This article contains affiliate links, which means we may earn a commission if you make a purchase through these links. It's a seamless way to support our work at no extra cost to you.
If you're itching to add some depth and flavour to your tunes, let's talk about Euclidean rhythms. In this article, we'll dive into what they're all about and why they're a game-changer for Eurorack musicians.
Diving Into the Theory
The Euclidean rhythm takes its name from Euclid, an ancient Greek mathematician who lived in the 4th century BC and is known for his influential work in mathematics, Elements. This rhythm is based on Euclid's algorithm, which is used to find the greatest common divisor of two numbers.
In other words, the concept of Euclidean rhythms revolves around evenly spaced beats. The algorithm takes the number of beats and steps and distributes the beats evenly across the steps. For instance, if you have 16 steps and 5 beats, the algorithm will allocate the beats evenly across the steps while maximizing the distance between them. The following image of a ring illustrates this example.
You can use this technique to create complex patterns of beats and rests that can add a unique flavour to your music. One of the most powerful aspects of Euclidean rhythms is their ability to create complex polyrhythms.
A polyrhythm is a pattern of beats that has more than one rhythm playing at the same time. With Euclidean rhythms, you can easily create polyrhythms that are based on the same underlying algorithm. This allows you to create complex and interesting patterns that are still coherent and easy to follow. With the help of Eurorack modules, you can create your own unique Euclidean rhythms and take your music to the next level.
The Theory of Euclidean Rhythms in Eurorack
There are a number of different ways to generate Euclidean rhythms in Eurorack music. You could apply the theory manually to a sequencer although there's one popular method that is to use a dedicated Euclidean rhythm module, such as the ALM Busy Circuits Pamela's New/Pro Workout. This module allows you to easily create Euclidean rhythms by adjusting a few parameters, such as the number of beats and the number of steps. Other modules facilitate the generation of Euclidean patterns.
Here are a few:
Ornament and Crime with Hemisphere firmware installed to use the Annular Fusion Euclidean Drummer app
Constellation by Acid Rain Technology
Euclidean Circles by VPME
A-Ryth-Matik by Modulove
and others
Once you have generated a Euclidean rhythm, there are a number of ways to use it in your Eurorack music. One common technique is to use the rhythm to trigger various sound modules in your system. For example, you might use the rhythm to trigger a drum, a bassline, and a lead, creating a complex and evolving musical texture.
Here are a few more examples of how you can use Euclidean rhythms in your Eurorack system:
Control the gate or trigger of an envelope generator. By doing this, you can create evolving and complex patterns of modulation that are synchronized with the rhythm of the music.
Control the modulation depth of a filter or other processing module. By doing this, you can create rhythmic patterns that sweep through the sound, adding accents, movement and interest.
Control the rate of a delay. This will create dynamic effects that are synchronized with the rhythm of the music.
Adjust the tempo, length, and other parameters such as 'reset' and 'rotate' with triggers. This will cause your patterns to evolve over time, adding even more complexity with a heightened sense of unpredictability to your compositions.
There are countless ways to use Euclidean rhythms in your Eurorack system, so don't be afraid to experiment and see what works best for you and your music!

Put Into Practice
Are you ready for a challenge? Let's put the theory of Euclidean rhythms into practice.
Imagine you have a 16-step sequencer and you want to create a beat that combines a kick, a guitar, a bell, a bongo, and a hi-hat.
The kick has a 4-beat pattern
The hi-hat has a 13-beat pattern
The first envelope has a 12-beat pattern
The second envelope has an 11-beat pattern
Your challenge is to manually create a 16-step pattern for each instrument using Euclidean rhythms and make these instruments play well together.
You'll need to use the Euclidean algorithm to distribute the beats evenly among the steps of the sequencer. Remember, the goal is to create a pattern that feels natural and musical, even though the beats are not evenly spaced. Once you've distributed the beats according to the theory, you can tweak the pattern by adjusting the velocity of the hits, or applying effects to each instrument.
With a little bit of experimentation, you can create a complex and compelling rhythm that will make people want to move their feet.
In Sum
Euclidean rhythms are a powerful tool for any Eurorack musician. They are based on a simple mathematical algorithm that can create complex and interesting patterns of beats and rests. With the help of Eurorack modules, you can easily incorporate Euclidean rhythms into your music and take your sound to the next level. So why not give it a try? Experiment with different parameters and see what kind of grooves you can create.
Affiliate links
A seamless way to support our work at no extra cost to you.