I was recently invited to take part in a performance of the British composer Cornelius Cardew's 'Treatise', along with roughly thirty other musicians, at University of Greenwich on guitar. For those not initiated, 'Treatise' is a mammoth piece, some two-hours long, of fiercely abstract improvised music (here's a live extract of one group of improvisers' take on it), guided not by conventional musical notation, but rather by a visual representation known as 'graphic notation'.
Coming from a conventional classically-trained background prior to turning to rock music, I had no real idea until the Cardew concert about graphic notation. Viewing the nearly 200-page score for the first time (an excerpt is shown above), I was as baffled as anyone by the mixture of circles, arrows, and diverging lines. I'd heard of Cardew, of course, along with his tutor Karlheinz Stockhausen; he was a composer, a member of free improvisation group AMM, and a strident Marxist in the 70s (as many were want to do in that decade), repudiating his previous output in the process. But I had no idea that an alternative system to conventional notation existed – that is until the gig, in which I turned up to the soundcheck sweating from having lugged a guitar and amp (about 100 watts) down from North London to Greenwich via bus and then the Docklands Light Railway.
It turns out that graphical notation was used by a number of contemporary modern composers and the avant-garde, including John Cage, György Ligeti, Xenakis, Krzystof Pendericki, and Stockhausen himself. If you can understand what on earth Cage was getting at with the score below, you've probably got a better grasp of graphic notation than I have: 


 
For the concert, I dispensed with any notions of playing 'ordinary' guitar riffs and chords; for such an abstract piece, there didn't really seem any point. Instead, I employed an E-bow; a kind of mini-synthesiser without any notes which achieves its affect by the user placing it close to guitar strings. The magnets within the E-bow, powered by a battery, produce a thundering sustained drone which, combined with effects like reverb, have been used frequently in popular music lore, from Jimmy Page's coaxing of guitar smoke in Led Zeppelin's 'Dazed & Confused' onwards. In addition, I used the handle part of a beater on the strings of the guitar.
There's something liberating about 'this' side of guitar playing; by that, I mean the improvisatory side of guitar playing instead of straightforward chord/solo conventions. Cardew undoubtedly was trained in conventional composition and notation, but with 'Treatise' he was trying to break out of this completely. Indeed, improvisation is built into the lifeblood of popular music. It's a liberating force that has been since in modern jazz and much left-field rock.
Conventional five-staff notation has become so ubiquitous that it has ingrained certain ideas in us: that if a note is higher up in a bar in a score than another note, then that must translate automatically to a higher up tone on the instrument. However, it wasn't always this way. In the non-Western world, prior to the conventional Western musical notation which has been adopted around the world, notation took on all kinds of different forms in the great ancient civilisations. These different systems of notation have been around for thousands of years, in contrast to Western notation, which we tend to think of as 'eternal', but in reality began only at some point in the middle-ages in comparison.

For example, India produced Swarilipi and the Bhatkhande System of notation among 
others, used in raga and other melodic modes in Indian classical music:

China, meanwhile, had the Qin tablature, which showed finger positions and stroke technique rather than notes:

But it was in Korea, with the Jeongganbo notation, that durations of notes was first indicated in all of the Far Eastern musical notation systems. It's possible that this could have partially been adopted and led to the conventional five-staff Western notation system which we use today.
Each square in the notation below indicates one beat:

Of course, we're so used to reading from left to right in the majority of the Indo-European languages (which you're doing right now reading this blog post) that it's easy to forget that many languages elsewhere are the opposite, going from right to left and from bottom to top on a page. This is evident from Hebrew and Arabic to Chinese Mandarin and Japanese. So it would have been with many of the scores above. By contrast, the musical notation produced in the Byzantine Empire (the largely Greek-speaking empire covering parts of modern-day Greece, Turkey, Italy, and others), is slightly more familiar, even if obviously still incomprehensible to most viewers, in that it ran left to right, and was separated into measures:



In a way, graphic notation is almost a kind of reminder, or return, to these pre-Western notations of music, in which interpretation was slightly more open to the listener, and the performances of the pieces were less rigid as in conventional notation.