The deceptive cadence

The dominant resolves, but not to the tonic chord: the bass rises a step to the submediant while the tendency tones keep their promises — the leading tone rises to the tonic degree and the second degree falls to it, which is why the third of the submediant chord is doubled. Everything resolves except the ear’s expectation, and the phrase is thrown back open; it is the standard way to refuse a close the harmony has fully prepared.

A deceptive cadence appears exactly where a full close is expected, and expected loudly, so the composer can reopen a phrase that seemed finished and extend it — into a longer period, or a coda that reopens material the listener thought was closed. Because every tendency tone still resolves correctly, the ear accepts the submediant as a legitimate answer to the dominant even while registering that the tonic never arrived — the tension the device exploits. It works best where the preceding material has made the authentic cadence feel inevitable.

• Doubling the root of the submediant instead of its third, the default habit for a root-position triad, which blocks the leading tone from resolving to the tonic degree without creating parallel octaves or an awkward doubling elsewhere.
• Letting the bass leap into the submediant instead of stepping up, which loses the smooth contrary motion that makes the deception convincing rather than merely wrong.
• Producing parallel fifths or octaves against the bass, an easy trap here since the bass moves by step rather than by the falling fifth most cadences train the ear to expect.
• Leaving the leading tone unresolved — sent down or sideways instead of up to the tonic degree — because the ear expects a different chord and the voice-leading discipline relaxes along with it.

• Jean-Philippe Rameau, Traité de l’harmonie réduite à ses principes naturels (1722), Book II, the broken cadence — Rameau’s cadence rompue: the fall of a fifth replaced by the rise of a step.
• Hugo Riemann, Vereinfachte Harmonielehre (1893), On the deceptive close — The dominant discharging onto the tonic’s representative — a real resolution onto a substitute.
• Ebenezer Prout, Harmony: Its Theory and Practice (1889), The chapter on cadences — The interrupted cadence and its doubling rule for the chord of arrival.