IV. Diatonic Harmony, Tonicization, and Modulation
Strengthening Endings with Cadential 6/4
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.
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 half cadences and authentic cadences 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]:
- 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.
- [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):
- Write sol ([latex]\hat{5}[/latex]) in the bass
- 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.
- 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:
- As always when dealing with the predominant area, watch out for parallel octaves between the predominant and [latex]\mathrm{cad.}^6_4[/latex].
- 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].
- Strengthening Endings with Cadential [latex]^6_4[/latex] (.pdf, .docx, .mscz of score). Includes unfigured bass exercises and analysis.
- 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. ↵
A kind of inconclusive cadence that occurs when a phrase ends on V. Occasionally, particularly in Romantic music, the final chord of a half cadence will be V⁷.
A cadence with the harmonies V–I. The harmonies are typically in root position. Authentic cadences can be further distinguished by their melody note in the I chord: an authentic cadence ending on 1̂ in the melody is a perfect authentic cadence, while one with 3̂ or 5̂ in the melody is an imperfect authentic cadence.
