This is a loose collection of stuff with which you can drill a rather busy, modern funk shuffle feel or triplet funk feel, a la Lopsy Lu or The Brecker Brothers' Inside Out:
OK, those examples are 40 years old, but people still play this way— if they're lucky, actually...
And this is indeed another practice method for use with Ted Reed's Syncopation— if you're not practicing that way, you'd better get on it. Talk to your teacher about it, or get some Skype lessons with me— something. This is how you learn to play. The examples here use the very famous first line of the very famous p. 37 exercise (which is on p. 38 of the new edition of the book):
We'll be using the Syncopation section of Reed— pp. x-x— reading the top line only, as is usual for that book. Play the book rhythm on the bass drum, except notes on the 2 and 4, which you play on the snare drum. We want to have a running snare drum backbeat, so if there's a rest or a held note on the 2 or 4, go ahead and add snare drum. Play quarter notes on the hihat or ride. Swing the 8th notes.
Next, do the same thing, but play entire line on the bass drum as written, plus the 2 and 4 on the snare, and the quarter notes on the cymbal. There will be some unisons between the snare and bass now. I haven't notated anything for the left foot here, but when your right hand is on the ride cymbal, you can add left foot on 2 and 4, or wherever you like.
The next few things are based on a very common Reed method, in which the RH/RF are played in unison, and the LH fills in the triplets. I usually move the RH to the snare occasionally to break up any multiple lefts, you can do this, or not:
Do this same method, except accent the 2 and 4 on the snare drum. If there is no snare on 2 or 4, add it:
Do that again, with quarter notes on the cymbal:
And with a jazz rhythm on the cymbal:
You could also do it with a straight shuffle rhythm on the cymbal if you are so moved. That gets to be a whole lot of activity when filling in the triplets, so I only bother with it when playing the simpler version.
As I'm further along in drilling this, I will occasionally go to the alternating-sticking version of the triplet way, with accents on the cymbals. On either the last measure of a line or the last two measures, like a fill. In this style of playing, doing this fill-like thing, I will play the snare drum fairly strongly— for the rest of this drill the snare should be played softly, except for the 2 and 4.
That adds up to a lot of stuff. You can rigorously play all these things with all the exercises, and it will take maybe 90 minutes to just play through it. If you've played that first triplet interpretation before, you can get through it much faster. Make about a 30-45 minute drill out of it, moving fairly quickly through the easy parts, combining methods, adding your own fills (alternating triplets on the drums or with both hands in unison are always good). We're interested in improvising, reading, and developing musically here, so you don't need to be too picky about getting every detail of the instructions exactly right.