Modulation to Closely Related Keys

Modulation is a change of tonal center within a piece — not just borrowing a chord for a moment (that's tonicization, from the last lesson) but genuinely re-establishing a new key as home, usually confirmed by a cadence in it. The smoothest way to get there is through a key that's already closely related to where you started.

Closely related keys are the ones that differ from your starting key by at most one sharp or flat: the relative minor/major, and the keys built on the dominant and subdominant (and their relatives). From C major, that's G major, F major, A minor, D minor, and E minor — five destinations, each one step around the circle of fifths.

The classic technique is pivot-chord modulation: find a chord that exists diatonically in both the old key and the new key, treat it as belonging to the new key from that point on, then confirm the new key with a cadence (typically V-I in the new key). Because the pivot chord itself doesn't sound foreign in either key, the ear accepts the reinterpretation without a jolt.

Modulating to the dominant is so common it's practically a default move in Classical-era form (a piece's second theme is expected to arrive there); modulating to the relative minor/major is nearly as common and especially natural since it requires no new sharps or flats at all — just a new sense of which note is home.