Kolmogorov Complexity: the Thing that gives Energy to Dance Music
Some of you liked my computer sciencey take on improvisation so I’m going to present a nerd’s view of another topic close to my heart.
I’m going to call it musical energy. Perhaps there is a formal term for this, but if so I don’t know it. From a DJ’s perspective, it’s the characteristic possessed by a tune that fills the dancefloor and gets the crowd moving.
Of course a tune has to be subjectively good to do these things as well, but that alone is not sufficient: there are plenty of great tunes that don’t have high energy. Nor does every tune in a DJ set have to be high energy — it’s fun, but not always desirable to run at 110% from start to finish.
Energy is not the same thing as tempo. Tempo is the number of beats per minute, a completely objective quality. Energy is a subjective modifier of tempo: to me, if I listen to two tunes with identical BPM, the one with higher energy feels faster.
Energy is not the same thing as busyness. Having more things happen at once doesn’t necessarily mean higher energy.
So what do we mean by energy, then?
I gave the answer away in the title
In information theory there’s this thing called Kolmogorov Complexity. The complexity of a given piece of information is defined as the shortest computer program, in a given language, that could reproduce the information.
For example, take the decimal number consisting of 1 followed by 200 zeros:
100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
In Python, I could express that as
10**200
which takes much less space than the original. But how about this one?
553527206377988085028250004204760250426513901637831154329418125409873767123121944013989197021710825182691896946905749882686222926272883076921556894389388071672122002722108452043935934972665104877104693
Good luck finding a way to shorten that one; it’s near enough random.
Music doesn’t work quite like this. For one thing, in information theory, white noise has maximum complexity, while to a human, it sounds like a fairly boring hiss. This is because our brains aren’t able to distinguish one white noise from another. Recall the definition of complexity:
the shortest computer program (in a given language) that could reproduce the information
I think this definition can work for musical energy, if we define
(1) the information = our subjective experience,
(2) the given language = whatever native code runs in our brains.
In other words, this elusive musical energy is the amount of work our brains have to do to understand what they’re experiencing.
Once you start thinking like that, it gives an insight into various musical phenomena. Bear in mind that the work your brain is doing can be either conscious or subconscious, but usually it’s the latter. Producers try to become conscious of this stuff, though they might disagree about how it works (other opinions are welcome in the comments below!).
Syncopation
Syncopation is when two musical themes appear out of phase with one another. Classic example embedded below: God is a DJ. I can’t actually think of an unsyncopated example in dance music because it’s such a common trick to use; not only because it raises energy, but also because it stops your lead synth from clashing with the kicks and snares in the mix, so each part can be mixed louder.
Given the lack of unsyncopated examples, how about I make my own (banging, yes I know)…
All three sections above (A, B, C) have the same tempo of kick drums; i.e. the speed at which people would dance. They also contain the same number of sounds. But A has no syncopation while C has a lot. I would say this means they rank in ascending order of energy.
My pet hypothesis is that to understand what’s going on in a rhythm, my brain has to create a sort of beat grid on which it can hang the various sounds. In A the beat grid is 120 beats per minute: every sound falls exactly on a beat. In B, the beat grid is 240 beats per minute, as the bongos fall halfway between the kicks and snares. In C — the most interesting — you need a grid of 480 beats per minute to understand the location of the first bongo hit, even though C is no more busy than B, and has the same tempo as A.
The bongo hits don’t even need to be very loud to make this work. They just need to be noticeable enough to trigger our brains into processing them.
Of course if you shift that bongo hit a touch earlier or later, then theoretically you’d need a much faster beat grid to explain its position in time. But that doesn’t work. Why? Our brains aren’t capable of conceiving that grid. They work by pattern matching, which I suspect means if they can’t process some extra complexity, they will usually match the simplest pattern they can process — and hence won’t do any extra work.
Hints of speech
There’s a corollary to that last part, which is this: if our music receiving brains can process something they probably will. A common trick in EDM is to throw in some sounds which vaguely resemble speech (using vocoders, formant filters, etc). Our brains have dedicated hardware for speech processing, so this engages more circuitry to process it, compared to equally busy sounds that aren’t speechlike.
