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For example, consider a modulation from C Major to E Major. These keys only share 3 notes in common, and are separated on the circle of fifths by 4 movements. They share no diatonic chords. Instead of trying to modulate directly between them, we can use a chain modulation. We could follow the circle of fifths, going major to major key until we reach E (C => G => D => A => E). Or we could shorten that by jumping every other 5th (C => D => E). C Major and D Major share the diatonic G Major chord. D Major and E Major share the diatonic A Major chord. This allows two common chord modulations to easily get from C Major to E Major without any disruptive transitions.
=== Parallel Key ===Parallel keys have the same root but different whole-half step patterns. For example, C Major and C Minor are parallel keys. Knowledge of [[Modes|modes]] offer us more parallel keys. Modulation between parallel keys is typically not as closely related as usual. For example, major/minor parallel keys only share 4 notes. However, because they retain the same tonal center, the change is not disruptive. [http://en.wikipedia.org/wiki/Pitch_axis_theory Pitch Axis Theory] is an extreme example of this. It uses chord progressions that all feature the same common note - sometimes this note is the root of every chord in the progression. The underlying chords do not necessarily
== Homework ==