Why Can a Pivot Chord Lead Music into a New Key?

The most interesting feature of common-chord modulation is that the notes of the chord do not change, yet its musical identity does. A pivot chord is a triad that belongs to both the original key and the new one. It is first understood through the old context, then reinterpreted through the new context.

In a move from C major to G major, an A minor chord offers a simple example. Within C major it can function as vi; within G major, the same notes—A, C and E—form ii. Hearing the chord alone does not prove that a modulation has occurred. If it is followed by D major and then resolves to G major, however, its earlier meaning is revised. The A minor chord was not merely another stop in C major; it prepared the dominant of the new key.

A modulation therefore does not happen because one chord suddenly transforms. Its function changes through the relationships around it. The value of a pivot chord is that it preserves continuity while creating direction: it does not abruptly sever the old key, but provides a point that the new key can take over. At the piano, an exaggerated pause or accent on the pivot often reveals too much too early. It is usually better to keep the phrase moving and let the new dominant and tonic gradually alter how the listener understands the chord that has just passed. What matters is not hearing a signpost, but sensing the road quietly change direction beneath the music.

https://viva.pressbooks.pub/openmusictheory/chapter/extended-tonicization-and-modulation-to-closely-related-keys/
https://musictheory.pugetsound.edu/mt21c/ModulationsWithDiatonicPivotChords.html