Secondary Dominants

Here’s a reduction of the beginning of Beethoven’s First Symphony in C major.

Notice that even though I said this music is in C major, two chords don’t make sense in our key.

  • The first chord is a C dominant seventh chord with a B flat.
  • And the fifth chord is a D dominant seventh chord with an F sharp.
So how do we make sense of this?

New Terms!

First we need to define a few terms.
  • Diatonic – music where all the notes belong in the key.
  • Chromatic- music where some of the notes don’t belong in the key. This requires accidentals in unexpected places.
  • Tonicize – to emphasize a note other than the tonic with chromatic notes preceding it. This involves mimicing tendency tone relationships (Ti to Do and Fa to Mi or Me).
  • Secondary leading-tone – a pitch that functions as a new tendency tone that mimics the Ti-Do relationship.

Chromatic Chords

Notice that C7 and D7 chords don’t make sense in C major, but they do make sense as V7 in other keys (F major and G major, respectively). So both chords are diatonic to other keys, but chromatic in this context of C major.
Also notice that each chromatic dominant seventh chord is followed by the expected chord in the diatonic key. C7 is followed by an F major triad. D7 is followed by a G major triad. The chromatic chords and chromatic pitches resolve in aurally sastifing ways that match what they would do in their diatonic keys.
  • C7-F
    • Bass:  Sings both roots, C and F.
    • Soprano: The third, E, acts like a leading-tone and resolves up to F. The secondary leading-tone. Note that it is diatonic here.
    • Alto: Sings the chromatic seventh, B flat, and resolves down by step to A.
    • Extra voices fill out the rest of the chords and part writing.
  • D7-G
    • Bass: Sings both roots, D and G.
    • Soprano: The chromatic third, F sharp, acts like a leading-tone and resolves up to G.
    • Alto: Sings the seventh, C, and resolves down by step to B.
    • Extra voices fill out the rest of the chords and part writing.
Both of these chords and their resolutions are things we have done before. The only thing that is new is the accidentals. These chords seem to function in both their original diatonic keys and C major at the same time. We call these chords secondary dominants, because of this dual function. They are dominants (dominant seventh chords) that tonicize secondary pitches. The dominant seventh on G, G7, in C major could be considered the “primary” dominant.

Labeling These Chords

So what do we write under the chords? Theorists have decided that their labels should reflect the borrowing of these chords from other keys, rather than just adding information to the diatonic Roman numeral.
  • Rather that I7, we call C7 in C major: V7/IV, said five-seven of four.
  • And instead of II7, we call D7 in C major: V7/V, said five-seven of five.
The slash notation shows that each chord sounds like a dominant seventh chord and we expect it to go to the chord underneath the slash, the secondary “tonic.” So V7/IV often goes to IV and V7/V often goes to V.

Finding Secondary Dominants

  1. Find a chromatic chord. (accidentals!)
  2. Find its root. It is a dominant seventh chord or major triad.
  3. Find the pitch a P5 below the root.
  4. This new pitch is the root of a diatonic major or minor triad.
  5. The chromatic chord is a secondary dominant. Label it V(7)/x. (x is the roman numeral of the diatonic triad in step 4.)
Example in C major
  1. You see a chord with D sharp, F sharp and B in music in C major. It has two accidentals D sharp and F sharp that don’t fit the key. This is a chromatic chord.
  2. The root is B, and it is a major triad.
  3. A P5 below B is E.
  4. E is the root of a minor triad, the mediant (iii) in C major.
  5. If the D sharp is the lowest note, the original chord is labeled V6/iii.

Writing Secondary Dominants

  1. Find the the root of the chord after the secondary dominant (the Roman numeral under the slash). It is a major or minor triad.
  2. Find the pitch a P5 above the root. This is the root of the secondary dominant. Write it in.
  3. Build a dominant seventh chord or major triad on this pitch. (Accidentals!)
  4. Resolve the chordal 7th (down) and the secondary leading-tone (up).
Example in G major
  1. You are asked to write a V7/IV going to IV in G major. The root of IV is C and is a major triad.
  2. A P5 above C is G.
  3. A G7 chord has the pitches G, B, D, and F. Note that the F natural requires an accidental.
  4. Part write as follows.
    • Bass: G-C (Do-Fa)
    • Upper voices (in any arrangment)
      • Secondary leading-tone B resolves up to C (Mi-Fa mimicing Ti-Do).
      • Chromatic seventh F resolves down by step to E (Te-La mimicing Fa-Mi).
      • D moves to C (Sol-Fa) to create an incomplete IV with three roots and a third.
Example in B minor
  1. You are asked to write a V65/V going to V in B minor. The root of V is F sharp and is a major triad.
  2. A P5 above F sharp is C sharp.
  3. A C#7 chord has the pitches C sharp, E sharp, G sharp, and B. Note that E sharp and G sharp require accidentals.
  4. Part write as follows. Remember that the secondary dominant is in first inversion and that with inversions both chords are complete.
    • Bass: Chromatic secondary leading-tone E sharp resolves up to F sharp (Fi-Sol mimicing Ti-Do).
    • Upper voices (in any arrangement)
      • C sharp common tone between both chords (Re-Re).
      • Seventh B resolves down by step to A sharp (Do-Ti). Note the normal diatonic accidental on Ti.
      • Chromatic G sharp moves to F sharp to double the root (La-Sol).