18. Polyrhythm & polymeter

This is the 18th episode and in the previous one we talked about time signatures and how we could count the strong beats for each one. If you haven't seen it and if you're not sure about time signatures, I'd recommend watching it first. Today we're going to see how to combine these rhythms to create polyrhythms.

POLYRHYTHM

Polyrhythm is the superposition of 2 rhythms that don't have the same number of beats, but are of the same duration. For example in a bar of 4/4, you could have 3 triplet half notes over 4 quarter notes. Then you have a polyrhythm of 3 over 4. The same duration - the bar of 4/4 - is divided in 3 by the triplets and by 4 by the quarter notes.

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These notes not being of the same length means that they'll become more offset as they'll play.

In the same way you could make other polyrhythms like 5 over 4 or 7 over 5 for instance. 
As long as the two rhythms that are layered fill the same amount of time, usually one bar, it will be a polyrhythm.

If I talk about polyrhythm, I also need to talk about polymeter.

POLYMETER

A polymeter is the superposition of 2 time signatures that don't have the same number of beats per bar, so their bar would be of different lengths.

Combining two rhythms that are not of the same length will mean that the more their patterns repeat, the more offset they'll become, even though each of their subdivisions can be of the same duration.

Let's have a look to see what I mean. This is a 3/4 over 4/4 polymeter.

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We'll have a bar of 3/4. So we'll play the first note, and leave the two others silent. That will be our pattern that will then repeat. It will make 1 e a 2 e a 3 e a 4 e a

And with the bar of 4/4, we'll play the first one, and leave the 3 others silent. That will make 1 e and a 2 e and a 3 e and a

Now if we layer these bars on top of each others, every quarter notes will be of the same length, and both rhythms start on the same beat. But you can see how the hits offset over time.
Because it's a 3/4 over 4/4 polymeter, the two patterns will synchronise again after 3 loops of the 4/4 pattern, or 4 loops of the 3/4 pattern.

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You can notice how this polymeter of 3/4 over 4/4 is similar to the polyrhythm of 3 over 4. They sound identical,  but at different speeds.

That is because their ratio is the same, 3 to 4. And that's probably the most important part, but we'll get back to it.

So to sum it up:
A polyrhythm is one length of time, usually a bar, divided in two different ways. So the notes won't have the same length in the two rhythms.
A polymeter is two rhythms built around the same type of notes, but the total length of the two rhythms are different.

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You can play this polymeter as is, having these hits played with different notes by different instruments or different drum sounds.

But you can also create a rhythm a bit more complex for each layer to see how they combine. That's where knowing where are the strong and weak beats of each time signature can be handy, as it gives you a good base to start with. Again, this is all explained in the previous video about time signatures.

But keep in mind that the ratio is everything. The simpler the ratio is between two meters, the easier the polyrhythm (or polymeter) is to internalise.

If the ratio between the two meters is very complex, like let's say 9 over 15, the polyrhythm will be more difficult to understand quickly.

If it kind of reminds you of the very first video of this series about consonances and dissonances, you're right! Combining rhythms kind of works like combining tones, where the simpler the ratio is between two frequencies, the more consonant they are.

If you want to learn more about the relationship between rhythms and pitches , you can watch Adam Neeley's conference about it on ableton's channel. It's a 45 minutes video talking about how polyrhythms and chords can be related, and then explain few things beyond that point, it very interesting.

The simplest ratio you can have between two rhythms is 2 over 3. Where an amount of time i divided in 2 in the first rhythm, and divided in 3 in the second rhythm.

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This particular polyrhym is called an hemiola and you can obtain it by combining a bar of 3/4 and a bar of 6/8.

The bar of 3/4 is divided in 3 beats, that can each be divided in 2, which gives us this "1 and 2 and 3 and"
And the bar of 6/8, is made of 2 groupings of 3 notes, which gives us "1 e and 2 e and".
So, see how we have this pattern of 2 repeating 3 times, and this pattern of 3 repeated twice.

The hemiola is kinda special because it is a polyrhythm, the same bar divided in two and in 3 beats, but at the same time it's a polymeter, as it's two time signatures combined, where all the subdivisions are of the same lengths.

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The simplicity of this polyrhythm maked it super effective and it have been used in countless musics and genres, from sub saharan African music to Renaissance pieces.

Quick note aside about the relation between pitch and rhythm: the term hemiola was also used by early Pythagoreans to talk about perfect fifths, describing de ratio of two lengths of two strings being 3 to 2. The shorter string would then make three vibrations in the same amount of time that the longer string makes two, producing a perfect fifths.
And that's the kind of things we talked in the very first video of this series.

If you want to see more about how to use the hemiola, you can also check the video of Jake Lizzio from Signals Music studio. A very cool video about the hemiola where he also use it for a composition.

Just before we wrap up this video let's make a last polymeter of 7/4 over 4/4 .

So the two rhythm will offset in a way that it would take seven loops of 4/4 bars, or four loops of 7/4 bars for these two meters to resynchronise.
If we write the first note of each bar, we end up with something like this, so we can see how these meters layer.

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If the length of this whole part was one bar, this would make a poly rhythm of 7 over 4, as there would be 7 beats over 4 beats.

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Which mean that if you can speed that up and internalise it well, writing a polymeter is a good way to learn its corresponding polyrhythm. And again, the simpler the ratio between the 2 rhythms, the simpler it is to learn, as the loop will be shorter.

Anyways so we have this polymeter of 7/4 over 4/4, let's see how it sounds with a bit more complex rhythms. I'll play kick and snare on the first and third beat of each bar of 4/4. And i'll decide the 7/4 in two, so it's more like two bars of 7/8, and I'll play open hi hat on the 1, 3 and 5, and close huh at on the 2, 4, 6 and 7.

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And this will conclude the end of this episode. Which may or may not be one of the last of this series. Though I will come back with a last episode kinda summing up everything viewed in this series with a, hopefully, useful document to download for free.

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