Science Sundays: James Sneyd – Mathematics and Music: the beauties of pattern

Dr. James Sneyd

Sneyd claims to have no answer to the question of whether mathematical and musical ability are necessarily linked, but hopes to show us how an appreciation and understanding of one field can enrich the other, and demonstrate common beauties not always apparent to the naked eye. He will briefly discuss some of his favorite moments in the joint history of mathematics and music. He believes we will find them amusing as well as interesting. Then he will give us a deeper look at patterns typically underlying mathematical research and show how such pattern constructions lie also at the heart of such things as musical improvisation and rhythmic patterns — not to mention Homeric poetry — which he promises will make an appearance.

James Sneyd, professor of mathematics, University of Auckland, Royal Society of New Zealand, states that, “For over 2000 years of Western culture, mathematics and music have been inextricably linked. Together with geometry and astronomy, arithmetic and music made up the four components of the quadrivium that formed the basis of the academic curriculum throughout antiquity and the medieval period. It can come as no surprise, therefore, that the greatest scientific philosophers and mathematicians, from Pythagoras and Aristotle to Euler and Helmholtz, have included music as a natural part of their scientific studies.”

Thus has arisen in the popular mind the notion of mathematician as musician — that somehow, a mathematical brain is peculiarly suited to the study of music, and vice versa.

“However, here be dragons,” Sneyd said. These historical studies, focusing on how musical scales are constructed using various fantastical combinations of mathematical fractions, expose only a superficial similarity between the disciplines. Just as music is so much more than scale construction, so is mathematics far more than mere multiplication of fractions. Both mathematics and music are — at heart — the construction of patterns, and herein lies a far more fundamental connection between the worlds of mathematics and music.

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