Here's the next in a series of posts designed to help students in search of partwriting help. In this post, I will discuss the notorious second inversion chords, or 6/4 chords (to use the figured bass). 6/4 chords are an unusually difficult topic, I've found, and I hope this post will clarify their use.
First, it is important to know that 6/4 chords are extremely unstable, unlike root-position or first-inversion chords. You could begin and end a piece on a root position chord and the piece would sound complete. You could not begin and end a piece on a second-inversion chord (in the common practice era) and have it sound final and complete. This lack of closure is due to the origins of the 6/4 chords in a variety of embellishing (non-chord) tones.
There are four types of 6/4 chords in common usage, each with its roots in a particular embellishing tone. The first type of 6/4 chord, and probably the most common is the cadential 6/4 chord. The cadential 6/4 is so called because it occurs most commonly at cadences. The cadential 6/4 chord originated from suspensions, as shown in the example below.
**You may wish to right-click on the image and open it in a new window: it will be larger and you may be better able to toggle back and forth between the text and the example.
In the first two measures (labeled (1)), we have a perfect authentic cadence written in four voices. If we suspend the notes of the tonic triad over the dominant bass, we get the cadential 6/4. The E and the C are retained from the tonic chord in the first half of the measure and they reappear over the bass G in the second measure of (2). The E resolves down to D, and the C resolves down to B: D and B in combination with the G produce the dominant chord. Notice the doubled G in the second chord: you should always double the bass in a 6/4 chord.
Also, notice the figures I use under the G in the bass: I use a roman numeral V to indicate the dominant harmony. 6-5 and 4-3 both indicate linear motions (i.e., suspensions) over the bass note of the V chord. There is an important difference between this figuration and V 6/4, which (in the key of C major) could be interpreted as a G major chord with a D in the bass. The hyphens (6-5 and 4-3) are key in making this distinction.
At some point in history, other chords began to intervene between the initial tonic and the cadential 6/4. As a result, it lost some of its suspension-like qualities. (3) above shows a cadential 6/4 chord with a ii6 chord in between the initial tonic and the cadential 6/4. In (4) above, the cadential 6/4 resolves to a V7 chord: note the figuration which shows 8-7, 6-5, and 4-3.
The next type of commonly encountered 6/4 chord is the passing 6/4 chord. The passing 6/4 came about as a result of passing tones between a bass arpeggiation of a triad. The example below illustrates.
The first two measures feature a voice exchange that prolongs the tonic harmony. The voice exchange occurs between the soprano and the bass: the C in the bass in the first measure is transferred to the soprano in m. 2; the E in the soprano in m. 1 is transferred to the bass in m. 2. To smooth out the voice leading, we add a passing tone, D, in the bass (highlighted in yellow). To give the D a little more oomph, we can harmonize it with notes from the dominant triad, as shown in the last two measures. Notice that I didn't call this chord a V 6/4 for two reasons: first, I want to emphasize its embellishing role. It's nowhere near as structurally important as the two tonic chords on either side. Second, I want to avoid confusion with the cadential 6/4 figures given above.
The next kind of 6/4 chord is the neighboring 6/4 (also called the pedal 6/4). As you may have guessed, this 6/4 chord has origins in neighbor tones and pedal tones. The example below illustrates.
We call this the neighboring 6/4 chord because the alto and tenor voices go up by step in the second half of the first measure and return from the notes they came in the second measure. Here again, I didn't label the harmony as a IV 6/4: I used n 6/4 to show its weak stature and to emphasize its role in prolonging the tonic harmony. One could also notated the linear motions of the voices as I did in the second half of the example. This 6/4 chord is also called the pedal 6/4 chord because the bass does not change (much like a pedal tone).
The final type of 6/4 chord in common usage is the arpeggiated 6/4. The arpeggiated 6/4 occurs when the bass line is arpeggiating a triad.
In the first two measures, the bass line is arpeggiating a tonic triad (note that I used only one roman numeral to indicate that the fundamental harmony stays the same; only the inversions change). The arpeggiated 6/4 occurs when the fifth of the chord is in the bass (on the first half of m. 2). The second two measures illustrate perhaps the most common occurence of the arpeggiated 6/4 chord (especially if you're a bass player!): in oom-pah or boom-chick figures. In measure 1, the tonic harmony remains in force through the whole measure, and we get the fifth of the chord in the bass on the second half of the measure. In measure 2, we get the fifth of the chord in the bass on the downbeat of the measure, and dominant harmony fills the measure.
