{"id":277,"date":"2012-12-13T19:57:41","date_gmt":"2012-12-14T00:57:41","guid":{"rendered":"http:\/\/dantepfer.com\/blog\/?p=277"},"modified":"2025-12-09T20:11:24","modified_gmt":"2025-12-10T01:11:24","slug":"hear-rhythm-become-pitch-before-your-ears","status":"publish","type":"post","link":"https:\/\/dantepfer.com\/blog\/?p=277","title":{"rendered":"Rhythm \/ Pitch Duality: hear rhythm become pitch before your ears"},"content":{"rendered":"

I just got home from a five-week tour in Europe and finally have some time to do what I call research. The way I see it, being a touring musician is a bit like being a scientist: you spend a bunch of time in the lab, and you find something that you’re excited about; then you have to go out and give a bunch of seminars to tell the world about it. But very soon you’re itching to get back to the lab, because you want to discover the next<\/em> thing. So here I am, at home and doing research, which for me, right now, in between practicing piano and writing tunes, means getting into a computer music programming environment called SuperCollider<\/a>.<\/p>\n

Yesterday I was fooling around with it and suddenly realized that with SuperCollider, I could do something I’d been wanting to do for years, which is to make a recording of rhythm becoming pitch, and back again. You see, rhythm and pitch are exactly the same thing, only at very different speeds. How’s that, you ask? Well, let’s start with the harmonic series:<\/p>\n

\"harmonic_series\"<\/a><\/p>\n

The harmonic series is what you get when you take a string, on a guitar, say, and start dividing it up. So let’s say you tune your string to a low C, the lowest note on the staff above. Then you divide it in two, so only half of the string is ringing. That note, as Pythagoras discovered a long time ago, sounds exactly an octave higher than the fundamental. Now you divide it in thirds, and you realize that that note is exactly an octave and a perfect fifth above the fundamental, a G. Now here’s the interesting part: the octave vibrates at exactly twice the frequency of the fundamental, and the octave + fifth vibrates at 3 times the frequency of the fundamental. In other words, divide a string in 2 and it vibrates twice as fast; in 3 and it vibrates 3 times as fast. And so on through the harmonic series \u2014 I’ve written down the first 8 notes of it above. The major third (E 2 octaves above the fundamental), for example, shows up when you divide the string in 5 and it vibrates 5 times as fast as the fundamental.<\/p>\n

How does this relate to rhythm? Let’s think about the interval of an octave. If we play a low C and the C an octave above that at the same time, we’ll have one note vibrating at one frequency and the other vibrating 2 times as fast. If you looked at the sound waves next to each other, they would look like this:<\/p>\n

\"octave_waves\"<\/a>Now consider just the crests of each wave, the moment where they reach their maximum. In the time between two crests of the bottom wave (the fundamental), the top one (the octave) crests twice. If we were to write this out in rhythmic notation, it would look like this:<\/p>\n

\"octave\"<\/a>

Octave (2\/1)<\/p><\/div>\n

That’s a very simple rhythm: 2 for 1. Any child can tap it on her knees. But did you know that if you sped a recording of her tapping this rhythm on her knees up about a hundred times, you would actually hear two pitches an octave apart? Don’t take my word for it, check it out:<\/p>\n\t