V7 Resolutions: Out with the Fifth!

If you read the previous music theory lesson, you learned that

The third of the V7 chord () resolves up by half-step to the tonic scale degree (). There is an exception to this that we’ll get to in this lesson.

The seventh of the V7 chord () resolves down by step to the mediant scale degree (). In a major key, the resolution is down a half-step; in a minor key, the resolution is down a whole-step. There are no exceptions to this rule: down with the seventh!

Out with the Fifth!

A triad has three chord tones: the root, the third, and the fifth. A seventh chord has four chord tones: the root, the third, the fifth, and the seventh.

In four-part harmony, the object is to create smooth voice leading from one chord to the next. Sometimes this is difficult without making certain sacrifices.

A common technique to make voice leading smoother is to leave a chord tone out of one of the chords. So, if we’re going to leave a chord tone out of a triad or seventh chord, which one should it be: the root, the third, the fifth, or the seventh?

Let’s look at each chord tone to see which one might work:

Root: We can’t leave the root of the chord out without making it a different chord.
Third: We can’t leave the third out of the chord without getting a hollow or empty sound. Sometimes this effect is desired, but not in traditional four-part harmony. Besides, if the third is missing, we don’t know if the chord is a major chord or a minor chord.
Seventh: If we leave the seventh out, the chord is no longer a seventh chord. So if you want a seventh chord, the seventh of the chord must be present.

This leaves us with one chord tone that may be left out: the fifth.

Complete and Incomplete Chords

Listen to the four-voice examples below. The first pair of chords is a triad, the second pair, a seventh chord. The first chord of each pair contains all the chord tones. In the second chord, the fifth is missing, and another root is in its place in the tenor voice.

When a chord has all of its chord tones, we’ll call it complete. When the fifth is left out, we’ll call the chord incomplete.

Listen carefully and you’ll hear that the incomplete chords sound perfectly acceptable without the fifth.

Why do you think that is?

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Do you remember the harmonic series? The third partial is a perfect fifth above the fundamental; it is one of the strongest harmonics, and is usually easy to hear. Because of its strength, we still perceive the presence of the fifth of a chord even when it is absent in four voices. Go back and listen again to the pairs of chords above. If you listen carefully, you might be able to hear the fifth in the second chord of each pair, even though it is absent.

I-V7-I (i-V7-i) Progressions

When writing a V7-I progression in four voices, there are three ways the V7 may resolve to the I chord using complete or incomplete chords. All three resolutions occur frequently in music literature. Think of these resolutions as three options. In other words when you resolve a V7 chord to a I chord, you have three choices as to how to resolve it. Some composers seem to favor one way over another, and some use all three with equal frequency. As you become more comfortable and fluent in four-part harmonization, you will discover that one resolution may work better than another depending on certain musical situations, such as voicing or spacing.

Option 1: The Complete V7 to Incomplete I

In this version of the I-V7-I progression, the third () and the seventh () of the V7 chord are in the soprano and alto respectively, and they resolve as they should (indicated by the arrows): the third moves up by half-step to , and the seventh moves down by step to . Remember, in the minor mode, we use the harmonic minor scale (raised ) so we get a half-step up to .

Now look at the tenor voice of the V7 chord. It has the fifth (D). In this particular voicing, there is nowhere for the tenor to move except to , creating a tonic chord with three roots and no fifth. The tenor should not move up to the E because it would result in a doubled third which is not desirable (see this music theory lesson for a review of chord doubling). If the tenor jumps from the D in the V7 down to a G in the tonic chord, the I chord would be complete, but there would be forbidden parallel fifths between the tenor and the bass. The complete V7 to the incomplete I, therefore, is the best solution given this particular chord voicing:

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Option 2: The Incomplete V7 to Complete I

I used vocal scoring for this next example because it makes it easier to see what’s going on. Here, the tenor has the fifth of the first I chord (G), and it stays on the G (the common tone) while the rest of the voices move to form a V7 chord. This results in an incomplete V7 chord (two roots and no fifth). When the V7 resolves to the final I chord, the tenor again stays on the G, creating a complete I chord:

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Option 3: The Complete V7 to Complete I

The only way to get from a complete V7 to a complete I is if one of the chord members of the V7 does not resolve normally. We know that there are no exceptions for the seventh of the V7 chord: it must always resolve down by step. The third of the V7 (), however, may resolve down to the fifth of the chord as long as it’s in an inner voice (the alto or tenor):

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In the example above, the third is in the alto. Instead of resolving “properly” to the tonic scale degree, it leaps down to the G, enabling the I chord to be complete. J.S. Bach favored this type of V7 resolution, especially in his chorale harmonizations.

Listen to the progression and notice that the V7 resolution sounds fine. Our ears are satisfied, even though the leading tone does not resolve as it should. This is because the soprano has the same C that the alto would have if it resolved up by half-step.

The best way to become fluent in the various I-V7-I progressions is to practice them in every major and minor key. You can download all three of them written out in all the keys on the Harmonic Progressions page, but try to practice them without reading the music.