The Geometry of Consonance

Big shout to Bruce Warila for the heads up...

SOURCE LINK

Invited Speaker: Dmitri Tymoczko

The Geometry of Consonance

Abstract
In my talk, I will describe five properties that help make music sound tonal — or “good,” to most listeners. I will then show that combining these properties is mathematically non-trivial, with the consequence that space of possible tonal musics is severely constrained. This leads me to construct higher-dimensional geometrical representations of musical structure, in which it is clear how the various properties can be combined. Finally, I will show that Western music combines these five properties at two different temporal levels: the immediate level of the chord, and the long-term level of the scale. The resulting music is hierarchically self-similar, exploiting the same basic procedures on two different time scales. In fact, one and the same twisted cubic lattice describes the musical relationships among common chords and scales.

Another Gem of Sound and Mysticism

VIBRATIONAL TRUTH -- Profusely illustrated and beautifully explained. Probably one of the single best webpages about the geometry of music I’ve ever found.