For my project I did a video presentation about the patterns and symmetries within music, specifically focusing on musical fractals. I decided this format was best so I could share both my own musical fractal as well as already existing musical fractals that exist in other composers’ music. While my video itself contains much of the mathematical overlap and main ideas I learned I will take the space here to write down both things said in the video, as well as things that I learned in the process of creating my project.

To start I’ll explain what a fractal is. A fractal consists of patterns that build off of one another to create something more complex and beautiful. Below this is a picture of a pythagorean tree fractal. Here we see it starts with a square, then there are two more squares added, then to each of those two more, and this pattern continues on and on.

A musical fractal, as I explain in the video, is some sort of property about the music whether that be a rhythm, tension, pitch, or something else that is a part of a bigger picture and is building off of other dynamics within the music to create this musical fractal. It can also be described as a symmetry or pattern found within music. One composer who was a master at using musical fractals was ​Johann Sebastian Bach. Many of these musical fractals occur within his canons, which makes sense since canons themselves have many fractal-like properties of starting with a melody then creating different variations of that melody at different speeds, styles, instruments, or even different keys.

In my project I wanted to be able to show these fractals in a way that helped the listener be able to visually see the patterns as well as hear them. To do this I found a program called Music Animation Machine (MAM) created by Stephen Malinowski. This app took audio files and created visualizations of the music from abstract images to lines and dots scrolling across the page (this was the visualization I used in my video presentation). Each series of lines and dots represents a different instrument part and in my presentation I showed the example of Bach’s Brandenburg Concerto #4, movement 3. Each note is represented by a dot and the lines are there for fluidity, duration, and aesthetic purposes. As the video plays there are numerous patterns and symmetries we can see. We notice similar melodies and themes occur and bounce around from instrument to instrument.

Finally at the end of my video presentation I showed my own original composition of a musical fractal. I tried to incorporate the same melody in different octaves as well as note lengths. Instead of simply summarizing the video I wanted to explain what I learned during this process and really a key take away I got from this project. After I had spent countless days and hours trying to make my musical fractal composition at least not sound awful, I began to realize that to create symmetries and fractals in music is something that can not be done by anyone, but is a skill that takes expertise in many disciplines to be able to create something that actually sounds beautiful and aesthetically pleasing. Bach was successful in his compositions of musical fractals because he understood both mathematics as well as music and how to incorporate them both to create something amazing. Bach not only relied on the calculations and math to create his music (like I mainly focused on), but he also understood that audiences don’t simply want to hear something completely predictable. Music is a creative process because of its originality; the way Bach uses not just mathematics to create his music, but also the element of surprise and other musical qualities makes Bach’s music authentic and beautiful.


DancingPhilosopher. ​Animation of an Imperfectly Self-Resembling Pythagoras Tree​. 16 Oct.

2019, bm. Accessed 3 June 2020.


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