Warning: if you are a die hard rhythm strummer, this post is probably not for you…

I have already mentioned chord inversions in several posts, but I never really discussed their actual usage.

In general, chord inversions are used to create more interesting and dynamic bass lines. If you are playing in a band, this is of course the responsibility of the bass player, but in a standalone arrangement, it is your responsibility.

Suppose we have the following chord progression:
|C – – – |Cmaj7 – – – |Am – – – |Am7 – – – |D7 – – – |G7 – – – | …

If you only use root position chords, the bass line will be
|c – – – |c – – – |a – – – |a – – – |d – – – |g – – – |
This isn’t wrong of course, but it’s a tad repetitive; also, the bass jumps around by large intervals. Again, this isn’t wrong in any way, but not very interesting.
We would like to tame that bass line and have it make a nice melody on its own, complementing the melody in the top voice.

Using inversions, we can write something like this:
|C – – – |Cmaj7/B – – – |Am – – – |Am7/G – – – |D7/F# – – – |G7 – – – | …
The bass line now goes:
|c – – – |b – – – |a – – – |g – – – |f# – – – |g – – – |
This is a nice melodic line on its own and it makes the chord transitions much smoother. If you spice it up with some voice leading, you get something really nice.

So, let’s look at the “rules” to best use chord inversions.

First inversions
First inversions can be used quite liberally; there are very few “rules” about them. Basically, you can use a first inversion in place of a root position chord anywhere you want.

The fact is, some chords should always be played in first inversion! The diminished triad is the typical example. It sounds much better that way. In root position the b5 interval between the root and the top voice is inelegant and very unstable (e.g. B° = (B D F)). In first inversion (D F B) the chord is more stable while still retaining a #4 between the two topmost voices.

Second inversions
Second inversions are a bit more touchy and need to be handled with some care.
The primary reason is that triads in second inversion are less stable than their root position and first inversion counterparts.
Let’s take the C triad. In root position we have (C E G) and in first inversion we have (E G C).
In both cases the bass is a stable scale degree.
But in second inversion we have (G C E): the bass is a rather unstable scale degree (the dominant), and additionally the chord contains a dissonant interval of a 4th between the bass and the second chord tone. For that reason second inversions are often called 6/4 chords: the intervals are (B 4 6).

A first “rule” regarding second inversions is that, if you double any chord tone, it’s got to be the bass. Doubling any other chord tone makes the chord brittle (try it and judge by yourself!).
But more importantly, there is also a limited number of situations where second inversions sound good; let’s review them quickly.

1. Passing 6/4 chords
Second inversions are often used as passing chords between a root position chord and its first inversion. For example: C – G/D – C/E. As you can see, in this case the bass line goes c – d – e, which is quite dynamic. That G/D is a passing chord: it doesn’t have any functional purpose.
(Needless to say, if you want to end the song with a perfect cadence, then C – G – C is the way to go!)

2. Pedal 6/4 chords
You will certainly recognize this one immediately: A – D/A – A.
This happens all the time in gospel, pop, etc.
Again, that D/A chord is only there to prolong and reinforce the tonic chord, while bringing some variety.

3. Cadential 6/4
This is a very frequent usage of the second inversion.
Instead of the traditional Dm – G – C (ii – V – I), we can play Dm/F – C/G – G – C. The C/G in this case is called a cadential 6/4 chord because it is part of the V – I cadence and makes the V stronger. For this to work, that C/G chord needs to be placed on a strong beat in the bar, so we will have: |Dm/F – C/G G |C – – – |.
Note how the first inversion Dm/F nicely leads to the cadence: the bass goes f – g – g – c.

In most other situations, second inversions are awkward and should be avoided.
But as always, the ultimate judge is your ear!

Fuller chords
Seventh chords (maj7, m7, dom7, …) can of course also be inverted. For example G7 (G B D F) has the following inversions:
Root position: (G B D F)
G7/B (B D F G)
G7/D (D F G B)
G7/F (F G B D)
If you play them, you will notice that these inversions become increasingly unstable.

Contrary to triads, there are no specific “rules” regarding these chords. This is because these chords are inherently dissonant. So the only “requirement” is to properly handle the dissonance, i.e. prepare it and resolve it..
For example, let’s take the Dm7 (D F A C) chord in C major. This chord obviously contains a dissonant b7 interval between the bass and the top voice. No matter what inversion you use, that C note will be the most active chord tone. So here is how we deal with it:
a) sound the dissonance as a consonant chord tone in a preparation chord
b) hold the chord tone as you transition to the Dm7 chord, moving the other chord tones appropriately
c) resolve the dissonant chord into the target chord

For example, we can prepare the Dm7 chord by playing an Am (A C E) chord first; this is because Am contains a (consonant) C note, which will become dissonant in the Dm7 chord. So we have Am -> Dm7 where the C note is held as a common tone (see voice leading).
In the C major scale, the dissonant C note is much more actively attracted by B than by D, so the resolution chord should contain B; the G chord is a logical choice.
So finally we have Am -> Dm7 -> G. Looks familiar? Well, now you know why! This chord sequence successively prepares a dissonance and resolves it, and this is why it sounds so good.

Of course, as usually, there are plenty of other possible choices.
It’s up to your ear to decide which solution sounds best.
Have fun!