Listen by numbers: music and maths

An article by: Marcus du Sautoy

I used to do a lot of counting as a trumpeter in my local youth orchestra. Sitting in the brass section, counting out rests so I didn’t crash in early with a fanfare, I began to realise that mathematics and music had even deeper links. It is certainly a connection people have commented on throughout the ages.

“Music,” wrote the great 17th-century German mathematician Gottfried Leibniz, “is the sensation of counting without being aware you were counting.” But there is more to this connection than counting. As the French baroque composer Rameau declared in 1722: “I must confess that only with the aid of mathematics did my ideas become clear.”

So is there really a link? Or is it crazy to try to connect the creative art of music with the steely logic of mathematics? Certainly the grammar of music – rhythm and pitch – has mathematical foundations. When we hear two notes an octave apart, we feel we’re hearing the same note, so much so that we give them the same name. (This is because the frequencies of the two notes are in an exact 1:2 ratio.)

Yet, while the combinations of notes we have been drawn to over the centuries can all be explained through numbers, music is more than just notes and beats – just as Shakespeare is more than just words from a dictionary. And it is in putting the notes together to create, say, the Goldberg Variations or Don Giovanni that I believe the true connection between mathematics and music reveals itself.

Read the rest of Marcus du Sautoy excellent article here Listen by numbers

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