Flat Majors & Secondary Dominants
If we look at this group of chords through the lens of C Major, we can describe some of them as non-diatonic chords in two main classes: flat Majors and secondary Dominants.
Flat Majors are Major chords which are outside (between) chords in a Major key center. They sit in the gaps between diatonic chords of a key. We get their names by comparing to what is ‘normal’ in Major keys.
In C, the normal E type chord in C Major is E minor. If we flat it, and make it Major, it can be viewed as a ♭III [uppercase III is a Major chord in letter position III]. This is a Major chord built on the lowered 3rd of the key. Same for the 7. The normal 7 is B diminished. Flat it, make it Major…B flat Major.
The complete flat Major sequence is ♭II, ♭III, ♭V, ♭VI, ♭VII. In C, these chords are D♭, E♭, G♭, A♭, & B♭. There is no ♭IV because this chord would be Fb, which is E Major, and E is in a different class [it’s a secondary Dominant].
Secondary Dominants are the V chord of any chord in the key. These chords are not in the key; they are outside as well. The only Dominant in a key is its own V chord. For C, G or G7 exists. So, we consider the V chord for the ii, iii, IV, V, and vi. I typically leave out the V of the viio chord.
These Dominants can be triads or Dominant 7 type chords.
the V of ii [V/ii] is A or A7. A or A7 is the Dominant of Dm.
the V of V [V/V] is D or D7. D or D7 is the Dominant of G. We could also just think of D as a Major II [we have options].
These are the only two secondary Dominants in this set of voicings. The complete list for C:
V/ii = A7; V/iii = B7; V/IV = C7; V/V = D7, V/vi = E7. Again, we typically don’t think 2ndary Dom for the viio chord. We can however and this chord would be F#7.
If we were to talk about a different Major key, all of these chords would mean something different to that tonic [root of the key].