— 2012 — Apr 16

Harmonic Intervals from Polyrhythms

by Anton Schwartz

Here’s a beautiful audio/video demonstration of a simple acoustic principle. Watch it first if you want to figure out for yourself what’s going on… or read on for an explanation.

First a little background about sound waves (skip it if you’re familiar): All sounds are vibrations of air molecules. Every sound that is a musical note is characterized by how many times per second the vibration occurs. Increasing the frequency of vibration raises the note’s pitch; decreasing it lowers the pitch.

When you play two notes together, the musical interval they form is determined by the ratio of the notes’ frequencies. When one note has twice the frequency of the other, the interval they make together is an octave. When the ratio is 3:2 (that is, when one note’s frequency is 50% more than the other’s), they form a perfect fifth interval.

The vibrations of musical sounds occur very rapidly, anywhere from dozens to thousands of times per second… much too fast for us to count and verify their frequencies by ear. So here’s a wonderful demonstration of how the frequency ratio of 3:2 actually produces the sound of a perfect fifth.

If we make a clicking sound over and over at a regular interval, and begin to speed up the interval, it will start to sound like a note. That’s what happens when we attach a card to a bicycle so that it flaps against the wheel spokes as we pedal.

If increasing a note’s frequency by 50% really raises the note by a fifth, then when we listen two sets of clicks, one 50% more rapid than the other, we ought to hear a perfect fifth interval. We have a rhythmic term for two sets of clicks where one is 50% more rapid: a 3-over-2 (or “3:2”) polyrhythm. So does a 3:2 polyrhythm sound like a perfect fifth?

This video clip demonstrates that it does. You don’t hear any pitches at the beginning, when the rhythm is played at human speeds. But as the tempo speeds up, the musical interval emerges.

If we were to do the same demonstration with a 4:3 polyrhythm, we would hear a perfect fourth instead of a perfect fifth.

Thanks to Loudon Stearns for the great demo!

5 Responses

  1. Frances Martin says:

    Thank you for this! Never knew that polyrhythms create harmonic intervals, but this demonstration is very clear about the direct relationship! Will share with my piano students… thanks again! Frances

  2. Carter says:

    I’ve known about this theoretically for a long time, and often wondered how it would sound. Thank you for a great demonstration.

  3. Sen says:

    Would the same if a rhythm was speeded up to 440 beats in a second it would produce the note A natural ?

    • Yes, a 3:2 polyrhythm at 440 beats per second (26,400 bpm) would produce the A above middle C and the E above that.

  4. Dana Bara says:

    Thanks for having this resource available. I couldn’t find the right set of Google keywords when I first learned about this phenomenon so I was struggling to find this again — but here I am!

    Thanks again for the beautifully simple illustration!!

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