In yesterday’s post I mentioned matchstick harmony.
Matchstick harmony is governed by a rule: It’s easiest for the ear to follow harmonies that move short distances on the lattice.
If you move by as few matchsticks as possible when going from triad to triad, you will generate a chord progression that “makes sense” to the ear.
Here’s a rather artificial matchstick chord progression in Mixolydian mode. All I do is flip from each triangle to the one that borders it. It isn’t great music, but it shows how moving small distances on the lattice can draw the ear to a distant spot and bring it back again.
Actually this progression does drag the ear along rather fast. The roots move by major thirds (solid lines) and minor thirds (broken lines), which are not the shortest distances on the lattice. I like those equilateral triangles — they make visualizing easier for me — but if I wanted to accurately show harmonic distance, the horizontal lines, showing movement by fifths, should be the shortest, and the broken lines, the minor thirds, should be the longest, with the major thirds in between.
Progressions that move left or right, by fifths, are easier yet to follow.