Modulation · Music theory
Changing key: directly, through a common chord, through the dominant of the new key or by enharmony, and how to recognize that it has happened.
Changing center
To modulate is to pass from one key to another, so that the ear accepts another tonic as the new center. A foreign chord is not enough: that would be a secondary dominant, or what is called a tonicization. For a modulation, the new key has to establish itself: it usually takes a cadence there, and more than a moment in that place.
A classical work in major usually goes to the key of the dominant, and one in minor to its relative. The closest keys, closely related, make an almost imperceptible change because they share almost all their notes. Distant ones are more striking: the modulation becomes an event.