Using Harmonic Polyrhythms

First of all a little summary of where we are at the end of Adam’s video, which if you haven’t watched already I would highly recommend doing so for a good overview.

• Rhythm is just harmony slowed down. (This is actually the statement that started me thinking about all this about 5 years ago)

• Polyrhythms are relative pulses that have similar ratios to those we hear as chords (made up of notes).

• Therefore, we could say that subdivisions of a pulse are simply intervals from the root pulse. If our pulse is 1/4 notes, a 5th is the polyrhythm 3:2, i.e. 3 pulses in the space or 2 pulses, or as we call them in music – triplets.

As it happens, we can link most of the scale degrees we use in the west* to commonly used subdivisions/polyrhythms (plus a few less commonly used but still pretty fun polyrhythms)

root – 1:1 – 1/4 notes / crotchets

2nd – 9:8 (9 notes in the space of 8 – 1/4 note nontuplets, or triplets of triplets)

4th – 4:3 (dotted 8ths/quavers)

5th – 3:2 (1/4 note triplets)

7th – 15:8 (or the ‘harmonic 7th’ 7:4 can be more useful for rhythmic applications)

octave – 2:1 – 8ths/quavers

Note I’m showing this with a keyboard playing the scale of C for no other reason than it’s easier to visualise.

Audio example: polyrhythmic ‘scale’ against a click:

Listening to the audio of this you really hear the comfort and simplicity of the easy intervals of perfect 4ths & 5ths, and the satisfying resolve of the octave. The other intervals are an acquired taste – you can learn to love them, they’re just unfamiliar at first. It’s like when you show someone a TV series you love and they’re pretty indifferent, but you know it’s just because they don’t know the characters yet..

Adam’s video kind of signs off saying all this is great but maybe only a really useful study for the future or for some kind of species that can perceive this stuff in the way we can tonal harmony.. when the fact is we do perceive, appreciate and enjoy them, they just play out on longer timescales. Think of the larger-scale rhythms we experience, like the regular groove of the change of seasons, or the repeating rhythm of your routine from day to day, week to week.. How about the contrast you feel when the tempo of a song picks up, or slows down, or the memory of chilling out on holiday when you’re back in work with a million things going on at once. We experience the flow of events in life like rhythms, whether they’re ordered into music or not.

While we might not be able to perceive them in the same way we can in their pitched range, we can still use the ideas from harmonic studies as long as we’re sensitive to what this frequency range (rhythm) is functional for.

Our brains are expert pattern recognisers, and as humans we find it deeply satisfying to recognise patterns. When we hear a note, our brains hear a repeating cycle and glue those together to hear it as one continuing note. If we hear one hand-clap in isolation, it doesn’t really mean much. Even two in a row is still a bit abstract. It takes a few to get going before we decide we’re hearing a rhythm.

This is the same reason that typically, a chord sequence will progress/move at a slower rate than a melody, because it takes our brains longer to make sense of what’s going on, to appreciate the chord. It takes us a good few repetitions of the frequency cycles for our brain to ‘get’ the pattern.

So here’s a kind of hierarchy/structure of events we have in the musical world, moving from faster rates to slower.

• A fixed frequency gives us a NOTE **

• Put these together to make a MELODY

• A series of melodic ideas will often follow a CHORD SEQUENCE

• A chord sequence may make a phrase or a SECTION of a song

• A few of these may make up a SONG or musical PIECE

• You might put these together to make a coherent ALBUM or LIVE SET or SYMPHONY for example

Maybe now is a good time to make a little disclaimer that there are obviously lots of exceptions to all the trends I’m bringing up here, and great music is built on breaking these kind of conventions and rules – mainly because we’re so comfortable with tonal harmony that people have explored it a lot and know how to make something complicated still sound good… anyway, moving on.

If we’re looking at different steps on this hierarchy, we’d expect slightly different disciplines for each.. if you try to change chords in a chord sequence as quickly as in an intricate melody, it will probably sound like a mess. As we deal with slower frequency structures, we need to move more slowly for them to be appreciated. So as chord changes need more time to develop than melodies, movements on the rhythmic level need to develop at an even slower rate than that.

If we say the tempo of a song is its ‘root’ that we base all the subdivisions from, the majority of music popularly listened to you could say works in a similar way to the idea of drone-based composition, where you have one note/root playing constantly, and melodies are built on top of that, creating tension & release but always pointing back to that root. This is basically the essence of a groove. We set up a rhythmic structure and everyone sticks to it, always referring back to the tempo and the common subdivisions that everyone’s agreeing on, for example 1/4s, 8ths and 16ths. (in harmonic terms, these are like root, an 8ve up, and another 8ve up).

You can make a lot of great music with that! Especially given all the tonal detail going on on top, different instruments, chords, melodies etc. But we also started making lots of other cool stuff in tonal music when we started moving that drone around and building off sequences of chords.

So in rhythmic terms, the root will be our tempo, our scales and chords are the subdivisions/repeating figures we build from there.

