The song came gushing out like an open hydrant on a hot summer day, but for Natalie Cole, it was a complicated kind of high. Minutes before she heard her breakthrough hit, “This Will Be,” on the radio for the first time in 1975, she had scored a heroin fix and was tripping down 113th Street in Harlem. Drugs were a recent mainstay; she started using heavily in college, during the substance-fueled psychedelic era (she still managed to get her degree, in psychology). Music, meanwhile, was her birthright — after all, she was the daughter of Nat King Cole, one of the most beloved singers of the 20th century. Growing up in the exclusive Hancock Park section of Los Angeles, she could wander into the living room and find the likes of Ella Fitzgerald, Louis Armstrong, Sinatra gathered round the family piano. Now that she had a big hit of her own, fame was proving to be a stronger stimulant. She kicked heroin, married one of her producers, had a son, had more hits, appeared on “The Tonight Show.”