node your exam review
First, the standard disclaimer for music theory discussions of this type. There are certain conventions which composers of Western art music followed during the period approximately from 1500 - 1850; this node is about one of those conventions. While 20th century classical music and popular music for the most part ignore many of the traditional conventions, they still come in handy quite often. There's a reason that these conventions ruled for so long, and if you're going to throw them out the window you better have a darn good reason. Now on to the good stuff...
Chords in second inversion, also known as 6-4 chords
You might want to review chord inversion at this point, if you're not clear on the basics. But, by means of introduction, a 6-4 chord is a chord made by stacking the notes an interval of a fourth above the bass and a sixth above the bass. The root of the chord is located a fourth above the bass. In real life, the symbol for these chords looks like (for example) I64, except without the 6 and the 4 aligned vertically with each other. I'm going to use 6-4 as a shorthand for this, since its more html friendly.
Traditionally, composers and theorists have considered chords (we're talking about just plain vanilla chords, no 7ths or notes outside of the key) in second inversion to be more dissonant than chords in first inversion or root position. The reason for this goes back to the rules of two-part counterpoint, in which intervals of a fourth are considered dissonant (which makes sense, as in terms of distance above root, the fourth is one of the last intervals to appear in the harmonic series of a note). In a 6-4 chord, the arguably most prominent interval (the interval which contains the root of the chord and the bass note) is a fourth. The dissonance of this prominent interval gives the entire chord a dissonant sound.
Additionally, in two-voice counterpoint, dissonant intervals of a fourth were often suspended over the bass, then resolved down by stepwise motion to a third. The notes in a 6-4 chord are similarly suspended in a clump above the bass note, which gives the chord it a top-heavy, unstable sound: go to a keyboard, play D G B (at the same time), and odds are you'll want to hear it resolving to D F# A -- notice that the motion of the G in that sequence is the same as a four-to-three suspension in two voice counterpoint.
Since 6-4 chords are so dissonant and unstable (and yes, plenty of that dissonant, unstable sound comes from the fact that for centuries composers have treated them as dissonant, unstable chords) they should be used sparingly, and have traditionally been used in only a few very specific situations. In most, if not all of these situations, 6-4 chords are analyzed as embellishments of the chords around them, not as chords which have harmonic function in their own right. Because of their instability, 6-4 chords don't usually stand harmonically on their own, rather only as part of a sequence, so it doesn't make sense to notate their harmonic function except as part of a sequence. I'm going to discuss these situations in terms of four-part harmony, because that's easiest, but they make sense in other contexts as well.
1. The Neighboring 6-4 (or pedal 6-4)
A neighboring 6-4 chord occurs when the bass repeats the same note, while the upper voices move (usually by stepwise motion) to a 6-4 chord and back down to the original chord, like so (in C):
Soprano: C C C
Alto: G A G
Tenor: E F E
Bass: C C C
I N6-4 I
(Because the bass note holds on the root of the first chord, and because the 6-4 chord resolves back down to the first chord, the neighboring 6-4 chord is treated as an expansion of the harmonic function of the chord which precedes and follows it.)
2. The Passing 6-4
A passing 6-4 chord occurs in the course of stepwise motion in the bass. Passing six four chords are often used to expand tonic, like this:
C B C
G G G
E D E
C D E
I P6-4 I6
3. Bass Motion and the 6-4 chord
Occasionally, while the other voices stay on the notes of some chord, the bass will arpeggiate the notes of the triad. During the course of this arpeggiation, of course, the chord is going to go through all its possible inversions, one of which is second inversion. Still, the entire passage is analyzed as a single chord, regardless of the motion of the bass.
Other times, when the bass holds the melodic line of the piece, 6-4 chords will occur as the other voices harmonize the bass melody. In this case, since the bass is no longer forming the harmonic foundation of the piece, the chords are not analyzed as necessarily being in the inversion which the bass implies (unless there is other reason to do so).
4. The Cadential 6-4
This is the most common use of the 6-4 chord, and if you listen to any kind of music for a little while you're almost sure to hear a cadential 6-4 chord or two. To explain the cadential 6-4 chord, we need to go back to the top-heavyness of the 6-4 chord which I discussed earlier. The upper voices in a 6-4 chord seem to hang rather uneasily over the bass. Were they to both move down in stepwise motion, keeping the same bass note, the resulting triad would be a stable root position chord. This upper voice motion provides a feeling of tension, and thus is often used to enhance the final cadences of a piece. What happens, basically, looks like this (in C):
E - D C
C - B G
G E
G C
V 6 - 5 I
4 - 3
The cadential 6-4 chord is approached in the same way as a V chord at a cadence point would be, and it is analyzed as a V chord with scale degrees 6 and 4 above the bass suspended. A cadential 6-4 chord must follow this suspended motion, scale degrees 6 and 4 above the bass must move down by step to their resolution. If the V chord in a cadential 6-4 is a seventh chord, then it is analyzed like this (in C):
E - D C
C - B G
G - F E
G C
V 8 - 7 I
6 - 5
4 - 3
The duration of the 6-4 suspended chord and its resolution is also important: as with any suspension in two-voice counterpoint, the 6-4 chord must come on a metrically strong beat, and its resolution on a metrically weak beat. Frequently, the 6-4 chord and its resolution together have the same rhythmic value as any other single chord in the piece does, and if this rhythmic value isn't equally divided between the two chords, the majority of the time goes to the 6-4 chord (one never sees a 6-4 chord which resolves quickly down, then holds on the V chord for a while). In fact, composers will frequently hit the cadential 6-4 chord and then go on for great lengths embellishing on it and building tension before resolving down to V.
Sources:
Kostka, Stephen and Payne, Dorothy.
Tonal Harmony. McGraw-Hill, 2000. p. 144-153
Personal notes, Music 31 class at
University of North Carolina at Chapel Hill, taught by Dr. Jocelyn Neal