Dave McKenna is, I think, not so well known as he should be. I have a large handful of his CDs, and the Ogg-Vorbis files ripped from those were the first things I put on my new Cowon D2. His style, like (say) that of Art Tatum or Fats Waller or Teddy Wilson, is instantly recognizable. The Wikipedia article at the link identifies the sources of his sound:

From the link above:

McKenna’s renditions usually begin with a spare, open statement of the melody, or, on ballads, a freely played, richly harmonized one. He often states the theme a second time, gradually bringing more harmony or a stronger pulse into play.

The improvisation then begins in earnest on three levels simultaneously, namely a walking bass line, midrange chords and an improvised melody. The bass line, for which McKenna frequently employes the rarely-used lowest regions of the piano, is naturally being played in the left hand, often non legato, to simulate an actual double bassist’s phrasing, the melody in the right. The chords are interspersed using the thumb and forefinger of the right hand or of both hands combined, if the bass is not too low to make the stretch unfeasible. Sometimes he also adds a guide-tone line consisting of thirds and sevenths on top of the bass, played by the thumb of the left hand.

His famous four-to-the-bar “strum” is achieved by the left hand alone, playing a bass note (root/fifth/other interval) plus third and seventh, leading to frequent left-hand stretches of a tenth, which is why these voicings frequently appear arpeggiated, with the top two notes being played on the beat, the bass note slightly before. These voicings are often subtly altered every two beats, for variety. This playing style is frequently mistaken for a stride piano, which it is clearly not, as it is of a four-beat nature, as opposed to the two-beat “oom-pah” of true stride piano, as exemplified by Fats Waller, James P. Johnson, and the like. McKenna usually reserves all-out stride for sections where a bassist would play half notes, i.e. ballads and Dixieland-tinged material. The result is the sound of a three piece band under one person’s creative control.

McKenna can weave a spontaneous melodic line, usually with lots of chromaticism and blues licks, over the bass line. The bass can be anything from single notes to repeated chords like a rhythm guitar to a full-blown stride piano, the latter often reserved for the height of a song’s development.

However, the most astonishing feature of McKenna’s playing is his infallible sense of time and tremendous swing. There is a highly constant, “objective” time in his left hand bass lines, and also his left-hand chords or chord fragments are very much on the beat. The right hand chords are often ahead of the beat, whereas the melody frequently lags slightly behind. This polyrhythmic tripartition gives rise to the compelling rhythmic drive of his playing.

Many players can play left-hand chords and right hand improvisation, or walk a bass line and improvise with the other hand. It is McKenna’s ability to add the third element of the harmony in the middle that defines his original approach. The main difficulty is not so much a pianistic as conceptual one. If you can HEAR the three parts, you can play them. If the effect of the music isn’t clear mentally, it won’t appear easily at the keyboard.

You probably should get a Dave McKenna CD. Try Shadows ‘N Dreams—here’s the tracklist (and at the link you can listen to segments):

1. Dream a Little Dream of Me
2. I Had the Craziest Dream
3. Me and My Shadow
4. You Stepped Out of a Dream
5. Darn That Dream
6. Shadowland
7. Deep in a Dream
8. Hit the Road to Dreamland
9. The Shadow of Your Smile
10. Dream ‘N’ Blue
11. Shadow Waltz
12. I’ll See You in My Dreams
13. We Kiss in a Shadow
14. I Have Dreamed