Doubling norms

In four voices something must be doubled: the root first, the fifth second, the third sparingly — and in an inverted chord, prefer doubling a tone other than the bass when the bass carries the third. The reasoning is functional, not numerological: tones with somewhere to go — thirds, and every tendency tone — resist doubling because two voices would owe the same resolution, while stable tones bear reinforcement. The rule yields to the line: a doubling that lets every voice move by step outranks a textbook doubling that forces a leap.

Doubling is decided at every chord of every four-voice texture, so the defaults are what make part-writing fast: root first, then whatever the lines want. The exceptions are as load-bearing as the rule — the deceptive cadence doubles the third of the submediant because the tendency tones demand it, and first-inversion chords choose their doubling by line rather than by formula. When a progression fights back, the doubling is usually the knob to turn.

• Doubling a tendency tone — leading tone or chordal seventh — so two voices owe the same resolution.
• Doubling the bass of a first-inversion chord by default, reinforcing the third instead of the stabler tones above it.
• Sacrificing stepwise lines to keep a textbook doubling, when the hierarchy exists to serve the lines.
• Omitting the third to make a doubling work mid-phrase, which leaves a bare, mode-less sonority before the end.
• Tripling the root mid-progression where a complete chord was available, spending fullness the final chord could have used.

• Ebenezer Prout, Harmony: Its Theory and Practice (1889), The opening chapters on harmony in four parts — The doubling hierarchy and its stated exceptions for inverted chords.
• Luigi Cherubini, Cours de contrepoint et de fugue (1835), The rules for counterpoint in four parts — The strict-style doubling discipline the harmony classroom inherited.