IV. Diatonic Harmony, Tonicization, and Modulation

John Peterson

Key Takeaways

  • Instead of using an inverted [latex]\mathrm{V^7}[/latex] chord to prolong tonic, composers sometimes use [latex]\mathrm{vii^{o7}}[/latex] or its inversions.
  • Each inversion of [latex]\mathrm{vii^{o7}}[/latex] can be used in the same way as a particular inversion of [latex]\mathrm{V^7}[/latex]. The pairings of [latex]\mathrm{V^7}[/latex] and [latex]\mathrm{vii^{o7}}[/latex] are based on the bass note each chord harmonizes.
    • [latex]\mathrm{vii^{o7}}[/latex] can be used anywhere that [latex]\mathrm{V^6_5}[/latex] or [latex]\mathrm{V^6}[/latex] can be used.
    • [latex]\mathrm{vii^{o}\begin{smallmatrix}6\\5\end{smallmatrix}}[/latex] or [latex]\mathrm{vii^{o6}}[/latex] can be used in place of [latex]\mathrm{V^4_3}[/latex].
    • [latex]\mathrm{vii^{o}\begin{smallmatrix}4\\3\end{smallmatrix}}[/latex] can be used in place of [latex]\mathrm{V^4_2}[/latex].

Chapter Playlist

Overview

Earlier, we saw how the tonic can be prolonged using essentially four kinds of progressions, which we categorized according to their basslines (see the summary section of that chapter for a reminder). In this chapter, we consider an alternative way to harmonize those same tonic-prolongation bass lines using a harmony that can substitute for V7: the . Example 1 shows a passage from Mozart’s “Agnus Dei” that uses viio7 and its inversions to prolong tonic. Below the actual version, a recomposition shows that the bass line from the actual version can also be harmonized with V7 and its inversions. As you listen, notice the differences in color between the two versions. You may hear that the actual version is full of a wonderful tension that is less present in the recomposed version.

Example 1. Using viio7 vs. V7 in Mozart, “Agnus Dei” from Requiem (0:06–0:20).

Before we address how this substitution works, here are three points we need to emphasize:

  1. The leading-tone chord as a triad is always used in first inversion viio6. This is because any other inversion creates a dissonance with the bass that composers tend to avoid.
  2. In minor, we need to remember to use ti [latex](\uparrow\hat{7})[/latex], not te [latex](\downarrow\hat{7})[/latex], to build the leading-tone chord. In other words, remember to raise the leading tone.
  3. In major, the leading-tone seventh chord’s quality is half diminished if we don’t alter it (e.g. in C major: B-D-F-A). Composers tend to prefer the sound of a fully diminished 7th chord, though, so we nearly always find that in major keys, composers lower the chordal seventh to make the chord fully diminished (e.g., in C major: B-D-F-A♭) (Example 2). You can use both, but viio7 is much more common than vii∅7, and we’ll see why below.

Example 2. Comparing qualities of leading-tone seventh chords.

Substituting the leading-tone chord in place of V(7)

Almost all inversions of [latex]\mathrm{vii^{o7}}[/latex] (plus [latex]\mathrm{vii^{o6}})[/latex] can substitute for an inversion of [latex]\mathrm{V^7}[/latex] (and [latex]\mathrm{V^6})[/latex] according to which note is in the bass (Example 3). What this means is that, for example, [latex]\mathrm{vii^{o7}}[/latex] can be used anywhere that [latex]\mathrm{V^6_5}[/latex] or [latex]\mathrm{V^6}[/latex] can be used. Similarly, [latex]\mathrm{vii^{o}\begin{smallmatrix}6\\5\end{smallmatrix}}[/latex] or [latex]\mathrm{vii^{o6}}[/latex] can be used in place of [latex]\mathrm{V^4_3}[/latex], and [latex]\mathrm{vii^{o}\begin{smallmatrix}4\\3\end{smallmatrix}}[/latex] can be used in place of [latex]\mathrm{V^4_2}[/latex].

[table id=43 /]

Example 3. Substituting viio7 for V7 according to which note is in the bass.

Luckily, there isn’t too much else to learn with respect to part writing. Continue to follow and to resolve active notes in the upper voices according to their tendencies. Example 4 reviews these tendencies and adds the one new note we haven’t seen yet in a dominant-function chord: le/la [latex](\downarrow\hat{6}[/latex]/[latex]\hat{6})[/latex]. Example 5 shows tonic prolongations involving viio7 and its inversions, and it compares each to a corresponding prolongation involving [latex]\mathrm{V^7}[/latex] and its inversions.

[table id=44 /]

Example 4. Tendencies of active notes in dominant-function chords.

Example 5. Writing with [latex]\mathit{vii^{o6}}[/latex] and [latex]\mathit{vii^{o7}}[/latex] and its inversions.

viio4/2

You might have noticed that [latex]\mathrm{vii^{o}\begin{smallmatrix}4\\2\end{smallmatrix}}[/latex] doesn’t correspond to an inversion of [latex]\mathrm{V^7}[/latex]. That’s because it’s built on le [latex](\downarrow\hat{6})[/latex], which isn’t in [latex]\mathrm{V^7}[/latex]. [latex]\mathrm{vii^{o}\begin{smallmatrix}4\\2\end{smallmatrix}}[/latex] is a very rare harmony because the expected resolution from le down to sol [latex](\downarrow\hat6-\hat5)[/latex] (see Example 4) occurs in the bass. So far, we’ve seen that sol [latex](\hat{5})[/latex] in the bass typically supports V or [latex]\mathrm{V^7}[/latex], and that’s also the case here: [latex]\mathrm{vii^{o}\begin{smallmatrix}4\\2\end{smallmatrix}}[/latex] goes to [latex]\mathrm{cad.^6_4}[/latex] (Example 6). Again, though, [latex]\mathrm{vii^{o}\begin{smallmatrix}4\\2\end{smallmatrix}}[/latex] is not a very common chord.

Example 6. Using [latex]\mathit{vii^{o}\begin{smallmatrix}4\\2\end{smallmatrix}}[/latex].

Using the leading-tone chord as a half-diminished seventh chord

vii∅7 presents voice-leading challenges that are not present with viio7 because it contains a perfect fifth between re [latex](\hat{2})[/latex] and la [latex](\hat{6})[/latex]. This is perhaps another reason that composers favor viio7 over vii∅7: with ∅7, we need to watch out for parallel fifths, as in Example 7. An easy way to avoid them is to always make sure that re [latex](\hat{2})[/latex] is above la [latex](\hat{6})[/latex] when you use vii∅7 or its inversions. The one time where this advice is impossible is with [latex]\mathrm{vii^{∅}\begin{smallmatrix}6\\5\end{smallmatrix}}[/latex], where re [latex](\hat{2})[/latex] is in the bass. Although it’s possible to avoid parallels with [latex]\mathrm{vii^{∅}\begin{smallmatrix}6\\5\end{smallmatrix}}[/latex], we’d recommend just using [latex]\mathrm{vii^{o}\begin{smallmatrix}6\\5\end{smallmatrix}}[/latex] instead.

Example 7. Using [latex]\mathit{vii^{∅7}}[/latex] and its inversions.

Assignments
  1. Prolongation at Phrase Beginnings using the Leading-tone Chord (.pdf, .docx). Asks students to write from Roman numerals, complete analysis, and realize figured bass.

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