Finding Gold in Music: The Golden Ratio and Rhythm Structure

The Golden Section, or Golden Ratio, has been a favorite endeavor of mine for years. The ratio itself is quite simple. B:A = A:(B+A), or “the small stands in relation to the large as the large stands in relation to the whole.” The Golden Ratio is represented by the Greek letter ‘phi’ which is correlated to the irrational number 1.6180339…


I’ve always loved the metaphorical reciprocity of this statement in a spiritual sense. For this reason, and the fact the Golden Ratio is abundant in nature, I’ve worked for many years to incorporate this relationship into musical systems of time and pitch.

I went back to my notebooks from the 90’s and they’re filled with scores of different applications of the Golden Section, but in the interest of clarity, I’m going back to the very beginning of my exploration and have decided to include you along the way.

Due to the complexity of integrating new pitch systems (getting my instruments to play notes they’re not built to play), I’ve decided to start with simple phi rhythms. I anticipate some false starts and dead ends, but I’m blogging about each step for a few reasons- not the least of which is keeping everything straight in my own head.

Golden Ratio Rhythm Elements V1.1

For version 1 of my experiment I decided to divide a 4 bar phrase (at 120 beats per minute) into its Golden Section ratios. Looking forward, I hope to use these points in time as the stressed beats of this rhythm system. Since I’m starting simple, there are only two points on our timeline.

Golden Ratio Rhythm

4 bars at 120bpm takes 8 seconds. Section A needed to be 1.618 times the length of Section B, so I simply had to solve for 1x + 1.618x = 8 to get B, which equals 3.056. Now, if we play a drum at the beginning (0sec), at both phi points (3.056s and 4.945s), we get only 3 hits across an 8 second period, which wonderfully celebrates the Golden Section, but does not make for a very interesting beat. There’s just not enough going on. When I next visit this, I will have broken down B into futher subsections (simply dividing by 1.618 each time) which will provide us with additional ‘phi-relevant’ points in time and also give us fodder for creating a more exciting beat.