The beat goes on: the geometry that makes music pleasing

Researchers uncover mathematical formula for rhythm and suggest our brains may be hardwired to respond to it. Whether it's Bach or Brubeck, a new study shows that composers repeat rhythmic patterns in their works in such a way that the part is a copy of the larger whole. A research team led by neuroscientists Drs. Daniel Levitin and Vinod Menon, from McGill and Stanford Universities, respectively, analyzed the scores of close to 2,000 musical compositions written by more than 40 composers over the last 400 years in a large variety of Western musical genres. They discovered a mathematical formula governing the rhythmic patterns to which every single piece of music conformed. "One of the things that we've known about music for a couple of decades is that the distribution of pitches and loudness in music follow predictable mathematical patterns," says Levitin. "Rhythm is even more fundamental to our enjoyment of music: it's rhythm that infants respond to first, it's rhythm that makes you want to get out of your chair and move, and so it's not really a surprise to discover that rhythm, too, is governed by a similar mathematical formula." The researchers found that all the musical compositions they studied shared the same "fractal" quality, where the part is a more limited repetition of the whole.