Secondary dominants, and the chord that arrives a bar early
Chords from outside the key that work as the dominant of a degree that is not the first, and why they make the next chord sound inevitable.
A song in C major has an A seventh chord in the middle of it. A seventh does not belong to the harmonic field of C: the sixth degree is A minor, and the C sharp the chord carries does not exist in the scale. And yet it sounds perfectly at home, because the next chord is D minor, and A seventh is the dominant of D. That is the mechanism: a chord borrowed from another key to do the dominant's job towards a degree that is not the first.
The V7 of each degree
Every degree that can be a tonic has a dominant of its own: the seventh chord a fifth above it. In C major:
- V7 of II — A seventh, resolving to D minor.
- V7 of III — B seventh, resolving to E minor.
- V7 of IV — C seventh, resolving to F major.
- V7 of V — D seventh, resolving to G.
- V7 of VI — E seventh, resolving to A minor.
E seventh prepares A minor; D seventh prepares G. Each of them contains a note foreign to the key, and it is that note — the leading tone of the arrival degree — that makes the next chord sound like a destination instead of a step.
The seventh degree is left off the list. B diminished cannot be the tonic of anything, so it gets no dominant; the rule is that you only prepare a degree that can sound like a centre.
What the chord actually does
A secondary dominant does, in miniature, what the main dominant does for the whole key: it creates a leading tone for the arrival chord and a tritone that resolves onto it.
A seventh has A, C sharp, E and G. The C sharp is D's leading tone, a semitone below it; the G sits a semitone above F, which is the third of D minor. Both resolve by semitone, exactly as B and F resolve to C and E in the main dominant.
For an instant the music behaves as if it were in D. Tradition calls this tonicisation: the degree gets, for one chord, the treatment of a tonic, and then the music carries on in its usual key. It is not modulation, because there is no change of centre; it is a one-bar detour.
Where they turn up
The commonest place is one bar before a diatonic degree the music wants to underline. The V7 of V is the most frequent of all, because it turns the arrival at the dominant into a small event:
The V7 of II opens half the songs that begin with a II–V–I; the V7 of VI prepares the return to the sixth degree after a deceptive cadence; the V7 of IV is the C seventh chord that appears out of nowhere before the F.
Chains
A secondary dominant can have a secondary dominant of its own. Chain them and the roots fall by fifths all the way to the tonic:
E, A, D, G, C. Each chord is the dominant of the next, and the only diatonic one on the list is the last. The ear follows because every resolution is a step of the circle of fifths, and the circle is the path it knows best.
What to take from here
A secondary dominant is the V7 of a degree that is not the first: a chord from outside the field, with the arrival degree's leading tone inside it, which makes the next chord sound inevitable. Every degree that can be a tonic has one; the seventh does not. Recognising them explains almost every "strange" chord in a popular chart, and the turnaround of the next reading is where they pile up most.