The plagal cadence

The close from the subdominant side: IV settles onto I with the tonic held as a common tone and the other voices falling by step. There is no leading tone in it — nothing strains — which is why the plagal close sounds like assent rather than arrival: it confirms an ending rather than making one, and the tradition most often places it after the true close.

Almost never the structural close of a phrase on its own — its usual place is right after a genuine authentic cadence, confirming an ending already made rather than making one itself. Its association with “Amen” is not incidental: without a leading tone to resolve, nothing in the progression demands the tonic, so the effect is assent rather than necessity, which is why church and hymn closes reach for it so often. The held common tone gives it a stillness no authentic cadence has, useful wherever a phrase needs to settle rather than arrive.

• Letting the tonic-degree voice leap away instead of holding it as the common tone between the two chords, losing the sense of settling rather than moving that the progression depends on.
• Sending an upper voice up by leap into the final tonic instead of down by step, trading the cadence’s quiet descent for a gesture that sounds like arrival rather than assent.
• Relying on it alone to end a phrase, asking a progression with no leading tone to supply the pull that only the authentic cadence provides.

• Jean-Philippe Rameau, Traité de l’harmonie réduite à ses principes naturels (1722), Book II, the irregular cadence — The subdominant’s rise of a fifth to the tonic as the mirror of the perfect fall.
• Hugo Riemann, Vereinfachte Harmonielehre (1893), On the plagal close — The arrival from the subdominant side, bypassing the dominant’s pull entirely.
• Ebenezer Prout, Harmony: Its Theory and Practice (1889), The chapter on cadences — The classroom account, including its customary place after the authentic close.