THE GEOMETRY OF MUSICAL CHORDS
Dmitri Tymoczko, Princeton University
Musical chords have a non-Euclidean geometry that has been exploited by Western composers in many different styles. A musical chord can be represented as a point in a geometrical space called an orbifold. Line segments represent mappings from the notes of one chord to those of another. Composers in a wide range of styles have exploited the non-Euclidean geometry of these spaces, typically by utilizing short line segments between structurally similar chords. Such line segments exist only when chords are nearly symmetrical under translation, reflection, or permutation. Paradigmatically consonant and dissonant chords possess different near-symmetries, and suggest different musical uses.
I’ve always found the link between music and math fascinating. These naturally occurring patterns that can be explained by numbers become mysterious when demonstrated through music. The artistic part of me is most alive in the questions and mystery of life. While the scientific part of me wants answers and to figure things out. But it’s not a struggle between two opposing viewpoints. It’s two parallel lines following a path through time. Hidden beneath the surface is infinity.