There are a lot of ways this tactic can be deployed, so here are a few good examples:
Hedflux — Music Is My Weapon: iTunes / Amazon / YouTube
GMS vs Eskimo — GMS-Kimo: Amazon / YouTube (surprised iTunes doesn’t have this)
Bushwacka — Feel It (Original): iTunes / Amazon (James Lavelle remix — slightly more modern dancefloor sound): Amazon CD / YouTube
The more escapist end of the dance music world will tend to avoid too much actual speech, because it’s too grounding, an everyday phenomenon that doesn’t excite the listener. Short repeated loops are common, though, as the unnatural repetition cancels the grounding effect.
Liminality
If your brain isn’t quite sure whether something is there or not, it’s going to expend extra effort to try and find out. So, sounds that exist at the threshold of perception are another way to give music more energy. The obvious way to do this — and most quality music will, especially classical — is to have some quieter things going on beyond the main lead.
But there are other ways to confuse us as well. One I particularly like is the perceptual threshold between pitched and unpitched sounds. This can be achieved in a variety of ways: short notes, pitch slides, frequency modulation… the detuned hypersaw (aka the “hoover”, a combination of multiple saw waves not quite in tune) has a sweet spot where it turns from a single note to chaotic noise. High pass filters, by removing the fundamental for our brains to latch onto, can exacerbate this. For a super high energy example of all these combined — and I warn you this is overstimulating in the best possible way — listen to Anmitzcuaca. Száhala is a computational linguist by training; I doubt it’s a coincidence that he makes use of these perceptual tricks.
(Sorry no links — possibly a bit too mental for the stores!)
Arrangements
Arrangements — the broader structures of tunes — tend to work best when they tread a line between predictability and unpredictability. Obviously, the more predictable an arrangement is, the less work your brain has to do to understand it.
Of course an arrangement can also be too unpredictable. I’m not quite sure where to fit completely bonkers arrangements into this framework — hello, breakcore! I think most people look for other things besides energy in dance music, like for example a degree of flow. So perhaps it’s correct to say that breakcore has more energy than everything else, but it comes at the expense of other things which I clearly didn’t care about that day I was dancing to breakcore.
Several genres of dance music depend on a build-and-drop structure, which again needs to tread the predictable/unpredictable line very delicately. That’s worth a whole other post another day.
Real audio versus synthesizers
Many, if not most EDM styles make heavy use of synthesizers — to give the music an otherworldly feel. Nonetheless producers often find that including just a small amount of real audio, perhaps heavily processed but nonetheless recorded via a microphone, adds a degree of depth to their tunes. I think the reason for this is also Kolmogorov complexity. The real world has a tonne of nuance that would take a very long time to reproduce by programming even the best synthesizers out there. It strikes the right balance between too predictable for our brains (like straight repetition) and too random for our brains (like white noise); surely not a coincidence either, considering that the real world is the same information stream that our brains evolved to process.
More creative ways to occupy the brain
I’m going to wind down with a fantastic tune that combines a lot of this stuff: Sasha’s “Who Killed Sparky”.
· The arrangement keeps varying things subtly; I suspect a few real world samples.
· Syncopation is everywhere; not just in the beat but in the 3-note lead synth line which is coprime with the number of semiquavers in the bar, in other words though the pattern stays the same each bar starts at a different part of it. (I think this may need two mental beat grids, or a single longer one, to keep track).
· The lead synth is in places driven through distortion at a level that makes it unstable — I suspect it’s right on the threshold of a tonal change and would sound very different if driven even slightly more or less. Keeping track of tonal changes in that synth definitely adds a lot of interest.
· No obvious vocals, but is that a choir-like sound just as the tune peaks? That would be vocals and liminality combined, then.
There’s one more thing that keeps varying in this tune, and that’s the use of space. One moment we have a dry sound with no reverb, the next a small room, eventually I like to imagine some sort of enormous cathedral in the mountains in outer space (if there was any sound in space which there isn’t, but you get the point). The cuts between these are extremely sudden, and not very predictable. I don’t think the untrained listener would consciously notice all this, but we have special hardware in our heads for processing spatial information in audio, and Sasha certainly makes use of it.
One of my favourite pieces of prog.
Footnote
A quick google shows me I’m not the only person to apply Kolmogorov complexity to music. This in particular caught my eye. While I don’t think its methods are sound and disagree with the conclusion (which would imply that simple music can never be beautiful), I like how it posits an evolutionary basis for perceiving beauty.
Thanks are owed to all those who introduced me to the wonderful tunes I’ve used as examples here:- if I remember rightly, Philippa, Matt, Rob, Dan/Jen/Josh, Tommo.
This blog is copied to Medium from my original which you can follow here.
