A three-over-four polyrhythm is comprised of sets of three equally spaced notes and four equally spaced notes that occupy the same timeframe. Typically both sides of the polyrhythm start together on the same note and utilize the same subdivision. If we look at a measure of 8th-note triplets in 4/4, we have a total of twelve notes that are divisible by both three and four. Quarter notes comprise the four side and will represent the pulse. The three side is created by playing every fourth triplet partial—one-trip-let, two-trip-let, three-trip-let, four-trip-let.

Exercise 1 demonstrates this with 8th-note triplets on the hi-hat and four quarter notes on the bass drum, while the three side of the polyrhythm is played on the snare.

Within an 8th-note triplet framework, you can displace either one or both sides of the polyrhythm to start on any partial of the triplet. The rhythm starts to get especially interesting when you double the subdivision from 8th-note triplets to 16th-note triplets. Doing this allows you to displace one or both sides of the polyrhythm into positions where none of the notes from either side are played simultaneously.

Let’s explore this using 16th-note triplets. There will be twice as many partials between each note of the four side of the polyrhythm. A great way to help internalize the spacing is by using a sticking pattern that fits evenly within it. There are eight 16th-note triplet partials between each beat of the three side, so let’s assign a common sticking pattern—RLRR LRRL. The three side becomes clear when you accent the first note of the sticking.

Exercise 2 displaces the three side forward by one 16th-note-triplet partial. The sticking pattern is phrased between the snare and two pairs of hi-hats.

In Exercise 3 we’ll move the three side forward by two more partials, to the “&” of beat 1.

There are eight permutations of the three-note grouping in this polyrhythm. Experimenting with each position will help you internalize the feel of the three side from every point in the measure.

You can also displace the four side. Exercise 4 moves the four-note grouping to the “&” of the beat, with the left foot on the hi-hat, while the sticking pattern is voiced on the toms. Start by getting familiar with how the tom and snare pattern sounds against the left foot before adding the bass drum.

Exercise 5 voices the hand pattern between a pair of ride cymbals, with the left-hand accents placed on the bell.

In Exercises 6 and 7, the four side of the polyrhythm is played with quarter notes between the bass drum and snare, while an embellished ride cymbal pattern sits on top. The left foot is free to experiment with all eight permutations of the three side. In Exercise 6, the three-note grouping starts on the fourth 16th-note triplet partial, while in Exercise 7 it starts on the eighth. Make sure to start the rhythm on the six remaining partials as well.

While still playing the three side with the hi-hat foot, let’s try a groove that accents the four side on the “&” of each beat with the ride bell. This time the three side starts on the fifth 16th-note triplet partial.

These rhythms get especially interesting when accenting the four side on less common partials. Exercises 9 and 10 have a syncopated right-hand pattern between the hi-hats and a stack. The stack accents the four side on the fifth 16th-note triplet partial. The kick and snare create a funky groove, and the three side is played with the left foot.

One of my favorite ways to play polyrhythms is within double bass grooves. In Exercise 11, the four side is voiced with bass drum doubles. The snare plays the three side starting on the third 16th-note-triplet partial.

In Exercise 12, both sides of the three-over-four polyrhythm start on the fifth 16th-note triplet partial of beat 1. We’ll use the hi-hat and stack pattern from Exercises 9 and 10 to accent the four side of the polyrhythm.

The next two examples use a similar double bass approach. However, this time we’ll play alternating three-stroke ruffs instead of doubles. Exercise 13 applies this to the four side of the polyrhythm on the second 16th-note triplet partial. The three side is played with the snare starting on the downbeat.

Exercise 14 is an embellished groove that moves the three-stroke ruffs in the bass drum to the three side, starting on the second partial. The four side starts on the downbeat with quarter-note cymbal accents.

Exploring all eight of the three-note permutations and all six of the four-note permutations can be a lengthy process. We’ve only scratched the surface of what you can do with these ideas to expand your rhythmic palette. Be creative, and come up with your own ways to explore all of the possibilities as well.

Aaron Edgar plays with the Canadian prog-metal band Third Ion and is a session drummer, clinician, and author. He teaches weekly live lessons on Drumeo.com. You can find his book, Boom!!, as well as information on how to sign up for private lessons, at aaronedgardrum.com.