I think you will enjoy this guest post by Daniel Y. of yoursound.today, a conceptual sound design and music platform.  He is also an artist and music producer from Bulgaria.

The Golden Ratio in Sound Design

The golden ratio – an aesthetic found in numerous places in visual art and nature, has been eluding many artists from ancient history to the present, and today it finds its place in sound design as well.
The golden ratio equals 1.618… and represents what one can describe as beauty found between the ratio between 2 different objects, dimensions and proportions. But while it definitely strikes an interesting visual aesthetic, can one really hear it? The short answer is yes, and people have already been using it in music composition for a while, even if unconsciously. One look at Mozart’s work and the golden ratio is all over the place, for example in terms of amounts of notes used in his musical scores–scores which are so big that it makes it hard to believe Mozart did it by accident. This leads us to even more strongly recognize his genius.
But that was a few hundred years ago. Today, the golden ratio is finally starting to find its place within sound design and before I tell you how, let me address any doubts again – yes, if done properly, one could hear it. But only when you listen and look for it and compare it to other sounds. While you cannot hear the ratio itself, the distinctive difference is a certain pleasantness and satisfaction that comes from listening to a sound in alignment with that ratio. If you want to quickly measure for yourself before we delve deeper into this topic, I suggest you to quickly open your favourite Plugin and align the Attack, Release, and Sustain of your sound so that it is in accordance to 1.618. (Simply pick a random number for one of the parameters and divide or multiply it by that number.) See if it sounds good to you.
Before I tell you how you can get more creative with it, let me briefly explain how it found its way into my own work. While music is seen as something engaging more strongly with the creative muscle, there is just as much mathematics and physics involved in it. And while various artists such as Leonardo da Vinci are known to have applied both creativity and mathematical analysis in their work, few are those who have done the same in the realms of music. I wanted to do that, so I started rigorously researching the mathematics of music. I found out differently tempered scales, psychoacoustics, and even some interesting ideas regarding to using chance in composition, but nothing really was what I wanted to do. Most people who use math in music usually focus on the composition of the piece which doesn’t always produce pleasant results. But with the development of technology and synthesis, new possibilities arose and allowed for new applications of math. Thus, I started experimenting with the golden ratio in a more fundamental part of music – the sound sources.
So, here’s how you can get creative with it and my personal recommendations:
ADSR – The main and most prominent way to apply the golden ratio is to ensure the Attack, Decay, Sustain and Release of the sound are in the right proportions (1.618) no matter what type of synthesis you use. You can actually pick only 3 of these parameters and leave the fourth at 0 if you wish (except for the attack).
Wavetable Synthesis – While you can use any type of synthesis your heart desires, in wavetable synthesis you can use geometrical shapes and image to form the wavetable itself and those can be images that also follow the golden ratio proportions. I personally use Serum, so a suggestion you can try if you have that plugin is to download an image of a golden ratio spiral and drag and drop it onto Serum’s wavetable section which will translate the image into sound. Interesting timbres are often the result of this.
LFOs – Using low-frequency oscillation on various aspects of the sound can give an interesting effect. To do this, one thing you can do is look at your tempo. If it is 120 BPM that is 2 beats per second and you can simply multiply 2 by 1.618 and set you LFO speed at 3.2 Hz. Then there will be a relationship between the sounds you play and the rhythm of the song.
Effects – Similarly to the ADSR you can create the same proportions using different effects but I recommend doing that with Reverb and Delay effects, as those, especially Delay, can give a specific feel to the sound.
Other things you can do include tampering with the tuning and pitch elements of your patch. This is great if you are working on an FX sound and want to experiment with the golden ratio.
There is still much room for examination of this topic within music and sounds, as we have barely scratched the surface here. While there have been attempts to create a tuning system implementing the golden ratio, there is still no such satisfactory musical scale. Also, the golden ratio has been found in many contemporary pop songs in terms of arrangement. There are many discoveries to be made on implementation of mathematics in sound, and experimentation is the key to that. So I encourage you to experiment!
About the author:
Daniel Y. is the founder of yoursound.today (A conceptual sound design and music platform) and also an artist and music producer from Bulgaria.