Yesterday, the show-business icon Carol Burnett celebrated her 90th birthday, and NBC aired its tribute special Carol Burnett: 90 Years of Laughter + Love, which taped last month. Burnett used to end episodes of The Carol Burnett Show, the sketch-comedy series that ran from 1967 to 1978, with “I’m So Glad We Had This Time Together,” a song that Burnett’s husband Joe Hamilton wrote for her. On last night’s special, Katy Perry, herself a kind of show-business icon, sang the song to Burnett.