Polymetre and polyrhythm
Polymetre and polyrhythm are two different ways of making a rhythm more complex, by having different parts phase in and out of sync with each other. Both feature different instruments playing in different metres at the same time, but in different ways.
First, let's picture a regular 4/4 bar of music as a single bar, divided into four even beats, which in turn are divided into four sixteenths.
Cohesive
In the rigid world of quantised, sequenced music, these smallest divisions are where you can place notes. Naturally, you can place notes wherever you want, but the simplified world of digital step sequencers makes these rhythmic distinctions clearer, both to describe and hear.
So, in this example, the drum and bassline parts can play together, fully in sync with each other, each able to start or stop a note at any of the sixteen evenly spaced points in the bar.
Having every part in alignment with all the others like this is such a common default, I'm not clear on whether there's a term to describe it, so let's tentatively call it cohesive, both a monorhythm and a monometre.
Polyrhythm
Polyrhythm involves keeping the bar the same length for all parts, but having more or fewer divisions in that bar where you can place notes, for only some of those parts. That way, the different parts phase in and out of sync with each other in terms of when they can have notes, but their bars always begin and end in sync.
Polyrhythm
The common triplet, when only played by some but not all parts, is essentially a very brief polyrhythm.
The only popular example of a lengthy polyrhythm I know of is N-Trance's "Set You Free", which features a piano playing an arpeggio in triplets throughout, while the rest of the song is simply 4/4.
Polymetre
Polymetre is the opposite of polyrhythm. It involves keeping the smallest division, where you can place notes, in sync across all parts, but making the bar (pattern, in digital step sequencer terminology) longer or shorter for some of them. This causes the start and end of their bars to go in and out of phase with the other parts, while their notes still conform to the same overall grid of sixteenths.
Polymetre
Good examples of polymetre can be found all over the Nine Inch Nails album The Fragile.
Exploiting ambiguity
As a special example, a bar with three 4/4 beats and a bar with four 3/4 beats contain the same amount of sixteenths (twelve), making them the same length. So in this specific instance, polymetre and polyrhythm become two different ways of expressing the same thing happening.
Ambiguous
This isn't the only example — any number with lots of divisors can be exploited in this way, by making a bar that many sixteenths long.
On a finer level, this is essentially how DIN sync works, and why it has 24, not 16 or 32, pulses per beat — to allow triplets.
24 pulses per quarter note
Pattern length
Apparently people steeped in Western music theory tend to consider polyrhythm and polymetre rare and advanced. This tends to surprise people used to making electronic music, as using polymetres can be as simple as changing the pattern length for only some parts while leaving most at the default bar-long 16 sixteenths.
Independent step sequencers (both analogue and digital) with arbitrary pattern lengths make this especially easy to do without having to think about the maths involved. See, for example, the layering of TB-303 parts on Hardfloor's "Acperience 1", and Autechre's use of the MC-202 in "Windwind", both of which add a little polymetre simply by using a shorter pattern length.
You can also play a long string of dotted eighths by hand, as with Fatboy Slim's "Santa Cruz".
Delay
Perhaps the most common thing in electronic music that's arguably hinting at polymetre is to feature a dotted eighth delay in a regular 4/4 track. The simplest version of this is to play a percussive arpeggio in eighth notes, and delay it in dotted eighths (as with Kraftwerk's "Autobahn"), or vice versa (as with Aphex Twin's "On"). That way, the delay fills in the gaps between the notes with fainter grace notes, making the melody sound far more complex than it actually is.
In summary, by using multiple different pattern lengths or clip lengths, a simple sequencer can easily create polymetres that add to the complexity and richness of a track. Even the humble delay effect can do something very similar.
Quotes
The futurism in Detroit really boiled down to the 909 drum machine for me, especially the claps, the hi-hats — particularly when you brought the metallic mid-range up in those, they just had this kind of rhythm that was such a beautiful forward momentum. Nearly like pushing yourself into the future. The 303, on the other hand, I love the squelchyness. I liked that it was sucking you in, but I didn't like so much when it got too hard and grating.
I think one of the things that enabled me to fuse those two things together was using very syncopated 16-note drum patterns on the 909 and oftentimes three or five-note polyrhythms (Actually polymetres — Zoë) on the 303. So that even as you were feeling the structure of the track and the normal four-bar eight-bar changes over top, there was this other melody and squelch and delayed line that never seemed to have a beginning or end. Those were the two things that came together that really made "F.U.", made "Substance Abuse". All over Train-Tracs, there's always some kind of melody that's looping in a different time signature.
— Richie Hawtin, 2019[1]
References
- "Signal Path: Richie Hawtin on His Origins as F.U.S.E. and How He Made Techno in the Early '90s" Maya-Roisin Slater, Fact, May 2019
Music theory: Arpeggio | Block chord | Broken chord | Circle of fifths | Interval | Music | Pitched tempos | Polymetre and polyrhythm | Rest | Swing | Velocity