# Thoughts on the Golden Ratio and colour.

Last Autumn, I posted an article talking about the Golden Rule. Here’s an excerpt from that post in which I quoted from Juliette Aristides’ book:

”Yet in a few places a remarkable physical phenomenon occurred- the clear and pleasing ringing of a musical tone. The new tones were created at the one half, two thirds and three quarters divisions of the string when measuring the string from right to left. When measuring the string from left to right, however, these tones are created at the one quarter, one third and one half divisions.

…these pleasing tones are called ‘harmonics’ or ‘musicial root harmonies’. They are the result of the string taking a new physical form called a sinusoidal wave when it is pressed at the one half, two thirds and three quarter division points. We now refer to these key positions along the string as the ‘octave’, the ‘perfect fifth’ and the ‘perfect fourth’ respectively….

….Curiously, the same ratios that are pleasing to our ears provide pleasing intervals to our eyes. Throughout history, master artists have used the harmonic ratios discovered by Pythagoras.”

This ratio is also known as the Golden Ratio or pi (3.14 relates the radius of a circle to its perimeter) and was shown by Leonardo da Vinci to relate the different parts of human anatomy in the Vitruvian Man (above). The Golden Ratio has also been shown to hold true for the spacing of nodes along a tree branch and the curve of a snail’s shell.

If music can be described, even only in part, by mathematics and composition likewise, could we not do that with colour?

Using 350-780 nm as the full spectrum, the octave would be found at 565 nm, the perfect fifth at 637 nm and the perfect fourth at 672.5 nm. These correspond to the following colours:

Energy in the visible electromagnetic spectrum has a range of approximately 350-780 nm.

There are two different ways to go about this. The first way is by taking the visible range as a whole and the octave being a half of this, then the perfect fifth and fourth as two thirds and three fourths respectively, like this:

These colours are at the opposite side of the colour wheel- no big surprise, since the colour wheel is based on the electromagnetic spectrum.

Back to the Golden Ratio: Theoretically for the golden rule to hold up, the colours should relate to each other along the electromagnetic spectrum in the same ratio- a whole, two thirds and one third.

Let’s analyze a couple of paintings and see what works.

First up is the most famous painting of all time:

Picked colours along the electromagnetic spectrum:

The main colours are at 1 and at 2/3rds of the spectrum. Let’s do another one- Bouguereau, known for his mastery of colour:

Now, that’s only two paintings and there are far, far more that we could analyze in the same way to see whether this holds true in general.

. It’s also possible that this holds true even if you zoom in on the spectrum and pick two random colours to represent 0 and 1- the colour that appears at two thirds along the line will form a Golden Ratio and therefore ‘go’ with the other two.

We could carry out many experiments along the same theoretical basis, but for now, it looks as though colour may follow the Golden Ratio by forming combinations pleasing to the eye and that we can use the electromagnetic spectrum together with the Golden Ratio as a basis for selecting colours that will go together and be aesthetically pleasing.

Please leave a comment if you have any thoughts on this topic!

This is really, deeply fascinating, Theresa.

And why not? The numbers are found everywhere, why not in the colour spectrum? I’d be interested to see how well this approach holds up in practical application- i.e., deliberately selecting colours for a work-in-progress using this method, rather than using it is a critical tool to analyse pre-existing work.

Its allways really interesting to read about the golden ratio !!! ” Der Goldene Schnitt” thats how we call it in germany.

thank you theresa!!! have a nice day!

The golden ratio is Phi 1.61803359 not pi 3.14 as you describe

Hi there,

Interesting efforts to present the golden ratio. However, correction suggested by J.D. above is past overdue. The ration is indeed 1,618 … Phi and not Pi (3,14) – Huge difference between the two.

Good luck

ES