IV. Diatonic Harmony, Tonicization, and Modulation

Strengthening Endings with Cadential 6/4

John Peterson

Key Takeaways

  • This chapter introduces the [latex]\mathrm{cad.}^6_4[/latex], an embellishment of the dominant that results from the combination of two embellishing tones a 6th and a 4th 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 6th above the bass falls to a 5th above the bass and the 4th above the bass falls to a 3rd 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 7th. 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 dominant’s desire for resolution: [latex]\mathrm{cadential}^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] is comprised of 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 6th and a 4th above the bass, and their appearance often intensifies our desire for 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 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 4th) with the bass. Composers therefore treat [latex]^6_4[/latex] chords in four special ways. 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 it isn’t a standalone triad), here are two additional reasons we favor 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 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. Since music is an auditory art, we prefer the label that expresses how the chord sounds.[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 6th and 4th 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


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]\begin{smallmatrix}6-5\\4-3\end{smallmatrix}[/latex] tell you how the [latex]\mathrm{cad.}^6_4[/latex] resolves. Those lines mean “keep this motion in the same voice.” That is, whichever voice has a 6th above the bass should fall to a 5th above the bass, and whichever voice has the 4th above the bass should fall to a 3rd above the bass.

Adding a 7th is easy, too! Whatever voice is doubling the bass moves down a step to take the 7th of the chord. This motion is reflected by the figures 8-7 (the octave above the bass moves down to a 7th 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 6th above the bass, it’s comparatively much rarer to leap to the 4th above the bass because it’s a dissonance. So especially avoid that.

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

  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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