Mathematics & Music: Cosmic Twins

A look at some of the deep connections between mathematics and music

“Music is the pleasure the human mind experiences from counting without being aware that it is counting.” — Gottfried Wilhelm von Leibniz (1646–1716)

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The connections between mathematics and music run deep. The subjects can be thought of as cosmic twins, born out of a tantalizing mixture of order and disorder. They both grow from foundations that are built on patterns: patterns made up of repetitions, ratios, number sequences, geometrical transformations, symmetries, combinations, variations, and more.

Music is, at its core, based on numbers and mathematical relationships. By the same measure, numbers and mathematical relationships can be transformed into music. To explore the many connections in detail, we would need to explain the core terminology of each field — far more information than would fit in this brief article. We will therefore touch on a few important relationships that will establish a foundation if you’re inclined to dig deeper.