Dave McKenna (1930 – 2008) is the undisputed master of left hand bass for jazz pianists. What he did with his left hand was much deeper than just that. He changed the function of the left hand often in his playing. His right hand was also exceptionally fluid and had a beautiful tone as if he were playing Chopin.
In the following video clip, he plays “Lulu’s Back in Town”. You can observe how he changes the function of his left hand. Towards the end of the clip, he modulates six times through increasingly ascending keys.
Here he plays “Serenade in Blue”. The camera is always on his hands. You’ll see that he has incredible economy of motion. He plays block chords, left hand bass, left hand “strumming” chords and so on. The secret to his “feel” is when he phrases the melody behind the beat, as singers often do, and plays bass on the beat and chords slightly ahead of the beat.
McKenna knew by heart something like a kabillion songs, and he could play them in any key. He often played medleys, with song-to-song connections ranging from the obvious to the somewhat obscure, but based around a theme. Here he is playing a Rodgers and Hart medley.