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Which chord belongs over each scale degree in the bass?
The eighteenth century’s standard harmonization of a scalewise bass, ascending and descending, in major and minor. The Rule is the thoroughbass player’s default map: it tells you what to play when the figures are silent, and it encodes which degrees carry stable harmony and which carry motion.
The Rule of the Octave is the thoroughbass player’s default map: harmonize a scalewise bass with 5/3 chords on the stable degrees — the tonic and the dominant — and chords of the sixth on the mobile degrees between them, enriched at the second, fourth and seventh degrees according to the direction of travel.
Rising through the octave, the standard harmonization gives the tonic its 5/3, the second degree 4/3, the third degree a sixth, the fourth degree 6/5, the dominant its 5/3, the sixth and seventh degrees sixths, and the tonic its 5/3 again.
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 minor ascent follows the major’s plan — stable degrees taking 5/3, mobile degrees taking a sixth — with two differences the mode forces.
Coming down, the minor mode reverts to its own scale: the seventh and sixth degrees are natural, and the chords above them are the minor dominant and the minor subdominant in first inversion.