absence

sound waves are oscillations between 2 points, therefore they are represented as edges.

the tritone interval maps to symmetrical opposite edges (C-F#) , (G-C#) , (E-A#) etc. result: full rotations along the 3 orthogonal edge loops generates the 3 diminished scales (C-A-F#-D#) (G#-B-D-F) (E-C#-A#-G) now lets trace the C major scale:

we can see the major scale is a hamiltonian path that visits each of the 3 orthogonal faces. there is a single missing edge that cleanly closes the loop though: G# this is where we get barry harris' 6th diminished scale (C major with an added G#). barry harris discovered the ONLY move that makes the major scale looping and self referential. we can now use the cube to generate our own scales:

looks like this on a piano:

sounds like this:

Dazed & Confused, September 1997.

Kaga-Yuzen Kimono

The Gaunt Bird of Famine

Marian Spore Bush