Inversions of V7 usually function as linear chords. These chords usually appear as complete chords, and resolve to complete tonic triads. The leading tone always resolves to tonic when appearing in an inverted V7.

The V6/5 has the leading tone in the bass (like a V6), and must resolve to a root position tonic triad. It often functions as a neighbor chord between two root position tonic triads, or as an incomplete neighbor with the bass leaping down into the V6/5 and resolving to the tonic triad in root position.

The V4/3 has scale degree two in the bass (like  a V6/4). It connects root position tonic and first inversion tonic triads, moving in either direction.

The V4/2 has the chordal seventh in the bass (the fourth scale degree). Since inversions of V7 resolve to tonic, and the chordal seventh always resolves down by step, V4/2 must resolve to I6 (or i6). It often occurs as a passing chord, following a V (triad) with the bass moving down by step creating a V4/2. It can occur as a neighbor chord between two I6 chords; it can also follow a IV or ii6, with the bass note holding as a common tone between the two chords.

I’ve posted on root-position dominant seventh chords before.

For our purposes, you don’t need to worry about the motion into and out of the chordal seventh for now.

I’ll add a posting to talk about dominant seventh chords in inversions (linear dominants).

Quick notes on using the mediant harmony (iii/III) and leading tone harmony (vii° in major and minor).

Mediant

Our main use of the mediant harmony will be to harmonize descending 1 – 7 – 6 soprano lines, where the LT does not resolve back to tonic. You can use iii/III to harmonize scale degree 7. The mediant harmony usually leads to IV/iv (ascending 2nd) or vi (descending 5th). Keep in mind that in minor, 7 will not be raised if III is used.

Leading Tone

The leading tone triad can be used a dominant substitute, but for now we’ll concentrate on using it as a passing chord in a tonic prolongation capacity.

Since vii° is a diminished triad, we will only use it in first inversion (to deemphasize the dissonant interval of the °5/+4 by putting it in upper voices – not combined with the bass). Since the root and fifth form a dissonant interval that wants to resolve, you do not double either chord tone. Always double the third (bass).

With the bass on the second scale degree, and the tonic prolongation function of the chord, you’ll find the LT triad happening with a 1 – 2 – 3 or 3 – 2 – 1 scale degree progression in the bass. The progression will be I – vii°6 – I6 (i – vii°6 – i6), or the reverse, I6 – vii°6 – I.

There are two ways to handle voice leading out of the LT triad. You can resolve the dissonant interval (°5/+4), or you can move in unequal 4ths/5ths. If you resolve the dissonant interval, the °5 will resolve in to a 3rd. The +4 will resolve out to a 6th. Resolving the °5/+4 will result in a tonic chord with doubled root and doubled third, and a missing fifth. If you move in unequal 4ths/5ths, the resulting triad will be complete. You must always move in contrary motion from the doubled third (scale degree 2) in the LT triad, to scale degrees 1 and 3.

Yes, this is a one-chord-only post.

The submediant (vi, VI) chord has three usages: as a tonic prolongation, as a deceptive resolution, and as a predominant chord.

The submediant as tonic prolongation

The submediant can be used after a tonic chord as part of a common falling 3rd progression. It almost always leads to a subdominant class chord.

RN:     I – vi – ii6 – V – I
Class: T – T – S  -  D – T

RN:     I – vi – IV – I (or I6)
Class: T – T – S  -  T

For both progressions, tonic is prolonged by the following of the submediant triad (through the shared chord tones of 1 and 3). For the second progression, the entire four-chord sequence can be analyzed as a tonic prolongation.

The submediant as substitution for tonic (deceptive resolution)

When vi follows V or V7 instead of I, the listener hears the “substitution” of the vi as a deceptive resolution. Some important things should be kept in mind.

• If the resolution happens at a cadence, we call the progression a Deceptive Cadence (DC). We only call it a deceptive cadence if it happens at a cadence.
• If it occurs anywhere else in the phrase, we call it a deceptive resolution, or deceptive progression.

V to vi almost always occurs in root position, and this is how we’ll handle it in our part-writing examples. Since the progression is an ascending second root movement, the general advice of upper voices moving in contrary motion to the bass is followed except for one important caveat: You must resolve the leading tone to tonic. Move the other two voices in contrary motion to the nearest chord tones, which will result in a doubled third (scale degree 1) of the submediant chord.

The submediant as a predominant chord

vi can move directly to V, functioning as a predominant chord. This type of function happens much more rarely than the above two functions, as it is a descending second progression. We see this type of movement more in the Romantic period. When you part-write this progression, you have to be careful not to write objectionable parallels, or end up with a doubled leading tone in the dominant harmony.