In summary:
First, it is important to know that 6/4 chords are extremely unstable, unlike root-position or first-inversion chords. You could begin and end a piece on a root position chord and the piece would sound complete. You could not begin and end a piece on a second-inversion chord (in the common practice era) and have it sound final and complete. This lack of closure is due to the origins of the 6/4 chords in a variety of embellishing (non-chord) tones.
There are four types of 6/4 chords in common usage, each with its roots in a particular embellishing tone. The first type of 6/4 chord, and probably the most common is the cadential 6/4 chord. The cadential 6/4 is so called because it occurs most commonly at cadences. The cadential 6/4 chord originated from suspensions, as shown in the example below.
**You may wish to right-click on the image and open it in a new window: it will be larger and you may be better able to toggle back and forth between the text and the example.
In the first two measures (labeled (1)), we have a perfect authentic cadence written in four voices. If we suspend the notes of the tonic triad over the dominant bass, we get the cadential 6/4. The E and the C are retained from the tonic chord in the first half of the measure and they reappear over the bass G in the second measure of (2). The E resolves down to D, and the C resolves down to B: D and B in combination with the G produce the dominant chord. Notice the doubled G in the second chord: you should always double the bass in a 6/4 chord.
Also, notice the figures I use under the G in the bass: I use a roman numeral V to indicate the dominant harmony. 6-5 and 4-3 both indicate linear motions (i.e., suspensions) over the bass note of the V chord. There is an important difference between this figuration and V 6/4, which (in the key of C major) could be interpreted as a G major chord with a D in the bass. The hyphens (6-5 and 4-3) are key in making this distinction.
At some point in history, other chords began to intervene between the initial tonic and the cadential 6/4. As a result, it lost some of its suspension-like qualities. (3) above shows a cadential 6/4 chord with a ii6 chord in between the initial tonic and the cadential 6/4. In (4) above, the cadential 6/4 resolves to a V7 chord: note the figuration which shows 8-7, 6-5, and 4-3.
The next type of commonly encountered 6/4 chord is the passing 6/4 chord. The passing 6/4 came about as a result of passing tones between a bass arpeggiation of a triad. The example below illustrates.
The first two measures feature a voice exchange that prolongs the tonic harmony. The voice exchange occurs between the soprano and the bass: the C in the bass in the first measure is transferred to the soprano in m. 2; the E in the soprano in m. 1 is transferred to the bass in m. 2. To smooth out the voice leading, we add a passing tone, D, in the bass (highlighted in yellow). To give the D a little more oomph, we can harmonize it with notes from the dominant triad, as shown in the last two measures. Notice that I didn't call this chord a V 6/4 for two reasons: first, I want to emphasize its embellishing role. It's nowhere near as structurally important as the two tonic chords on either side. Second, I want to avoid confusion with the cadential 6/4 figures given above.
The next kind of 6/4 chord is the neighboring 6/4 (also called the pedal 6/4). As you may have guessed, this 6/4 chord has origins in neighbor tones and pedal tones. The example below illustrates.
We call this the neighboring 6/4 chord because the alto and tenor voices go up by step in the second half of the first measure and return from the notes they came in the second measure. Here again, I didn't label the harmony as a IV 6/4: I used n 6/4 to show its weak stature and to emphasize its role in prolonging the tonic harmony. One could also notated the linear motions of the voices as I did in the second half of the example. This 6/4 chord is also called the pedal 6/4 chord because the bass does not change (much like a pedal tone).
The final type of 6/4 chord in common usage is the arpeggiated 6/4. The arpeggiated 6/4 occurs when the bass line is arpeggiating a triad.
In the first two measures, the bass line is arpeggiating a tonic triad (note that I used only one roman numeral to indicate that the fundamental harmony stays the same; only the inversions change). The arpeggiated 6/4 occurs when the fifth of the chord is in the bass (on the first half of m. 2). The second two measures illustrate perhaps the most common occurence of the arpeggiated 6/4 chord (especially if you're a bass player!): in oom-pah or boom-chick figures. In measure 1, the tonic harmony remains in force through the whole measure, and we get the fifth of the chord in the bass on the second half of the measure. In measure 2, we get the fifth of the chord in the bass on the downbeat of the measure, and dominant harmony fills the measure.
In summary:
There are four kinds of 6/4 chords: cadential, passing, neighboring, and arpeggiated.
All 6/4 chords are substantially less stable than root-position or first-inversion triads. (In fact, some would argue that they're not chords at all but rather amalgamations of embellishing tones.)
The cadential 6/4 always occurs in a metrically strong position. The passing and neighboring 6/4 chords virtually always occur in weak metrical positions. The arpeggiated chord can occur in strong or weak metrical positions.
Always double the fifth of the chord in 6/4 chords. The fifth of the chord is equivalent to the bass note in all cases.