The Geometry of Music, by John Baez

torus_music

The geometry of music revealed!  The red lines connect notes that are a major third apart.  The green lines connect notes that are a minor third apart. The blue lines connect notes that are a perfect fifth apart.

Each triangle is a chord with three notes, called a triad.  These are the most basic chords in Western music.   There are two kinds:

A major triad sounds happy.  The major triads are the triangles whose edges go red-green-blue as you go around clockwise.

A minor triad sounds sad.  The minor triads are the triangles whose edges go green-red-blue as you go around clockwise.

This pattern is called a tone net, and this one was created by David W. Bulger.  There’s a lot more to say about it, and you can read more in this Wikipedia article:

http://en.wikipedia.org/wiki/Neo-Riemannian_theory

and this great post by Richard Green:

https://plus.google.com/u/0/101584889282878921052/posts/bgpNTT8WqHx

The symmetry group of this tone net is important in music theory, and if you read these you’ll know why!

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