Inuitive links between musical chords and geometries
Familiar relationships between sets of musical notes, such as transposition between chords, directly translate into geometrical structures such as this Möbius strip — where each dot represents a whole class of equivalent two-note chords — or into more complex structures with many dimensions.
Composers have an understanding of these geometries without
realizing it, says music theorist Dmitri Tymoczko of
Wandering around these spaces, Tymoczko and his collaborators have found subtle relationships between progressions of chords that traditional musical theory would classify as unrelated — for example, between progressions in Mozart’s Fantasy in C-minor and in Beethoven’s Ninth Symphony, the team reported in the April 18 Science.
Callender, C., I. Quinn, and D. Tymoczko 2008. Generalized voice-leading spaces. Science 320(April 18):346.
Rehmeyer, J.J. 2008. The eometry of music: Music as an audible exploration of hyperdimensional geometries. MathTrek (March 7). Available at [Go to].