IV. Diatonic Harmony, Tonicization, and Modulation

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 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 . 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 through the fifth of the chord while the upper voices sustain the chord in some way. It may prolong any harmony, and we don’t typically bother recognizing it in analysis.

The table in Example 6 below 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 tonic (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 fourth). 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 (, , , or ) because the kind of [latex]^6_4[/latex] determines the label. For [latex]^6_4[/latex] chords, the Roman numeral by itself isn’t a sufficient label—the type also needs to be included.

Passing [latex]^6_4[/latex]

The is a [latex]^6_4[/latex] chord built on a 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 (e.g., [latex]\mathrm{IV^6-pass.^6_4-ii^6}[/latex]), not of different function (e.g., [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 pass[latex]^6_4[/latex]:

  1. Write the entire bass. 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 pass.[latex]\mathbf{^6_4}[/latex]. Just like with [latex]\mathrm{cad.^6_4}[/latex], to spell [latex]\mathrm{pass.^6_4}[/latex], determine what notes are a fourth and sixth above the bass. One voice will double the bass, just like in [latex]\mathrm{cad.^6_4}[/latex].
  3. Write the entire soprano. The soprano should be a line that moves by step, not the static line.
  4. Fill in inner voices, making them move as little as possible.

Example 2. Writing with pass.[latex]\mathit{^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 (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. 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 n.[latex]\mathbf{^6_4}[/latex]. 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 sixth and fourth above the middle bass note. One voice will double the bass.
  3. Write the entire soprano. For the soprano, choose either an upper-neighbor line 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 fifth of a chord while the upper voices sustain the chord. It’s commonly found in, for example, ending bass (Example 3) or waltz-style accompaniments (Example 5). Unlike the other types, [latex]\mathrm{arp.^6_4} typically doesn’t need to be labeled in analysis. Example 5 identifies it using figures, but it’s not necessary to do so—each measure could simply be labeled as I.

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

Summary: 6/4 chord types

The table in Example 6 summarizes the characteristics of the three [latex]^6_4[/latex] chord types that should be labeled in analysis. When you come across a [latex]^6_4[/latex] chord in analysis, remember to stop and ask yourself what type it is (passing, neighboring, or cadential) and label it appropriately.

[table id=45 /]

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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