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...this is very similar to some other things we've been doing here lately, like the Stick Control applications on the drumset. Basically identical in fact, except the Stone thing is geared towards funk and the ECM feel, and this is more about basic solo vocabulary in jazz— and rhythmic interpretation for ensemble playing in general. Basic, non-timekeeping rhythmic functionality on the drum set.
We'll use the one-line exercises starting on page 34 of Progressive Steps to Syncopation— current edition. Here's one measure of line 1 from on p. 34:
As I always do with this book, we're going to re-interpret the stems-up part, and ignore the stems-down part. We'll use a very common method for orchestrating that rhythm on the drum set based on long notes and short notes; short notes are untied 8th notes; long notes are everything else— tied 8th notes, quarter notes, and dotted quarter notes. Play the short notes on the snare drum with your left hand, and the long notes on the bass drum:
First play the cymbal (any cymbal, with your right hand) in unison with all of the notes:
Then play the cymbal only on the long notes— the bass drum notes:
Next play the short notes with both hands in unison, and long notes on bass drum only:
This is all simple enough that you can easily begin moving your hands around the drums and cymbals, and begin thinking about the melodic shape of what you're doing.
Let's look at the line 4 exercise:
The top line played on snare drum and bass drum, according to the short note/long note system, playing the cymbal along with all notes:
Then cymbal on the long notes only:
Short notes with both hands in unison— these unison notes can be played on any two drums, or on the snare drum with any cymbal:
Where there are two or more running 8th notes, you could also play them with an alternating sticking, with the hands on the same drum, or on different drums:
When doing that, I prefer to play the right hand on the &s, and the left hand on the beat. You could also do the alternating sticking on the cymbal-on-long-notes way.
Play through the one-line exercises with all of these interpretations, then begin working on the long syncopation exercises beginning on page 38. Move the hand parts of the exercises around the drums and cymbals, and change from one interpretation to the next without stopping. Then improvise your own solos while trading 4s or 8s.
Listen to some 50s-60s Roy Haynes (Out of the Afternoon, Misterioso by Thelonious Monk), Frankie Dunlop (the tune Jackie-ing, and the albums Criss Cross, or Monk's Dream by Thelonious Monk), and Billy Higgins (Art Deco by Don Cherry) to hear these types of things played in actual music.
Download this one page list of basic orchestrations if you haven't already memorized them.