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I will assume you understand basic diatonic harmony to even be asking this question.

The principle of doubling in harmony is a reference to the common practice of four-part harmony: soprano (S), Alto (A), tenor (T), and bass (B). Triads have only three tones: a root, a third, and a fifth. Therefore, in four-voice harmony, one of those chord members must be doubled. So here are the basic principles. But remember, music is art, not science. There are always exceptions, and times when a different doubling is preferred. At any rate here are what I call the "Standard Doubling Procedures."

Root position triad: double the root

First inversion triad: double the root or the fifth. Do not double the third.

Second inversion triad: double the fifth (in this case, the bass).

A few exceptions:

In a progression from V-vi, double the third of the vi chord, which is the tonic scale degree.

In a ii6 - V progression, double the third of the ii chord (the bass) it tends to strengthen the progression as it is doubling the subdominant scale degree.

vii6 chord, usually has the third doubled, sometimes the fifth, but NEVER the root because the root is the leading tone.

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