Secondary dominants

A 7-chord that does not belong to the key is usually a dominant in disguise: it points at the chord that comes next.

The dominant of another chord

A secondary dominant is the dominant 7th of a chord other than I: the V7 that belongs to that chord’s own key. It is written V7/x (“five of x”). The one on V is the “five of five”, V7/V. In C major:

There is no V/vii°, because a diminished chord is not a stable target. In C the notes outside the key are C♯ (in A7), D♯ (in B7), B♭ (in C7), F♯ (in D7) and G♯ (in E7).

How they behave

A secondary dominant usually resolves to its target: D7 → G, E7 → Am. The out-of-key note is the target’s leading tone, so it rises by a half step: F♯ → G, G♯ → A. The music briefly leans toward another key without really changing key: a tonicization. Chains of secondary dominants follow the circle of fifths (E7 → A7 → D7 → G7 → C, lesson 10.4).

A 7-chord on a degree other than V, with a note outside the key, is almost always a secondary dominant. Look at the chord that follows.

For the bass

The root still moves down a 5th (or up a 4th) into the target. The out-of-key 3rd is an excellent approach note: over A7 the line moves C → C♯ (the 3rd of A7) → D.