Benoît Mandelbrot died on Thursday. I hadn’t realized the founder of chaos theory, the man who coined the word “fractal” to describe a concept he had discovered, was still alive. Fractals haven’t even been around for 30 years? But yes, that’s right; his original book was published in 1982.
For me there are two essential concepts in his work. The first is that many things do not get simpler the more closely you look at them. His classic statement of this insight was the question “How long is the coast of England?” If you measure it with a yard stick you’ll get one number. If you measure it with a foot-long ruler you’ll get another, larger number. If you measure it microscopically, you’ll get a much larger number. You could say that the length is, actually, infinite, getting larger and larger the more closely you measure.
What makes it even more interesting, though, is that he defined a class of functions that produce that kind of complexity. The most famous of those, when graphed, produces the famous “Mandelbrot Set.” The images of this set, usually brilliantly colored, are incredibly complicated and beautiful, but the function that produces it is very simple:
f(z) = z² + C
That’s it. That’s all you need to do to create those gorgeously complex pictures. You pick a constant number (C), and run the function over and over. You compute f(C). Then you take the result, and put it back into the function, computing f(result). You do that over and over (or better yet your computer does it for you) until either the results start shooting off to infinity, or stabilize at a single value. (Meaning, F(Z) = Z, so the results stop changing.) If it stabilizes, you put a point on the graph for C, because it’s in the set. You can color that point depending on how fast it stabilizes. And you do that enough, and you get those gorgeous pictures.
Breathtaking beauty and complexity, from calculations you could do with a pencil if you just had enough time. This is an illustration of one of the core principles of my atheism: Some of the most beautiful things in the world are created not by deliberate intention, but by the endless repetition of very simple processes. Glaciers, forests, ocean waves, clouds, light on water — they are far too complex to create intentionally.
Which brings me to generative music. Music is much simpler than nature, for the most part, and obviously you can create very beautiful music intentionally. But you can also create very beautiful and complex music from very simple pieces, if you loop them repeatedly and feed them back into each other. One of my favorite examples of the latter is Brian Eno’s Discreet Music.
It’s more than 30 minutes long, but it’s created from two brief musical phrases (something like seven seconds for one, and eighteen seconds for the other). He had both phrases in a synthesizer with a recall system (the EMS Synthi A, an early sequencer) which played them repeatedly. Since they were different lengths, they combined in different ways every time they looped.
He treated them with an equalizer to change the timbre of the notes, and then fed them into a long tape delay system. (A literal loop — five feet or so of tape.) Then he let that all run more or less unattended as he answered the phone, did other things, and occasionally injected something new into the mix. 30 minutes of that recording filled the first side of the classic album.
The result is beautiful and soothing and never boring, and I have loved it since the first time I heard it a quarter-century or so ago. (Come to think of it, I think I bought that album the same year Mandelbrot wrote his book.)
And today, perhaps in unintentional honor of Mandelbrot, I recorded a version of that piece on harmonica. I played the two basic phrases on a chromatic harmonica (the melodies themselves are very simple diatonic pieces in C or G minor, depending on your viewpoint), using an octave generator on the harmonica. I recorded each of them into a separate loop, leaving lots of space around them. I started both running, and fed them into a ten-second loop with a very long decay time. The two short phrases immediately started interacting in unpredictable ways, and it was very soon recognizable as “Discreet Music.”
Rather than modifying the loops with equalizers or a synthesizer, every once in a while I would play the phrases again, higher or lower on the harmonica, or with different settings on the octave generator, or with different embrochure. Those fed into the long delay and became part of the mix. The piece is (arbitrarily) about 15 minutes long, and for at least half that time I was just sitting and listening to the loops.
The result is not perfect (small flubs playing the phrases, or playing them a bit too loud, in a few spots) but I like it a lot. The original is better, but hell, this is all harmonica. And it was performed entirely live; what you hear is a direct two-track recording with no editing at all, other than fading it in and fading it out.
There’s a lot more to hear at harmonitronica.com, ranging from ambient pieces like this to very aggressive blues riff sampling to some lighthearted pieces. There’s even a political piece, and a gospel song, and I will be posting more pieces in the weeks to come. And stay tuned for the next time you can see some live harmonitronica.