Researchers find music has its own geometry

April 18th, 2008 - 1:47 pm ICT by admin  

Paul McCartney

Washington, April 18 (ANI): It is very well acknowledged that music has rhythm and beat but now it seems that it has a shape too.

In the wake of centuries of attempt to seek deep connections between music and mathematics, a research team concludes that music does have geometry.

More than 200 years ago Pythagoras reportedly discovered that pleasing musical intervals could be described using simple ratios.

And the idea of the so-called musica universalis or music of the spheres emerged in the Middle Ages as the philosophical idea that the proportions in the movements of the celestial bodies — the sun, moon and planets — could be viewed as a form of music, inaudible but perfectly harmonious.

Now, three music professors - Clifton Callender at Florida State University, Ian Quinn at Yale University, and Dmitri Tymoczko at Princeton University - have devised a new way of analysing and categorising music to reduce musical works to their mathematical essence, suggesting that mathematics is a more fundamental language of nature than music.

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 different geometries,” Tymoczko.

“Our methods are not so great at distinguishing Aerosmith from the Rolling Stones. But they might allow you to visualize some of the differences between John Lennon and Paul McCartney. And they certainly help you understand more deeply how classical music relates to rock or is different from atonal music,” Tymoczko added.

The trio has outlined a method called geometrical music theory that translates the language of musical theory into that of contemporary geometry.

They take sequences of notes, like chords, rhythms and scales, and categorize them so they can be grouped into families.

They have identified a way to assign mathematical structure to these families, so they can then be represented by points in complex geometrical spaces, much the way x and “y coordinates, in the simpler system of high school algebra, correspond to points on a two-dimensional plane.

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

They trio expects that this achievement will allow researchers to analyse and understand music in much deeper and more satisfying ways.

“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,” said Tymoczko, an assistant professor of music at Princeton.

“You could create new kinds of musical instruments or new kinds of toys,” he said. “You could create new kinds of visualization tools — imagine going to a classical music concert where the music was being translated visually. We could change the way we educate musicians. There are lots of practical consequences that could follow from these ideas,” Tymoczko added.

According to Rachel Wells Hall of the Department of Mathematics and Computer Science at St. Joseph’s University in Philadelphia, the work represents a significant departure from other attempts to quantify music.

She said that their effort stands out both for the breadth of its musical implications and the depth of its mathematical content.

The study is published in the April 18 issue of Science. (ANI)

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