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IV. Diatonic Harmony, Tonicization, and Modulation
Strengthening Endings with Cadential 6/4

### Core Idea

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

### Explanation

This chapter introduces the \mathrm{cadential}^6_4 (\mathrm{cad.}^6_4), an embellishment of the dominant that results from the combination of two embellishing tones a sixth and a fourth above the bass note sol (\hat{5}). We label the \mathrm{cad.\ }^6_4 and its resolution to V(7) as one unit: \mathrm{V}\begin{smallmatrix}(8-7)\\6-5\\4-3\end{smallmatrix}.

Any chord that normally approaches V can approach \mathrm{cad. }^6_4. Most commonly, this is one of the strong predominants.

When resolving \mathrm{cad.}^6_4, 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 theaddition 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 ^6_4 (\mathrm{cad.}^6_4).

The authentic cadence in Example 1 involves a V7 that has been embellished by \mathrm{cad.}^6_4. We use the word “embellished” intentionally here because the \mathrm{cad.}^6_4 comprises two embellishing tones that appear over sol (\hat{5}) 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 “\mathrm{cad.}^6_4.” Although the \mathrm{cad.}^6_4 often shows up at cadence points, it may show up anywhere in a phrase as an embellishment of V(7).

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

A note on ^6_4 chords.

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

Labeling cadential 6/4

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

The chord appears after a strong predominant. If we label it \mathrm{I}^6_4, we'd be implying that a predominant goes to tonic, which is not the sound we hear, given that sol (\hat{5}) is in the bass.

\mathrm{V}^6_4 reflects the chord’s sound as an elaboration of V, whereas I^6_4 reflects the chord’s spelling only.If you're not convinced by the sound of the chord argument, try playing the passage in Example 1, but stop on the \mathrm{cad.}^6_4. 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 \mathrm{cad.}^6_4 surely sounds more unstable than stable.

Writing with cadential 6/4

Spelling cadential 6/4 in four voices

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

Write sol (\hat{5}) 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 \mathrm{cad.}^6_4 to avoid parallels. The other will take the unused note from step 2.

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Example 2. Spelling cad.\mathit{^6_4}.

Voice leading with cadential 6/4

Resolution

Cadential ^6_4 can resolve either to a V triad (Examples 3a, 3c) or a V7 chord (Examples 3b, 3d). The lines in the label ^{6-5}_{4-3} tell you how the \mathrm{cad.}^6_4 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).

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Example 3. Resolving cad.\mathit{^6_4}.

Approaching cadential 6/4

Since the \mathrm{cad.}^6_4 embellishes the dominant, any harmony that approaches V can also approach \mathrm{cad.}^6_4. 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 \mathrm{cad.}^6_4.

Motion into (and out of) the \mathrm{cad.}^6_4 is usually very smooth. Avoid leaping to a member of the \mathrm{cad.}^6_4. 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 cad.\mathit{^6_4}.

Assignments

Strengthening Endings with Cadential ^6_4 (.pdf, .docx, .[mscz](https://v

### Key Quote

In Example 1, the embellishing tones are a passing tone and a suspension.

### Application Scenarios

The authentic cadence in Example 1 involves a V7 that has been embellished by \mathrm{cad.}^6_4. We use the word “embellished” intentionally here because the \mathrm{cad.}^6_4 comprises two embellishing tones that appear over sol (\hat{5}) 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 “\mathrm{cad.}^6_4.” Although the \mathrm{cad.}^6_4 often shows up at cadence points, it may show up anywhere in a phrase as an embellishment of V(7).

Example 1. cad.\mathit{^6_4} in Joseph Boulogne's String Quartet no. 4, I, mm. 45–47 ([1:26–1:30](https://open.spotify.com/track/1ULeiOZtuBKhTKiWYZtghD?si=c2d202263ec948bf)).

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

\mathrm{V}^6_4 reflects the chord’s sound as an elaboration of V, whereas I^6_4 reflects the chord’s spelling only.If you're not convinced by the sound of the chord argument, try playing the passage in[[B]] Example 1[[/B]], but stop on the \mathrm{cad.}^6_4. 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 \mathrm{cad.}^6_4 surely sounds more unstable than stable.

### Key Terminology

embellishing tones authentic cadence second inversion cadential 6/4 suspension dissonance authentic cadential cadence passing phrase tonic

### Related Links

Chapter Playlist addition of a seventh using a strong predominant 1:26–1:30 pdf docx mscz
Source: https://viva.pressbooks.pub/openmusictheory/chapter/cadential-64/
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