Magical Patterns
April 22, 2016
Roger Antonsen

Did you know that you could hear numbers?

(Published in Aftenposten April 22, 2016, in Norwegian.)

The world of music, consisting of sounds, tones and frequencies, is full of patterns. Here is a little video about the simplest patterns that exist and how we can hear numbers.

For example, the video discusses the relationship between the length of a string and the frequency that results when we play the string: The string length and frequency we hear are inversely proportional to each other.

When I got the idea for this video, I reached out to my friends at the Department of Physics at the University of Oslo. There, Associate Professor Arnt Inge Vistnes, who teaches the physics of oscillations and waves, loaned me the box you see in the video. On the box, two identical strings are fastened next to each other. Their lengths can be adjusted in order to experiment with different sounds.

In the video, I experiment with making one string shorter than the other. What must the lengths of the strings be for the sounds to play well together and produce harmony?

Music and sound are exciting topic that there are great mathematical analyses of. If you are interested in digging into some of this, there are a number of good books, such as Dave Benson's book Music: A Mathematical Offering.

For example, it is impossible to tune a guitar perfectly using only pure ratios like 3/2 and 4/3. Rather, we use equal tempered tunings, and then the point of departure is the square root of two. However, that is another story.

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