Researchers Convert Music to Mathematics

May 7, 2008

Researchers claim to have discovered that music has geometry--and to have found a way of reducing musical works to their mathematical basics.

Dmitri Tymoczko (Princeton University), Clifton Callender (Florida State University), and Ian Quinn (Yale University), say they have devised a “geometrical music theory” that, as explained in a piece in Science (April 18), suggests that music can be expressed as mathematical shapes. The researcher's approach involves assigning mathematical structures to families of chords, rhythms, and scales. This then leads to a finer grasp of music’s nature and evolution.

"The most satisfying aspect of this research," said Tymoczko, "is that we can now see that there is a logical structure linking many, many different musical concepts." The history of music, he said, can be represented as a "long process of exploring different symmetries and different geometries.”

"Conceptualizing music," Tymoczko noted, "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. 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."

However, Tymoczko also pointed out that "Our methods are not so great at distinguishing Aerosmith from the Rolling Stones." But they might allow anyone to "visualize some of the differences between John Lennon and Paul McCartney." McCartney's tunes tend to look more traditional, he said, while Lennon's tend to be more "rock." Nonetheless, the research, he indicated, would help in understanding "more deeply how classical music relates to rock or is different from atonal music.”

Sources: Exclaim News, Daily Princetonian, Princeton News