The cadential 6/4 chord occurs as part of a two-chord progression of I6/4 – V (minor, i6/4). This two-chord progression happens at ends of phrases, and offers a melodic cadence (descending step-wise motion to 2 and/or 1), and occurs as part of a dominant harmony ending in either a half cadence or carrying on to resolution on tonic and an authentic cadence.

Some important things to keep in mind:

• The cadential 6/4 is not a tonic-functioning harmony, which is why we avoid labeling it with a RN of I (i). It really is part of a dominant function (the entire two-chord progression is D-Class).
• The cadential 6/4 always occurs on a strong beat (metrically).
• In four-voice partwriting, the bass of the 6/4 chord (scale degree 5) is always doubled. The other chord tones (scale degrees 3 and 1) are tendency tones.
• The tendency tones of a cadential 6/4 chord always resolve down by step from 3 – 2, and from 1 – LT.
• Both parts of the two-chord progression (C6/4 to V) have scale degree 5 in the bass.
• The cadential 6/4 to dominant progression functions the same way that a root position V chord would. The C6/4 progression never occurs as part of a tonic prolongation.

Uses and Function

Triads in first inversion provide the following uses and function:

• They expand the number of possible bass pitches, thereby providing the opportunity for melodic bass lines.
• They allow for greater hierarchy of function by avoiding root position V – I movement away from cadences.
• They provide more prolongation opportunities through root to first inversion movement (and vice versa).

Prolongation and Voice Exchange

Moving from root position to first inversion (and vice versa) are often accompanied by a voice exchange between the soprano and bass lines. In a voice exchange of this sort, the inner voices remain unchanged. The soprano moves to the chord tone that the bass previously had, and the bass moves to the chord tone the soprano previously had.

If you start with a root position triad, say a tonic chord, place the third in the soprano. The root will be in the bass. Moving to a first inversion triad of the same type, the bass will move from the root to the third of the chord. The soprano can then move down from the third to the root of the chord.

Prolongation and the V6

Using a V6 between two tonic triads provides another possible tonic prolongation progression. Instead of labeling the movement according to the soprano motion, we refer to the lower neighbor motion in the bass line (scale degrees 1 – 7 – 1).

Parallel First Inversion Triads

First inversion triads in close position do not have a perfect fifth. This property allows for composers to string together parallel first inversion triads by stepwise movement, usually as part of a transitional passage. When first inversion triads move in parallel motion we do not label them with Roman numerals, because they do not have a harmonic function based on their root. We use the figured bass indication of 6 under each chord, ending with a 5 and the Roman numeral. In other words, we label the harmony of the chord before the parallel first inversion triads, and the chord after the last first inversion triad, but nothing in between.

In four voices you will have parallel octaves in this type of progression. You need to use an alternate doubling technique, where you alternate between doubling the root of one chord, then the third of the next, alternating until the progression of parallel chords has ended.

To harmonize a melody, follow the steps below.

1. Analyze the melody
   1. determine the key
   2. label the scale degrees of the melody
2. Pick Harmonies
   1. It is very helpful to write out all the possible harmonies for each melody note (following the given harmonic rhythm)
   2. Remember that once you pick a harmony, it affects future possible choices, much like species counterpoint.
   3. Try to think in groups of harmonies by function. Write out the cadence first. Look to start with a tonic prolongation pattern. Look for possible voice exchanges between the soprano and bass parts.
3. Write the bass line, choosing between root position and first inversion triads (if you haven’t already) to create an interesting melodic contour.
4. Check for objectionable parallels between the given soprano and your composed bass line. Fix if needed.

These rules apply for major and minor first inversion triads.

(1) Double the root or the fifth, preferably, of a first inversion triad. Only double the third if it provides the best possible voice leading.

(2) Don’t double the bass of a V6 chord, ever. The bass of V6 is the LT. Leading tones in the bass are always resolved.

(3) A change of position from V to V6 requires that the LT in the upper voice for the root position V change to a new chord tone. This change avoids doubling the LT. The upper voice change is usually from scale degree 7 to 2, so that the original LT can still resolve to 1. You want to resolve the original LT, as well as the new LT in the bass.

(4) When moving from root position to first inversion, or vice versa, the best voice leading is a voice exchange. (The bass and the soprano swap chord tones.)

(5) When a voice exchange is not possible, one voice must remain static.

(6) To avoid parallel octaves between root position and first inversion chords of different harmonies, approach and leave the doubled chord tone by oblique or contrary motion.

(7) Chordal figuration (chordal skips or changes of position) can be used to avoid parallel fifths and octaves.