An introduction to modulation
Hear a move into a closely related key and name the chord that makes the turn.
A new tonic
Modulation is a move into another key: a new tonic becomes the anchor of the music. Most often music moves into closely related keys, whose signatures differ by no more than one sign. For C major these are G major, F major and the relative minors of all three: A, E and D minor.
The sign of a modulation is a new accidental: in G major F♯ appears, the leading note of the new tonic, and the dominant of the new key is built on it.
From C major to G major: F♯ appears
Practice: Where does it modulate? (1)
Practice: Closely related keys
The pivot chord
A smooth modulation passes through a pivot chord, a triad that belongs to both keys. The ear takes it in the old key, and what follows shows it already belongs to the new one.
C major and G major share the C major, E minor, G major and A minor triads. A minor is vi in C major and ii in G major; after it the dominant of G major confirms the new tonic.
From C major to F major: B♭ in the V7 of the new key
From C major to A minor: G♯, the leading note of A minor
A new key is confirmed by a cadence: dominant (often V7) → new tonic. Until the cadence comes, a new accidental may be only a passing tonicisation.