

Turning Rhythm into Tone


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.

Octave Waves

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:

Quarter note, eighth notes

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.

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  1. I posted this in the comments on the original blog, but I thought I would re-post it here as well:

    I think these sorts of illusions are really cool.

    However, the situation is even stranger than you describe.

    One thing has to do with pitch. You describe pitch as being how fast the sine wave moves up and down. True, sine waves do indeed have pitches. But what you are describing is actually frequency, which is not the same thing. In addition to the commonly-known pitches of pure tones and harmonics, there are also a lot of really weird ways to make pitches where there is no sound at all at the frequency you hear the pitch at.

    So then what is pitch? The truth is nobody is quite sure. Let me rephrase that: lots of people are sure, but nobody has been able to convince everyone else that they are right.

    Another weird thing is with octaves. The reason octaves are significant is because two pitches that are otherwise the identical but separated by one octave are very hard to tell apart, even though the frequency of one is twice the other, and we are normally sensitive to much smaller frequency changes. Nobody is entirely sure why that is, either, but it doesn’t appear to be part of the mechanics of the ear. Also, if you combine two sounds that are off by one octave, you only hear one pitch (which you can hear in your illusions),

    There are also weird things that happen with rythms. When do we hear two sounds as a rhythm, and when do we hear them as two independent sets of sounds? There are a lot of rules regarding this, including where the sounds are coming from, whether they start at the same time, whether things like loudness and frequency changes sync up, and so on. It is possible to manipulate this on the fly by playing with these parameters, but two periodic sounds that start off seeming like separate sources will tend to fuse into one rhythm the longer you listen to them, only to be suddenly broken up again when one sound does something the other doesn’t. You may even notice this when listening to the examples here (I did at least).

    Another interesting thing has to do with how our ears and brains handle sequential sounds. If two sounds are too close together, you won’t hear the second. There are even cases where a later sound will make you unable to hear a sound that came before it!

  2. Really interesting post and great comment theblackcat!

    I’m not nearly learned enough to get that deep but I have a couple of observations.

    The way we hear sound, and music specifically, also has a social component. I think a case can be made for something fundamentally physical about how we hear the perfect intervals but after that all bets are off. All the different scale traditions around the world and throughout history point to a certain plasticity in how we perceive sound and make use of it aesthetically. Mind you, this should come as no shock as perception is in the brain and brains are the most plastic of organs.

    That link reminded me: passenger jets harmonise. Usually I can hear three distinct notes. I suspect that they’re caused by the air rushing over the skin of the aircraft, the propulsion system and the pressurising system for the cabin air.

    I’ve never tried too hard to figure out that harmony, partly because my ear training sucks, and partly because when I get to the point of listening to the plane sing to me I’ve long since sunken in the half-conscious limbo of too many hours in the air.

    That said, they seem harmonically related, and aren’t unpleasant to hear together. I also suspect that the fact that all three vibration sources are acting on the same resonance cavity might have something to do with it.

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