IV. Diatonic Harmony, Tonicization, and Modulation

John Peterson

Key Takeaways

  • This chapter introduces the [latex]\mathrm{cadential}^6_4[/latex] [latex](\mathrm{cad.}^6_4)[/latex], an embellishment of the dominant that results from the combination of two embellishing tones a sixth and a fourth above the bass note sol ([latex]\hat{5}[/latex]). We label the [latex]\mathrm{cad.\ }^6_4[/latex] and its resolution to V(7) as one unit: [latex]\mathrm{V}\begin{smallmatrix}(8-7)\\6-5\\4-3\end{smallmatrix}[/latex].
  • Any chord that normally approaches V can approach [latex]\mathrm{cad. }^6_4[/latex]. Most commonly, this is one of the strong predominants.
  • When resolving [latex]\mathrm{cad.}^6_4[/latex], be sure to follow the figures such that the sixth above the bass falls to a fifth above the bass and the fourth above the bass falls to a third above the bass.

Chapter Playlist

So far, we’ve seen that the dominant can be strengthened, particularly at authentic cadences, by the addition of a seventh. We also saw that both and are commonly strengthened using a strong predominant. In this chapter, we look at another way to strengthen the the dominant’s drive toward resolution: the cadential [latex]^6_4[/latex] [latex](\mathrm{cad.}^6_4)[/latex].

The authentic cadence in Example 1 involves a V7 that has been embellished by [latex]\mathrm{cad.}^6_4[/latex]. We use the word “embellished” intentionally here because the [latex]\mathrm{cad.}^6_4[/latex] comprises two embellishing tones that appear over sol ([latex]\hat{5}[/latex]) in the bass. In Example 1, the embellishing tones are a passing tone and a suspension. These embellishing tones happen to always be a sixth and a fourth above the bass, and their appearance often intensifies the expectation to hear a cadence, hence the name “[latex]\mathrm{cad.}^6_4[/latex].” Although the [latex]\mathrm{cad.}^6_4[/latex] often shows up at cadence points, it may show up anywhere in a phrase as an embellishment of V(7).

Example 1. [latex]cad.\mathit{^6_4}[/latex] in Joseph Boulogne’s String Quartet no. 4, I, mm. 45–47 (1:26–1:30).

A note on [latex]^6_4[/latex] chords.

[latex]^6_4[/latex] chords are special because they involve a dissonance (the fourth) with the bass. Composers therefore treat [latex]^6_4[/latex] chords in distinct ways, which fall into four categories. To acknowledge their special usage, each variety of [latex]^6_4[/latex] chord has its own label that relates to how the chord functions. Future chapters will introduce the remaining [latex]^6_4[/latex] chord types.

Labeling cadential 6/4

You might have noticed that the [latex]\mathrm{cad.}^6_4[/latex] in Example 1 involves the notes B[latex]\flat[/latex], G, and E[latex]\flat[/latex], which spells a tonic triad in second inversion in the excerpt’s key. Why are we labeling this chord [latex]\mathrm{V}^6_4[/latex], then? Besides the fact that [latex]\mathrm{cad.}^6_4[/latex] arises from the combination of two embellishing tones (and therefore isn’t a standalone triad), here are two additional reasons to use the label [latex]\mathrm{V}^6_4[/latex] over I[latex]^6_4[/latex]:

  1. The chord appears after a strong predominant. If we label it [latex]\mathrm{I}^6_4[/latex], we’d be implying that a predominant goes to tonic, which is not the sound we hear, given that sol ([latex]\hat{5}[/latex]) is in the bass.
  2. [latex]\mathrm{V}^6_4[/latex] reflects the chord’s sound as an elaboration of V, whereas I[latex]^6_4[/latex] reflects the chord’s spelling only.[1]

Writing with cadential 6/4

Spelling cadential 6/4 in four voices

To spell [latex]\mathrm{cad.}^6_4[/latex], do the following (Example 2):

  1. Write sol ([latex]\hat{5}[/latex]) in the bass
  2. Determine what notes are a sixth and fourth above the bass. Choose one of those notes to place in the soprano. The other will go in an inner voice in step 3.
  3. Fill in the inner voices: one voice will double the bass, which is a necessity in [latex]\mathrm{cad.}^6_4[/latex] to avoid parallels. The other will take the unused note from step 2.

Example 2. Spelling [latex]cad.\mathit{^6_4}[/latex].

Voice leading with cadential 6/4

Resolution

Cadential [latex]^6_4[/latex] can resolve either to a V triad (Examples 3a, 3c) or a V7 chord (Examples 3b, 3d). The lines in the label [latex]^{6-5}_{4-3}[/latex] tell you how the [latex]\mathrm{cad.}^6_4[/latex] resolves, indicating “keep this motion in the same voice.” That is, whichever voice has a sixth above the bass should fall to a fifth above the bass, and whichever voice has the fourth above the bass should fall to a third above the bass.

Adding a seventh is just as straightforward: whatever voice is doubling the bass moves down a step to take the seventh of the chord. This motion is reflected by the figures 8-7 (the octave above the bass moves down to a seventh above the bass).

Example 3. Resolving [latex]cad.\mathit{^6_4}[/latex].

Approaching cadential 6/4

Since the [latex]\mathrm{cad.}^6_4[/latex] embellishes the dominant, any harmony that approaches V can also approach [latex]\mathrm{cad.}^6_4[/latex]. Most commonly, though, these are the strong predominants IV and ii6 (Example 4).

Two guidelines apply here:

  1. As always when dealing with the predominant area, watch out for parallel octaves between the predominant and [latex]\mathrm{cad.}^6_4[/latex].
  2. Motion into (and out of) the [latex]\mathrm{cad.}^6_4[/latex] is usually very smooth. Avoid leaping to a member of the [latex]\mathrm{cad.}^6_4[/latex]. While composers do occasionally leap to the sixth above the bass, it’s comparatively much rarer to leap to the fourth above the bass because it’s a dissonance, so that in particular should be avoided.

Example 4. Approaching [latex]cad.\mathit{^6_4}[/latex].

Assignments
  1. Strengthening Endings with Cadential [latex]^6_4[/latex] (.pdf, .docx, .mscz of score). Includes unfigured bass exercises and analysis.

  1. If you're not convinced by the sound of the chord argument, try playing the passage in Example 1, but stop on the [latex]\mathrm{cad.}^6_4[/latex]. Does it sound stable? Probably not. Tonic chords are associated with stability and a sense of “home,” while dominants are associated with a desire to resolve. The [latex]\mathrm{cad.}^6_4[/latex] surely sounds more unstable than stable.

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