Practically everything about music is rooted in mathematics: harmony, rhythm, melodic patterns. Performing music reinforces parts of the brain used when doing maths. And some studies have even show that children who play instruments are able to complete complex mathematical problems better than peers who do not play instruments. But there are some composers who explicitly based their working methods and musical structures on mathematical principals. Here are five pieces of classical music inspired by mathematics.
PHOTO: Ecole polytechnique Université Paris-Saclay
1. Johann Sebastian Bach: The Art of Fugue
Bach’s masterpiece is a prime example of mathematical precision in music. It consists of 14 fugues and 4 canons, all based on a single theme, out of which the composer generates all sorts of intricate patterns and recursions. Some have even argued that the structure is based on the Fibonacci sequence and the golden ratio.
2. Olivier Messiaen: Quartet for the End of Time
Messiaen famously used prime numbers as a structural device in this widely-celebrated work, written while the French composer was a prisoner of war in German captivity: as the piano plays a sequence of 17 chords, the cello plays a melody with 29 notes, creating a continually shifting, non-repeating pattern that evokes both a sense of unease and timelessness.
3. Iannis Xenakis: Metastasis
Continuing our list of music inspired by mathematics: Xenakis, an architect and composer, used complex mathematical models in his compositions. And ‘Metastasis’ is fine example, based as it is on principles of probability theory and incorporating architectural concepts like hyperbolic paraboloids. In particular, Xenakis drew inspiration from Einstein’s theory of relativity, which views time as a function of matter and energy rather than a linear, universal flow. In ‘Metastaseis,’ this is reflected in how the piece progresses through changes in intensity, register, and density of scoring, rather than relying on traditional time-based structures like fixed tempos or time signatures. The result is a piece of intense physicality.
4.Arnold Schoenberg: Various Works
Of all music inspired by mathematics, Schoenberg’s must be the maths-iest among them. His 12-tone technique, which he used in many compositions, is in some ways more maths than music (or at least some would argue so), based as it is on the organisation of all 12 notes of the chromatic scale into a specific order. What emerged was a highly structured approach to composition.
5. Karlheinz Stockhausen: Gruppen
This piece, in which three different orchestras are arranged in a horseshoe shape around the audience, uses mathematical formulas to determine various aspects of the composition. The foundation of Gruppen is a 12-pitch tone row (a sequence of 12 notes), which Stockhausen used to structure every other aspect of the piece. Even the tempo is mathematically -derived – calculated by translating the pitches in the tone row into tempo ratios.
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