Modulation to remote keys
It is also useful to understand modulation from the standpoint of conceptual procedures. This page looks at some of those procedures.
Using diminished seventh chords
Modulation to more remote keys can be accomplished by making use of a particularly striking quality of the diminished seventh, namely its symmetry. Since the diminished seventh chord is symmetrical, it can be spelled in any of four ways, in each case the new spelling resulting in a shift of leading tone. By shifting the leading tone, the diminished seventh chord can resolve to four different triads and thus function as a dominant chord in four different keys.
Study these examples carefully. You will notice that the first line has the four possible inversions of the diminished seventh chord in the key of C major, resolvoving logically to the I chord in various inversions. The other four lines show the same diminished seventh chords, in the same positions, but spelled as if they were viiº7 in the keys of Eb, A and F#, respectively. Thus, by respelling the same enharmonic diminished seventh chords, these chords can function as vii7 in four different keys. Note the the keys themselves—C, Eb, F# and A—form a diminished seventh chord.
By starting a progression in the key of C and then respelling the diminished seventh chord enharmonically, one can quickly modulate from C major to the fairly distant keys of Eb, A and even F#. Since diminished seventh chords can move easily to either the minor or major mode, the final key can either be major or minor.
Look at this example and listen carefully to the resultant sound. In each instance, the diminished seventh chord sounds identical in equal temperament, but is spelled different enhamonically. According to the enharmonic spelling, the chord can resolve to any of four key centers, spaced apart by minor thirds.
Using Change of Mode Modulation
Another modulation technique is related to the concept of using mixture chords. Once a chord has been borrowed from a neighboring mode, that chord can be reinterpreted to be a pivot chord in a more distantly related key.
Here is a simple passage that begins in C major, uses a mode change of the vi chord to create a V of D and create a sense of modulation up a step. Once this moduation occurs, the IV chord is given a change of mode to iv minor, allowing a clear iv-V-I cadence in F major.
By Common Tone Modulation (Mediant relationship)
This technique relates to the concept of using Mediant chords. Once a composer has taken the liberty of moving creating a mediant chord within a diatonic key—using Ab major in the key of C, for example—the composer can then use that Ab chord as a pivot to a new key. The Ab could become IV in the key of Eb, or even V in the key of Db—a modulation to the Neapolitan:
By Chromatic Pivot Chords
Ultimately, we begin to reach the maxim of Max Reger: "any chord can follow any other chord!" It's all question of good voice leading and of creating a modulation and chord progression that is convincing. Voice leading is really the key—if the individual contrapuntal lines make logical sense and move in fairly smooth succession, many shifting chromatic harmonies can be created, and the ear accepts them due to the smooth logic of the individual voice movement. This is true for Bach, and it's true for the most modern of contemporary classical compositions.