The “Non-Euclidian” Geometry of Music
An interesting piece over at New Scientist describes a new way to visualize music. Dmitri Tymoczko, of Princeton, is the creator of these new “music maps:”
In these maps, a single point corresponds to a chord. The scheme is constructed so that a point representing a chord with the notes C and G has a position next to combinations of nearby notes on the scale, such as the chord containing the slightly higher-pitched “sharp” notes C# and G#.
The shorter the distance from one point in the map to another, the better the chord transition sounds to the ear. So, for example, only a short step exists between points representing two musical intervals known as the “perfect fourth” and “perfect fifth” – a standard transition that pervades all types of Western music, even rock.
Short steps can exist between less conventionally linked chords. The non-standard chord progressions of the E minor piano prelude, written by the 19th century composer Frederick Chopin, move along very short lines in these maps. Music theorists have previously struggled to explain why the succession of chords he used sounded so pleasant.
By contrast, a much longer distance – and a much more jarring transition – exists between two close notes at the low end of the scale to a close pair at the high end.
An example, using Chopin, can be found here. It’s in Quicktime. Tymoczko believes these maps can be used as pedagogical aid for new composers.