Music, mathematics link uncovered

The connection between music and mathematics has always fascinated scholars. Now, 200 years after Greek philosopher Pythogoras discovered the orderliness of music, researchers have uncovered its secret structure.

A team of three music professors has devised a new way of analysing and categorising music that takes advantage of the deep, complex mathematics they see enmeshed in its very fabric, the 'Science' journal reported.

The trio - Clifton Callender of Florida State University, Ian Quinn of Yale University and Dmitri Tymoczko of Princeton University - has outlined a method, known as "geometrical music theory", that translates the language of musical theory into that of contemporary geometry.

In fact, the researchers took sequences of notes, like chords, rhythms and scales, and categorised them so they could be grouped into "families". They have found a way to assign mathematical structure to these families, so they can then be represented by points 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 scientists 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. The whole point of making these geometric spaces is that, at the end of the day, it helps you understand music better.

"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.

"But to me, 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 geometries.

"Our methods are not so great at distinguishing Aerosmith from the Rolling Stones. But they might allow you to visualise some of the differences between John Lennon and Paul McCartney," Prof Tymoczko wrote.