In one sense, it must have been easy for early jazz pianists to figure out what to do with their left hand.
If you played jazz piano in the 20's, the default LH technique was stride. Oom-pah, oom-pah, oom-pah. Once you mastered the basic stride pattern, you'd develop a few variations and be all set.
If you played bebop in the 40's and early 50s, you'd play shell voicings to give the bass player some room to walk bass lines. Later, perhaps you'd adapt Bill Evans' rootless method to your own style.
In every era of jazz, there were one or perhaps two main ways to use your left hand. In a way, each jazz piano style can be largely defined by its main left hand technique.
Jazz piano students frequently ask me what to do with their left hand while playing standards. There are so many options available that it can seem overwhelming at times. And even when we master each approach, which one expresses what we ourselves want to express in this post-modern musical age?
These questions are best answered by each of us individually, and indeed, every one of today's prominent jazz pianists has found his or her own solution to this problem. The first step is to master each approach. Take a standard like Autumn Leaves or All The Things You Are and learn to play it using each of the left hand techniques I've listed below (along with a pianist who used the technique). Once you can do this, you'll be able to decide "on the spot" which approach to use with each tune you play, or if you want to mix them up or develop your own variations on the basic methods.
Here are the most common left hand techniques for jazz piano:
1. Stride (Fats Waller)
2. Shell voicings (Bud Powell)
3. Root plus 3rd and 7th (Bill Evans when playing solo)
4. Rootless voicings (Bill Evans in trio setting)
5. Low 5th up to a chord built in 4ths (McCoy Tyner)
6. Adding inner-voice movement (Keith Jarrett)
7. Doubling RH solo down an octave or two (Oscar Peterson)
8. Walking bass (Lennie Tristano, Dick Wellstood)
There are others, too, such as contrapuntal motion, but this is a good list to start with. Take some time and really learn each technique. Then you'll be able to play with a wider stylistic palette and become a more confident and fluent improviser.
Good luck with your music!
Here's a good list of tunes to practice the above styles on.
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