Sevenths and secondary dominants: Bach chorales

Sevenths and secondary dominants give Bach's harmony its drive. They also come with strict rules about where they go next.

Sevenths

The 7th resolves down by step and is never doubled.

CorrectThe 7th of V7, F(A), falls by step to E

Non-dominant 7ths (ii7, IV7, vi7) must be prepared: the 7th sounds in the same part in the chord before.

Correctii6/5 to V to I: the 7th of ii7, C(S), is prepared in chord I, held, then falls to B

Inversions of V7

In C major, V7 is G, B, D, F. In every inversion the 7th, F, falls to E and the leading note, B, rises to C.

V6/5: B, the leading note, in the bass

It goes to I, with the bass rising.

CorrectV6/5 to I: B(B) rises to C, and the 7th, F(T), falls to E

V4/3: D, the 5th, in the bass

It goes to I or I6.

CorrectV4/3 to I: D(B) falls to C, B(S) rises to C, and the 7th, F(A), falls to E

V4/2: F, the 7th, in the bass

It goes to I6, with the bass falling.

CorrectV4/2 to I6: the 7th is in the bass, so F(B) falls to E

Root position V7

A complete root-position V7 usually resolves to an incomplete I, with a tripled root.

CorrectComplete V7 to incomplete I: C tripled, no G

Leaving out the 5th of V7 lets you resolve to a complete I.

CorrectV7 without its 5th, D, to a complete I

Secondary dominants

A secondary dominant is the dominant (or dominant 7th) of a chord other than the tonic. It must resolve to its target chord: the chromatic raised note rises, and the 7th falls. In C major:

D7 goes to G (V7/V).

CorrectV7/V to V: F#(A) rises to G, and the 7th, C(S), falls to B

A7 goes to Dm (V7/ii).

CorrectV7/ii to ii: C#(T) rises to D, and the 7th, G(S), falls to F

E7 goes to Am (V7/vi).

CorrectV7/vi to vi: G#(A) rises to A, and the 7th, D(S), falls to C

C7 goes to F (V7/IV).

CorrectV7/IV to IV: the 7th, Bb(A), falls to A