Much of the time when I enter WolfamAlpha I feel the way archeologists must have felt confronting Egyptian hieroglyphics before the deciphering of the Rosetta Stone or—to cast things the other way and into the future—the way the scientists in 2001, A Space Odyssey felt in the presence of the monolith. I know it's magnificent but I don't know how to work it—not properly, at least.
The latest instance of my admiring frustration has been caused by WolframTones, which, as the tagline has it, is "an experiment in a new kind of music." It's a sonic working out of the principle that wonderfully complex objects can be created from the interplay of a few remarkably simple mathematical rules. (Shades of chaos theory, Mandelbrot fractals, and, I suppose too, natural selection.)
The music appears visually as rectangles containing a pattern of coloured squares, looking rather like an embroidery or knitting pattern. Clicking on it causes music to result. But this isn't just a matter of passive appreciation: you can create and manipulate the rules that govern the patterns. To help innumerates like me, WolframTones offers you 15 basic styles – classical, hip-hop, world, etc., along with controls that let you choose timing, scales from hundreds of possible mappings, and the "instruments" from among dozens and dozens of midi possibilities. The possible combinations and permutations are astronomical. You can then download a link to your particular composition—which can be played online at the WolframTones website or emailed as a midi attachment. Here, for example, is my utterly unremarkable, maundering bit of "ambient" music and, following the sound file, the visual pattern that "generated" it.
If you're interested in the hows and wherefores of this, there's a fair bit of explanation available, a portion of which follows:
How does one take a pattern generated by a cellular automaton, and render it as music? The key idea of WolframTones is to take a swath through the pattern:
and tip it on its side, and treat it as a musical score:
And for the truly curious, at the bottom of the "Generate a composition" screen there's a modest link offering "information about controls," which will go into some detail about the mathematical rules and structures.
If you do whip up a cantata over the holidays, send us the link by way of a comment.