Mathematics in Music

“The mind counting without being conscious that it is counting.” That’s how the the philosopher Leibniz described listening to music.

Cognitive scientists have become very interested in the ways the brain grasps musical patterns. It turns out there are overlaps between musical and linguistic and mathematical ability, which have spawned all kinds of theories about how music arose in prehistory. 

Also maths has changed in recent times. It’s no longer just about numbers. It’s about groups and symmetries and chaos and complexity. Mathematicians are in search of patterns, and music is all about pattern-making. 

The Greek-French composer Iannis Xenakis conjured sounds out of Bernouilli’s equations, and Brownian motion.

All this was revealed in a brilliant lecture on music and symmetry, given by Marcus de Sautoy as part of the Swedish Radio Symphony Orchestra’s Interplay series. Symmetry is something music has at the very basic level of sound. 

"Look at the make-up of a single sound on a 3-d oscilloscope, and you find the more pure and beautiful the sound, the more symmetry it has. The purest sound of all is a sine wave, and that looks like a circle. And a circle has infinite axes of symmetry."

Why do we choose one rather than another? Because it captivates us, for a reason we can’t quite define. It may because in some way the progression bends the rules, or actually breaks them. Bach broke the rules quite often, but that doesn’t mean we lesser mortals can do it (as I was often reminded as a student, after handing in a ham-fisted chorale harmonisation). If we could define the thing that gives that special x factor to harmonic progressions, we could produce them to order, or get a computer to do it.

There’s a need to find a pattern with that extra something that is used also when composing music, because a perfect pattern on music is boring, which opens the door to a new world. 

Read the Full article at Telegraph

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