Tymoczko (pronounced tim-OSS-ko), who spent this past academic year as a composer in residence at the Radcliffe Institute for Advanced Study, has developed a way to represent music spatially. Using non-Euclidean geometry and a complex figure, borrowed from string theory, called an orbifold (which can have from two to an infinite number of dimensions, depending on the number of notes being played at once), Tymoczko’s system shows how chords that are generally pleasing to the ear appear in locations close to one another, clustered close to the orbifold’s center. Sounds that the ear identifies as dissonant appear as outliers, closer to the edges.

The system “allows you to translate these half-formed intuitive understandings into very precise, clear language,” says Tymoczko, an assistant professor of music at Princeton. “Personally, I find that incredibly cool.” So, apparently, did Science, which recently published his mathematically based exposition—the only music-theory paper the journal has accepted in its 127-year history.

For a map that would represent music accurately, Tymoczko needed a shape folded once to acknowledge the circular nature of octaves, and again to reflect the existence of two different combinations that produce the same result—for example, A plus C sounds the same as C plus A. “On a piano, there are many, many different ways of playing the same chord,” Tymoczko says. “I’ve collapsed all the different ways of playing a chord into a single point on the map.”