The octave rule, major descending

Falling through the octave, the harmonization mirrors the ascent with one signature difference: 5/3 on the tonic, sixths on the seventh and sixth degrees, 5/3 on the dominant — then 4/2 on the falling fourth degree, the dominant seventh passing its dissonance into the bass so the fourth degree resolves down into a sixth on the third, and 4/3 on the second degree closing home. The descent is where the Rule teaches the seventh in the bass: the 4/2’s bass tone is itself the dissonance, and its stepwise fall is the resolution.

The descent handles closes and laments: falling basses carry more cadential weight, and the Rule’s 4/2 station is the standard way a dominant hands its tension down into a running line. It is also the door to the evaded cadence and every V4/2–I6 formula — the same motion, met one scale degree at a time — and the reason a falling bass so often sounds like an ending being prepared.

• Placing a 5/3 on the descending fourth degree, ignoring the 4/2 that gives the descent its engine.
• Failing to resolve the 4/2’s bass down by step, when the bass itself carries the dissonance.
• Letting parallel fifths form between upper voices as the hands fall — the descent breeds them between fifth-related stations.
• Doubling the leading tone inside the closing 4/3.

• Fedele Fenaroli, Regole musicali per i principianti di cembalo (1775), The rules for accompanying the scale (descending) — The Neapolitan per-degree assignments for the falling bass, 4/2 at the fourth degree.
• François Campion, Traité d’accompagnement et de composition selon la règle de l’octave (1716), The règle de l’octave — The original two-directional map.