In the video below, made in 1941, Thomas Wright "Fats" Waller (1904-1943) performs "Honeysuckle Rose," one of his best known compositions. It's an example of a "soundie," which are "three-minute American musical 16mm films, produced ... between 1940 and 1946, each containing a song, dance and/or band or orchestral number.... The films were displayed on the Panoram, a coin-operated film jukebox or machine music, in nightclubs, bars, restaurants, factory lounges, and amusement centers." The "woman on the piano" is Vivian Brown, who appeared in a number of soundies.