Direct (Dominant) Modulation
We can jump quickly between keys without worrying about more complex modulation. We use the dominant of the new key.
We've looked at both diatonic and major minor modulation to get between two different keys. Both relied on playing a sequence of chords where the hand-over between keys was done using chords that shared as many notes as possible. All the notes were shared in a diatonic modulation, and two out of three in a major-minor modulation.
This is the diagram from the previous tutorial again. You can see that it takes five chords to play the modulation. This may be too long.
Instead we can skip everything else but the dominant seventh chord, in orange. We can go directly from A to G7 to C. Because it doesn't use pivot chords it won't sound very smooth, but it gets us where we are going.
When we follow the full modulation sequence, we can play the orange dominant chord with or without the 7. When we jump, playing the seventh is almost essential.
Why it works
The dominant seventh has a stronger pull towards the root of a key than any other chord. If you play the G7, you are instantly drawn towards C. Recall that when we used the dominant seventh (the orange chord) in the chord maps, we always followed it with the root chord (in red).
The same thing is happening in these modulations, we are playing the dominant seventh to indicate to the listener that we're heading for the root of the new key. It is such a strong force that the listener instantly knows where we are going, and understands that the key has changed.
The final key in each modulation diagram can't be reached by either a diatonic, or a major-minor modulation. It has to use the direct modulation.
In the diagram we are heading for E♭. The full set of chords suggest playing the dominant without its seventh first (B♭), then playing it with a seventh (B♭7). Whether you do this, or just go straight to the B♭7, you are jumping directly to the new key.
Because the A and B♭ chords (the dividing line between the keys) don't share any notes, the modulation is called "chromatic". Not all direct modulations are chromatic; but that's just a matter of naming. They all work exactly the same way: you go straight to the dominant seventh and then to the root of the new key.