Thinking of it like this, we can do a few things..

We can use inline-rhythm (the rhythm of one voice) like a melody, changing between subdivisions to create tension/release and decorations in the same way you would in a scale. Going back to our original scale diagram we could make a simple rhythmic melody using the root and its octaves (8/16/32), 5ths (triplets/6lets), 4th (4:3), major 3rd (5:4). Cool. This is one step further on from just setting up a drone, now moving into the territory of making rhythmic melody, and a source of A LOT of fun in itself. Listen to a latin bongo or quinto solo for an organic application of this kind of thing in a rhythmic setting.

Taking this even further, we can start having fun with this idea of harmonic polyrhythms – we can use one set, like a ‘chord’ or ‘scale’ to set up a foundation to build on. Let’s take a major triad. Using C as a visual guide again, Root/major 3rd/5th, C/E/G. The Root is going to be our tempo, whatever else we play that is going to feel like home. Other voices can be phrased against this in 5:4 (major 3rd, 1/4 note quintuplets) or 3:2 (perfect 5th, triplets), and as long as there are repeating and recognisable phrases/figures, you will begin to hear the patterns and the music in there (though it will sound random at first).

Bearing in mind we might need to tweak things a little bit to end up with music that’s actually nice to listen to, we can always ‘transpose’ one of these note-rates up or down an octave to make a bit of space in the music, whilst achieving the same harmonic effect. Instead of 1/4 note quintuplets (5:4) they could be 1/8 note quintuplets (5:2), and the voice doing triplets could be 1/2 note triplets (3:4).

We can change ‘chord’ to make a new section with a different feel. If we go from our ‘I’ chord of a major triad to one built on the 4th, IV (F), then relative to our original tempo we’d now have our voices playing IV (F) 4:3, VI (A) 5:3, and I (C) 2:1.

So now we’ve got a section with voices and repeating figures in the original tempo (1/4 notes, 8ths & 16ths), dotted 8ths (4:3), and 5:3 (and/or related ‘octaves’ of these). Because the original tempo is still being represented, you could probably pull this off without rocking the boat too much. That said, this is where voicing and emphasis come into play – if you decided to say, put a loud repeating kick drum on the 4:3 (IV) polyrhythm, the listener might hear that as a new pulse, with the other rhythms building off of that. In this case, we’ve basically achieved a metric modulation – this is something people have been playing around with for decades. In this instance, because we’re just doing another major triad, it would seem like the whole song had just sped up by a third. However, if the root is still being represented and emphasised, it should just feel like a pretty weird gear change, or scene change if you like. You could say this is similar to chord inversions, or adding different bass notes to chords.

How about another chord to complete a nice simple chord progression of I/IV/V.. so to make the V chord we’ve got V (triplets), VII (septuplets?) and II (9:8, nontuplets, i.e. triplets of triplets). Things can start to get slippery here because now the root tempo is not being represented anywhere, it’s like we’ve let go of the side of the pool and are now just swimming in a polyharmo-rhythmic soupy wonderland. Again, this is likely to have the effect of just feeling like another metric modulation, or tempo change…However, the skill of composing in this way would be to make it still feel like it resolves if you come back to your original ‘home’ tempo/chord.

Because of how long it takes to ‘set up’ and recognise a polyrhythm, you won’t really be able to move through these sections or ‘scenes’ that fast without it seeming pretty random and unlinked. Essentially each time you move ‘chord’, it’s like setting up a new groove. To be able to follow the piece as a whole might take a bit of practise, in the same way as you don’t notice the pacing of a film or the form of a symphony the first time you see or hear one – you just experience it – buy the ticket and take the ride. Once you’ve experienced a few and maybe have even studied it, it’s just another level of detail that you can appreciate, and tool to create with.

All this stuff will sound weird at first. Changes in what we find appealing happens slowly, Asimov called it social inertia. Imagine someone from the 11th century hearing a beautifully complex chord like a min7add9 chord, or something like The Rites of Spring (even contemporary audiences had trouble with that one). Lots of people have already made a lot of great music using polyrhythmic concepts which could be described in the terms I’ve outlined here, but perhaps thinking of it in this way will give people a different framework, or a basis/reason to compose polyrhythmic ideas in certain directions.

This is all just scratching the surface of course – I’ll be updating this blog with plenty more ideas in the same vein… Cheerio.

* – as these are perfect ratios, it’s actually the equivalent of Just Intonation, which in the range of pitches we hear most harmony in, has a few problems.. if you’re interested, check out more info here.

** – On a side note, if we go higher than notes, we actually move into the realm of timbre/tone – in the 1950s Karlheinz Stockhausen made ‘Kontakte’ by playing a series of sine waves on a loop at stupidly fast speeds, finding out that by doing so could make all sorts of sound textures, essentially using additive synthesis – a reverse version of a Fast Fourier Transform (FFT – what a spectrum analyzer does; instead of picking out the frequencies of a sound, you play frequencies together to make a new sound).