Can You Hear the Golden Ratio?

Is there a way to calculate beauty? Or a secret formula to a well-composed painting or the part of a song that makes your heart race? Turns out there is a “golden ratio” that shows up in many of the designs that captivate and delight us!

You might be familiar with the image of the inside of a nautilus shell or the way the individual scales of a pinecone spiral outward at the base. Like some kind of code from the great beyond, the golden ratio appears to show up all around us.

Very often, this is represented in the visual world but is it also happening in the music we make! You might never listen to your favorite song the same way again after this article.

Let’s start with the basics.

What is this “golden ratio”?

It really begins at a fundamental level for humans. Some scientists believe that the ratio appears to be designed into our works of art and architecture because it is the flow of imagery that is easiest for our brains to quickly scan and understand! ¹

With this ease comes a sense of pleasure, and thus, we tend to replicate that feeling as we create.

This is why many people have found it in works like the Mona Lisa, the Pyramids of Giza, and the Parthenon.

So, what’s going on here mathematically?

The golden ratio is the irrational number Phi. Irrational essentially means the number goes on and on with no end digit, like the better-known number Pi. If you were to round it, Phi is generally equal to 1.618.

To explain it in mathematical terms, it’s the number you find when you divide a line into two partS so that the longer part divided by the smaller part is equal to the entire length divided by the longer part.

So in the case of the rectangle below, if you were to divide the long side of the rectangle (21+13)=34 by the short side (21). You’d get 1.619, or Phi. Do this with the rest of the rectangles you see, and you’ll find that the long side divided by the short side will be Phi.

But what does this have to do with music?

It took me a while to understand exactly what was happening with the golden ratio. But you don’t really have to understand the numbers to start seeing the golden ratio in the world all around you! Including—much to our surprise—the world of classical composers.

As you’ll see in the video below, musicians and mathematicians have been looking at music for a while now and are finding that Phi isn’t just for the visual arts. You can find these “Phi moments” in music!

Is this just a coincidence? Or was it intentional? Maybe used as a way to set up creative constraints to make something spectacular?

Once you’ve heard a Phi moment, you’ll start asking yourself, what’s going on here? The PBS Digital Studios series Sound Field dove into this question and here’s what they found…

If your a fan of the behind-the-scenes world of music or music history, make sure you check out Sound Field. They explore everything from the origins of funk music to the way technology has reshaped the music we listen to today!

The Phi Moment Experiment

Give that experiment they mentioned a go. Take your favorite song and find out how many seconds it has. Then, multiply that by .618. Now, head to that point in the song and see what you find. I gave it a try with a few of my favorites and the vast majority were either at a high point in the song or just reaching it!

This got me thinking, is there a Phi moment in concerts? In playing a series of songs with their own Phi moments is there ever a point in a concert that is a phi moment? One that really is happening unintentionally?

I don’t have an answer but the next time you’re at a concert, maybe you could do an experiment to see when the crowd’s favorite tune comes on.

Let us know what you find!

Put your Phi glasses on and do some digging of your own. Where are you finding Phi? Share this story with a friend! Who knows, maybe they’ve been recognizing Phi moments for years without knowing they were out there.

Whether you’re excited by the mathematics of it all, the beauty, or even the randomness of the world, the idea of a Golden Ratio probably explains some little corner of this planet that you know about.

Really, the best part about it is how knowing about this ratio can leave us walking through the world with a little more awe.

Stay beautiful & keep laughing!

-Liesl

This article originally published May 10, 2019.