Polyrhythms - A Quick Theory Lesson

This article is to inform people about what polyrhythms ACTUALLY are, and furthermore clear the air about the musical devices they are often mistaken for: polymeters, and rhythmic displacement.

As you probably all know (prog-metalheads and fans of Meshuggah, TesseracT, Periphery, Porcupine Tree and the like), a lot of the time musicians and composers ofter get labelled with using polyrhythms. A lot of the time, the term "polyrhythm" is used to describe - in Porcupine Tree's case - a PolyMETER; in Meshuggah's case, Rhythmic Displacement. Allow me to explain the theoretical difference between the three devices in question.

Polyrhythms

A polyrhythm is two types of tuplets layered over each other and played simultaneously: a common example being a triplets over quavers; a less common and considerably trickier example (often found in Chopin and Liszt) would be something like a septuplet (7) over semiquavers. A good example of this would be in Brahms's 4th Symphony, First Movement:



You'll find polyrhythms all over the place here, however the strongest I feel is at around about 3:12, quite short but very clear between the lower and higher stringed instruments. It's a fairly straightforward example, as it's only a three over 2. For more complex examples, they are dotted all over Chopin's "Nocturnes" for piano, or you could watch this video:



There's 5 over 4 covered in that one, and I think a 7 over 2 at one point.



Polymeters

A polymeter is a different story altogether, and generally speaking a lot easier to hear and pull off, although it's obviously objective to the difficulty of the polymeter. This device is where two (or more) time signatures are being phrased simultaneously, e.g. the drums, keyboards and bass playing in 4/4 and the guitars playing in 5/8 (Porcupine Tree - Anesthetise). One vital point, however, is that the time signatures HAVE TO RESOLVE (can be described as a "rhythmic cadence"), meaning that if it is a 4/4 over 5/8 polymeter, then the 4/4 pattern will have to be played 5 times for the 5/8 to fit. If the 5/8 or 4/4 pattern is forced to resolve then it's something different entirely. A great example, as aforementioned would be in Porcupine Tree's tune Anesthetise:



The polymetric sequence occurs at 5:08. No other section in this song is polymetric, except for when Gavin goes nuts at 11:17, where hit snare is arguably polymetric (we'll get onto that later). More examples:



Not self promoting at all *cough*, but it illustrates my point at 2:00, in which the keyboard and harp are playing in 3/4 and the bass and drums are playing a 4/4 pattern. Also at 1:12, where the strings, piano and open hi-hat are playing in 3/8 and the the other instruments are playing in 4/4. Another:



At 4:56 the hi-hat (later the whole drumkit) is playing in 5/8 and the bass is playing in 6/8.



Rhythmic Displacement

This is possibly the most common device, and is used EVERYWHERE, heavily in technical metal. This is where a continuous pulse (often a cymbal) is lilted slightly by instruments phrasing in another time signature, pushed to resolve after a certain number of bars. Very different to a polymeter! An example would be as follows:

5/8, 5/8, 5/8, 5/8, 5/4, 1/4

(all over a 4/4 pulse: it works out because the pattern adds up to 32 quavers, which is divisible by a 4/4 pulse)

Another:

11/8, 11/8, 5/4

(same principles)

Meshuggah use this technique a HELL of a lot, splattered all across Nothing in almost every single riff. It is also used melodically in a lot of Jazz and Classical (Herbie Hancock favours this technique and often phrases in fives). A few examples:



The beginning of this song has the riff phrased like so:

7/8, 7/8, 7/8, 7/8, 2/4 over a 4/4 pulse. More examples:



3:08

5/4, 5/4, 5/4, 1/4



Why this is just a THEORY

If you are a musician and you are reading this, then you may be asking "well, isn't a polymeter just a sped up polyrhythm", or vice versa, and to that I can only say: isn't forte just a louder version of piano? You would be right however, a polymeter IS a slowed down polyrhythm. Let me explain:

The way a polyrhythm is constructed is exactly like a polymeter. To create a polyrhythm, you first have to decide which numbers you are using (let's say triplets (3) and semiquavers (4) for now), then you have to divide the beat up by the product of those two numbers (in this case 12). The triplets would appear on every fourth 12th note, and the semiquavers on every third 12th note. Here's a scrappy little diagram:

