V. Diatonic Harmony, Tonicization, and Modulation

Prolongation at Phrase Beginnings using the Leading-tone Chord

John Peterson

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 for a reminder). In this chapter we consider an alternative way to harmonize those same tonic prolongation basslines using a harmony that can substitute for V7: the leading-tone chord (meaning the triad or 7th chord built on Ti (\hat{7})) (Example 1).

Example 1. Using viio7 vs. V7 in Mozart, “Agnus Dei” from Requiem. Recording: 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). That’s 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 (\uparrow\hat{7}), not Te (\downarrow\hat{7}), to build the leading-tone chord. In other words, remember to raise the leading tone.
  3. In major the leading-tone 7th 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-Ab) (Example 2). You can use both, but viio7 is much more common than vii{\o}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 viio7 (plus viio6) can substitute for an inversion of V7 (and V6) according to which note is in the bass (Example 3). What this means is that, for example, viio7 can be used anywhere that V\begin{smallmatrix}6\\5\end{smallmatrix} or V6 can be used. Similarly, viio\begin{smallmatrix}6\\5\end{smallmatrix} or viio6 can be used in place of V\begin{smallmatrix}4\\3\end{smallmatrix}, and viio\begin{smallmatrix}4\\3\end{smallmatrix} can be used in place of V\begin{smallmatrix}4\\2\end{smallmatrix}.

Bass note \mathrm{V}^{7} \mathrm{vii}^{\circ7}
Ti (\hat{7}) \mathrm{V}\begin{smallmatrix}6\\5\end{smallmatrix} \mathrm{vii}^{\circ7}
Re (\hat{2}) \mathrm{V}\begin{smallmatrix}4\\3\end{smallmatrix} \mathrm{vii}^{\circ}\begin{smallmatrix}6\\(5)\end{smallmatrix}
Fa (\hat{4}) \mathrm{V}\begin{smallmatrix}4\\2\end{smallmatrix} \mathrm{vii}^{\circ}\begin{smallmatrix}4\\3\end{smallmatrix}

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

Luckily, there isn’t too much new to learn with respect to part writing. Continue to follow and continue 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 (\downarrow\hat{6}/\hat{6}). Example 5 shows tonic prolongations involving viio7 and its inversions, and it compares each to a corresponding prolongation involving V7 and its inversions.

Active note Resolution
Ti (\hat{7}) Do (\hat{1})
Re (\hat{2}) Do (\hat{1})
Fa (\hat{4}) Mi (\hat{3})
Le/La (\downarrow\hat{6}/\hat{6}) Sol (\hat{5})

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

Example 5. Writing with viio6 and viio7 and its inversions.

viio4/2

You might have noticed that viio\begin{smallmatrix}4\\2\end{smallmatrix} doesn’t correspond to an inversion of V7. That’s because it’s built on Le (\downarrow\hat{6}), and Le (\downarrow\hat{6}) isn’t in V7. viio\begin{smallmatrix}4\\2\end{smallmatrix} is a very rare harmony because its bass note, Le (\downarrow\hat{6}), resolves down to Sol (\hat{5}) (we saw that Le (\downarrow\hat{6}) resolves to Sol (\hat{5}) in Example 4). So far we’ve seen that Sol (\hat{5}) in the bass typically supports V or V7, and that’s also the case here: viio\begin{smallmatrix}4\\2\end{smallmatrix} goes to cadential \begin{smallmatrix}6\\4\end{smallmatrix} (Example 6). Again, though, viio\begin{smallmatrix}4\\2\end{smallmatrix} is not a very common chord.

Example 6. Using viio\begin{smallmatrix}4\\2\end{smallmatrix}.

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

vii{\o}7 presents voice-leading challenges that are not present with viio7 because it contains a perfect fifth between Re (\hat{2}) and La (\hat{6}). This is perhaps another reason that composers favor viio7 over vii{\o}7: with {\o}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 (\hat{2}) is above La (\hat{6}) when you use vii{\o}7 or its inversions. The one time where this advice is impossible is with vii{\o}[latex]\begin{smallmatrix}6\\5\end{smallmatrix}[/latex], where Re (\hat{2}) is in the bass. Although it’s possible to avoid parallels with vii{\o}[latex]\begin{smallmatrix}6\\5\end{smallmatrix}[/latex], we’d recommend just using viio\begin{smallmatrix}6\\5\end{smallmatrix} instead.

Example 7. Using vii{\o}7 and its inversions.

Assignments

  • Assignment 1: Includes short writing from Roman numerals, analysis, and figured bass

 

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