The triplet is a fundamental subdivision in jazz. It’s normally thought to provide the essential swing feel (even though the straight-eighth feel predominates at faster tempos). The most common example in drumming is the ride-cymbal beat (Ex. 1). Most comping vocabulary in jazz relates to the easy, natural flow of Ex. 2.
The off-beat triplet provides a terrific means to inject rhythmic tension because it goes against the 4/4 grain. Play Ex. 3 using two hands, and then play the off-beats with just the left hand (Ex. 4), combined with the ride and hi-hat from Ex. 1. Also try separately practicing the bass drum (Ex. 5) and hi-hat (Ex. 6) while playing the ride pattern. Off-beat triplets can begin and end anywhere in the bar, although the final triplet of beat 4 often works best (for starting and stopping à la Philly Joe Jones). Use in your music as desired.
Peter Erskine has played with Weather Report, Steps Ahead, and the Stan Kenton Orchestra, and holds an honorary doctor of music degree from Berklee College Of Music. http://petererskine.com