Roots falling in thirds

Roots falling by thirds — I to vi to IV to ii — share two tones at every join, so the harmony changes color more than it changes place: each step keeps most of the previous chord and lowers its foundation. The motion is gentle and accumulative, gathering subdominant weight as it falls, and it asks for a cadence to spend what it has gathered — the chain itself never resolves anything.

The falling-thirds chain is the soft opening gambit of the tradition — it deepens a tonic into its relatives without committing to travel, which suits beginnings, codas, and any passage that should breathe rather than drive. Because each join holds two common tones, it is also the easiest sequence to sing and the safest to write; the craft lies in knowing it must hand off to a dominant to end.

• Treating the chain as a progression that can close, when nothing in it resolves and a cadence must follow.
• Moving the common tones unnecessarily, which surrenders the smoothness that is the motion’s whole character.
• Falling a third too far and arriving on chords that undermine the key rather than deepening it.
• Letting the outer voices drift into parallels at the joins where both must move.

• Jean-Philippe Rameau, Traité de l’harmonie réduite à ses principes naturels (1722), Book II, root motion by thirds — The third as the next natural root motion after the fifth, bound by its common tones.
• Fedele Fenaroli, Regole musicali per i principianti di cembalo (1775), The rules for the movements of the bass — The falling-thirds movimento among the standard bass motions.