Function — why chords pull

Play G–C–D–G, then play it again but stop on the D. Something audibly stays open. The last step is missing, and the ear supplies it on its own.

Within a key every chord has a role, and three of them carry nearly everything. A spatial image makes them concrete: the tonic (I) is home, the resting point where a song may end. The subdominant (IV) is a step outside the door — away from the resting point, without urgency. The dominant (V) stands at the threshold and pulls back with the strongest tension. The D left hanging was that dominant.

The reason for the pull is a single note, the leading tone. It sits a half step below the root and is part of the dominant chord; that half step strives upward into the resting point. It's the same half step as in the melody layer and the same interval principle — the entire harmonic pull rests on one half step.

From this comes the short catalog of cadences, the ways of arriving: the authentic cadence V–I as the expected resolution, the plagal IV–I as the softer variant (the amen of church music), and the deceptive cadence V–vi, where a minor relative follows instead of the resting point. The deceptive cadence proves the pull is real: only an expectation can be broken.