Modulation is the process of changing key.
Although most modulations use the progression V-I or V7-I, sometimes music can pass into a new key without any preparation from the new dominant chord. This is called direct modulation.
Here is an example from the opening of Mozart’s Rondo Alla Turca K331, 3rd movement. The first seven bars are all tonic chords, first in the home key of A minor, and then in the modulation key of E minor, until the perfect cadence in bar 8. There is no dominant chord in the new key of E minor at the point of modulation – the music moves directly into the new key.
This means we have three ways to modulate:
1. With a pivot chord: e.g ii=V – V7 – I
2. Without a pivot chord: V7 – I
3. Direct modulation: moving immediately to chord I