Resolving dominant 7th chords
When resolving V7 chords, it is always important to remember to find the "active" tones and resolve them first. Active tones are tones which want to move to a specific note in the next chord.
A good example of an active tone is a leading tone. When the leading tone is present in any dominant function chord (such as V, V7, vii, or vii7), it wants to resolve up a half step to the tonic. All dominant function chords have a leading tone in them. It is particularly important to resolve this note correctly when it is in the soprano voice.
Sevenths of chords are another type of active tone. Sevenths are present in all kinds of diatonic 7th chords and secondary 7th chords, and they all want to resolve down by step to the the next scale tone directly below. (In other words, the note below may be either a whole or a half step below the 7th of the chord.) The seventh of the dominant seventh chord is the 4th step of the scale.
Leading tones are the 7th step of the scale that is located a HALF STEP below the tonic note. In major, that is where the 7th scale degree is found, but in minor, you will have to raise the 7th step of the scale to make it become a leading tone. The tone a whole step below the tonic in minor is not a leading tone. It is called the subtonic note.
Note: this is tricky! Because the two types of active tones I have mentioned above (leading tones and 7ths) are both present in a V7 chord, there can be some confusion about their resolution since both these notes are associated with the number 7. It is very important to have a clear idea which one is being referred to when discussing the resolution of V7 chords.
Therefore, I will always refer the the 7th step of the scale by the name "leading tone" and the seventh of the chord will be referred to as "the seventh".
This is the reason it has to be perfectly clear is because:
leading tones resolve UP
7ths resolve DOWN
It is so easy to mix up the two if you start thinking of them both as 7ths of something!
When musicians talk about "7ths", they are usually talking about either an interval of a 7th, or seventh chords. So I try never to use the word 7th to refer to the seventh step of the scale in a chord (unless I say the whole phrase "seventh step of the scale"). The seventh step of the scale is not the 7th of the chord in a V7 chord.
“Problems” resolving root position V to I
There are three ways to deal with the voice-leading problems that come up when moving V7 to I, tripling the root of the tonic chord of resolution (and leaving out the 5th), voicing up the V7 chord so that it is incomplete, or “frustrating” the leading tone (ONLY if it is in an inner voice) by moving it down to the fifth of the tonic chord rather than resolving it up to the tonic.
As you might observe from these three methods, there is some flexibility with resolving the leading tone when it is not in an outer voice, but there is no flexibility about resolving 7th of chords: they need to move down by step.
Of the three methods, using an incomplete V7 chord is quite often the best solution, since it allows the active tones to resolve as desired, and results in a normal doubling in the chord of resolution.
1 - one possibility: the tripled toot
If you have a four-voice V7 to I progression (both chords root position) where the V7 chord contains all four notes (we call that “complete”) and the leading tone is in the soprano, the correct resolution will create a tripled root. This is often referred to as “complete to incomplete.”
This is because the bass voice must move to the tonic note and the leading tone in the soprano must also resolve to the tonic note. The 7th of the V7 chord must also resolve down by step to the third step fo the scale.
This leaves one note remaining, the 5th of the V7 chord (which is the 2nd step of the scale) not knowing exactly where to go. Since you already have two roots and a third, you will be thinking you should move this note to the fifth of the tonic note to complete the chord. But this is not an option, as it creates parallel fifths with the bass voice (even when moved in contrary motion to the bass!)
If we are in the key of c major, our V7 chord is GBDF. Here is how the resolution above happens:
The G is in the bass and must move up to C since both chords must be in root position. The leading tone B is in the soprano, so it must resolve up to C also. The F, the 7th of the chord, must resolve down by step to the note E. So far, then, we have two C’s and an E in our tonic chord. But no G.
The D has no particular place it is required to go, unlike the other three notes. You might figure that it seems obvious that you should move it to the missing G, but this is what creates the parallel 5ths (G-D moving to C-G).
The only correct solution when given this situation is to move the 5th down to the tonic note, creating the three-roots-and-a-third doubling. This is the best solution, and the correct method to solve this problem. [Note: Bach sometimes chooses instead to move this note up to the 3rd step of the scale instead, creating a tonic chord with two roots and two thirds. But this is not the preferred solution.]
However, you may find this resolution causes you other problems if the tonic chord is not the final chord of the progression. The typical problem is that with three of the same note in the tonic chord, you may have a very hard time moving ahead to any other chord without creating parallel octaves somewhere in the solution.
If you have a choice about how the V7 chord is voiced (as in realizing a figured bass in a chorale style example) you may wish to avoid the tripled root altogether by utilizing one of the next options described below.
2 - a good alternative: the incomplete V7
If you find yourself in the situation above, (both root position chords and LT in the soprano) you might wish to avoid the whole tripled root solution by voicing up the V7 chord differently, as an incomplete chord, if you have the option of changing it. Leave out the 5th of the chord, and double the root of the chord instead. This version is referred to as “incomplete to complete.”
For example, in the key of C major, as above, our V7 chord contains the notes GBD & F. In this case we would create our voicing of the V7 chord so that it has two G’s, B and F, instead.
Even with the leading tone B in the soprano, it will be easy to resolve from the incomplete V7 to a tonic chord with the root doubled. This is the simplest of the three methods.
The G in bass moves to C. The leading tone B in soprano resolves to C. The 7th, F, resolves down to E. This leaves the remaining G to just remain on G to complete the chord.
It is a very simple solution, creating smooth voice leading, keeping the common tone, and arriving at a complete tonic chord with the root doubled.
3 - another option: the “frustrated” leading tone
The LT is “frustrated” in this solution because it does not get to resolve to the tonic the way it wants to. This option is only available if the leading tone is in an inner voice. That way it is not so noticeable that is has not resolved correctly. If you are given homework where there is a complete V7 chord but the leading tone is NOT in the soprano (or the bass, since both chords are root position) then this could work. This is another way to get to a complete tonic chord with the root doubled. Both chords have all their notes, to this version is referred to as “complete to complete.”
In C, with our V chord GBDF, we have all the notes but the B is in the alto or tenor voice. The G in the bass must move to the C. The 7th of the chord, F, must also move down by step to E. But the leading tone B does not go up to C - instead it goes down a third to the note G. That means so far we have a C, an E, and a G. So the remaining D note in the V7 chord can move down a step to C to give us the root doubling we need in our tonic chord.
This solution also creates good choice leading and doubling. If you don’t think of doing it however, and you resolve the notes where they “want” to go (meaning you take the B up to C), you will end up with that same tripled root problem discussed above. Frustrating the leading tone is the way to undo that.