IV. Diatonic Harmony, Tonicization, and Modulation

6/4 chords as forms of prolongation

John Peterson

Key Takeaways

This chapter introduces three additional [latex]^6_4[/latex] chords beyond cadential [latex]^6_4[/latex].

  • Passing (pass.) [latex]^6_4[/latex] involves a passing tone in the bass that has been harmonized by a [latex]^6_4[/latex] chord. It typically prolongs tonic or predominant harmonies, and it always occurs between two chords of the same function.
  • Neighbor (n.) [latex]^6_4[/latex] involves a static bass above which two of the upper voices perform upper neighbor motion. It typically prolongs tonic or dominant harmonies, and the chords on both sides of it are always in root position.
  • Arpeggiating (arp.) [latex]^6_4[/latex] involves a bass that arpeggiates through the fifth of the chord while the upper voices somehow sustain the chord. It may prolong any harmony, and we don’t typically bother recognizing it in analysis.

The table in Example 6 summarizes the characteristics of each of the three types of [latex]^6_4[/latex] that we advocate labeling in analysis.

Chapter Playlist

So far we’ve seen that the T area is most commonly prolonged using dominant-function chords, especially inverted [latex]\mathrm{V^7}[/latex]s. In this chapter we look at some additional, less common ways to prolong not only tonic chords, but also dominant and predominant chords. Earlier, we saw how [latex]^6_4[/latex] chords are treated in special ways because they contain a dissonance with the bass (the 4th). We’ve already learned about [latex]\mathrm{cad.^6_4}[/latex]. Here, we turn to the three other ways [latex]^6_4[/latex] chords can be used: passing [latex]^6_4[/latex], neighboring [latex]^6_4[/latex], and arpeggiating [latex]^6_4[/latex]. Note that in analysis whenever you encounter a [latex]^6_4[/latex] chord, you should stop and identify which kind it is (cadential, passing, neighboring, or arpeggiating) because the kind of [latex]^6_4[/latex] determines the label. Please don’t just throw down a Roman numeral and move on—make sure you label [latex]^6_4[/latex] chords according to their type.

Passing [latex]^6_4[/latex]

The is a [latex]^6_4[/latex] chord built on a passing tone in the bass (Example 1). It’s most commonly found prolonging tonic or predominant harmonies. Importantly, the chords on both sides of the [latex]\mathrm{pass.^6_4}[/latex] are always the same function. For example: [latex]\mathrm{IV^6-pass.^6_4-ii^6}[/latex]. They are not of different function: [latex]\mathrm{IV^6-pass.^6_4-I}[/latex].

Example 1. [latex]\mathrm{pass.^6_4}[/latex] in Beethoven, Piano Sonata Op. 14, No. 1, I, mm. 50–57 (1:28-1:42).

Example 2a demonstrates the steps for writing [latex]\mathrm{pass.^6_4}[/latex] to expand tonic, and Examples 2b and 2c show several ways [latex]\mathrm{pass.^6_4}[/latex] can prolong the predominant area. Note that each of these progressions can also work backward (e.g. [latex]\mathrm{I^6-pass.^6_4-I}[/latex] also works).

To write with [latex]\mathrm{pass.^6_4}[/latex]:

  1. Write the entire bass.
    1. You should have three notes in stepwise motion where the first and last notes belong to the same functional area (T or PD). The middle note will be your passing tone.
  2. Spell the [latex]\mathrm{pass.^6_4}[/latex].
    1. Just like with [latex]\mathrm{cad.^6_4}[/latex], to spell [latex]\mathrm{pass.^6_4}[/latex] determine what notes are a 4th and 6th above the bass.
    2. One voice will double the bass, just like in [latex]\mathrm{cad.^6_4}[/latex].
  3. Write the entire soprano.
    1. Choose a line that moves by step. Don’t choose the static line.
  4. Fill in inner voices making they move as little as possible.

Example 2. Writing with [latex]\mathit{pass.^6_4}[/latex].

