The simple authentic cadence

The standard close: the bass falls a fifth (or rises a fourth) from dominant to tonic, both chords in root position, while each voice keeps its cadential promise — the leading tone rises to the tonic degree, the second degree falls to it, and the remaining voice holds or steps to the nearest chord tone. When the soprano itself arrives on the tonic the close is full; let the soprano end on the third or fifth, or put either chord in inversion, and the same progression closes less finally.

This is the cadence reserved for real endings — the close of a phrase, a period, a section, or an entire piece — wherever the harmony must resolve every tendency tone at once and leave nothing outstanding. The full and imperfect forms do real formal work: a soprano off the tonic, or either chord inverted, produces a close firm enough to punctuate a phrase without claiming to end it, so the imperfect form carries the interior articulation while the full form is saved for the true close.

• Leaving the leading tone to fall or leap away instead of rising to the tonic, the single resolution the cadence depends on above all others.
• Doubling the leading tone, which forces a choice between parallel octaves and a leading tone that never resolves.
• Moving the bass and soprano in parallel fifths or octaves on the approach to the tonic, the classic outer-voice collision of the V–I motion.
• Calling the cadence a full close while leaving the soprano on the third or fifth of the tonic chord, when that is the imperfect form regardless of how convincing the bass motion sounds.
• Letting the second scale degree leap away instead of falling by step, trading a stepwise resolution that sounds inevitable for one that sounds assembled.

• Fedele Fenaroli, Regole musicali per i principianti di cembalo (1775), The rules of the cadences (the simple cadence) — The Neapolitan grading of the closes begins here: the plain dominant-to-tonic fall.
• Jean-Philippe Rameau, Traité de l’harmonie réduite à ses principes naturels (1722), Book II, the perfect cadence — The fundamental bass falling a fifth as the defining motion of closure.
• Hugo Riemann, Vereinfachte Harmonielehre (1893), On the cadences — The close as the completion of the functional circuit, tension discharged onto the tonic.