Mixture Chords and Mediant Relationships
Mixture Chords (Modal Borrowing)
The concept of "mixture chords" as they are often called in theory textbooks is a simple one. Rather than only availing oneself of chords in the prevailing key (along with the secondary dominants), one can "borrow" harmonies from the parallel major or minor.
Based on this principle, many other possible chord progressions can be conceived through the concept of modal borrowing or mixture. Here are a few to consider:
Borrowing from the minor mode
The greater complexity of the minor mode affords the composer a great wealth of material to use when writing major key music.
The Diminished seventh chord
We have already discussed the diminished seventh chord, which is really a borrowed harmony, making use of the harmonic minor scale. Anytime you use a diminished seventh chord (B-D-F-Ab in the key of C) when in a major key, you are using a mixture chord. So, one down...
Subdominant minor, Supertonic half-diminished (use of b6)
Another commonplace example is the use of the subdominant minor triad in a major key. This is commonplace due to the principle of harmonic polarity, where the minor triad can be conceived as arising from the reciprocal series. Thus, in C major, use F minor. This progression often has a sentimental feeling to it:
Similarly, the relative subdominant, the ii chord, which is naturally a minor triad or a minor seventh chord in the major mode, can be voiced as a diminished triad or, more commonly, a half-diminished seventh chord. Often this will appear in first inversion, giving the chord an additional feeling of a IV minor with an added sixth.
Minor tonic (use of b3)
The minor tonic is always an interesting and expressive shift of mode, even when the intended ultimate cadence is to be to a major key. One of the most striking examples of course is the shift from major to minor in the opening of Strauss' Also Sprach Zarathustra (aka 2001:A Space Oddysey).
Lowered Submediant (use of b3 and b6 combined)
By using both the lowered third and lowered 6th scale degrees, a bVI major triad can appear in the major mode.
When the bVI appears in place of vi in a deceptive cadence when in a major key, the result is often quite striking:
Lowered seventh
The use of the lowered seventh degree of the scale is striking in a major key. In music not afraid to express the Mixolydian mode, a bVII triad can be employed. This is rare in classical music, although extremely common in Rock music (the "na-na-na-" coda in Hey Jude, for example—a passage that is softened by the shared common tone between the bVII and the IV). Here is progression with bVII in relationship both to IV and to V.
The use of the lowered seventh can also provide an opportunity for the dominant triad to take on a minor inflection, significantly softening the effect of the I to V progression.
Borrowing from the major mode
Borrowings from the major mode when in minor are less common, probably because the minor mode is less in need of enrichment. However;
Raised 3
Of course, one can always voice the tonic triad as major when in minor, if a brightening effect is desired. This was the common final cadence in a minor key during the Baroque era, the so-called Picardie Third. But within Romantic music, I was often voiced as a major triad within a minor key environment for poetic effect, especially in Lieder and Chanson (German and French art songs) with strong tendencies towards word painting.
Raised 6
This can provide for a brightening effect by turning the subdominant triad into a major triad when in a minor mode.
It also is common when combined melodically with the raised 7, resulting in chord progressions that occur over the melodic minor scale:
Raised 7
This is of course is the common borrowing in minor, resulting in the standard dominant seventh chord when in the minor mode.
Mediant Harmonies
Mediant harmonies refer to the use of triads that are not specifically part of the key, but can be moved to smoothly due to the existence of common tones between two given chords. These common tones exist by virtue of the roots of the chords being a third apart—thus the concept of mediant relationship and thus "Mediant Harmony."
The concept of mediant harmonies is related to the concept of borrowing if we consider that often, mediant harmonies are identical to chords that can function as secondard dominants. The difference here is that they do not function as secondary dominants, resolving down a fifth, but instead serve as shifts in harmonic color in an otherwise diatonic progression. The following examples will clarity this concept.
III Major when in a Major Key
III major is of course functionally the V/vi, but sometimes a harmony can simply go to from I to III or from V to III and then on to another harmony, where the III major does not function as the V of vi:
IV Major in a Major Key
Similarly, using the VI major can give a brightening to the root movement to the relative minor. Think of this is as the "parallel major of the relative minor."
In brief, any two chords can move from on to the other through the exercise of a mediant relationship.
NEXT: 6E Harmonic Polarity and Mixture Chords in Beethoven's Waldstein Sonata