Have you ever tried to improvise over a left hand "vamp." You know, those repeating patterns that Keith Jarrett and others have popularized?
If you have practiced vamps, then you've probably been frustrated at one time or another that you can't always keep the left hand pattern going exactly the same every time while you improvise freely with your right hand.
Well, there's the hint: (whisper) Keith Jarrett doesn't play it exactly the same each time either.
I mean, he could play it the same way each time if he wanted to, but he usually doesn't. (For proof of this, check out the official transcription of his legendary Koln Concert.)
What happens is that the LH vamps adapt to what he plays with his right hand. If the RH plays something fast, then maybe the LH leaves out a note or two. Or if the RH accents a particular beat, then the LH may hit that accent too, or whatever.
My point is that there's a relationship between the two hands, even when playing repeating LH patterns. A fluid relationship, where the characteristic sound of the vamp is repeated in each measure, even as some of the notes and rhythms continually change.
Here's Keith Jarrett playing one of his signature gospel-jazz vamps:
Keith Jarrett Solo Piano
When you practice vamps, start by playing the pattern exactly the same each time. Then, after it becomes natural, start varying it a little. When you add the right hand's improvisation, you'll already be a little flexible to accommodate anything your right hand wants to play. Your left hand can be a dynamic, responsive rhythm section, even while playing a seemingly repetitive pattern. At first this might seem difficult, but in the long run it's actually easier. Have fun!
If you're a Keith Jarrett fan, I have a whole series of videos devoted to showing you his pianistic techniques in my jazz piano course. You can check it out HERE.