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 sustain the chord in some way. It may prolong any harmony, and we don’t typically bother recognizing it in analysis.
The table in below summarizes the characteristics of each of the three types of [latex]^6_4[/latex] that we advocate labeling in analysis.
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 (cadential, passing, neighboring, or arpeggiating) 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 passing (pass.) [latex]^6_4[/latex] is a [latex]^6_4[/latex] chord built on a passing tone in the bass ( ). 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]).
demonstrates the steps for writing [latex]\mathrm{pass.^6_4}[/latex] to expand tonic, and and 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]:
- 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.
- 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].
- Write the entire soprano. The soprano should be a line that moves by step, not the static line.
- Fill in inner voices, making them move as little as possible.
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 ( ). 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. demonstrates the steps for writing [latex]\mathrm{n.^6_4}[/latex] to prolong tonic, and shows the voice leading to prolong V.
To write with [latex]\mathrm{n.^6_4}[/latex]:
- Write the entire bass. The bass will be three of the same note, typically do–do–do or sol–sol–sol ([latex]\hat1-\hat1-\hat1[/latex] or [latex]\hat5-\hat5-\hat5[/latex])
- 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.
- 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.
- Fill in the inner voices, making them move as little as possible.
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 arpeggiations ( ) or waltz-style accompaniments ( ). Unlike the other types, [latex]\mathrm{arp.^6_4}[/latex] typically doesn’t need to be labeled in analysis. identifies it using figures, but it’s not necessary to do so—each measure could simply be labeled as I.
Summary: 6/4 chord types
The table in
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.
| 6/4 chord | Label | Characteristics |
|---|---|---|
| Passing | [latex]\mathrm{pass.^6_4}[/latex] |
|
| Neighboring | [latex]x^{5-6-5}_{3-4-3}[/latex] |
|
| Cadential | [latex]\mathrm{V}\begin{smallmatrix}(8-7)\\6-5\\4-3\end{smallmatrix}[/latex] |
|
- [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.
A type of motion where a chord tone moves by step to another tone, then resolves by step in the same direction. For example, C–D–E above a C major chord would be an example of neighboring motion, in which D can be described as a passing tone. Entire harmonies may be said to be passing when embellishing another harmony, when the voice-leading between the two chords involves mainly passing tones (as in the passing 6/4 chord).
A type of motion where a chord tone moves by step to another tone, then moves back to the original chord tone. For example, C–D–C above a C major chord would be an example of neighboring motion, in which D can be described as a neighbor tone. Entire harmonies may be said to be neighboring when embellishing another harmony, when the voice-leading between the two chords involves only neighboring and common-tone motion (as in the common-tone diminished seventh chord).
A melodic, "horizontal" statement of a triadic harmony; in other words, each note of a triadic harmony played in succession (rather than simultaneously). Also referred to as a "broken chord."
A common embellishment of the cadential V chord, in which the fifth of the V chord (re, 2̂) is replaced with the sixth (mi/me, 3̂) and the third (ti, 7̂) is replaced with the fourth (do, 1̂). The sixth and fourth form a 6/4 chord, hence its label. The cadential 6/4 resembles a I6/4 in its pitch content.
A 6/4 chord built on a passing tone in the bass, most commonly found prolonging tonic or predominant harmonies. Importantly, the chords on both sides of the passing 6/4 are always the same function.
A kind of 6/4 chord that embellishes a harmony with neighbor motion. This is usually labeled with figures, e.g., with 5-6-5 in one voice and 3-4-3 in another.
A 6/4 chord that results from an arpeggiated bass line (e.g., if the bass line alternates between the root and fifth of the same chord).