There's a very big history with the drum set and jazz drumming in that the drum set developed around the time that jazz started to make its way into the music scene through the Americas, especially through the south part of the Americas, coming out of New Orleans style of music. To get a basic understanding of jazz drumming you want to have a good idea about what to play in your time portions of your body. What I mean by time, I'm talking about the patterns that give out the time which would be your ride cymbal, your left foot hi hat, or your hi hat foot.
The best place to start with jazz playing is to understand the pattern or what we call the ostinato to play in jazz. That would be a pattern on your ride cymbal playing one, two, and three, four, and one, two, and three, four. It sounds like this.
Typically you want to aim for the body portion of the ride, and you want to get a nice tone from your cymbal rather than just hitting it really strong. I'm also using thinner sticks to get a little bit more of a jazz tone to my playing. Typically what you're going to start doing is playing two and four on your left foot with that. Just playing, one, two, three, four, one, two, three, four. As you play them together it sounds like this. One, two, ready, play.
Now, as drummers, we spend a long portion of our time developing independence and coordination against that pattern. The best thing to do would maybe start with just some quarter notes on either the bass drum or the snare drum against this pattern. In addition, notice that I've tuned up my bass drum and tuned my snare drum down to create more of that jazz tone we're looking for.
What I'm going to play right now is just quarter notes on my bass drum against this pattern boom, boom, boom, boom or one, two, three, four so you can hear what's called a walking bass line against it. One, two, three, four.
In addition I'm now playing heel down which is just the pivot from my ankle, and I'm playing it lightly. It's called feathering the bass drum just to back off of it. You could do the same thing with snare, separately, to develop your snare hand against that pattern. One, two, three, four.
And though there are infinite patterns that you could play against that in addition to changing that time pattern, that right there is a good place to start to develop the independence you need for jazz drumming.