Euler’s Number and the price of fish
A short listening exercise for you: This morning, I turned two streams of data into music. One of these ditties expresses the first 48 digits of the transcendental number e through the medium of handbells. The other ‘plays’ the metric tonnes of salmon sold, day by day, in the second quarter of 2010 on the London Stock Exchange.
Any idea which is which?
The popular science press is awash with music projects of this ilk – a genre of sound art known as ‘data sonification’. If you’re looking for a sonification project that’s guaranteed to go viral, first identify a datastream with sufficient exotic charm to lure the discerning journalist. Anything far too big or small to imagine is particularly fitting – data from quark collisions, junk DNA and coronal mass ejections are good – numbers of double-decker buses won’t cut it. Spit out this datastream, map it number by number onto notes, chords or rhythms et voila! You have a texbook sciart project: a string of inscrutable music with science running all the way through it like a stick of Blackpool rock.
I have to be honest and say I’m unconvinced by some of the data sonification oeuvre. Arguably, music from data can be an entertaining way to get some more arcane research projects into the public consciousness. These catchy numbers, for instance, recently helped to make the ATLAS detector talk of the town – and that’s no bad thing. Of course sonification is nothing new. The Geiger Counter sonifies the presence of ionising radiation. And musical instruments can be thought of as machines for sonifying human gestures (especially the theremin). Admittedly, I occasionally dabble with sonification. I’ve recently been grapping with some optical flow algorithms, for instance, which I’m using to make music from the flight of butterflies in London Zoo. I think sonification projects should point up the salient attributes of a body of data, revealing barely discernable patterns and relationships, for instance. And – more importantly – should somehow express the purpose of the datastream (tricky to do – but therein lies the art). Check out these sonified sorting algorithms for example (by @andrut).
Sonified sorting algorithms (@andrut)
They’re let down by some cheesy general midi sounds but nevertheless let you hear a jumble of data gradually being sorted from big to small. Fascinating – and very different to the species of sonification that I personally find irksome. I have a problem with sonifications that express very little about the data stream under scrutiny, apart from the fact it’s made up of numbers.
Take my hastily prepared bell tune, for example, a digit-by-digit sonification of Euler’s Number (e). In case you’re wondering, it’s song number 1 on the list. There’s enough to say on e, its cosmic significance and its applications, to fill a library. Just for starters, this beautiful number can be used to express the decay of isotopes or capacitive charge or the growth of populations. Embedded in integrals, it enables us to analyse the world using new geometries (for instance with Fourier and Laplace transforms – indispensible tricks that make me feel like I’m putting on my psychonautic maths glasses). But when I hear tune 1, all I can sense is that e is made of a seemingly random stream of digits.* My ‘Euler music’ might as well be about the price of fish.
This technique I’ve used isn’t dissimilar to one which has been heard quite a lot this week, as musicians have been sonifying pi, digit by digit, for ‘Pi Day’. You can hear various entries on YouTube (Ryan has written about a rather fine example on this blog). Yes, many of them sound beguiling – but do they express anything beyond the fact that pi is irrational, like e? If you close your eyes, do you sense anything, erm, circly? Listening to these paens to pi, I feel there’s something slightly disappointing about the mappings many of the composers have used to turn numbers to notes. Somehow, their digit-by-digit sonifications reduce pi, a number of universal significance, into something quotidian. Sadly, many express the number in decimal then map it onto an eight-note, diatonic, tempered Western scale. About as cosmic as representing the surface of Jupiter with Lego bricks.
Maybe my analysis is unfair, too prescriptive or simply oversensitive. Perhaps there’s nothing wrong than music whose sole aim is to make the observation that pi is made of a never-ending, random* stream of digits. That, in itself, may be a sufficiently interesting music project. But here’s the rub – these numbers are random and random music is boring. Don’t take my word for it. There’s a raft of psychology (to be filed under The Bleedin’ Obvious) that relates arousal to the complexity and novelty of art and music. This work is summed up neatly by the Wundt Curve (1974). Put simply, we find music boring if it’s too predictable or too random. We seem to love the stuff in between – the music that presents us with that glorious, sonic game, where musical patterns sometimes meet, sometimes defy, our expectations.
So, that sums up my gripe about certain kinds of data sonification. Of course, regardless of its origins, responses to music are largely down to personal taste. With this in mind, I felt I should seek a second opinion on this thorny topic. So I went to the experts: MC Zirconium and DJ Bongoboy, aka Project Moonbase, a duo of self-styled ‘retro futurists’ with an encyclopaedic knowledge of scientifically-inspired music. Unsurprisingly, they’re no strangers to the world of data sonfication, a genre Zirconium has described as ‘the extreme sport of music’. Over a salmon tikka, Bongoboy summed up their approach: ‘“More important than “have we discovered the Higgs boson?” or “how did the universe ultimately begin?”, the key questions for us are 1. Does it have a beat? and 2. Is there a corresponding ukulele tuning?”‘
‘I like my sonification to fill me with terror’, Zirconium added. ‘If I am listening to radiation emanating from distant parts of the universe, I want to feel horrified by the scientific majesty of it all.’
Well said Sirs! With that in mind, I’ll sign off with this little treat: my Euler’s Number music mixed with my sonatina on salmon sales. Put on your unitards, tune your ukeleles into the cosmic background radiation and imagine a mighty salmon dancing in spectral space. Dance my pretties, dance!
* They are random – but I’m lacking the space and the maths chops to describe the species of randomness we are dealing with here.
My next article may be of special interest to Steampunk friends. It features a short chat with a man in a tall hat that made me change my opnions on the way the artists cut up and resample past technologies.