Secondary Dominants

[Toxikator]

This is Copypasta from the FLipside's music theory forum.

Criticisms, expansions, etceteras welcome!

For those not in the know, secondary dominant chords are (almost always major) chords which function as the V chord in the key of the chord that follows them.

If that makes NO sense to you, think about the V chord in C Major: G. In the key of CMajor, we call it "V", but it could also technically be described as a "V/I" (read "five of one"). this logic can be "transposed", if you will, to any chord in the key. For example, the "V" chord itself has it's own V; we calculate it by pretending, briefly, that we're in the key of Gmaj instead of CMaj. In GMaj, the V chord is D.

So, in the key of C, the DMajor chord (sometimes written II) is a V/V chord; it is the dominant chord OF the dominant chord. The dominant will follow it, and it can be analyzed as a V-I in Gmaj, where the G (I) is then also written as a V, which then resolves to I in CMaj.

Like a really short modulation.

There are all sorts of uses for secondary dominants, but right now there are two in particular that I'd like to focus on.

The first way you can use a secondary dominant is to accent a circle progression; this is the way I've just demonstrated.

Because the motion from the secondary dominant to its resolution is circular, the secondary dominant can be used in place of it's nearest diatonic relative in a circle progression.

Consider the common I-ii-V-I. If we wanted, we could replace the ii with a II (aka a V/V); the only difference is the quality of the third, so the chord is very nearly diatonic; this replacement accents the circular motion from ii-V by making the ii chord major; not only does this create a conflict with the key that needs resolving, but the major chord resolves to its own "tonic" in the V chord better than the minor does.

As a result, this trick is most effective when performed (in major keys) on the ii and vi scale degrees (it can work on the iii scale degree as well, but the resolution to a diminished chord is not a very strong one).

Of course, an observant reader might note that, for example, the motion from I-IV is very similar to the motion from V-I in the key of IV (almost like a V/IV-IV) and wonder if it can be exploited the same way it is my making the minor ii and vi into major II and VI; yes it can.

The dominant chord is unique to a major scale in that, if you add a diatonic 7th to the chord, you'll have a major-minor 7th chord (AKA dominant 7th; in jazz notation, often simply written as "7"). that V7 chord has a particular tendency toward the tonic. By contrast, the other major chords diatonic to a scale (I and IV) have major-major 7ths, which do not have as strong a tendency to resolution. Here again we can use our secondary dominant tricks by adding a m7 to the I chord (or the IV, but as with the iii, it resolves to the viio scale degree, which is not usually effective). By playing CEGBb instead of CEGB, we create a tendency for the I chord to "resolve", rather than just move, to the IV chord; this is the same trick we used with the ii and vi.

Those three chords represent the essence of the first kind of secondary dominant usage, which is to change the quality of a diatonic chord in order to accent a circle progression.

the other kind of use is one that's a bit more specific, but which has a really cool sound

I don't doubt that anyone who's still READING has heard this progression used at least once, and wouldn't be surprised if they wondered how on earth it worked. It was employed very frequently by Bach and his contemporaries and is to this day a favorite way of utilizing secondary dominants.

It is characterised by a chromatic ascension in the bass voice; half-step up, another half-step up.

When moving from one chord to another chord that is immediately above it (IV to V, V to vi, etc.), there are a couple of issues. The first is voiceleading, which is very difficult when chords share no tones which are all adjacent. This trick helps work through them, and also helps strenghten the typically weak motion of chords by a step.

Let's consider the V chord in Cmajor: G. suppose we want to get to the vi chord; A. Well, what's the secondary dominant of A? though A is minor, it's dominant would still be major (assuming the harmonic form), so that's EG#B. Notice that, if we put this chord in first inversion, there's a G# in the bass. G# is a half-step ABOVE G, and a half-step BELOW A. Therefore, if we play V - V6/vi - vi, our bassline goes G-G#-A; the classical chromatic ascent that defines this progression.

For ANY two chords a step apart, the V6/second will create a chromatic ascent. However, this progression is MOST effective when moving from a Major chord to a minor chord; in other words, V-vi or I-ii; it CAN work also for the IV-V progression. The reason it doesn't work very well for the others is that they either directly touch the viio chord, or else (in the case of ii-iii) the secondary dominant IS on the vii degree; this means that, in order to be made major, TWO tones must be raised, which sounds odd. However, for the special case of ii-iii, the progression has a sort of cousin which has a similar effect: rather than using ii-VII-iii, you use ii-vii-iii; the minor vii chord still has a dominant quality over the minor iii chord. Of course, in the original root-first inversion-root position, the bassline is not chromatic; if we invert all the chords once more, to first inversion-second inversion-first inverson, we can put the chromatic ascent in the bass. So for the ii-v/iii-iii motion, you need to invert the chords again.

for these progressions, adding a 7th is typically a poor choice: the reason for this is that these progressions (excepting the IV-V/V-V) resolve to a minor chord, meaning the added 7th creates an ambiguity about resolution rather than a tendency toward it.

(Author's note: When I use the arabic numeral "6", I mean "first inversion". It should be superscripted but KvR doesn't seem to like the [sup] tags.

[Km7]

Thanks for this post, I am sure it would be useful!
I would summarize as follows:
Secondary dominants (and sub-dominants as well) result in a tonicization of the chord after them, for which they serve as dominants. They are usually major in order to provide the less stable leading tone, which is a half-step away from the root of the tonicized chord (the temporary tonic) and is captured by its gravity.
Secondary dominants have diatonic roots. They are build upon the scale degree which is a perfect fifth above the degree on which the tonicized chord is build. From what is said, one can easily deduce that for example, the diminished chord on the seventh degree doesn't have a secondary dominant -> 1) perfect fifth above the VII degree is outside of the scale and 2) the diminished chord cannot serve as a temporary tonic because it is very unstable and doesn't have an actual root.
Whether one will alterate the two tones of the diminished chord on the seventh degree when building V/iii (in order to provide a leading tone) depends on the situation and should be judged by the composer. If yes, we have two chromatic tones simultaneously, which in highly diatonic context would sound too surprising, if no, the effect would be weaker (as v-i). Another way to tonicize the iii chord is to use vii/iii (this is valid for the other chords, as well).
Same about the choice for usage of the secondary V7 of a minor chord (and also depends on the style). Nevertheless, it is true that the minor third is not so pure as the major third, it is away from the fourth and has less gravitational power, but the fourth still resolves to it.