Neighbor [latex]^6_4[/latex]

The neighbor (n.) [latex]^6_4[/latex] consists of a static bass over top of which two voices have upper-neighbor motion (Example 3). Sometimes [latex]\mathrm{n.^6_4}[/latex] is called pedal [latex]^6_4[/latex], a name that reflects the static pedal in the bass. It’s most commonly found prolonging I or V. Example 4a demonstrates the steps for writing [latex]\mathrm{n.^6_4}[/latex] to prolong tonic, and Example 4b shows the voice leading to prolong V.

Example 3. Neighbor and Arpeggiating [latex]\mathit{^6_4}[/latex] in Josephine Lang, “Dem Königs-Sohn.”

To write with [latex]\mathrm{n.^6_4}[/latex]:

  1. Write the entire bass.
    1. The bass will be three of the same note, typically dododo or solsolsol ([latex]\hat1-\hat1-\hat1[/latex] or [latex]\hat5-\hat5-\hat5[/latex])
  2. Spell [latex]\mathrm{n.^6_4}[/latex].
    1. The [latex]\mathrm{n.^6_4}[/latex] will be over the middle bass note. As with [latex]\mathrm{cad.}[/latex] and [latex]\mathrm{pass.^6_4}[/latex], determine a 6th and 4th above the middle bass note.
    2. One voice will double the bass.
  3. Write the entire soprano.
    1. Choose either to put one of the upper-neighbor lines in the soprano or the static line. Unlike with [latex]\mathrm{cad.}[/latex] or [latex]\mathrm{pass.^6_4}[/latex], [latex]\mathrm{n.^6_4}[/latex] will more frequently have a static line in the soprano.
  4. Fill in the inner voices making them move as little as possible.

Example 4. Writing with [latex]\mathit{n.^6_4}[/latex].

Arpeggiating [latex]^6_4[/latex]

Arpeggiating (arp.) [latex]^6_4[/latex] is typically created when the bass leaps to the 5th of a chord while the upper voices sustained the chord. It’s commonly found in, for example, ending bass arpeggiations (Example 3) or waltz-style accompaniments (Example 5). It’s not typically worthwhile to recognize it with an analytical symbol in analysis (often that just clutters the page). If you wish to do so, we recommend using figures to identify it as in Example 5, but we don’t typically advocate doing so.

Example 5. Arpeggiating [latex]\mathit{^6_4}[/latex] in Sophie de Auguste Weyrauch, Six Danses No. 3.

Summary: [latex]^6_4[/latex] chord types

Characteristics of the three [latex]^6_4[/latex] chord types that we advocate labeling in analysis are summarized in the table in Example 6. It’s worth emphasizing one more time that when you come across a [latex]^6_4[/latex] chord in analysis, stop and ask yourself: is it passing, neighboring, or cadential, and label it appropriately. The table in Example 6 can help you differentiate between these three types.

[latex]\begin{smallmatrix}6\\4\end{smallmatrix}[/latex] Chord Label Characteristics
Passing [latex]\begin{smallmatrix}6\\4\end{smallmatrix}[/latex] - PT in bass
- Outer chords are same function
Neighboring X[latex]\begin{smallmatrix}5--6--5\\3--4--3\end{smallmatrix}[/latex] - Static bass
- Upper neighbor motion in two upper voices
- Outer chords are the same
Cadential V[latex]\begin{smallmatrix}(8--7)\\6--5\\4--3\end{smallmatrix}[/latex] - Sol ([latex]\hat{5}[/latex]) in bass
- [latex]\begin{smallmatrix}6\\4\end{smallmatrix}[/latex] on stronger beat

Example 6. Summary of [latex]\mathit{^6_4}[/latex] chord types.

Assignments
  1. [latex]^6_4[/latex] chords as forms of prolongation (.pdf, .docx). Asks students to review previous concepts, write from Roman numerals, write from figures, and analyze excerpts.

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