The art of fugue has a thousand faces

We live in a highly specialized world. Everyone masters only a tiny fraction of the entire reality. As a consequence, we often forget the overall picture. A reminder to the intrinsic unity of reality comes (not so) unexpected from Johan Sebastian Bach and his masterpiece: the Art of Fugue.

The Art of Fugue is the musical testament of Bach. It consists of 14 fugues and 4 canons of increasing complexity. All the pieces are based on variations of a single main subject. The work is highly experimental. Bach stretched the contrapuntal techniques to their limits and came up with an impressive collection of interrelated pieces. No instrumentation is provided within the score. Indeed, this music is quite abstract and perhaps should be read rather than heard.

subject of The Art of Fugue

The main subject of The Art of Fugue.

The Art of Fugue is not only one of the best compositions ever written, but is also a pointer to other fields outside the musical domain. The work has deep relationships with mathematics, biology, linguistics and architecture.

The Art of Fugue is related to mathematics. The entire work can be regarded as a fractal structure based on recursion and self-similarity. The concept of recursion is the key to understanding both fractals and self-similarity. Recursion is the process of embedding some constructs within other constructs of the same kind. This process leads to self-similarity. Fractals display self-similar patterns. In other words, a fractal appears the same at every scale. The Art of Fugue exploits recursion, since it is based on a single musical pattern, which is restated at different levels of resolutions. Therefore, the musical structure becomes self-similar, and the work as a whole can be regarded as a musical fractal.


Fractal objects appear the same at every scale.

The Art of fugue is related to biology. Life is astonishingly diverse. Biologists estimate that nearly 2 million species live on planet Earth. There are creatures as strange as the dumbo octopus, and as regal as the tiger. Nevertheless, all life forms are based on a simple molecule: the DNA. The DNA consists of four bases (guanine, adenine, thymine and cytosine), that combined together are capable of generating every living system. Likewise, the Art of Fugue is based on a simple musical molecule: the main subject. This short string of musical information is responsible for the variety and richness of the entire work. Indeed, the subject is musical DNA, which carries all the information needed to generate the highly complex musical structures that characterize the Art of Fugue.


The Dna is the base of life.

The Art of fugue is related to linguistics. The similarities between musical and natural language have always been explored by philosophers, musicologists and linguists. Both the languages are based on syntax. In particular, the syntax of the natural language can be represented by a generative grammar. A generative grammar provides a small set of rules, that can generate all the correct grammatical sentences of one language. The Art of Fugue has its own set of rules, which considered together form a kind of musical generative grammar. The musical grammar consists of the basic rules of the counterpoint such as the inversion, diminution and augmentation, which directly shape the musical sentences. Thus, a small set of rules can generate the entire richness of the Art of Fugue.

The Art of Fugue is related to architecture. Both music and architecture are interested in structures. Music organizes sonic spaces, while architecture organizes physical spaces. Likewise, they both share the compositional process. In particular, architects have always been obsessed by the organizational process based on modules. For example, the Parthenon entirely relies on the golden ratio. The length of the temple, the height of the columns as well as the Parthenon’s façade can all be obtained from the golden ratio. Also, the architect Le Corbusier used a similar prime generator called modulor. Indeed, he exploited the modulor while working on Notre Dame du Haute and the Unite d’Habitation. The similarities between this architectural process and the compositional process used by Bach are striking. All of them are based on a single molecule of DNA that encodes the genetic instructions for the different kinds of compositions.


The Parthenon is based on the golden ratio.

The Art of Fugue in particular and the music in general are invaluable tools to understand the reality as a whole. Indeed, they can unveil the secret network that connects the different aspects of reality altogether. In this sense, listening to the Art of Fugue is not only a compelling aesthetic experience, but also a multidimensional journey that provides the listener extra-information about the structure of the world itself.


6 thoughts on “The art of fugue has a thousand faces

  1. Cool article. Have you ever read the book “Godel, Escher, Bach”? It’s a really fascinating book that looks at how music, geometry and the Incompleteness Theorem all share similar underlying structures. Based on this post, I think that you would really like it. Be warned though, the mathematics are not watered down, so you have to have a solid background in mathematics to wade through it.

    • Thank you for your comment Zbraiser. “Godel, Escher, Bach” is one of my favourite book. I think the way Hofstadter related the three domains is just amazng. Of course, many of my ideas are (in)directly influenced by his work.

    • Thanks for your thought ATheoryofMusic. You are right! The art of fugue is such a wonderful piece of music. Every contrapunctus is a masterpiece. It took me years to “understand” the inner complexity of most of the contrapuncti, and of course I’m far from done.

  2. Pingback: Top 10 classical composers of all time – Part 2 | Musikalkemist

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