Incommensurable Loops

Music For Airports, at least one of the pieces on there, is structurally very, very simple. There are sung notes, sung by three women and myself. One of the notes repeats every twenty-three-and-a-half seconds. It is, in fact, a long loop running around a series of tubular aluminium chairs in Conny Plank's studio. The next lowest loop repeats every twenty-five-and-seven-eighths seconds or something like that. The third one every twenty-nine-and-fifteen-sixteenths seconds or something. What I mean is they all repeat in cycles that are called incommensurable - they are not likely to come back into sync again.

Eno, Imagination Conference, 1996 (source)

Many of my own records, particularly the ambient pieces, were created using such systems. For example, a number of tape loops, each with different musical elements and of different length, were allowed to overlay each other arbitrarily. Because of the differing lengths it could have been several years before they fell back into sync, and so the music always appeared different.

Eno, The Independent, 1996 (source)

And Music For Airports is one of the products of that. What happens with that piece is that... well, I'll take one of the four pieces there. There's one piece that is just groups of voices singing long notes. And each long note was actually a very long loop of tape, so each single note repeats at a regular cycle. But each of the cycles of repetition is of a different and complexly related length. The relationships between the lengths aren't simple, they're not six to four. They're like 127 to 79, or something like that. Numbers that mean they would constantly be falling in different relationships to one another.

Eno, quoted in Tannenbaum 1985 (source)

There are many versions of this story, and Eno often uses the phrase incommensurable - a piece of mathematical jargon¹ - to describe the process behind his early ambient works: loops that drift out of synchronisation and are unlikely to realign for long periods. The approach is most prominent on Music for Airports (1978), as he references above, but it also provides the core of Discreet Music (1975), Thursday Afternoon (1985), as well as his installation work - at first using auto-reverse cassette decks, then multiple CD players set to shuffle mode, and later, software. Whether Eno completely abandoned the approach isn’t clear, but with the advent of computers his generative work appears to rely more on rule-based probabilistic models, where sound events are assigned likelihoods of occurring - for example, designing a piece on the principle “small modal note shifts within a few tones are likely; large leaps in octave, unlikely.” see here

The incommensurable loops idea really fired my imagination back in 2001 when I first read these interviews where Eno was remarkably forthcoming about his methods. I quickly set about making several loop-based pieces using the equipment I had to hand - some old tracker software and my PC soundcard (my “studio” at this point consisted of a cassette four-track recorder, which was great for linear recording but didn’t lend itself to this purpose). I “tricked” the tracker software into playing the samples and looping them, then by filling in blank bars - i.e. no further samples to be played - they would continue for any duration I wanted.

This was productive and a thrilling excursion away from the traditional rock approach I was used to, but obviously a bit derivative. I differentiated myself a little by not slavishly copying Eno’s sound palette and instead using what I had at my disposal - guitar with associated effects pedals, trumpet (not very expertly played; I hid my poor intonation in layers of an analogue delay pedal), and old Casio keyboards (as a poor substitute for 1970s synthesisers). I can look back on such works now with a bit of nostalgia and enjoy the naivety. Not every musical utterance needs to be an earth-shattering artistic statement, and actually, some of them hold up okay.

Sometime in the mid-2000s, whilst designing my website, I hit upon the idea of presenting such loop works as online entities². In interviews about generative work - his Ambient albums and others - Eno often references the fact that the music is infinite, never likely to repeat in exactly the same combination. Although this is a mathematical exaggeration - given enough time the loops would come into synchronisation again - it’s as good as infinite. This presents a problem for presenting such pieces via traditional means. In the case of Discreet Music, for example, the length was limited to the duration of one side of an LP. This was extended for Thursday Afternoon to the length of a CD (famously 74 minutes, at the insistence of Sony to accommodate Beethoven’s Ninth Symphony). Eno’s experiments with the KOAN software (Generative Music 1 and referenced several times in his 1995 diary) in the late ’90s raised the idea of the “seed” information being released as a 2.5” diskette - so the music could go on creating itself for as long as the user wished. The drawback in the ’90s was that people didn’t generally want to sit around a beige PC to listen to their music - this was the era of stereos, CDs, Walkmans.

I started to wonder about playing audio over the web. This was a long way from the early days of the Internet, when crunchy lo-fi sounds were played over RealPlayer; thanks to Napster, the MP3 was king and audio on the web was suddenly accessible. Most browser functionality, however, was geared toward embedding single sounds within a website - alerts, annoying background music, and so on. Anything more complex (laughably simple now!) in those days was built using Flash. I set about learning a little about how to program Flash, following a few tutorials, and with a bit of head-bashing worked out that the same trick I’d played on my tracker software - instigating several loops and just letting them run - worked in Flash too. I turned it into a small front end with a volume control and play/stop button.

This was before I had undertaken any formal learning in music programming (I think I was lucky that Flash handled everything in the background and pretty much needed a single line like "play sound1.mp3 loop=true" but I was fairly experienced in hacking together websites and working with code from my day job. Looking back, I’m amazed that I got something to work in the days before dedicated forums and co-pilot-like tools.

Of course, things move on - Flash became outmoded with modern browsers and HTML5. At some point, I deleted the “infinite music” bit of my website and mentally archived it. I was perhaps at that point a bit embarrassed by my youthful efforts as much as wanting to excise the dead tech. Much later I began to experiment with the Web Audio API (yielding several web-based works), and the idea of loops and “ambient webpages” (see Landscape) came up again. They were now easy to implement within the browser, and I made a few experiments.

To finish Eno’s story - with the advent of smartphones he got his wish that everyone suddenly had a high-fidelity audio device in their pocket, with processing power far outstripping even the most advanced PCs of the KOAN era. He made several successful apps such as Bloom, and by the time Reflection (2017) was released, he was able to finally realise a piece of generative music both as a fixed release and as an ever-evolving app: the best of both worlds³.

On embarking on refreshing this website after a few years of neglect, I had to delve into the archives and came across the files that drove the original “Infinite Music” Flash app. Whilst the old code is now just e-rubbish, the original loop files were all intact, and on auditioning a couple I began to wonder if the idea could be resurrected using the Web Audio API. It’s a trivial piece of programming really - fetch the files, load them into buffers, and set them to loop indefinitely. Although I admit to using some AI co-piloting judiciously to improve my rusty coding skills (most of which involved telling it not to add various bells and whistles) and to put a new minimal gloss on the front end. I marvel at being able to create something in an hour or two that took me days of frustration back in the day. They’re not perfect - in fact, looking back on them now, I realise one crucial error I made was not to include enough silence in these compositions - they’re very busy and information-packed. I could, of course, retrospectively fix that up, but that didn’t feel in the spirit of the project. I may, in due course, create some new pieces on this principle and incorporate everything I’ve learned since those early Flash experiments.

Sheffield, November 2025

In mathematics, “incommensurable” describes two quantities whose ratio cannot be expressed as a ratio of two integers, meaning they have no common measure. ↩
I’m struggling to date the work precisely, I mentioned it in an email to a friend in 2007, it definitely appears on an archived version of my website from 2008. ↩
Sadly for me, it was exclusive to Apple, and being a PC user I’ve never actually heard the app version. ↩