Researchers uncover music’s secret structure

April 18th, 2008 - 1:04 pm ICT by admin  

Washington, April 18 (IANS) More than 200 years after Pythagoras discovered the orderliness of music, three professors have devised a way of analysing music that takes advantage of the deep, complex mathematics seemingly enmeshed in its very fabric. Writing in the April 18 issue of Science, they have outlined a method called “geometrical music theory” that translates the language of musical theory into that of contemporary geometry.

Clifton Callender of Florida State University, Ian Quinn of Yale and Dmitri Tymoczko of Princeton took sequences of notes and categorised them so they could be grouped into “families”.

They have found a way to assign mathematical structure to these families, so they could then be represented by in complex geometrical spaces.

Different types of categorisation produce different geometrical spaces, and reflect the different ways in which musicians over the centuries have understood music.

This achievement, they expect, will allow researchers to analyse and understand music in much deeper and more satisfying ways.

“The music of the spheres isn’t really a metaphor - some musical spaces really are spheres,” said Tymoczko. “Having a powerful set of tools for conceptualising music allows you to do all sorts of things you hadn’t done before.”

“You could create new kinds of musical instruments or new kinds of toys,” he said. “You could create new kinds of visualisation tools - imagine going to a classical music concert where the music was being translated visually.”

“But to me,” Tymoczko added, “the most satisfying aspect of this research is that we can now see that there is a logical structure linking many, many different musical concepts.

“To some extent, we can represent the history of music as a long process of exploring different symmetries and different geometries.”

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