Exploring Music's Complexities

Fractal Music


Fractal geometry, a relatively new field of math, provides a means to create mathematical descriptions of sound. It differs from classical geometry in that it doesn’t use formulas to define shapes; it uses iteration (1). Fractal shapes are made in two steps. First, a rule is made about how to change a shape. This rule is applied to the shape again and again, through infinity.

The notion that a relationship exists between music theory and mathematics dates back to the Ancient Greeks who described the relationship as the “harmony of the spheres”. Today, researchers are utilizing fractal geometry to define these relationships.

This geometry permits one to get a sense of the whole when looking at the smallest part.   Because all music genre follow the patterns of fractal motion it was determined that it should be possible to produce music using fractal methods.The notion that a relationship exists between music theory and mathematics dates back to the Ancient Greeks who described the relationship as the “harmony of the spheres”. Today, researchers are utilizing fractal geometry to define these relationships.

This possibility was researched in 1989 by KENNETHJ.Hsu*AND ANDREASJ.Hsu (2) who noted preliminary analysis of a few compositions by Bach and others indicate the potential for making a numerical analysis of music.   They found that the musical effects of a composition could be expressed as deviations from fractal geometry.

Two groups of computer-generated music exist: music in which a computer generates the score, which could be performed by humans, and music which is both composed and performed by computers. There is a large genre of music that is organized, synthesized, and created on computers (3). Other programs can produce sequences of notes using computer music languages such as MaxMSP, SuperColider, Csound, Pure Data and ChucK on most personal computers (3).

Computer programs are also now available to improvise existing music. Musical phrases are extracted from existing music and repeatedly played to create algorisms to identify patterns. Improvisation software uses these computer algorithms to recombine musical phrases extracted from existing music. Utilizing machine learning and pattern matching the result is “in the style” of the original music.

Dave Cope, a pioneer in computer generated music, has used software program to great effect with composers such as Bach and Mozart (his program Experiments in Musical Intelligence is famous for creating “Mozart’s 42nd Symphony”), and also within his own pieces, combining his own creations with that of the computer (4).

What does all this mean to musicians? Will one have to be a computer savvy musician in the future? Could computers ever put all musicians out of work? For some, these advances in artificial intelligence will certainly be warmly embraced, permitting the making of certain types of music easier and cheaper to create. It also may help to auto-generate certain compositions.

Interesting though this is, others say that while music bears similarities to mathematics it is not the same. One of a composer’s goals is to create something that evokes feelings in listeners. For the mathematician something is either true or false. Mathematics does not create emotions: it creates something logically consistent (5). Perhaps a better proposition is that sound is a better determiner than music.

In June of 2016, Google launched a project designed to expand the use of technology to make music. While attempts to use computers to make music are not new, Google’s is unique in that it has enormous computing power and is making its tools available to everyone. Building on the research conducted in the 1950s and the rapid development of computer equipment, the program hopes to assist musicians stay on the cutting edge in concert with mastering their instruments of choice. Samples of songs produced with Artificial Intelligence can be heard at Google’s Magenta Music on YouTube.


  1. Dallas, George. What are Fractals and Why Should I Care?   https://georgemdallas.wordpress.com/2014/05/02/what-are-fractals-and-why-should-i-care/ Retrieved 04/20/2017.
  1. Browne, Malsome W. J.S. Bach + Fractals = New Music     http://www.nytimes.com/1991/04/16/science/j-s-bach-fractals-new-music.html? pagewanted=all Retrieved 04/20/2017.
  1. Computer Music. From Wikipedia, the free encyclopedia.   https://en.wikipedia.org/wiki/Computer_music.
  1. McFarland, Matt. Google’s artificial intelligence could transform the way we make music. http://www.chicagotribune.com/bluesky/technology/ct-google-computers-creating-songs-project-magenta-20160606-story.html. Retrieved 04/20/2017.
  1. Fraser, Colin. Is music really math? https://www.quora.com/Is-music-really-math. Retrieved 04/20/2017.

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