Polyrhythms have always been in all my favorite tracks even before I knew what polyrhythms were. Radiohead, Mars Volta, Aphex Twin and Tool being some great examples.
I had my first experience with poly rhythms when I was a very young guitarist playing in a death metal band. It was always unimaginative 4/4 rhythms, mostly down-strokes which worked great for heavy distorted guitar based metal. We occasionally got progressive with the arrangements, but only because we had a great keyboardist that glued us all together. On one of our sessions, an older, hippy, slightly nuts looking guy came to join us. He played guitar in the most odd way, I remember thinking, it fits and sounds cool as hell but i didn't have a clue what he was doing and it was just a simple 3 note pattern. 10 years on, and from what I know now, it was a 3 over 4 polyrhythm!
Even before I knew what a 3 over 4 pattern was, I loved poly rhythmic music. All my favorite music included polyrhythms, bands like Tool, who I have been fascinated with, and still am, Radiohead, who explore more and more polyrhythms throughout their musical journey, Techno music, Minimal being a big one, Ambient, Philip glass and Aphex twin. If you don't know these people, I'd highly recommend checking them out!
Polyrhythms are everywhere, polymeters are used everywhere and Syncopated euclidean rhythms are everywhere. I loved all this music without even knowing they followed and shared similar techniques, theorys or rhythmical mathematics.
After my heavy metal guitar phase, I got into electronic music and found certain tracks gave me that similar feeling, simple notes but mesmerising rhythms. I started learning with the DAW Steinburgs Cubase and I worked mostly with MIDI. It really made me realise the different patterns, sequences, quantitation and time signature options available. I needed to understand how music explores them. It made me want to know how to utilise them.
This is when I found Polyrhythms.
I explored the internet learning how, when, why, and I was left confused due to the terminology and the conflicting ideas on what a polyrhythm is.
The tutorials either describing these rhythms as an arrangement and meter process, or a pattern confined within a repeating rhythm. This is because in the electronic music production a lot of educators are calling poly meters, poly rhythms! There is a difference, but they do share a similar concept, which is multiple rhythms playing at the same time, or, to put it into math, fitting an odd number of beats or subdivisions into an even number of beats or bars.
As mentioned above, the term poly, whether is poly rhythm, meter or metric, refers to working with odd and even numbers of beats, bars or subdivisions, together.
Hopefully the following sheds some light onto what that all means.
What are Polyrhythms?
The term Polyrhythm describes multiple rhythms played together, and this is especially noticeable when an odd number of beats, or subdivision of beats, are played with an even number of beats, or subdivision of beats. In other words, the first beat of the rhythm will always play at the same time with the other beats spread out evenly in time. So imagine counting 1, 2, 3 with a second person counting 1, 2 ,3, 4 at the same time, but ensuring both counters count the 1 at the same time every time. To achieve this, it means 1, 2, 3 needs to be counted at a slower speed than counting 1, 2, 3, 4.
To put this another way, within a 4/4 meter, an even number of beats is typically used per bar, In Dance music a floor to the floor beat is described when a kick drum is played on each of the 4 beats, spaced out evenly within the bar. If we were to display this on a 16th grid it would look like this. x---x---x---x---
But what if you decide to also use an odd number of beats to accompany the 4/4 pattern?
If we were to add a second pattern to this, let say 3 beats, or 3 subdivision of beats (depending on the quantised grid you want to use) then you would be creating a 3:4 polyrhythm. For it to be classed as a polyrhythm, the initial beat of both patterns need to start at the same time, on every beat, or bar, counting 1, 2, 3 and 1, 2, 3, 4 at the same time, but ensuring that number 1 is counted at the same time on both the 4;4 and 3;4 patterns.
I have purposely chosen a 3:4 pattern as this grid is available on most sequencers or DAW's by selecting a triplet grid, the 3;4 pattern I have described would look like this.
A 5:4 example would look like this
and a 7:4 would look like this
What are time signatures?
Before I explain what polymeters are, it is important for you to understand what a time signature is. I have kept the time signature examples in this tutorial brief, but if you wanted a better understanding you will find a wealth of easy to follow information on the internet for this topic.
A time signature is made up of 2 numbers to express how many beats are in a bar. The first number tells us the beat or note length and the second number tells us how many of these, spaced out equally, will fill a bar. For example, 4/4 means that 4 quarter notes equals 1 bar or music, a 3/4 time signature means 3 quarter notes make up a bar of music. As a computer musician, this terminology would be most recognisable when setting our quantization grid as per the screen shot below.
A 4/4 quantised grid
What are Polymeters?
Now you understand time signatures, polymeters should be far easier to understand than polyrhythms, this is due to the fact that standard quantization grids are used and shared between the different rhythms, but instead, multiple time signatures will be played together, eg 4/4 pattern played with a 3/4 pattern will be classed as a polymeter. This will be made obvious when looking at the arrange page as the phrases or rhythms will repeat on different bars. Again like polyrhythms this is noticeable when using and even number pattern such as 4/4 with an odd numbered pattern such as 3/4, 5/8 or 7/8.
The following shows an arrangement example of a 4/4 (top) vs a 5/4 (bottom) pattern. As you can see the 4/4 pattern repeats every bar where as the 5/4 pattern extends past the bar (5 beats). Both patterns played together means the phrase wont repeat until bar 5 and again on bar 10, this can be really useful to make 2 repetitive rhythms or phrases sound far more interesting.
Using Euclidean patterns in Polyrythms and Polymeters
To put it simply, Euclidean Rhythms are patterns that are spaced out equally within a bar/ phrase or time frame. I am not going to talk about the mathematical equations used to work out the spacing but I have included a video tutorial below from Omri Cohen, which demonstrates using an euclidean sequencer to create rhythms and polymeters.
Euclidean patterns work extremely well with polymeters. Due to the predictable nature of the patterns, the euclidean equation helps playing s combination of different time signatures more pleasing to the ear. A Euclidean sequencer is extremely fun to play with, however the patterns can be programmed quite easily using standard MIDI.
The video example below also mentions using the sequencer to create polyrhythms, although the patterns demonstrated are not typically polyrhythms (more of a micro polymeter) both rhythms share the same grid, the initial beat on both patterns repeat at the same point and they share the same time signature, however the second rhythm using odd numbers is used to accent beats of the first rhythm. This type of rhythm doesn't strictly fall into the polyrhythm category above and could instead be described as an syncopated rhythm, but as you will hear, it sounds great.
There is a number of youtube tutorials which cover this better than I can describe it in words, so would recommend the following
https://www.youtube.com/watch?v=htbRx2jgF-E&t=378s from ANDREW HUANG
From Transmission Samples
Differences between polyrhythms and polymeters
I hope this means we will see more understanding and more experimentation with polyrhythms and poly meters in western music, as I for one think it's the secret sauce to a great groove and a mesmerising record.