Music. Maths. Perhaps it’s the variables involved, amplitudes, frequencies, wavelengths, that make music so easy to talk of in terms of mathematics, and more so than other artforms. 

The two share a close history. Remember Pythagoras? The square on the hypotenuse is equal to the sum of the squares on the other two sides (for a right angled triangle)? You may also know the story of Pythagoras and the blacksmith; how upon hearing the consonant and dissonant strikes of the various hammers he was able to derive the proportional relationship an object’s mass has to its pitch. 

In his Harvard Norton Lectures, Leonard Bernstein explores the idea that sound, language, music, all share the same root, and how the secrets of the harmonic series of overtones might’ve played a part in the founding of human speech.

Then there’s Bach of course, the symmetry of whose music has been explored in countless scholarly articles...

Bach and musical symmetry

Bach and the musical torus 

More on the much loved mathematical donuts later!

Emily Howard

Emily Howard is one composer who looks to mathematical and scientific concepts for inspiration. Her new Sound Investment piece will explore exponential growth and decay, extreme states, explosion and implosion and these ideas might be wrought in music, itself ‘derived’ from her Soliloquies & Dialogues solo percussion work, R. 

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Howard read mathematics and computer science at Oxford, before focusing her post-grad studies on music. Her commitment to collaboration between mathematicians, scientist and musicians led to the founding of PRiSM, RNCM’s Centre for Practice & Research in Science & Music.

Simonyi Professor for the Public Understanding of Science, Marcus du Sautoy is a colleague of Howard's. Our friends at NMC hosted their inaugural Listening Club with Howard and du Sautoy as guests during lockdown. One idea discussed is how a higher dimensional entity such a music is rendered, locked in two dimensions, and how composers are constantly having to evolve new notation to counter this interdimensional problem. 

This could be likened to how we, in our three dimensional world, might experience the tesseract, a cube in four dimensional space. 

Take Howard's recent Orchestral Geometries for LSO: Torus, sphere, Antisphere. The composer likes to imagine walking on these higher dimensional, and sometimes negative curvature shapes; how might these, often highly abstract, objects be rendered in pitch, timbre, and rhythm?

In our recent BCMG Chats, Howard mentioned the influence of Iannis Xenakis on her creative practice, and it’d be remiss for a blog about music and maths not to feature the Greek architect-composer. Bálint András Varga’s Conversations with Xenakis is a great starting point for those looking to know more about the maths of Xenakis's music, and how composer wove complex mathematical concepts like set theory, stochastics processes and game theory into his music. Training as an architect comes with its fair share of engineering mathematics, after all.

George Lewis

George Lewis has played extensively with the idea of probability in his music (as have so many) and is well known for his pieces featuring musically adept computers. His interactive trio for trombone, two pianos and interactive music system features an AI ‘player’ piano that responds to the playing of the human pianist. 

The human pianist here, Amina Claudine Meyers, claimed she could not discern the AI's playing from that of a human. 

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Julian Anderson

Computers have played a Promethean part in the development of music. Spectrograms could not be produced without them - the visual representation of a sounds frequency content. 

Spectralism is a cornerstone of Julian Anderson’s music. The composer joined our NEXT students for a workshop preparing Grisey’s Vortex Temporum for performance, Grisey himself an exponent of spectralism. Anderson studied with Grisey’s contemporary, Tristan Murail, another composer who used relationships between harmonic spectra as a compositional springboard.

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Despite all the maths and science, Howard extols the importance of making space in her music for life and all its rich experience. Mathematics may underpin our universe regardless of human life, but music only makes sense with ‘us’ there.