Extended Tonicization and Modulation to Closely Related Keys
Brief tonicization — a secondary dominant that momentarily brightens a single chord before returning to the home key — is common and does not disturb the sense of a single tonal center. When that temporary tonicization extends across multiple chords or an entire phrase, and especially when the music cadences in the new key, the effect crosses a threshold: what began as tonicization becomes modulation. Modulation means the listener's sense of tonal center genuinely shifts to the new key, at least temporarily.
Closely related keys are those that share most of their scale degrees — differing by only one accidental from the home key. From any major key, the five closely related keys are: the relative minor (vi), the dominant major (V), the subdominant major (IV), the supertonic minor (ii), and the mediant minor (iii). From a minor key, the closely related keys are the relative major (III), the dominant minor or major (v/V), the subdominant minor (iv), the subtonic major (VII), and the mediant major (VI). Because closely related keys share most of their pitches, modulations to them are smooth and common in tonal music.
The clearest sign of a modulation (as opposed to mere tonicization) is a cadence in the new key — particularly a PAC. The process typically involves: (1) establishing the home key, (2) introducing the pivot chord, a chord that is diatonic in both the old and new key and is retrospectively reinterpreted as a new function, (3) applying a secondary dominant or diatonic dominant of the new key, and (4) cadencing in the new key. Once the new key is confirmed by cadence, Roman numerals are calculated relative to the new tonic until another modulation or return to the home key occurs.