Songwriting and the Golden Mean

Written by Gary Ewer
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The Golden Mean, also called the Golden Ratio, is a mathematical ratio that artists, architects and musicians have used in the construction of their art form for centuries. Let’s skip all the mathematical complexities and jump to a simple description, and then see how composers have used this in their music to determine if there’s a way of using it in songwriting forms.

If you start with the two whole numbers 0 and 1, adding them together gives you 1. Now take 1 and 1 and add them together, giving you 2. Proceed in this manner, adding the last two numbers of the sequence together to get the next number. This sequence (called the Fibonacci Series) looks like this:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144…

If you take any two adjacent numbers, and divide the smaller number into the larger number, you get a number somewhat close to 1.618. And in fact, the further along the sequence you go, the resulting division of the small number into the adjacent larger number gets you closer and closer to 1.618. That number is called the Golden Mean.

That ratio, 1.618, has been used by artists, architects and composers as a way of helping to structure their artistic creations. For example, Da Vinci drew faces that were 1.618 times longer than they were wider. The Parthenon is 1.618 times longer than it is high.

In music, the composer Bela Bartok used the Golden Mean to structure his compositions. In his “Music for Strings, Percussion and Celesta,” Bartok had musically important events occurring in bar numbers represented by the Fibonacci Series.

But is there a way for songwriters to use the Golden Mean? And why would you want to?

The Golden Mean occurs naturally in the world around us. For example, a snail’s shell spirals outward following the Golden mean: if you measure across the largest bump on the sprial, you’ll find that it’s 1.618 times larger than the smaller bump beside it. Many artists have believed that if you can fit your music into a construction determined by the Golden Mean, you’ll be injecting a kind of natural beauty, similar to Da Vinci’s portraits.

But how could you do this in songwriting? Applying Golden Mean to your songs might require you to compose much of your song, and then go back and apply Golden Mean proportions. In any case, here are some ideas:

1. Measure the length of your song in seconds, and then have some important event occur at the 1, 2, 3, 5, 8, etc – second mark. For example, the bridge of a song will naturally want to occur at that moment.
2. Take the length of your song, multiply it by 0.618, and you’ll get a spot in your song that’s almost two-thirds of the way along. Let something significant happen there (perhaps a cymbal crash followed by a momentary silence, a change of time signature, etc.) Let it be the climactic point of your song.
3. Change something about the instrumental accompaniment at different spots along the Fibonacci series.
4. Work backwards through your song, finding moments to make significant events occur along a backwards-running Fibonacci series.

And this suggestion comes from songwriter Stephen Wilcox from Australia: “Another variation I use is to divide the two sections before and after the golden mean point by the golden mean again… and have events occur at these points also, resulting in golden means within the golden mean. It has been a major breakthrough for my songwriting…”

If you’ve been using Golden Mean or any other interesting mathematical construct to work out some aspect of your musical compositions, please feel free to post them below. I’d love to hear from you.
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