Mathematics and Music: A Lifelong Friendship

Whenever I used to hear the name Pythagoras, I would immediately think of the equation a^2 + b^2 = c^2. However, as I learned more about the ancient Greek mathematician, I realised that there was a lot more to him. He was also a fascinating philosopher, innovator and, like me, a musician—though he was a much more important one. He is thought to have invented the monochord, one of the first stringed instruments and a device that is also used as a scientific lab instrument. He used mathematical principles to investigate the relationship between pitch and the lengths of the monochord string, applying proper proportions and ultimately creating the Pythagorean Circle that led to the circle of fifths.

Once I discovered Pythagoras’ contributions to mathematics and music, I began to contemplate the many similarities between the two disciplines. Music is intrinsically mathematical and often composed based on ratios and proportions, Pythagoras’ favorite concept. But is there such a thing as overdoing it on the math when composing a concerto or an opera? Can too much consciousness of mathematics overwhelm the music?

When I listen to Bach and Handel, I can see the counterpoint mathematically in my mind, creating beautiful layers. Sometimes this hinders me from simply enjoying the sound. It is especially distracting with more modern music when harmonies are jagged and tri-tones abound. I wonder what Pythagoras would have thought of Schoenberg’s 12-tone technique. Would he hate it? Or would he admire its ingenuity? To many, music is a kind of language. Like all languages, it has changed in accordance with societal preferences. I believe this is an indication of progress.

Although I sometimes yearn for proportion and clean lines when I listen to Webern or even to the radio, I am still able to admire the beauty that chaos can create. I hope Pythagoras was able to do the same.