Work by researchers at Waterloo Engineering demonstrates how advanced algebra can help reveal the deep patterns and symmetry at the heart of music.
Dr. Olga Ibragimova, a former PhD student in computational mechanics, and Dr. Chrystopher Nehaniv, a professor of systems design engineering, used group theory - a branch of mathematics that studies symmetry and transformations - to examine melody.
Their analysis revealed symmetrical relationships in many melodies that help explain why certain musical phrases feel cohesive and complete.
“Our goal was to build a clear mathematical bridge between abstract algebra and the experience of listening to music,” Ibragimova said.
“When we think of melodies as shapes we can transform, it becomes clear that composers have been using these kinds of symmetries intuitively for centuries.”
Go to The secret math behind catchy melodies for the full story.