What is a chord that is common to both the original key and the modulated key called?

A chord that is common to both the original key and the modulated key is referred to as a pivot chord. This term is significant in music theory, particularly when discussing modulation—the process of changing from one key to another within a piece of music. The pivot chord serves as a transitional bridge that allows for a smooth shift between keys, as it belongs to both the starting and destination keys.

For example, if you are modulating from C major to G major, a common chord such as G major can function as a pivot chord because it appears naturally in both keys. This commonality aids in maintaining harmonic coherence during the modulation process, making the transition feel seamless to the listener.

The other terms provided have different meanings; for instance, a pivotal chord is not a standard term used in music theory, while dominant and subdominant chords refer to specific chord functions within a key, but they do not necessarily facilitate modulation between two keys.