Thurs., Feb. 7; 8 p.m. Sat., Feb. 9; 2 p.m. Sun., Feb. 10.