Though we all know that our senses don’t see the world as it is — what we perceive as an image is a bunch of photons bouncing off of an object, what we perceive as sound is a series of pressure waves hitting our eardrums — we live mostly separated from this fact. We can’t actually perceive the differences between the real world and our perception of it, so it’s an easy thing to ignore. That’s why things like optical illusions are so cool: they find a way to get past our perceptive defenses and show us how our brains are really processing the stimuli around us.
It’s also why jazz pianist Dan Tepfer’s recent post about rhythm-pitch duality rocked my world.
When playing with a computer-music programming environment called SuperCollider, he realized that he could speed rhythms up until they became pitches, much like a helicopter’s rotor gearing up for takeoff. The cool thing about this was not the fact that rhythm could become pitch, but what happened when he combined two rhythms together and sped them up.
Let’s back up and introduce you to the harmonic series. Long ago, a mathematician (most say it was Pythagoras) discovered that if you divide a vibrating string (say, a guitar string) in two, the frequency of the resulting tone will be twice that of the original tone when the string was undivided — this is called the fundamental. (A third of the string vibrates three times as fast, a fourth four, etc.) A tone at twice the frequency of its fundamental is an octave above that fundamental — low C to high C, for instance. Dan’s demonstration image explains this nicely: the bottom wave is the fundamental, the top wave is twice the frequency.
If you were to turn the crests of the waves into rhythms, you’d get a single beat for the bottom and a beat at double the speed on the top. Like so:
When Dan entered this rhythm into his program and sped it up, it sounded like this. Listen to that clip, and you’ll hear a perfect octave. That’s because he’s created the same frequency relationship that occurs in an octave, and sped it up until our brains no longer perceive them as singular events, instead hearing them as a single tone. It lets us hear exactly what’s happening when pressure waves reach our eardrums.
But this is just the tip of the iceberg. He does this with perfect fifths, minor thirds, even whole triads — that is, not just two notes, but three. Check it out.
Featured image by flickr user xdestineex.