I enjoy improvising piano in what I call (perhaps incorrectly) a "honky-tonk" or "ragtime" style, usually involving a steady stride or two-step in the left hand, and playing over that with lots of syncopation in the right hand. Harmony usually consists of majors and sevenths.
I am always impressed when I hear the introduction of other chords, fleetingly introduced (perhaps in a chromatic manner); they seem to be slipped in while transitioning from I to IV chords for example. I am assuming they are augmented or diminished chords, but I have never understood the theory of which ones to use and where.
Is there a systematic way of thinking about this, or is it - just - what sounds great?
EDIT: Here is the only quick example I could think of, off the top of my head. (Can you tell I have young kids -- please excuse the example). See middle of the piano solo at exactly 2:15 there is a chromatic bit. What is going on there, harmonically? And in general what harmonic principles is the piano player using throughout (e.g. at 1:41, and throughout piano solo 1:57 to 2:18).