-------------------------------------------------------------------------------------------------------------------------------------------------------

/            /            /            /            /            /            /            /            /            /            /            /
t                                                   t                                                   t
sq                                  sq                                   sq                                  sq

-------------------------------------------------------------------------------------------------------------------------------------------------------

/ = 12th note
t = triplet
sq = semiquaver

-------------------------------------------------------------------------------------------------------------------------------------------------------

Now this is all within one beat, and automatically becomes a polyrhtyhm, but if you slow each 12th not down to quavers then this becomes a 3/8 over 2/4 polymeter. This can be applied to any tuplets or time signatures you can think of. So essentially, the only difference between polymeters and polyrhythms is speed and notation. However, as I said before, it is just like saying that quiet is the same as loud, only a lot quieter.

Hope that helped!

There are also compound meters where measures of different lengths are simply tacked onto one another, which would be required for Clarke's example.

 

clarke2001 wrote:   But why? Why can't parallel 4/4 and 5/8 can stop abruptly somewhere in mid-bar and proceed together in let's say 3/4? Or there's another term for it?

I believe the point is that if they're not in the pattern Alex is describing then the time signatures are not actually matching up and you've just accidentally started playing free jazz, not that you're divinely bound to follow rules. Switching in the middle of a bar would be jarring, though, since I think the instruments would not be on the same beat so there would have to be a space for some people to catch up and for some to slow down to the new time signature. 

clarke2001 wrote: The Pessimist wrote: Polymeters A polymeter is a different story altogether, and generally speaking a lot easier to hear and pull off, although it's obviously objective to the difficulty of the polymeter. This device is where two (or more) time signatures are being phrased simultaneously, e.g. the drums, keyboards and bass playing in 4/4 and the guitars playing in 5/8 (Porcupine Tree - Anesthetise). One vital point, however, is that the time signatures HAVE TO RESOLVE (can be described as a "rhythmic cadence"), meaning that if it is a 4/4 over 5/8 polymeter, then the 4/4 pattern will have to be played 5 times for the 5/8 to fit. If the 5/8 or 4/4 pattern is forced to resolve then it's something different entirely. A great example, as aforementioned would be in Porcupine Tree's tune Anesthetise: But why? Why can't parallel 4/4 and 5/8 can stop abruptly somewhere in mid-bar and proceed together in let's say 3/4? Or there's another term for it?

Yep The other term is what I would call Rhythmic Displacement (RD) (phrasing in odd time meters, like Jay said - although he used the term "compound polymeters", which I've never heard before but I figure is just a form of RD?), like I mentioned Just as my examples resolve at the end, they can also "resolve" in the middle too, it's still RD nonetheless For something to be absolutely polymetric, it has to be linnear if you see what I mean... although it's an easy mistake to make as sticking a renegade bar in a different time sig. somewhere in the middle would still sound polymetric.

Hope that clears it up a bit...

And Xanatos:

No.

If you think music theory is worthless, why read a post about music theory? If you don't want to hear about music theory that's fine. Most people are like that. Going into a post about music theory to tell people not to use music theory is stupid. You enjoy music your way, let other people enjoy it the way they want to. A lot of us *like* theory.

Proletariat wrote: This is the perfect example of why western music theory should not be applied to popular and folk music and stick with the academic stuff.

What is the fundamental difference between popular and academic music that makes music theory only valid to discuss one but not the other?

I've always assumed polyrhythms resolved within the bar, while polymeters are resolved over several bars. Have to admit that I've never thought about it long enough to know whether that is true or not or whether it matters an awful lot.

I disagree. For most, you are what you practice. If you practice polyrhythms, they become part of what your subconscious creative will produce. Your ear will rarely reach for odd chords if you haven't played and experimented with them, and even if it does, you will have difficulty finding them.

Im not saying one shouldn't know theory but that as one that may know music theory you needn't expect others too especially since alot of us are just rock fans after all. you were obviously aggrivated that many of us don't know the difference doncha know

Proletariat wrote: Im not saying one shouldn't know theory but that as one that may know music theory you needn't expect others too especially since alot of us are just rock fans after all. you were obviously aggrivated that many of us don't know the difference doncha know

Edited by daslaf - February 09 2011 at 19:47