The chain of sevenths

Add a seventh to every chord of the falling-fifths circle and the sequence becomes self-perpetuating: each seventh is prepared as a common tone from the chord before, strikes with the new root, and falls by step to become the third of the chord after — which has meanwhile acquired its own seventh the same way. The voices alternate holding and falling in pairs, and the dissonance is passed hand to hand down the whole chain until the dominant spends it on the close.

This is how tonal music sustains tension over a span: the plain circle travels, but the chain of sevenths leans the whole way, each resolution instantly re-armed. It is the harmonic floor under countless sequences from the concerto grosso to the Romantic song, and at the keyboard it teaches the deepest thoroughbass habit — sevenths are not events but a relay, prepared, struck, and handed on.

• Striking a seventh unprepared mid-chain, when each is available as a common tone from the previous chord.
• Resolving a seventh upward to complete the next chord, which breaks the relay the chain depends on.
• Writing every chord complete, when the alternation of complete and incomplete voicings is what keeps the parallels out.
• Doubling one of the sevenths, putting the same falling obligation in two voices.

• Jean-Philippe Rameau, Traité de l’harmonie réduite à ses principes naturels (1722), Book II, the succession of sevenths — The fundamental bass in fifths carrying its dissonance from chord to chord.
• Carl Philipp Emanuel Bach, Versuch über die wahre Art das Clavier zu spielen, Part II (1762), Part II, on the chords of the seventh and their resolution — The keyboard realization of the chain: preparation by tie, resolution by step.
• Fedele Fenaroli, Regole musicali per i principianti di cembalo (1775), The rules for the movements of the bass — The movimento drilled with sevenths throughout the Neapolitan school.