"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 [a composer in residence at the Radcliffe Institute for Advanced Study] has devised a new way to map music that aims to do just that. (...) 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.” - Amira

"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 conceptualizing 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," Tymoczko added, "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." Understanding music, the authors write, is a process of discarding information." http://www.princeton.edu/main... - Amira