Week 6

Inverting a chord simply means changing the order of the notes so that a note other than the root of the chord is in the bass.
It's important not to confuse root and bass. The root is the note on which the chord is built, while the bass is the bottom note of the chord—even if it is not the root.
For example, in a C major chord, C is the root, whether or not it is the bass note. As you probably know by this point in your piano studies, the notes of a C major triad are C, E and G, in that order.
Here is a C major triad with the root, C, in the bass:
This chord is in root position.
If we move the C up so that the next note of the chord, E, is on the bottom:
... we get a C major triad in first inversion. Note that the notes of the chord are still C, E and G, so this chord must be a C major chord even if C isn't the bass note.
If we now invert the chord a second time, we'll have a C major chord in second inversion:
Here, G is the bass note.

A chord has as many possible positions as it has notes. Since our triad above has three notes, there are three possible positions: root position, first inversion and second inversion.
Since root position is not itself an inversion, a triad has two possible inversions. We can extrapolate this rule thus: The number of possible inversions of a chord equals the number of notes minus one.

Inverting seventh chords

Let's now turn to four-note chords and take a look at a very common chord, the dominant seventh. Here is the dominant seventh chord in C major, in root position:
Note that the dominant seventh is built on the fifth scale degree of any key. The fifth note of the C major scale (i.e., the fifth scale degree) is G.
The notes of this chord, from bottom to top, are G, B, D, F.
Now let's take a look at the chord inversions. If B (the second note of the chord) is on the bottom, this chord is in first inversion:
If the third note, D, is the bass note, our seventh chord is in second inversion:
Finally, if the fourth note, F, is in the bass, the dominant seventh chord is in third inversion:
Note that when determining the inversion, we're only concerned with the bottom note—the remaining notes can be in any order. It's therefore the bass note that determines the inversion.
This concludes our second lesson on chord inversions. Practice hard and you'll soon be an expert!