Wednesday, 11 August 2010

The sine wave and quantum beats

s long as I'm mucking about trying to find parallels between quantum mechanics, set theory, and rythm, I set about with a bit of a musical experiment on my trusty korg electribe mx as piped through my soundcraft lexicon mixer's drum plate. The tubes in the electribe give the drums a predictable warmth, while the plate adds room overtones and depth.

The problem is no doubt simple from a purely musical or musician's perspective, but interesting from a mathematical one.

Just like an ordinary sine wave, we simply build a rythm that alternates parts from one measure to the next. For example, we can build a rhythm consisting of bass drum, snare, and decorate it up top with a constant closed hihat (with an open on the last half beat).

Our bass drum hits on [1, 5, 9, 13], where as our snare is on [3, 6, 9, 12]. What we end up with is a pretty straightforward bossa nova, with the intersection of both parts occuring on the half four [9]. Enter the sine wave: we alternate the bass and snare every other measure! (Incidentally, the effect that this has - if I first switch that opening snare to an opening kick - is a binary alternation between bossa nova and rock-steady beat!).

Granted this is the simplest way of looking at our beat composition and arrangement, but the best way I can think of to introduce the analogy. But think of the tapestry we could weave when we apply more sophistication to this schema? Like introducing limits, Integration/Differentiation, partial derivatives to the same set of numbers? (Note: I haven't figured all this out myself yet - still some of the results I've observed are really interesting - not to mention they groove, albeit in ways you probably don't expect!) It's probably possible to build this on e.g. complex functions, while keeping the groove. Then you're in uncharted territory, sweet stuff, you're sailing in blue oceans. Of course, there's more than just these musical variables to tweak.

When combined with acoustic instruments, the intent is hopefully to sincerely emulate "the groove" within the prescribed toolset with this added rythmic complexity as part of the mix. But like everything I'm into at the moment, I've kind of ripped the machine down to its parts to muse and dwell on particular small bits of the problem that fascinate me. Hopefully I'll get down to proper business with it soon enough!

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