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Music and maths 1: ___flow___

As a composer I’ve always been interested in numbers and maths, and the way they relate to music. Maybe it comes from playing around on my Dad’s old DOS computer, making bleepy minimalism, or perhaps it comes from first learning about the harmonic series at school, and how timbre arises from the physical properties of instruments. Either way, numbers and mathematics are central to my work as a composer, and the elegance and power of mathematical processes are an ongoing source of artistic inspiration for me.
In this series of blog posts I’m going to be looking at some of the ways composers throughout history have explored music through numbers, and sharing some of my own approaches to composition.
In this first post I’m going to be looking at one of my own pieces: ___flow___, one of my most numerically-based recent works. I’ve not chosen to write about it first because I think it’s the best of the works I plan to cover, but because it uses a couple of simple mathematical tools which could be adapted or applied in lots of different contexts, and so may be of practical interest to any composers reading this who may be interested in exploring this way of working.
In early 2018 I was approached by the web hosting company Bytemark, who were sponsoring a conference at the University of York. The conference facility included a dedicated audio-visual projection space, which wasn’t going to be used. Bytemark had the idea of commissioning a work to be exhibited in this space, which would highlight their role as a corporate sponsor.
After some discussions, we agreed on the idea of an audio-visual piece based on the data flow into and out of Bytemark’s York servers. Armed with this data, I went into my studio to see what could be done with it.
This data came in the form of 14 channels of data, 7 incoming and 7 outgoing, covering a period of two weeks, recorded as streams of values, each corresponding to the average bandwidth per half-hour. You can see this data represented as a graph below. As we can see, the outgoing data has a regular 24-hour cycle, while the incoming data is much less clearly structured, with unpredictable peaks and troughs. I had to find a way to create a musical structure from the differing characteristics of these data streams.

As the conference was going to last all day, with people coming and going at all times, I wanted the piece to be able to run indefinitely, and to be appreciable to people coming in at any point. I decided to compress the 14-day data set into an hour, so the 24-hour cycle lasts about 5 minutes, and to use the peaks and troughs in the data to control the intensity of the music at any given time.
I composed fourteen melodic fragments, one for each channel. These fragments are played back at a speed and pitch determined by the amount of data moving through the corresponding channel. For example, a relatively inactive channel will play though its fragment as a series of slow bass notes, whereas a very active one will rise to the top of the texture as a quick, high melody.
By applying this simple mathematical process to all fourteen channels a texture is produced which follows the overall contour of the data in intensity and expresses the relationships between different channels through the foregrounding of different melodic fragments. In addition to this, each of the seven “dual” channels, that is the corresponding incoming and outgoing channels, were assigned a different instrumental sample, further distinguishing the different material.
I partnered this musical texture with a corresponding visual one. Each new note is represented by the appearance of a dot within the projection space, which drifts up or down depending on whether it’s an incoming or outgoing channel. Dots emerging from the same channel are linked by lines, and each pair of channels is assigned a position in horizontal space and a colour, which becomes lighter or darker depending on the rate of data flow.
You can see the piece installed in situ in the video below. As you can see, the effect is atmospheric and immersive. The five-minute/24-hour cycle means that the texture is always changing, and different sounds and melodies come slowly in and out of focus.

The work was well received by the conference goers, and was exhibited again in October at the Centre for Contemporary Art in Glasgow, as part of the 2018 Sound Thought festival.
___flow___ serves as an illustration of how a simple mapping of numerical sequences onto musical parameters – in this case speed and pitch – can be used to control and structure a piece. By writing the melodies I had control of the overall sound-world, but the large-scale shape of the music came entirely from the data, as did which melodies are prominent at any given time.
As composers we can choose when and how to allow processes to take control, when to make decisions ourselves and how complex or simple to make the processes we use. We may not think of ourselves as “mathematical” composers, but it’s a rare composer who uses no systematisation at all. Acknowledging this, and understanding what possibilities are available to us, can only give us more control over the music we write.
In the rest of this series I’ll look at how other composers have explored mathematical possibilities in writing a huge variety of different types of music, from early music to minimalism to sculpted noise. Stay tuned!

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Posted by author: Desmond Clarke
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