That last example had two question marks instead of roman numerals. What were those chords, D major and E major, doing in the key of C major? Don’t they know C major has no sharps or flats? Let’s take a closer look at that section:
These non-diatonic chords almost sound as if they’re dominant function chords, but how can that be possible if they’re not even in the same key as the example? Looking closer we see that the E major chord is moving to an A minor and the D major chord is moving to a G major. Which chords are dominant in the key of A and G?
E major and D major!
These types of chords are commonly called: Secondary Dominants. Dominant meaning they serve the dominant function of pushing or moving us to a resolution and secondary meaning they come from a different key. Any diatonic major or minor chord can be proceeded by a secondary dominant. Remember to find the dominant of a key you just have to count 5 notes up in the major scale. Here are all of the chords of C major proceeded by a secondary dominant:
Notice that instead of V/IV there’s a V7/IV. This is because V/IV is indistinguishable from I (in this context they’re both C major), but adding the 7th makes it obvious that’s its a secondary dominant.
This is also possible for vii0 chords, just use the 7th chord of the secondary key instead of the 5th.
Other types of non-diatonic chords
Borrowed chords – these are chords that are borrowed from the parallel minor/major key. They have the benefit of not needing to resolve to a specific place and are a great way to expand the tonal sound of a piece. The most common borrowed chords to show up in a major key include the bIII, iv, v, bVI, and bVII.
Passing chords – these are chords that are thrown in to help move from one place to another. For instance, in a chord progression that went from C major, to C# major, to D major the C# major would be considered a passing chord.
Augmented 6th chords – These are chords with a very specific set of resolutions and uses. Most collegiate music theory curricula cover Augmented 6th chords in the 3rd or 4th semester. They’re defined by an augmented 6th interval between scale degrees bVI and #IV. Click here for more info on the Augmented 6th chord.
Here’s another reharmonization of Star Spangled Banner using borrowed chords, passing chords, and Augmented 6th chords.