Start with a basic 3:2 polyrhythm, written with 8th notes representing the 3 side. Notated here for cymbal and snare drum:
The native */4 meter for this is 3/4— that's the shortest */4 meter that can hold the uninterrupted pattern in a single measure. We get that by playing that pattern twice:
To be clear, this is not necessarily about a literal 3:2 polyrhythm, with three pulses played against two pulses. It's about fitting a running dotted-8th note rhythm into */4 meters— mainly 2/4 or 4/4. The 3 side of the polyrhythm, the 8th notes, just represent the context— the implied subdivision of the time signature. Our main interest is the dotted 8th notes:
As these rhythms occur in nature, they don't always start the same way. Here's the above pattern starting on its second beat:
Extend the pattern one more beat to put it into 4/4. The dashed “imaginary” barline divides the measure in half, which will be significant in a moment.
Now the weird/interesting part— reverse the pattern to start with the second half first:
...we see that same type of move in clave-based music, with 3-2 and 2-3 clave orientations, and we see it in Brazilian music. It's not so weird if we think of the rhythm as two measures of 2/4 rather than 4/4; I use a single measure of 4/4 only because it's common in modern North American music. The idea of reversing the parts may seem strange in the first place, but it certainly must have evolved organically. I think it's only seems strange because we're imposing a “1” on music that isn't as 1-centric as we are accustomed to— at least in the musics where these rhythms first came into common usage.
PROOF THIS IS NOT SOME JIVE I'M JUST MAKING UP:
The rhythms resulting from the above system turn up everywhere in nature. Two quick examples, using that last rhythm: it is the same as this common bossa nova rhythm, frequently mislabeled “bossa clave.” Here it is in a complete groove:
And it occurs in DC Go-go music— it's the bass drum rhythm that is the foundation of the entire style:
Now, the end game here is not to theorize about rhythm. I'm more interested in developing a fairly complete funk drumming vocabulary with a few simple drumming ideas, based on these concepts. The vocabulary already exists— I just want to turn it into a method. It's also good to understand the extent to which this 3:2 polyrhythm is truly the life blood of African-American music, and Afro-Latin music, and all of their derivatives. Without this, we would all be playing marches.