Tag Archives: Geometry

Transformations and their musical counterparts.

This post is written in Binary Form.

When thinking about the relationship between numbers and music, often what first springs to mind are the proportional differences between the physical objects that generate musical intervals on which harmony and melody is so often based. The famous story of the blacksmith’s workshop and Pythagoras is sometimes used to illustrate this. Pythagoras was said to have been walking past a workshop where the sound of anvils of different weights were being struck, with each weight producing a different tone. Sounding together the result was consonant or stable. Upon investigation Pythagoras, it is said, realised that the pleasing aural result was accompanied by the pleasing integer proportion between the weights of the hammers, 6, 8, 9 and 12.

When one considers music in its own isolated discipline bubble, it might seem that it has a unique place beside mathematics (historically, music forms a pillar of the quadrivium alongside geometry, astronomy and athematic). However, perhaps the real power lies in the hands of numbers, and their ability to describe nature and her patterns.

“Numbers are a universal medium for the embedding of patterns of any sort, and that for that reason, statements seemingly about numbers alone can in fact encode statements about other universes of discourse”

Douglas Hofstadter, in his forward to Gödel’s Proof (Revised Edition)

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