A better way to visualize chord progression tendencies
To music folks, an interesting diagram coming out along the way of my current research on the foundations of music:
This diagram shows the typical directions in which chords change within diatonic harmony — not as hard rules, but as tendencies. These relationships are usually introduced using compact schematic progressions like the inset at upper left, which emphasizes common resolution pathways (including those involving ii, V, and I) but gives little intuition for how all the diatonic chords relate to one another as a system.
A clearer approach is to arrange the chords themselves in a sensible geometric way, namely on the Circle of Thirds, where chords drawn from the same diatonic scale sit in a natural relational order. Once drawn this way, the structure becomes immediately visible: the familiar tonic–subdominant–dominant–tonic tendency emerges naturally as a clockwise rotation around the circle.


