Elizabeth Gudrais in Harvard Magazine:
Humans seem to have an instinct for music. Certain songs have a quality that makes us want to tap our toes and sing along. We can’t quite say what makes good music, but we know it when we hear it. Sheet music, which tells musicians very precisely which notes to play and when, provides little clue to that mystical ingredient, but Dmitri Tymoczko ’91 has devised a new way to map music that aims to do just that.
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.