The circle of falling fifths

Roots falling by fifths — each chord’s root becoming the fifth of the next — is the strongest progression the diatonic system has, and run in sequence it visits every chord in the key before arriving home. The bass alternates falling fifths and rising fourths to stay in register, the upper voices bind the chords with common tones and steps, and the one diminished fifth in the bass — between the fourth and seventh degrees — is the seam that keeps the circle inside the key.

It is the default engine of tonal motion: when a passage must travel — an episode, a transition, a stretch between two arrivals — the circle supplies direction without invention, and the ear rides it as inevitability. Partimento players drilled it until it was reflex, and it underlies more repertoire than any other progression; recognizing a segment of the circle collapses whole passages into one idea.

• Letting parallel fifths or octaves form between chord pairs, the standard hazard of any pattern repeated without a check at each link.
• Replacing the diminished fifth in the bass with a perfect one, which walks the sequence out of the key.
• Doubling the leading tone or the root of the diminished chord at the vii° station.
• Running the full circle where the phrase needed only a segment, arriving back at the tonic the harmony just left.

• Jean-Philippe Rameau, Traité de l’harmonie réduite à ses principes naturels (1722), Book II, the fundamental bass in fifths — The fifth as the most natural root motion — the theoretical ground of the sequence.
• Fedele Fenaroli, Regole musicali per i principianti di cembalo (1775), The rules for the movements of the bass — The partimento movimento: the bass falling a fifth and rising a fourth.