IV. Diatonic Harmony, Tonicization, and Modulation

John Peterson

Key Takeaways

• This chapter introduces how composers add a seventh to the dominant to strengthen its pull toward the tonic. There are three ways a V7 can resolve to tonic:
• The default resolution: where all resolve according to their tendencies.
• Incomplete V7: where the fifth is omitted from the V7 and the V7‘s root is doubled instead to create a complete tonic.
• Leading-tone drop: where the leading tone in a complete V7 leaps down to sol ($\hat{5}$) to create a complete tonic.

The phrase in Example 1 ends with a similar to those we saw and wrote in the Introduction to Harmony, Cadences, and Endings chapter. Here, however, the V chord contains an extra note, fa ($\hat{4}$), that transforms it from a into a . Since the seventh adds dissonance (and therefore instability) to the chord, it strengthens the pull of the V chord toward I. Compare the sound of the excerpts in Example 2.

Example 1. A PAC involving V7 in Margaret Casson’s The Cuckoo

Example 2. A PAC involving: (a) only triads and (b) a V7 chord.

# The Default Resolution of V7 to I

When the notes of a complete V7 chord resolve according to their typical tendencies, we end up with a tonic triad that has three roots and one third—no fifth (Examples 3a and 3b). This is a completely normal, expected, and common resolution of V7 to I. It’s okay to leave out the fifth here since it doesn’t provide essential information about the chord. By contrast, the root and third are essential: the root determines the chord’s name, and the third determines its quality.

The resolution in Example 3c, where re ($\hat{2}$) goes up to mi ($\hat{3}$), is very uncommon, and such an unusual doubling in the tonic chord (two roots, two thirds) usually leads to voice-leading problems. We suggest avoiding this kind of resolution.

Example 3. Default resolution of V7.

To resolve V7 to I using a default resolution:

1. Write the entire bass: sol to do ($\hat{5}$–$\hat{1}$)
2. Write the entire soprano by choosing an active note to place in the soprano over V7, then resolving that note according to its tendency. Example 4 shows the tendencies for active notes in V7.
1. If you are writing in minor, remember to use ti ($\uparrow\hat{7}$), not te ($\downarrow\hat{7}$) in V7 to make the chord major!
3. Fill in the inner voices by asking “what do I have, what do I need, and what is the tendency of those notes?”

[table id=38 /]

Example 4. Tendencies of active notes in V7.

# Alternative Resolutions of V7 to I

Sometimes a composer may want the tonic chord to be complete rather than the incomplete chord that occurs in the default resolution. Two alternative resolutions of V7 make it possible to create a complete I. Note that the steps for writing remain the same as for the default resolution: write the entire bass, write the entire soprano choosing an active note over V7, then fill in the inner voices together as a pair by asking “what do I have, what do I need, and where do those notes go?”

### Incomplete V7

Examples 5a and 5b show a resolution where the fifth has been omitted from the V7, allowing that chord to resolve to a complete I. When we omit the fifth, we need to select a note to double in order to retain our four-voice texture. The only note we can double is the root, since doubling ti ($\uparrow\hat{7}$) or fa ($\hat{4}$) would create parallel octaves when both voices resolve according to their tendencies (Examples 5c and 5d).

Example 5. Alternative resolution of V7 involving an incomplete V7

It’s also possible to create a complete I from a complete V7, but in order to do so, we have to allow a tendency tone to move somewhere other than its expected resolution. Example 6 shows how this is possible using a leading-tone drop.  Here, ti ($\uparrow\hat{7}$) drops down to sol ($\hat{5}$) in an inner voice. This works because: (1) ti ($\uparrow\hat{7}$) is not a dissonant note; (2) ti ($\uparrow\hat{7}$) is in an inner voice, so it’s not too noticeable; and (3) ti ($\uparrow\hat{7}$) is the closest note that can move to sol ($\hat{5}$) in the tonic without causing parallels.

Example 6. Alternative resolution of V7 involving a leading-tone drop.

Two things are worth emphasizing here:

1. Use the leading-tone drop only in the alto or tenor voice to hide the fact that it’s not resolving as expected.
2. The leading tone always leaps down to sol ($\hat{5}$), never to mi ($\hat{3}$), which is further away than sol ($\hat{5}$).

# Summary

Example 7 summarizes the three possible ways to resolve V7–I. You may notice that we have not discussed how V7 works in . V7 is much less common in a HC since the HC is already unstable, and adding a seventh makes it that much more unstable. Since such a cadence more often appears in Romantic music, Janet Schmalfeldt (2011, 202) has termed HCs involving V7 the “19th-century HC.”

Example 7. A summary of possible resolutions of V7. 