Composer Reveals Music’s Hidden Geometry
Composers often speak of fitting chords and melodies together, as though sounds were physical objects with geometric shape. Now composer Dmitri Tymoczko, an assistant professor of music at Princeton University, is using topology and non-Euclidean geometry as a way of understanding how music is constructed.
His findings resulted in the first paper on music theory the journal Science has printed in its 127-year history.
Making graphical representations of music is not a new idea. Most people are familiar with the five-line musical staff, on which notes that appear physically higher represent sounds that have higher pitch. Other common representations include the circle of fifths, which illustrates the relationships between the 12 notes in the chromatic scale as though they were hours on a clock’s face.
To understand the melodic relationship between chords, Tymoczko connects the points with lines that represent how they have to change their notes to get from one chord to the next.
One of Tymoczko’s musical spaces resembles a triangular prism, in which points representing traditionally familiar harmonies such as major chords gather near the center of the triangle, forming neat geometric shapes with other common chords that relate to them closely. Dissonant, cluster-type harmonies can be found out near the edges, close to their own harmonic kin.
Tymoczko says that composers have traditionally valued harmonic consistency that does not require that the listener jump far from one region of the space to another too quickly. “This idea that you should stay in one part of space,” he says, “is an important ingredient of our notion of musical coherence.”
< Back to latest Music and Health
